IEEE MTT-V054-I12B (2006-12B) [54, 12b ed.]

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DECEMBER 2006

VOLUME 54

NUMBER 12

IETMAB

(ISSN 0018–9480)

PART II OF TWO PARTS SPECIAL ISSUE ON 2006 INTERNATIONAL MICROWAVE SYMPOSIUM

2006 Symposium Issue

“Bridge to the Future” was the theme of the 2006 IEEE MTT-S International Microwave Symposium, held on 11-16 June 2006 in San Francisco, CA

IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY The Microwave Theory and Techniques Society is an organization, within the framework of the IEEE, of members with principal professional interests in the field of microwave theory and techniques. All members of the IEEE are eligible for membership in the Society upon payment of the annual Society membership fee of $14.00, plus an annual subscription fee of $16.00 per year for electronic media only or $32.00 per year for electronic and print media. For information on joining, write to the IEEE at the address below. Member copies of Transactions/Journals are for personal use only. ADMINISTRATIVE COMMITTEE K. VARIAN, President S. M. EL-GHAZALY J. HAUSNER K. ITOH M. HARRIS D. HARVEY

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IEEE Periodicals Transactions/Journals Department Staff Director: FRAN ZAPPULLA Editorial Director: DAWN MELLEY Production Director: ROBERT SMREK Managing Editor: MONA MITTRA Senior Editor: CHRISTINA M. REZES IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES (ISSN 0018-9480) is published monthly by the Institute of Electrical and Electronics Engineers, Inc. Responsibility for the contents rests upon the authors and not upon the IEEE, the Society/Council, or its members. IEEE Corporate Office: 3 Park Avenue, 17th Floor, New York, NY 10016-5997. IEEE Operations Center: 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331. NJ Telephone: +1 732 981 0060. Price/Publication Information: Individual copies: IEEE Members $20.00 (first copy only), nonmember $77.00 per copy. (Note: Postage and handling charge not included.) Member and nonmember subscription prices available upon request. Available in microfiche and microfilm. Copyright and Reprint Permissions: Abstracting is permitted with credit to the source. Libraries are permitted to photocopy for private use of patrons, provided the per-copy fee indicated in the code at the bottom of the first page is paid through the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. For all other copying, reprint, or republication permission, write to Copyrights and Permissions Department, IEEE Publications Administration, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331. Copyright © 2006 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Periodicals Postage Paid at New York, NY and at additional mailing offices. Postmaster: Send address changes to IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331. GST Registration No. 125634188. Cover photo: by Carl Wilmington, courtesy of the San Francisco Convention and Visitors Bureau photo library, used with permission.

Digital Object Identifier 10.1109/TMTT.2006.888688

DECEMBER 2006

VOLUME 54

NUMBER 12

IETMAB

(ISSN 0018-9480)

PART II OF TWO PARTS

SPECIAL ISSUE ON 2006 INTERNATIONAL MICROWAVE SYMPOSIUM

2006 Symposium Issue

MICROWAVE SYMPOSIUM PAPERS

An Integrated Subharmonic Coupled-Oscillator Scheme for a 60-GHz Phased-Array Transmitter ...... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ .. J. F. Buckwalter, A. Babakhani, A. Komijani, and A. Hajimiri Novel Approach to the Synthesis of Microwave Diplexers ....... ......... ........ ....... G. Macchiarella and S. Tamiazzo High-Speed Digital-to-Analog Converter Using Schottky Diode Samplers ...... ..... K.-O. Sun and D. W. van der Weide Uniaxial and Radial Anisotropy Models for Finite-Volume Maxwellian Absorber ...... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... K. Sankaran, C. Fumeaux, and R. Vahldieck Sparse Macromodeling for Parametric Nonlinear Networks ..... ......... ........ ......... ......... . M. Ma and R. Khazaka Theoretical Justification of Space-Mapping-Based Modeling Utilizing a Database and On-Demand Parameter Extraction ...... ......... ........ ......... ....... ... ........ ......... ......... ........ S. Koziel, J. W. Bandler, and K. Madsen Dynamic Deviation Reduction-Based Volterra Behavioral Modeling of RF Power Amplifiers .. ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... A. Zhu, J. C. Pedro, and T. J. Brazil Low-Loss Differential Semicoaxial Interconnects in CMOS Process .... . . J.-D. Jin, S. S. H. Hsu, M.-T. Yang, and S. Liu An Empirical Bipolar Device Nonlinear Noise Modeling Approach for Large-Signal Microwave Circuit Analysis ..... .. .. ........ ......... ......... ........ ......... ......... ........ ....... P. A. Traverso, C. Florian, M. Borgarino, and F. Filicori Multiport-Amplifier-Based Architecture Versus Classical Architecture for Space Telecommunication Payloads ........ .. .. ........ ......... ......... ........ ......... ......... ........ ......... .. A. Mallet, A. Anakabe, J. Sombrin, and R. Rodriguez Monolithic Broadband Gilbert Micromixer With an Integrated Marchand Balun Using Standard Silicon IC Process ... .. .. ........ ......... ......... ........ ......... ......... ..... S.-C. Tseng, C. Meng, C.-H. Chang, C.-K. Wu, and G.-W. Huang

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(Contents Continued from Page 4269) Design and Analysis of Low Flicker-Noise CMOS Mixers for Direct-Conversion Receivers .... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... J. Park, C.-H. Lee, B.-S. Kim, and J. Laskar Silicon-Integrated Differential Bandpass Filters Based on Recursive and Channelized Principles and Methodology to Compute Their Exact Noise Figure .... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .. .. S. Darfeuille, J. Lintignat, R. Gómez-García, Z. Sassi, B. Barelaud, L. Billonnet, B. Jarry, H. Marie, and P. Gamand Full-Wave Analysis of Inhomogeneous Deep-Trench Isolation Patterning for Substrate Coupling Reduction and -Factor Improvement ... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .. S. Wane and D. Bajon A Broadband Single-Stage Equivalent Circuit for Modeling LTCC Bandpass Filters ... ... ..... Y.-S. Tsai and T.-S. Horng Distortion Analysis of Ultra-Wideband OFDM Receiver Front-Ends .... ........ . ........ .... M. Ranjan and L. E. Larson A Metric for the Quantification of Memory Effects in Power Amplifiers ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ...... J. P. Martins, P. M. Cabral, N. Borges Carvalho, and J. C. Pedro Hybrid Space-Discretizing Method—Method of Moments for the Analysis of Transient Interference . ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .. R. Khlifi and P. Russer InAs/AlSb HEMT and Its Application to Ultra-Low-Power Wideband High-Gain Low-Noise Amplifiers ...... ......... .. .. ........ ......... ......... ........ ........ B. Y. Ma, J. Bergman, P. Chen, J. B. Hacker, G. Sullivan, G. Nagy, and B. Brar AlGaN/GaN -Band 5-W MMIC Amplifier ... ........ ......... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ .. A. M. Darwish, K. Boutros, B. Luo, B. D. Huebschman, E. Viveiros, and H. A. Hung -Band Heartbeat Detector Measuring From Four Sides of a Human Experiment and Spectral Analysis of a Low-Power Body ... ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ........ C. Li, Y. Xiao, and J. Lin Evaluations of Specific Absorption Rate and Temperature Increase Within Pregnant Female Models in Magnetic Resonance Imaging Birdcage Coils .... ......... ........ ......... ......... ....... D. Wu, S. Shamsi, J. Chen, and W. Kainz Linearity Improvement of HBT-Based Doherty Power Amplifiers Based on a Simple Analytical Model ....... ......... .. .. ........ ......... ......... ........ ......... ........ Y. Zhao, A. G. Metzger, P. J. Zampardi, M. Iwamoto, and P. M. Asbeck RF Chipset for Impulse UWB Radar Using 0.13- m InP-HEMT Technology .. ......... ......... ........ ......... ......... .. .. ........ ......... .. Y. Kawano, Y. Nakasha, K. Yokoo, S. Masuda, T. Takahashi, T. Hirose, Y. Oishi, and K. Hamaguchi Study of 2-bit Antenna–Filter–Antenna Elements for Reconfigurable Millimeter-Wave Lens Arrays .. ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ....... C.-C. Cheng and A. Abbaspour-Tamijani Two-Port Vector Network Analyzer Measurements in the 218–344- and 356–500-GHz Frequency Bands ...... ......... .. .. ..... A. Fung, D. Dawson, L. Samoska, K. Lee, T. Gaier, P. Kangaslahti, C. Oleson, A. Denning, Y. Lau, and G. Boll A Distortion-Cancelled Doherty High-Power Amplifier Using 28-V GaAs Heterojunction FETs for W-CDMA Base Stations ......... I. Takenaka, K. Ishikura, H. Takahashi, K. Hasegawa, T. Ueda, T. Kurihara, K. Asano, and N. Iwata A 60-GHz-Band 12-Multiplier MMIC With Reduced Power Consumption ... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ... M. Ito, S. Kishimoto, Y. Hamada, and K. Maruhashi EM-Based Monte Carlo Analysis and Yield Prediction of Microwave Circuits Using Linear-Input Neural-Output Space Mapping ........ ......... ........ ......... .... ...... ........ ......... ......... ... J. E. Rayas-Sánchez and V. Gutiérrez-Ayala A 10-Gb/s Reconfigurable CMOS Equalizer Employing a Transition Detector-Based Output Monitoring Technique for Band-Limited Serial Links .... F. Bien, H. Kim, Y. Hur, M. Maeng, J. Cha, S. Chandramouli, E. Gebara, and J. Laskar CMOS Active Bandpass Filter Using Compacted Synthetic Quasi-TEM Lines at -Band ...... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ..... C.-K. C. Tzuang, H.-H. Wu, H.-S. Wu, and J. Chen Testing High-Frequency Electronic Signals With Reflection-Mode Electroabsorption Modulators ..... ......... ......... .. .. .. R. L. Van Tuyl, G. E. Höfler, R. G. Ritter, T. S. Marshall, J. Zhu, L. Billia, G. M. Clifford, W. Gong, and D. P. Bour Very Compact High-Gain Broadband Low-Noise Amplifier in InP HEMT Technology ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ....... S. Masuda, T. Ohki, and T. Hirose Low-Loss Integrated-Waveguide Passive Circuits Using Liquid-Crystal Polymer System-on-Package (SOP) Technology for Millimeter-Wave Applications ..... ......... ........ ......... ......... .. K. S. Yang, S. Pinel, I. K. Kim, and J. Laskar Information for Authors .. ........ ......... ......... ........ ......... .......... ........ ......... ......... ........ ......... ......... . 2006 INDEX OF MTT TRANSACTIONS

4372 4381 4397 4412 4422 4432 4440 4448 4456 4464 4472 4479 4489 4498 4507 4513 4522 4528 4538 4548 4556 4565 4572 4580

........ ......... ........ ......... ......... ........ ..... Available online at http://ieeexplore.ieee.org

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An Integrated Subharmonic Coupled-Oscillator Scheme for a 60-GHz Phased-Array Transmitter James F. Buckwalter, Member, IEEE, Aydin Babakhani, Student Member, IEEE, Abbas Komijani, Member, IEEE, and Ali Hajimiri, Member, IEEE

Abstract—This paper describes the design of an integrated coupled-oscillator array in SiGe for millimeter-wave applications. The design focuses on a scalable radio architecture where multiple 2 oscillator array dies are tiled to form larger arrays. A 2 for a 60-GHz transmitter is fabricated with integrated power amplifiers and on-chip antennas. To lock between multiple dies, an injection-locking scheme appropriate for wire-bond interconnects is described. The 2 2 array demonstrates a 200 –MHz locking range and 1 4 array formed by two adjacent chips has a 60-MHz locking range. The phase noise of the coupled oscillators is below 100 dBc/Hz at a 1-MHz offset when locked to an external reference. To the best of the authors’ knowledge, this is the highest frequency demonstration of coupled oscillators fabricated in a conventional silicon integrated-circuit process. Index Terms—BiCMOS integrated circuits, coupled oscillator, mutual injection locking, phased arrays.

I. INTRODUCTION

U

NLICENSED operation in the 59–64-GHz band is stimulating novel radio architectures for millimeter-wave integrated circuits. The available bandwidth offers gigabit/second data rates, and high absorption at 60 GHz is an important feature for dense networking. Transceiver circuits that operate at millimeter-wave frequencies have been demonstrated in silicon germanium (SiGe) fabrication technologies [1]–[3]. However, the integration of a complete phased-array transceiver with antennas on a single chip offers new design choices and opportunities [2]. Phased-array designs at the 24-GHz industrial–scientific–medical (ISM) band have demonstrated new receiver circuit architectures [4]–[9]. This paper demonstrates the application of a new circuit approach based on coupled-oscillator arrays for millimeter-wave phased-array designs in a standard SiGe integrated-circuit technology. To maintain phase coherence between phased-array elements, oscillators on different dies must be phase locked. While coupled phase-locked loop architectures can maintain the phase relationship between neighboring oscillators [7], [8], coupled oscillators are well suited for fully integrated phased-array circuits. The wavelength at 60 GHz allows for several array

Manuscript received March 28, 2006; revised August 23, 2006. J. F. Buckwalter was with the Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125 USA. He is now with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093 USA (e-mail: [email protected]). A. Babakhani, A. Komijani, and A. Hajimiri are with the Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125 USA (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885581

Fig. 1. Coupled-oscillator scheme for fully integrated phased-array transmitter. Each oscillator drives a transmit chain with a DAC controlled phase shifter, power amplifier, and antenna.

elements to be located on a single die. Consequently, an oscillator can be placed on each die or at each transmit element. One particular advantage of an on-chip coupled-oscillator array is the distribution of the carrier frequency between different transmit elements. Previous integrated phased-array implementations distribute 16 phases across the entire chip, results in large amounts of silicon area dedicated to wiring and high power consumption [4]. Global frequency distribution becomes increasingly difficult at millimeter frequencies. By co-locating an oscillator at each transmit stage, closer control of the delay mismatches between the local oscillator and the mixer stage is possible. Scalable architectures are particularly appropriate for creating large phased arrays by tiling several dies. In Fig. 1, scalability is demonstrated for a phased-array transmitter. The phased array requires phase coherence between all elements. Since each chip requires frequency generation, neighboring chips are injection locked to ensure phase coherence. If oscillators are located at each antenna element, injection locking can lock the oscillators both on-chip and between chips. This tiling approach is useful not only for phased arrays, but also for applications where the separation between antennas might be several wavelengths. Consequently, this design approach focuses on an injection-locking scheme appropriate for an onand off-chip coupled-oscillator array. In this transmitter implementation, a two element by two element (2 2) array of transmitter cells is integrated on a single

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chip with antennas. In [5], array scalability originally motivated investigation into a coupled-oscillator topology. This paper expands on the design details of the coupled-oscillator array by describing the interconnect structure for subharmonic injection locking, as well as the circuit implementation of the injectionlocked voltage-controlled oscillator (VCO). Additional results illustrate the circuit operation in the time domain. The measured results show that the phase noise of each element can be suppressed when locked to an external source across a single chip, as well as across two chips. In Section II, we summarize the analysis of coupled oscillators and explain the motivation of using these circuits for fully integrated phased-array elements. In Section III, we discuss the circuit design of the coupled-oscillator cell and the coupling network. Finally, the results for the coupled-oscillator array are presented and compared to the performance of individual oscillators in Section IV. II. COUPLED OSCILLATORS Adler described the unilateral locking phenomena in coupled oscillators [10] and Kurokawa later studied the microwave dynamics [11]. The basic phase relationship between neighboring oscillators is (1) where and are the phase difference and natural frequency detuning between the local osis the carrier frequency, is cillator and an injected signal, the quality factor for the oscillator, and and are the oscillator and injection currents. The locking range is defined as and allows the phase difference to twice theoretically vary from 90 to 90 . The frequency detuning relationship is demonstrated in [10]. Increasing the locking range or decreasing . The passive is possible with increasing components of the tank bound the oscillator and strongly affect the oscillator phase noise. From a testing standpoint, we use the injected current to control the locking range Bilateral oscillator arrays were first proposed by Stephan [12]. York and Compton [13], York et al. [14], and York and Itoh [15] proposed coupled oscillators for electronic beam steering through injection at the periphery of the array. The effect of bilateral injection locking is to modify the behavior in (1). In this case, the phase dynamics of the array produce a linear phase gradient across the array. In [15], the dynamics for a coupled-oscillator array with bilateral and external injection locking for beam steering are described as

(2) where and are the frequency detuning and phase difference between the th and osciland are the external injection current and lators, and phase, respectively. The continuum dynamics for beam steering have been studied by Pogorzelski et al. [16] and experimental

Fig. 2. Impact of different dielectric mediums for the interconnect scheme and the radiation network. The coupled oscillators will not necessarily be separated by half a wavelength at the subharmonic frequency. The coupled oscillator is connected by a transmission line with attenuation  and propagation constant . The impedance on the line is Z .

results have recently demonstrated the array pattern for oscillator arrays of discrete components [17]. In integrated circuit implementations, the process, voltage, and temperature (PVT) variations between different oscillators introduce phase errors between neighboring elements. For process variations, the design is subject to less variation across a single die than across different wafers. Therefore, the frequency range ensures the locking of the array must be greater when considering locking between different dies than locking between oscillators on a single die. Other characteristics of coupled-oscillator dynamics are worth consideration. First, the phase noise increases with the frequency detuning between neighboring oscillators [18]. Additionally, the phase noise limits the allowable frequency detuning. As the edges of the locking range are approached, the oscillators can lose lock. For this reason, coupled-oscillator arrays have found a limited 60 is necessary between array role in beamsteering since elements for beamforming. Secondly, stability analysis of coupled-oscillator dynamics demonstrates the possibility of unwanted modes in large arrays [19], [20]. Instead of exploiting the phase relationships in (1) and (2) to control the beam angle, this study instead relies on injection locking solely as a means to distribute and phase lock the carrier signal across a single chip and between neighboring chips. The locking range consequently must be large enough to satisfy the PVT variations in a particular integrated-circuit technology. Slight supply variations shift the natural frequencies of neighboring oscillators, as will be demonstrated in Section IV. The relative phase control of each transmit stage is independently provided with digital-to-analog (DAC) controlled mixers for beamforming and data modulation. This circumvents many of the problems of relying on coupled-oscillator dynamics for beamsteering. Finally, we consider the coupled-oscillator network as it applies to the phased-array transmitter. The distance between neighboring oscillators that are co-located with the antenna is dictated by the half-wavelength spacing in air or, if a silicon lens is used to focus the antenna pattern, in silicon [2]. This is illustrated in Fig. 2. One of the advantages of using a silicon lens is that the distance between array elements will be much shorter since silicon has a dielectric constant of 11.9. However, the coupling network in a standard silicon process will be located in the metal stack and, consequently, propagate through

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a different dielectric, i.e., silicon dioxide. It is interesting to consider the number of wavelengths of the th subharmonic of the oscillator frequency that separate the neighboring elements (3) where is the dielectric constant of the silicon dioxide and the could be chosen to minimize the attenuradiating medium. ation over the interconnect. The choice of the subharmonic frequency will be discussed in Section III. Notably, if the first suband the radiative dielectric is air, harmonic is used the interconnect will be approximately one-half of the subharmonic wavelength. However, if the radiative dielectric constant is instead silicon, the interconnect length is reduced to 0.14 of the subharmonic wavelength. By matching the impedance of the oscillator source to the coupling interconnect, the impact of the propagation constant is primarily reduced to the role of attenuation on the coupling signal. One final consideration regarding the use of coupled-oscillator arrays for beamsteering applications involves the phase jitter of each oscillator. Ideally, neighboring oscillators should have identical phases, but the phase noise of each oscillator is independent and the limited injection-locking bandwidth between oscillators causes a statistical variation, known as phase jitter, that corrupts the mean phase between the neighboring oscillators. The cycle-to-cycle phase jitter between two oscillators can be expressed as (4)

is the power spectrum of the phase of each oswhere cillator and is assumed to be identical for both oscillators. In many cases, the power spectrum of the phase can be estimated . Consequently, the from the measured phase noise phase noise of each oscillator must be suppressed sufficiently through injection locking to minimize the phase error between neighboring elements. Any contribution to the phase jitter will degrade the beam pattern and induce an error vector for data communication.

III. SCALABLE TWO-DIMENSIONAL (2-D) COUPLED-OSCILLATOR ARRAYS The basic coupled-oscillator topology is shown in Fig. 3. The 2 2 phased array contains four oscillators at each transmit (TX) stage. The block diagram demonstrates the implementation of the oscillator cell. Each oscillator is designed to operate at 40 GHz. Isolating the oscillator from the power amplifier and antenna is critical because on-chip coupling is difficult to accurately model and severely degrades performance through pulling between the oscillator and power amplifier [21]. By shifting the oscillator frequency to 40 GHz, the unwanted coupling is reduced. The oscillator is divided to 20 GHz and mixed with the 40-GHz signal to achieve the 60-GHz in-phase (I) and quadrature (Q) components.

Fig. 3. Coupled-oscillator schematic. The oscillators are coupled along two dimensions. The coupling network operates at one-third the carrier frequency.

A. Interconnections Coupling between different dies requires considering the interconnect. If wire bonds are used to provide the interconnect between two dies, frequencies above 20 GHz are strongly attenuated through poor matching and reflections. These losses reduce the injected current strength between the neighboring dies and weaken the locking range described in (2). Tiling chips at half-wavelength spacings keeps the inter-chip spacing small 200 m and minimizes the wire-bond inductance. Consequently, we choose to injection lock at a subharmonic of the local oscillator frequency. The first subharmonic at 20 GHz is available from the carrier generation scheme described above and illustrated in Fig. 3. Since the static dividers provide I and Q signals, we propose an I/Q scheme for coupling within a 2-D array of oscillators. In Fig. 3, the 20-GHz I signal is coupled along the -axis while the Q signal is coupled along the -axis. Consequently, each oscillator in the integrated 2 2 array receives an I and Q subharmonic signal from its neighbors. Coupled oscillators can simplify the distribution of high-frequency carrier energy over a phased array. However, electromagnetic simulations indicate the on-chip antenna will radiate substantially within the silicon substrate and silicon–dioxide metal stack since the dielectric constant of silicon is much higher than air [2]. The presence of a global transmission line interconnect grid absorbs part of this radiated energy. The transmission-line structure for the coupling interconnects was modified to reduce the absorption of radiated energy. The interconnect transmission line is illustrated in Fig. 4. The ground plane is a bathtub, which shields the differential interconnects from the substrate similar to the transmission lines described in earlier microwave and millimeter-wave designs [22], [23]. The bathtub ground plane, however, is severed every 200 m to avoid the absorption of radiated millimeter-wave energy. The differential coupling signal travelling in the transmission line is relatively unaffected by the severed ground plane since the return currents in this structure are localized. IE3D simulations

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Fig. 4. Interconnect structure with severed bathtub to prevent coupling to integrated antenna.

Fig. 6. Injection locking and VCO topology.

where is the saturation current, is the base–emitter is the thermal voltage. If we assume that the voltage, and bases are driven with a differential ac-coupled injection signal , the sinusoidal dependence in the exponent is expressed through the series expansion

Fig. 5. Measured interconnect S -parameters over 1 mm of interconnect.

indicate that the characteristic impedance of the lines changes by less than 5%. A segmented-ground transmission-line test structure was fabricated to compare the -parameters with a regular bathtub transmission line. The measured -parameters are compared in Fig. 5 and demonstrate that the loss of the segmented transmission line over 1 mm is around 3 dB and did not vary much between the segmented and normal transmission-line structure at 20 GHz. However, the measured return loss is increased by 3 dB at 20 GHz due to the severed ground plane. B. Frequency Doubler Since the injected signal is a subharmonic of the oscillator frequency, the injected frequency must be multiplied. At each oscillator, the I and Q injection signals are provided from the neighboring oscillators. Injection locking with both I and Q subharmonic signals increases the second harmonic power since . A circuit schematic for the frequency doubler and oscillator is shown in Fig. 6. The I/Q signals are picked up by a receiver that drives back-to-back bipolar devices. These transistors are biased below the forward active region to generate strong second harmonic content through recallows control over the tification. Changing the bias voltage injected current at the second harmonic. The basic collector current dependence on the base–emitter diode voltage is (5)

(6)

Odd harmonic terms cancel when the injection current is added at the collector. One back-to-back transistor pair is driven by I, the other one by Q. Since the second harmonic remaining at the collector has a 180 phase difference (90 multiplied by 2), the differential signal is generated for oscillator coupling. Consequently, the even harmonics remain in the current injected into the VCO tank circuit. Additionally, resistor degeneration at the emitter of the bipolar transistors provides common mode rejection. Emitter in the emitter degeneration is introduced with the resistor and the base–emitter voltage changes to (7) where is the common mode current. Recalculating (5), the differential collector current for the I and Q paths is

(8)

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Finally, the difference of the expressions in (8) gives the desired injected signal

(9) The injected current is twice the frequency of the I/Q signals and depends quadratically on the amplitude of the injected current. Adding the currents in (8) gives the total current through the emitter resistor

(10) The bias current is constant through the stage, but depends on the input power as the differential current did in (9). For small current levels, this transcendental equation can be approximated . In this with a series for the exponential dependence on case, (11)

When the tail resistance is small, , and the total current depends on the power of the injected signals. For larger power levels, the total current saturates as . For a tail resistance of 20 , this current is roughly 1.3 mA. Substituting (11) into (9), the differential mode current is

Fig. 7. Current injected into the VCO at oscillator and subharmonic frequency.

design, we chose 20 for the tail resistance as a tradeoff between the desired injection current and the rejection of the subat the tail resisharmonic frequency. Additionally, varying tance can provide a dc bias that puts the bipolar devices closer to the forward active region. This effect is plotted in Fig. 7 for V. Now the injection current depends weakly on the input subharmonic power and the injection current remains fixed at around 4 mA. However, the circuit also provides less rejection of the subharmonic energy. Consequently, the subharmonic energy is efficiently converted to the oscillator frequency energy through the use of a frequency-doubling scheme. Now we turn our attention to the coupling of the injected signal into the VCO.

(12) C. Injection-Locked Oscillator

For large power levels, the total differential current saturates at (13) Hence, the differential injection current contains only energy at the twice the subharmonic and the amplitude of the injection signal is independent of the injected power level. For , the differential current swing should be greater than 1 mA. However, this equation only describes the current when no dc bias is provided across the base–emitter junction. In reality, the base–emitter voltage drop can also be fixed to increase the amount of injection current. An ADS simulation of the complete frequency doubling circuit is demonstrated in Fig. 7. The simulation is performed as a function of the injected subharmonic voltage swing. Different values of tail resistance and base–emitter voltage are shown in the plot. The results provide a comparison for the amplitude of injected current at the subharmonic and carrier frequency. Larger resistance provides more rejection of the subharmonic frequency, but limits the current injected into the tank. For this

Energy can be injected at many different points of the oscillator core. Injection-locked frequency dividers inject energy in the tail of a cross-coupled differential pair [24]. However, the tail is useful primarily for superharmonic injection locking because the emitter or source node of the differential pair is a virtual ground at the oscillator frequency. Alternatively, coupled oscillators have been proposed for quadrature generation [25], [26]. These schemes use a differential pair connected in parallel to the cross-coupled pair in the oscillator core to inject energy. The sizing of these devices and injection current control the coupling strength. This topology can be difficult to implement at millimeter-wave frequencies because the parasitic loading can result in a narrow or reduced the tuning range. Other papers have shown direct injection locking for quadrature generation through a separate differential stage that drives a ring oscillator [27]. For this design, the frequency-doubler output is coupled into the VCO core with a coupled transmission line. The coupled transmission line is part of the VCO tank circuit to reduce the effect on the oscillator tuning range. Unfortunately, the coupled transmission line also limits coupling strength. -parameter simulations of coupled transmission lines in this fabrication technology are shown in Fig. 8. The simulations are swept

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Fig. 8.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

S -parameters for coupled transmission lines in injection-locked VCO.

for three different transmission-line lengths. At 40 GHz, the coupling between the injection-locking circuit and the VCO depends on the coupling length. The 50- m lines show a 15-dB coupling strength between the two circuits while the 200- m lines provide 7-dB coupling. Interestingly, the coupling reaches a maximum around this value and decreases at higher frequencies. In this case, the total inductance of the transmission-line tank of the VCO limited the coupled transmission-line section length to 100 m, providing 10-dB coupling. The lower coupling strength at 20 GHz provides additional rejection of the subharmonic energy. The coupled transmission line rejects the subharmonic frequency by 5 dB for the 100- m length compared to the oscillator harmonic frequency. On the left-hand side of the schematic in Fig. 6, a simple cross-coupled nMOS VCO is shown. The oscillator tank consists of the combination of the transmission line and coupled transmission for inductance and varactor diodes. The tuning range of the VCO is over 4 GHz, approximately 10% of the carrier frequency. Notably, the oscillator self-mixing enhances the frequency tuning range at 60 GHz by the ratio of 3 : 2, and the tuning range should remain 10% of the oscillator frequency. IV. RESULTS The coupled-oscillator array was constructed in IBM 8HP, a 130-nm SiGe process with bipolar and CMOS devices. The of the bipolar devices is 210 GHz. The array is maximum shown in Fig. 9 and occupies an area of 3.5 mm 5 mm. The wavelength of a 60-GHz signal determines the spacing between is roughly on-chip antennas. In air, the array spacing 2.5 mm. However, the array is intended to radiate through the die substrate where a silicon lens is used to absorb the radiated energy [2]. Consequently, the array spacing is designed and the array spacing is 0.7 mm. Unfortunately, for the element spacing is too restrictive given geometry considerations for the on-chip antenna and the array spacing was chosen for 1.7 mm. This limits the beamsteering and causes undesirable sidelobes, but is still useful for the proof-of-concept. The enlarged version of one cell shows the antenna, which resides approximately 200 m from the five pads on the lower metal layers, as well as the power amplifier, DAC controlled phase

Fig. 9. Chip microphotograph for complete 60-GHz transmitter with a close-up view of one array element.

shifter, mixers, and injection-locked VCO. The antennas are placed on the lower metal layers to provide better power coupling to the silicon lens. The coupling interconnects run along the top and right-hand side of the cell to four pads that allow wire bonding to a neighboring dies. Each oscillator consumes 25 mA for the static frequency divider and 125 mA for the oscillator, frequency doubler, and coupling buffers. The current is increased by the use of the quadrature injection locking scheme since each oscillator drives four 50- buffers. The VCO frequency varies between 35.5–39.5 GHz, falling 3.5 GHz below the desired range of 39–43 GHz. The tuning curve for each of the oscillators is shown in Fig. 10. The variation in the oscillator tuning range varies with location. The southern oscillators have a higher natural frequency than the northern oscillators. Additionally, the output power of these oscillators is approximately 3 dB lower. To prevent coupling between the antenna and large power supply connections on chip, the power supply was provided along an axis perpendicular to the on-chip antennas in the microphotograph in Fig. 9. Consequently, both northern oscillators are located closer to the power supply pads and the resulting drop in power seems most likely due to voltage drop along the supply lines. As the oscillators are tuned together, the locking range determines the usable oscillator frequency range. To characterize the performance of the coupled-oscillator array, a VCO test structure is initially measured under injection-locking conditions. The phase noise of the free-running oscillator, as well as the locked oscillator is demonstrated in

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2

Fig. 10. Tuning range for each oscillator in 2 2 array. The difference between the natural frequencies of each oscillator is greatest near the highest frequencies.

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Fig. 12. Locking range for the VCO as a function of injected power.

Fig. 11. Phase noise of reference, injection-locked oscillator, and unlocked oscillator. Fig. 13. Testing scheme for the coupled-oscillator array.

Fig. 11. The locked oscillator phase noise tracks the injected reference with 6-dB higher phase noise. The injected signal is at 20 GHz and the phase noise is measured at 40 GHz. Consequently, there is a 6-dB penalty in the phase noise of the locked on-chip oscillator. At 1-MHz offset, the phase noise of the locked oscillator is 112 dBc/Hz. The injection-locking characteristics are measured as a function of injection power. In Fig. 12, the carrier frequency is measured as a function of dBm, the the injected subharmonic frequency. At locking range is around 60 MHz and increases to 320 MHz dBm. To verify these locking-range results, we at compare the expression for the locking range to these measured is results. If the locking range is 320 MHz and the tank around 10 at 40 GHz, mA

MHz GHz

mA

(14) Comparing this to our simulations in Fig. 7 provides agreement about anticipated injection current levels. In Fig. 13, the testing scheme for the coupled oscillator is illustrated. The external reference drives a 20-GHz signal through a power splitter and an I/Q coupler. The second signal from the power splitter is divided down to 10 GHz and used to trigger

an Agilent 81600C oscilloscope. The I/Q signals from the coupler are delay matched to externally lock the coupled-oscillator array. The I signal is fed to the East edge and the Q signal is fed to the South edge. Additionally, the locking is controlled on-chip through the bias voltage of the frequency-doubling circuit, as described in Section III. For testing the 2 2 array, each oscillator can be probed with the high-speed sampling head in the oscilloscope or the spectrum analyzer. The oscillator behavior is studied by observing the 20-GHz injection-locking signal of the oscillator. In Fig. 14, the phase noise of the 2 2 coupled-oscillator array structure is shown with and without injection locking. In this case, the average phase noise of each oscillator is around 93 dBc/Hz at 1-MHz offset. Next, a 10-dBm external reference is injected at the northeast and southeast oscillators. The , was set to draw 8 mA injection current, controlled with per cell. The oscillator phase noise was consecutively measured without changing the operating conditions. The phase noise of the injection-locked VCOs is around 114 dBc/ Hz at 1-MHz offset. The locking range for the array under these conditions is approximately 200 MHz. The operation of the locked array is limited by the natural frequency and power variations for each oscillator. This also affects the phase noise of each oscillator in

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Fig. 16. Phase noise of northwest oscillator as a function of frequency detuning.

Fig. 14. Phase noise of each oscillator in 2 and (bottom) with injection locking.

2 2 single chip array: (top) without

Fig. 17. Phase noise of oscillators across a 1

Fig. 15. Phase of each oscillator in array across locking range.

the array. This supply and bias mismatch dominates the process and temperature variations that might occur on-chip. The phase of each oscillator can also be measured at 20 GHz with a high-speed sampling scope. The externally injected signal is used to trigger the high-speed scope. The phase progression of each oscillator is demonstrated in Fig. 15 and is normalized to zero to provide relative comparison of the phase. The maximum oscillator phase variation is at most 60 to 80 over the 200-MHz locking range. This locking range is measured at the subharmonic frequency, but the phase variation is calculated for the actual carrier frequency. Voltage variations strongly influence the locking range. Note that the southern oscillators tend to have a greater phase range due to the weaker oscillator current. Any phase offset between the oscillators can be compensated with the DAC controlled mixer that provides phase shifting.

2 4 array with two different dies.

Additionally, the frequency detuning between the reference and the oscillator was scanned to measure the change in the phase noise in Fig. 16. As demonstrated in [18], the phase noise changes as a function of the frequency detuning depending on the frequency offset. The curve qualitatively agrees with those predictions as the phase noise increases near the edges of the locking range. To achieve the best phase-noise performance across a grid of oscillators, the frequency detuning of all the oscillators should be minimized. Finally, a 1 4 oscillator array is measured in Fig. 17 with an external injection signal of 10 dBm at the NE oscillator of die #1. The testing scheme described in Fig. 13 is altered to include a second die. The coupling ports of the two chips are wire bonded together and the southern oscillators on both chips are turned off. As before, the spectrum analyzer and oscilloscope can probe each of the oscillator injection locking ports to measure the array behavior. The locking range under these conditions is roughly 60 MHz and is reduced partly because only the in-phase signals are used to injection lock the array. The phase noise of the locked oscillator closest to the external reference is 110 dBc/Hz at a 1-MHz offset. Each consecutive oscillator has phase noise of 105, 107, and 108 dBc/Hz. The phase noise would ideally increase across the array. Instead, the irregular shift in phase noise may result from the natural frequency detuning between the neighboring oscillators. Nonetheless, the

BUCKWALTER et al.: INTEGRATED SUBHARMONIC COUPLED-OSCILLATOR SCHEME FOR 60-GHz PHASED-ARRAY TRANSMITTER

Fig. 18. Oscilloscope waveforms for 20-GHz injection signals across 1 array.

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low phase noise across the two chips is encouraging for demonstrating larger arrays by locking on-chip oscillators to off-chip reference signals. The phases of each oscillator in the 1 4 array are shown in Fig. 18. The phase shift introduced between the two dies is nearly 180 , while the phase difference between the on-chip oscillators is smaller. This is presumably related to the difference in the injection strength between chips, as opposed to between oscillators on the same chip. This degradation in the injection frequency can also result in the lower locking range of the 1 4 array. The impedance of a short (0.2 mm) wire bond can be estimated as nH GHz and induces mismatch in the interconnect between two dies. V. CONCLUSION This paper has described the implementation of a coupled-oscillator array integrated in an SiGe process for millimeter-wave applications. The coupled oscillator employs quadrature subharmonic injection locking to couple neighboring phased-array elements both on-chip and between chips with wire-bond interconnects. Measurements of the oscillator array demonstrate reduced phase noise when locked to an external reference. The locking range was measured to be 200 MHz for the oscillators on a single die and is limited by the process and voltage variations that exist over the large die area. ACKNOWLEDGMENT The authors acknowledge the support of the Defense Advanced Research Projects Agency (DARPA) Trusted Foundries Program for access to the 8HP technology. Additionally, we thank the Rogers Corporation, Rogers, CT, for the generous donation of the duroid. REFERENCES [1] S. Reynolds et al., “60 GHz transceiver circuits in SiGe bipolar technology,” in IEEE Int. Solid-State Circuits Conf., Feb. 2004, pp. 442–444.

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[2] A. Babakhani et al., “77 GHz four element phased array receiver with on-chip dipole antennas in silicon,” in IEEE Int. Solid-State Circuits Conf., Feb. 2006, pp. 180–181. [3] B. Razavi, “A 60 GHz direct-conversion receiver,” in IEEE Int. SolidState Circuits Conf., Feb. 2005, pp. 400–402. [4] X. Guan et al., “A fully integrated 24-GHz eight element phased-array receiver in silicon,” IEEE J. Solid-State Circuits, vol. 39, no. 12, pp. 2311–2320, Dec. 2004. [5] J. Buckwalter et al., “Quadrature subharmonic coupled oscillators for a 60 GHz SiGe scalable phased array,” presented at the IEEE MTT-S Int. Microw. Symp., Jun. 2006. [6] H. Hashemi et al., “A 24-GHz SiGe phased array receiver-LO phase shifting approach,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 614–626, Feb. 2005. [7] J. J. Lynch and R. A. York, “A mode-locked array of coupled phaselocked loops,” IEEE Microw. Guided Wave Lett., vol. 5, no. 7, pp. 213–215, Jul. 1995. [8] J. F. Buckwalter, T. H. Heath, and R. A. York, “Synchronization design of a coupled phase-locked loop,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 952–960, Mar. 2003. [9] A. Hajimiri et al., “Integrated phased-array systems in silicon,” Proc. IEEE, vol. 93, no. 9, pp. 1637–1655, Sep. 2005. [10] R. Adler, “A study of locking behavior in oscillators,” Proc. IEEE, vol. 61, no. 10, pp. 1380–1385, Oct. 1973. [11] K. Kurokawa, “Injection locking of microwave solid-state oscillators,” Proc. IEEE, vol. 61, no. 10, pp. 1386–1410, Oct. 1973. [12] K. D. Stephan, “Inter-injection-locked oscillators for power combining and phased arrays,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 10, pp. 1017–1025, Oct. 1986. [13] R. A. York and R. C. Compton, “Measurement and modelling of radiative coupling in oscillator arrays,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 3, pp. 438–444, Mar. 1993. [14] R. A. York, P. Liao, and J. J. Lynch, “Oscillator array dynamics with broadband N -port coupling networks,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 3, pp. 438–444, Mar. 1993. [15] R. A. York and T. Itoh, “Injection and phase-locking techniques for beam control,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 11, pp. 1920–1929, Nov. 1998. [16] R. J. Pogorzelski, P. F. Maccarini, and R. A. York, “Continuum modeling of the dynamics of externally injection-locked coupled oscillator arrays,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 471–478, Apr. 1999. [17] R. J. Pogorzelski and F. F. Chiha, “A demonstration of the coupled oscillator based agile beam receiver concept,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3584–3588, Nov. 2005. [18] H.-C. Chiang et al., “Phase noise in externally injection-locked oscillator arrays,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 11, pp. 2035–2042, Nov. 1997. [19] K. D. Stephan and S. L. Young, “Mode stability of radiation-coupled interinjection-locked oscillators for integrated phased arrays,” IEEE Trans. Microw. Theory Tech., vol. 36, no. 5, pp. 921–924, May 1988. [20] J. J. Lynch and R. A. York, “Stability of mode-locked states of coupled oscillators,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 8, pp. 413–418, Aug. 1995. [21] B. Razavi, “A study of injection locking and pulling in oscillators,” IEEE J. Solid-State Circuits, vol. 39, no. 9, pp. 1415–1424, Sep. 2004. [22] A. Komijani, A. Natarajan, and A. Hajimiri, “A 24 GHz, 14.5 dBm fully integrated power amplifier in 0.18 m CMOS,” IEEE J. SolidState Circuits, vol. 40, no. 9, pp. 1901–1908, Sep. 2005. [23] A. Komijani and A. Hajimiri, “A wideband 77 GHz, 17.5 dBm fully integrated power amplifier in silicon,” IEEE J. Solid-State Circuits, vol. 41, no. 8, pp. 1749–1756, Aug. 2006. [24] H. R. Rategh and T. H. Lee, “Super-harmonic injection-locked frequency dividers,” IEEE J. Solid-State Circuits, vol. 34, no. 6, pp. 813–821, Jun. 1999. [25] R. Aparicio and A. Hajimiri, “A noise-shifting differential Colpitts VCO,” IEEE J. Solid-State Circuits, vol. 37, no. 12, pp. 1728–1736, Dec. 2002. [26] A. Mazzanti, F. Svelto, and P. Andreani, “On the amplitude and phase errors of quadrature LC-tank CMOS oscillators,” IEEE J. Solid-State Circuits, vol. 41, no. 6, pp. 1305–1313, Jun. 2006. [27] P. Kinget et al., “An injection-locking scheme for precise quadrature generation,” IEEE J. Solid-State Circuits, vol. 37, no. 7, pp. 845–851, Jul. 2002.

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James F. Buckwalter (S’01–M’06) received the B.S. degree in electrical engineering from the California Institute of Technology, Pasadena, in 1999, the M.S. degree in electrical engineering from the University of California at Santa Barbara, in 2001, and is currently with the California Institute of Technology working toward the Ph.D. degree in electrical engineering. From 1999 to 2000, he was a Research Scientist with Telcordia Technologies, where he was involved with rate-agile burst-mode electronics under a next-generation Internet Defense Advanced Research Projects Agency (DARPA) project. During Summer 2004, he was with the IBM T. J. Watson Research Center, Yorktown Heights, NY, where he developed new equalization techniques for high-speed serial links. In 2006, he joined Luxtera, Carlsbad, CA, where he developed high-speed circuits for optical interconnects. In July 2006, he joined the faculty of the University of California at San Diego, La Jolla, where he is currently an Assistant Professor of electrical engineering. His research interests are high-speed serial links, mixed-signal circuit design, and microwave and millimeter-wave integrated circuits. Dr. Buckwalter was the recipient of the 2003 Analog Devices Outstanding Student Designer Award and a 2004 IBM Ph.D. Fellowship.

Aydin Babakhani (S’03) received the B.S. degree in electronics engineering from the Sharif University of Technology, Tehran, Iran, in 2003, the M.S. degree in electrical engineering from California Institute of Technology, Pasadena, in 2005, and is currently working toward the Ph.D. degree at the California Institute of Technology. Mr. Babakhani is the vice chair of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Metro LA/SFV joint sections MTT-S Chapter 17.1. He was the recipient of the Grand Prize of the 2006 Stanford–Berkeley–California Institute of Technology Innovators Challenge, the 2005 International Solid-State Circuits Conference Analog Devices Inc. Outstanding Student Designer Award, and the 2003 California Institute of Technology Special Institute Fellowship and Atwood Fellowship. He was also the 1998 Gold Medal recipient of the National Physics Competition and the 1999 Gold Medal recipient of the 30th International Physics Olympiad, Padova, Italy.

Abbas Komijani (S’98–M’99) received the B.S. and M.S. degrees in electronics engineering from the Sharif University of Technology, Tehran, Iran, in 1995 and 1997, respectively, and is currently working toward the Ph.D. degree at the California Institute of Technology, Pasadena. From 1997 to 1999, he was a Senior Design Engineer with Emad Semiconductors, Tehran, Iran, where he was involved with CMOS chipsets for voiceband applications. From 1999 to 2000, he was a Senior Design Engineer with Valence Semiconductors, Irvine,

CA, where he was involved with data converters for voice over Internet Protocol (VoIP) applications. His research interests include high-frequency power amplifiers, wireless transceivers, phased-array architectures, and delta–sigma data converters. Mr. Komijani was the recipient of the 1991 Silver Medal of the National Mathematics Olympiad, the 2000 California Institute of Technology Atwood Fellowship, the 2004 IEEE Custom Integrated Circuits Conference (CICC) Best Student Paper Award, the 2005 Analog Devices Outstanding Student Designer Award, the 2006 Grand Prize of the Stanford–Berkeley–California Institute of Technology Innovators’ Challenge, and the 2006 Outstanding Ph.D. Student Award presented by the Association of Professors and Scholars of Iranian Heritage (APSIH).

Ali Hajimiri (S’95–M’99) received the B.S. degree in electronics engineering from the Sharif University of Technology, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the Stanford University, Stanford, CA, in 1996 and 1998, respectively. From 1993 to 1994, he was a Design Engineer with Philips Semiconductors, where he was involved with a BiCMOS chipset for global system for mobile communications (GSM) and cellular units. In 1995, he was with Sun Microsystems, where he was involved with the UltraSPARC microprocessor’s cache RAM design methodology. During Summer 1997, he was with Lucent Technologies (Bell Laboratories), Murray Hill, NJ, where he investigated low-phase-noise integrated oscillators. In 1998, he joined the faculty of the California Institute of Technology, Pasadena, where he is currently an Associate Professor of electrical engineering and the Director of the Microelectronics Laboratory. He is a cofounder of Axiom Microdevices Inc. He authored The Design of Low Noise Oscillators (Kluwer, 1999). He holds several U.S. and European patents. He is on the Guest Editorial Board of the Transactions of the Institute of Electronics, Information and Communication Engineers of Japan (IEICE). His research interests are high-speed and RF integrated circuits. Dr. Hajimiri is a Fellow of the Okawa Foundation. He is an associate editor of the IEEE JOURNAL OF SOLID-STATE CIRCUITS. He is a member of the Technical Program Committee of the International Solid-State Circuits Conference (ISSCC). He has also served as an associate editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART II: FUNDAMENTAL THEORY AND APPLICATIONS. He is a member of the Technical Program Committees of the International Conference on Computer Aided Design (ICCAD). He was a guest editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was selected to the top 100 innovators (TR100) list in 2004. He was a recipient of the Teaching and Mentoring Award presented by the California Institute of Technology. He was the Gold Medal winner of the National Physics Competition and the Bronze Medal winner of the 21st International Physics Olympiad, Groningen, The Netherlands. He was a corecipient of the International Solid-State Circuits Conference (ISSCC) 1998 Jack Kilby Outstanding Paper Award, two-time corecipient of CICC’s Best Paper Award, and a three-time recipient of the IBM Faculty Partnership Award, as well as the National Science Foundation (NSF) CAREER Award.

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Novel Approach to the Synthesis of Microwave Diplexers Giuseppe Macchiarella, Member, IEEE, and Stefano Tamiazzo

Abstract—A procedure for synthesizing microwave diplexers is presented. It is based on the evaluation of the characteristic polynomials of the diplexer including the three-port junction connecting the TX and RX filters (two types of junctions are considered, suitable for waveguide and coaxial diplexers modeling). The novel method is particularly suited for small separation between the two diplexer channels: as known, this is the most difficult case in the diplexers design, due to the strong interaction between the TX and RX filters. The proposed synthesis approach offers noticeable design flexibility, as it allows the synthesis of the two composing filters independently of their connections to the diplexer, taking into account at the same time the interaction produced in the diplexer junction. Moreover the choice of the filters topology is absolutely arbitrary (the number of poles and the transmission zeros of the two filters have to be specified). The proposed method has been validated by the design and fabrication of a diplexer for global system for mobile communications base stations. Index Terms—Circuit synthesis, diplexers, microwave filters.

I. INTRODUCTION

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ICROWAVE diplexers are typically employed to connect the RX and TX filters of a transceiver to a single antenna through a suitable three-port junction. The increasing development over the last years of mobile communication systems has stimulated the need for compact high-selectivity diplexers to be used in both combiners for base stations and millimeter-wave point-to-point radio links. Although some efforts have been made in the past for their exact synthesis [1]–[3], the most employed approach used today for the design of microwave diplexers is based on optimization. The RX and TX filters composing the diplexer are first designed independently of the diplexer (the mutual loading effects produced by the connection of the two filters to the three-port junction are so discarded). The whole diplexer structure is then numerically optimized (if possible, using full-wave modeling) by minimizing a suitably defined error function [4], [5]. Generally this approach gives satisfactory results when the initially designed diplexer presents a frequency response sufficiently close to the required mask (as in the case of well-spaced TX and RX channels). However, when the diplexer channels are very close or even contiguous, this “brute force” approach may become too time consuming (even with the current computer-aided design

Manuscript received September 30, 2006; revised July 7, 2006. G. Macchiarella is with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, 32-20133 Milan, Italy (e-mail: [email protected]). S. Tamiazzo is with Andrew Telecommunication Products, 20041 Agrate Brianza, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885909

(CAD) tools). The convergence could also become problematic due to the large number of “local minima,” which characterizes the error function to be minimized. To bypass such difficulties, the initial synthesis of the two filters should be carried out by taking into account the reciprocal loading, which is produced in the three-port junction [6]. Even with first-order network models for the filters and the three-port junction, such a design approach may produce acceptable results for a practical diplexer realization if tuning elements are employed in the structure [2]. In the case a high accuracy is required (e.g., when the tuning elements are not allowed), the first-order design previously described may represent a very good initial point (even for contiguous channels diplexers) for the full-wave optimization of the overall structure (in this case, the convergence to an acceptable solution can be achieved with very few iterations). It must, however, be observed that, to the authors’ knowledge, there is no synthesis procedures in the literature for diplexers employing filters with arbitrary topology (those presented in [1]–[3] refer to inline Chebyshev filters without transmission zeros). The purpose of this study is to present a general synthesis procedure for diplexers employing TX and RX filters with arbitrary topology (i.e., producing complex transmission zeros with a predefined symmetry [8]). The interaction between the RX and TX filters through the specific three-port junction employed in the diplexer is taken into account during the synthesis and the best performances are obtained when the two channels of the diplexer are very close (and even contiguous). The procedure begin with the iterative evaluation of the polynomials associated to the overall diplexer once suitable constraints are posed on the reflection and transmission parameters of the diplexer. The characteristic polynomials [8] of the RX and TX filters are then evaluated with a polynomial fitting technique, and the synthesis of these filters is realized separately from the diplexer, using well-established methods [11], [12] (the filters topology depends on the imposed transmission zeros, assigned at the beginning of the synthesis procedure). The derivation of the diplexer polynomials was originally introduced in [9] for a simple shunt connection of the input ports of the two filters; here, two further types of three-port junctions have been considered, well representative of practical diplexers implementations. II. CONFIGURATION OF THE DIPLEXER A microwave diplexer is generally composed of two bandpass filters with the two input ports connected through a three-port junction (Fig. 1).

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Fig. 1. General architecture of a diplexer.

Fig. 3. Resonating junction in combline diplexers. Grey rectangles represent the metallic rods composing the coupled array. M (0; 1) and M (0; 1) are the first couplings in the two filters (not included in the junction).

1

Fig. 2. Different diplexer junctions considered in this study. (a) Type-I junction. (b) Type-II junction.

Fig. 4. Frequency mapping: From [9].

Several structures can be employed for implementing the three-port junction, depending on the operating frequency, filter technology, electrical requirements, mechanical constraints, and so on. In this study, attention has been focused on two categories of junctions, which represent a large class of practical diplexers implementations. The equivalent circuits of these junctions are shown in Fig. 2. The first network [see Fig. 2(a)] represents an equivalent circuit for a rectangular waveguide -plane tee-junction (with a suitable choice of the reference sections [10]). The transformer can be evaluated, as a first apratio and the susceptance proximation, from the waveguide dimensions with the formulas reported in [10]. The second junction type [see Fig. 2(b)] is typically found in diplexers employing coupled coaxial cavities. In this case, the common node is realized by adding an extra resonator besides those of the TX and RX filters. Fig. 3 schematically shows a possible implementation of such a junction in case of inline comb filters. The synthesis of the diplexer is carried out in a normalized bandpass frequency domain, defined by the usual low-pass . Fig. 4 frequency transformation shows the correspondence among the relevant frequency points of this transformation, together with the definition of and . , The passband limits of the RX filter are represented by , while those of the TX filter are , . Note that are not, in genthe two inner passbands limits eral, geometrically symmetric with respect to (consequently ). The two low-pass prototype filters (RX and TX) in the normalized frequency domain can be characterized separately from the diplexer through their characteristic polynomials. These are

related to the filters’ scattering parameters [8]

f

=

f

f

,

B

=

f

0

f

.

(1) where the polynomials and have degree (order and have degree of TX filter), and the polynomials (order of TX filter). Note that these polynomials have the highest degree coefficient equal to 1 (it is assumed that the number of poles for the two filters is larger than the number of and have the transmission zeros). The polynomials highest degree coefficient given by and , respectively (these values determine the return loss at the passband limits [8]). The TX and RX transmission zeros then completely define and . the normalized polynomials To evaluate the scattering parameters of the overall diplexer, the cases corresponding to the different junctions considered in this study must be analyzed separately. Note that only the scattering parameters relevant for diplexer synthesis will be consid. ered III. DEFINITION OF DIPLEXER POLYNOMIALS Assuming the overall diplexer is a lossless three-port network, four polynomials are required to define its scattering pa-

MACCHIARELLA AND TAMIAZZO: NOVEL APPROACH TO SYNTHESIS OF MICROWAVE DIPLEXERS

rameters in the low-pass normalized domain (2) is imThe highest degree coefficient of , , , and posed equal to 1 with , , and suitable normalizing corepresent the poles of efficients. Note that the roots of are the reflection zeros at the the network, the roots of common node of the diplexer (port 1 in Fig. 1), and the roots of and are the transmission zeros in the TX and RX path, respectively.

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Note that the degree of the above polynomials (the diplexer . Moreover, being the highest order) is equal to equal to 1, the polynomials degree coefficient of and are normalized as specified at the beginning of this section. For the evaluation of the remaining polynomials, the foland can be derived for the lowing expressions of considered diplexer topology:

A. Diplexer With Type-I Junction [See Fig. 2(a)]

(9)

Let consider the input admittance at port 1 (3) and are the admittances at the input ports of the where TX and RX filters with ports 2 and 3 terminated with the reference load. These admittances can be expressed as function of the TX and RX characteristic polynomials defined in the Section II

Substituting (1) and (4) in the above equations and comparing and are derived as follows: with (2),

(10)

(4) where

(5) and have the highest degree coefLet observe that and , respecficient equal to 1 and their degree is and is and . tively; the degree of Substituting (4) in (3), the following expression for is obtained: (6) The parameter of the diplexer can be expressed as funcas follows: tion of (7)

(i.e., the number of It can be observed that the order of , transmission zeros in the TX path) is equal to being the number of TX filter transmission zeros. with This means that in addition to the zeros imposed by the TX filter, additional zeros appear in the diplexer response (the zeros ). Note that these zeros do not satisfy the symmetry reof quirements of the imposed zeros (i.e., they are arbitrarily disis placed in the complex plane). Similarly, the order of , with being the number of RX filter transmission zeros (the same considerations on the additional zeros with and of hold for as well, exchanging with ). B. Diplexer With Type-II Junction [See Fig. 2(b)] To simplify the low-pass equivalent circuit for the type-II junction, it is assumed that the resonating frequency of the junction node coincides with . The shunt resonator is then replaced in the normalized frequency domain by the capacitance . The diplexer polynomials can be derived analytically as in the previous case, obtaining the following expressions:

Substituting (6) in (7) and considering definition (2) of , , , and are finally the following expressions for obtained:

(8)

(11)

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Let observe that, in this case, the number of poles (and reflecbecause of the capacitance . tion zeros) is The number of transmission zeros at infinity in the TX and RX path of the diplexer is also increased by one, again due to the resonant nature of the junction node. Finally, the considerations regarding the number of and roots presented for the type-I junction hold for type II as well.

IV. PROCEDURE FOR EVALUATING THE CHARACTERISTIC POLYNOMIALS In Section III, analytical expressions have been derived, which relate the overall diplexer polynomials to the characteristic polynomials of the RX and TX filters defined in (2). A procedure will be now introduced, allowing the evaluation of these latter polynomials, once suitable constraints are posed on the reflections and transmission parameters of the diplexer. In this way, the reciprocal loading produced by each filter on the other through the three-port junction is taken into account during the synthesis of the filters (which can be carried out independently of the diplexer, employing one of the well-established methods available in the literature [8], [11], [12]). Let consider the first constraint, which is imposed on the reflection coefficient at the input port of the diplexer: the typical requirement is constituted by an equiripple response in the RX and TX channels with a prescribed minimum level of return loss. Unfortunately, to the authors’ knowledge, an analytical method does not exist for the evaluation of the reflection zeros at the ), producing a input port of the diplexer (i.e., the roots of perfect equiripple response in the TX and RX bands. An approximate solution has been found, however, by assigning to these zeros the pure imaginary values resulting from the synthesis of the TX and RX filters, generated independently of presence of the diplexer, with a general Chebyshev characteristic (including, if desired, complex transmission zeros). Surprisingly by using this approach, at the end of the synthesis procedure, a deviation of no more than 2 dB between the return loss actually presented by the synthesized diplexer and the ideal equiripple response has been obtained. In case of a type-II junction, one of the reflection zeros is imposed by the capacitance . This zero has to be specified , with the requirement that it in the normalized domain does not affect the quasi-equiripple response determined by the other (pure imaginary) reflection zeros. This goal is achieved by a pure real value (a good choice has proven to assigning to ). This condition determines the value of . be The other constraint concerns the transmission zeros of the TX and RX filters: it is assumed that these zeros (i.e., the roots and ) are imposed a priori. of polynomials - and -paAs a consequence, these zeros also appear in rameters of the diplexer [from (10) or (11)]. A. Evaluation of the Diplexer Polynomials The synthesis procedure consists first in the derivation of the , , , and having inidiplexer polynomials tially assigned the junction topology, the reflection zeros at the input port of the diplexer, and the transmission zeros of the TX

and RX filters. Note that, assuming a lossless overall diplexer, the unitary condition of the scattering matrix imposes that

(12) depends only on the imposed Note also that for both junction types. reflection zeros being The evaluation of the diplexer polynomials is carried out iteratively according to the following steps. Step 1) Initialization: the RX and TX filters are synthesized independently of the diplexer with a general Cheby, , shev characteristic (i.e., the polynomials , , , and are generated given the number of poles , the return loss in the two channels, and the transmission zeros of the two filters). To this purpose, well-established techniques are available in the literature [8], [11], [12]. The diplexer reflection zeros are obtained from the and (for a type-II junction, a furroots of is added). An initial estimate of ther zero and is then available from the above polynomials. and are evaluated using polyStep 2) Begin iteration: and nomial convolution: Step 3) Evaluation of and : the required return loss and ) is imposed in the two channels ( at the normalized frequencies

(13) and are obtained by solving the above linear system. Applying the spectral factorization is then evaluated from its technique to (12), roots (the poles of the diplexer). and : the roots of the Step 4) New estimation of polynomial are computed with and (type-I junction) or (type-II junction). The roots are sorted with increasing imagroots are assigned to inary part. The first and the last roots are assigned to (it is assumed that the RX band is below the TX band). and are generated from their roots (the highest degree coefficients are equal to 1 for both of these polynomials). and Step 5) Convergence verification: the roots of are compared with those evaluated at the previous iteration. The procedure iterates from point 2 until

MACCHIARELLA AND TAMIAZZO: NOVEL APPROACH TO SYNTHESIS OF MICROWAVE DIPLEXERS

the maximum relative difference between new and old roots is below a prescribed level. It has been found that the convergence is typically obtained within 5–10 iterations. In case of a type-II junction, parameter is not given explicis instead specified). However, the itly (the reflection zero can be derived from inspection of and value of (11)

of

and

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as follows: polyfit polyfit

, , Finally, and the difference of

(17) , and ,

and

are obtained from the sum , as follows:

(14) where and represent the second highest degree coefficient of the two polynomials. (18) B. Computation of

and

Filter Polynomials

The second step in the diplexer synthesis is the computation of the polynomials characterizing the TX and RX filters (i.e., , , , , , and ). and can be immediately computed at the end of the iterative procedure. In and are known from the imposed transmission fact, zeros, and the coefficients and can be evaluated from and using (10) or (11) as follows:

Type-I junction

Type-II junction

(15)

To obtain the remaining polynomials, it is necessary to first and , as described in the evaluate the polynomials following. and be the roots of and , respecLet and are known at the end of the itertively (note that and ative procedure). Using (8) or (11), the values can be computed from the following expressions:

(16) where is given by for a type-I junction and for a type-II junction. Now, from the knowledge of the by degree of and ( and , respectively), one finds that the number of unknowns (the coefficients of these polynomials) is just equal to the computed values with (16). A least square polynomial interpolation then allow the derivation

C. Consideration on the Accuracy As in all design approaches of microwave filters based on the equivalence between lumped and distributed models, the accuracy of the proposed synthesis method depends, first of all, on the normalized bandwidth employed in the low-pass–bandpass transformation. In this case, such bandwidth depends on the difference between the outer bandpass frequencies of the TX and RX filters: as a consequence, the accuracy increases by reducing both the TX and RX bandwidth and their separation. The best performance of the proposed synthesis approach is then expected with contiguous channel diplexers composed of narrowband filters. V. DESIGN OF DIPLEXERS WITH TYPE-I JUNCTION Here, the circuit design of a waveguide diplexer with an -plane tee-junction will be employed to demonstrate the effectiveness of the novel synthesis technique. The RX and TX filters are all poles, inline Chebyshev filters composed of waveguide cavities coupled through inductive iris [13]. Their design will be carried out with reference to the classical network model constituted by waveguide sections cascaded with shunt-inductive reactances [13]. The design specifications for the waveguide diplexer are the following (two almost contiguous bands have been required, being the new synthesis technique specifically suited for this condition). • RX filter (all poles): : 20 dB. Passband 14.9–15.1 GHz; return loss : 7. Number of poles • TX filter (all poles): : Passband 15.15–15.35 GHz; return loss 20 dB. : 7. number of poles mm, The waveguide WR62 has been selected ( mm), determining the following values for the parameters of the tee-junction equivalent circuit [10] and . The characteristic polynomials of the diplexer have been evaluated with the iterative procedure illustrated in Section IV, ob-

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Fig. 6. Equivalent circuits for waveguide filters. (a) Prototype topology defined by the coupling matrix elements. The blocks are impedance inverters; elements are frequency invariant reactances. (b) Denormalized wavethe guide filter topology [13], [14].

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Fig. 5. Computed response of the waveguide diplexer (polynomial model).

taining the following values (the polynomial coefficients are reported in descending order):

(Fig. 6(a) shows the correspondence between the prototype ele). ments and the coupling matrix elements The parameters of the waveguide filter model [see Fig. 6(b)] are then obtained de-normalizing the prototype with the following formulas [13], [14]:

(19)

Fig. 5 shows the computed polynomial response of the diplexer, obtained from the scattering parameters (2). Note that the maximum deviation of the return loss from the ideal equiripple condition is less than 2 dB. The following step in the diplexer design has been the synthesis of the low-pass prototype of the RX and TX filters from , , and the computed characteristic polynomials and , , and (note that and coincide with and because are all pole filters are the coefficients considered here). Using well-known techniques available in the of the inline literature [8], the normalized coupling matrix canonical prototype is first derived from the filter polynomials

where ( and are defined in Fig. 4), is the : velocity of light, and is the cutoff frequency of . Let us observe that the TX and RX filters synthesized here are not synchronous (i.e., the cavities resonate at frequenare different from each other). We also observe that, cies in order to obtain the required impedance levels at the reference sections of the tee-junction, a further unit inverter (realized with ) has been introduced at the a waveguide section of length filters inputs. The length of the waveguide section in Fig. 5(b) is then given by (20) and computed for the Table I reports the matrices two filters (the elements of the first two diagonals are reported

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TABLE I COUPLING MATRIX ELEMENTS OF SYNTHETIZED TX AND RX FILTERS

TABLE II PARAMETERS OF THE DENORMALIZED TX AND RX FILTERS

Fig. 8. Simulated response of the contiguous waveguide diplexer designed with the novel procedure.

characterization of the overall diplexer structure [4], [5], [7]. As previously stated, in case of contiguous-band diplexers, a good starting point for such optimization procedures is a mandatory requirement for obtaining the convergence to an acceptable solution. To give an idea of the starting point obtainable with the novel design procedure, the waveguide diplexer considered here has been redesigned imposing two contiguous bandwidths: the corresponding simulated response is shown in Fig. 8. VI. DESIGN OF DIPLEXRS WITH TYPE-II JUNCTION

Fig. 7. Simulated response of the designed waveguide diplexer (bold curve). TX and RX filters are represented by the circuit model in Fig. 6(b). For comparison, the ideal polynomial response is also reported (light curve).

because all the others elements are equal to zero); the parameters and are given in Table II. The result of the diplexer simulation, based on circuit models, is shown in Fig. 7: the agreement with the ideal polynomial response (also reported in Fig. 7) can be considered satisfactory (the discrepancies are mainly due to the variation with frequency of the equivalent inverters parameter [14]). It has then been assessed that the novel design procedure produces satisfying results when the waveguide diplexer is represented with a network elementary model. Nevertheless the obtainable accuracy is typically acceptable for a practical diplexer realization if tuning elements (screws) are included in the fabricated device [2]. When an high accuracy is instead required (no tuning elements allowed), the design results obtained here represent a very good starting point for optimization procedures based on full-wave

Here, the design of a diplexer with a type-II junction is illustrated. The technology concerned here is that of the generalized comb filters employed in base stations for mobile communication [17]. As depicted in Fig. 3, the resonating node is realized by means of an additional resonator coupled to the first RX and TX cavities. The following requirements considered for the diplexer synthesis refer to a typical global system for mobile communications (GSM) combiner operating at 1900 MHz. • RX filter: Number of poles: 10. Band: 1845.5–1915.5 MHz. : 22 dB. Return loss Transmission zeros (MHz): 1830, 1928.5, 1932.1, 1942.8. • TX filter: Number of poles: 9. Band: 1925–1992 MHz. : 22 dB. Return loss Transmission zeros (MHz): 1890, 1905, 1910. Note that the high selectivity required calls for several transmission zeros (both in TX and RX filters). These zeros are implemented though couplings between nonadjacent resonators. The design procedure begins, as in the previous case, with , , , the evaluation of the diplexer polynomials . The imposed zeros of (reflection zeros of the and diplexer) have been obtained from the roots of the characteristic and . These polynomials (with , polynomials

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Fig. 10. Topology of the diplexer low-pass prototype. Each black node represents a unit capacitance in parallel with a frequency invariant susceptance (M (k; k )); the solid lines are admittance inverters (M (i; j )). The input node (gray) is the parallel of the capacitance c with the unit source conductance; TX and RX loads (white nodes) are unit conductances.

Denormalization of the Diplexer Low-Pass Prototype

Fig. 9. Response of the diplexer with type-II junction evaluated through the characteristic polynomials (upper graph). The lower graph shows an expanded view of jS j in the two passbands.

and , ) are computed through the method described in [11], imposing the generalized Chebyshev characteristic with the required transmissionzeros. The additional normalized reflection zero (imposed by the resonating junction) has been assigned to 1.5 (as suggested in Section IV). Fig. 9 shows the diplexer frequency response obtained from the computed polynomials. in the two passbands: it It also reports a close-up view of can be seen that the maximum peak-to-peak deviation of with respect to the equiripple condition is less that 1.5 dB. It is interesting to observe that, in addition to the imposed transmission zeros, the diplexer response exhibits additional transmission and ), which contribute to the zeros (i.e., the zeros of diplexer selectivity in the two filters stopband. Continuing with the synthesis procedure, the normalized cais obtained with (14) and the polynopacitance , , , , , and are computed mials with (15)–(18). Two suitable low-pass prototypes have been then synthesized from such polynomials. The chosen topology of the prototypes is constituted by the cascade of triplets and/or quadruplets blocks, determining the required transmission zeros (the method described in [12] has been used for the synthesis). Fig. 10 shows the resulting topology of the overall diplexer. Note that the required transmission zeros in the RX filter has been implemented through the cascade of four triplets, while the transmission zeros in the TX filter are obtained with a triplet cascaded with a quadruplet. The method described in [15] could also be employed for synthesizing the low-pass prototype of the overall diplexer (Fig. 10) in a single pass.

The diplexer low-pass prototype (Fig. 10) is globally charand acterized by means of the coupling matrices obtained from the synthesis [12]. These matrices must be de-normalized for obtaining the parameters of filters and resonating junction to be used in the physical dimensioning of the diplexer (they are the coupling coefficients, resonating frequencies, and external ’s [16]). Using the properties of the coupling matrices and inverting the low-pass–bandpass transformation adopted here (Fig. 4), the following expressions are obtained ( and are defined in Fig. 4): resonant junction

(21)

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Note that and represent the coupling coefficients between the input resonating node and the first TX and RX resrepresents the external of the resonators, respectively. onating junction loaded by the source conductance. and are the external ’s determined by the loads at ports 2 and 3 of the diplexer on the last resonators in the TX and RX filters. The following values have been obtained for the synthesized diplexer. • TX filter: : [0.0239, Main path coupling coefficients 0.0177, 0.0168, 0.0185, 0.0148, 0.0138, 0.0204, 0.0295]. ; Cross-coupling coefficients: ; ; . (MHz): [1963.77 1960.46 1943.24 1959.64 1959.5 1937.67 1956.38 1958.6 1958.43]. • RX filters: : Main path coupling coefficients [0.0257, 0.0190, 0.0177, 0.0187, 0.0186, 0.0176, 0.0181, 0.0183, 0.0280]. ; Cross-coupling coefficients: ; ; ; . (MHz): [1875.02 1878.18 1862.8 1880.24 1892.07 1879.21 1896.56 1877.32 1899.54 1880.23]. • Resonating junction parameters: (MHz): 1917.36. : 5.21. External . First TX coupling: . First RX coupling: From the above parameters, the physical dimensioning of the diplexer can be performed, employing well-known methods available in the literature [16], [17].

Fig. 11. Top view of the fabricated diplexer.

Fabrication and Testing

Fig. 12. Measured (solid line) and simulated (dashed line) diplexer response. From [9]. (Color version available online at http://ieeexplore.ieee.org.)

For validating the novel method, the designed diplexer has been fabricated employing comb coaxial cavities coupled through apertures in the common walls and tuned with screws at the inner conductor open end. Nonadjacent couplings have been realized with suitable capacitive or inductive probes. The required external ’s are obtained through taps on the inner rod and ) of the last resonators in each filter ( and on the rod constituting the resonating junction . A schematic draw of the realized diplexer is shown in Fig. 11. The length of the cavities in each filter is approximately (where the wavelength is evaluated at the center of each filter passband). The diplexer cover (not shown in this figure) includes the tuning screws employed for alignment purposes. Fig. 12 reports the measured attenuation and return loss of the diplexer with the best realized alignment in the two passbands. For comparison, the simulated response of the diplexer (obtained from the diplexer polynomials) is also reported in this figure. It can be observed that the agreement between the measured and simulated curves is very satisfactory (measurement accuracy is scarcely above 80 dB for the relatively high noise floor

of the scalar network analyzer employed; however, the agreement in the two passbands is well evident). VII. CONCLUSION An innovative approach to the synthesis of microwave diplexers has been presented. The main feature of this approach is the evaluation through an iterative procedure of the characteristic polynomials associated to a specific diplexer topology (two types of three-port junctions connecting the RX and TX filters have been considered). The characteristic polynomials of the filters are then evaluated from the diplexer polynomials, and their synthesis is performed separately from the diplexer (the filters topology is arbitrary with allowed complex transmission zeros). The synthesized filters take into account the mutual loading effect produced by their connection to the three-port junction. The simulation of the synthesized diplexer (described with a network model) gives a quasi-equiripple response in the TX and RX frequency bands (the response deviates less than 2 dB from the perfect equiripple characteristic in all cases

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considered). The novel synthesis approach gives the best performance with very close diplexer channels (even contiguous). The design accuracy may be poor, on the other hand, with widely spaced channels because the polynomial models of microwave filters become more and more inaccurate as the normalized bandwidth increases (in fact, the normalized bandwidth employed in the bandpass—low-pass transformation depends on the difference between the outer limits of the TX and RX bands). By applying specific de-normalizing formulas (presented in this paper for the considered diplexer topologies), suitable parameters can be evaluated allowing a first-order dimensioning of the diplexer. The design results can be then employed either for the fabrication of the diplexer (if tuning elements are allowed in the structure) or as a starting point for a full-wave optimization of the overall structure when very high accuracy is required (as in case of no tuning elements employed). Two implementations of the synthesis procedure have been reported, concerning waveguide and coaxial diplexers. The validation of the procedure in case of diplexers employing tuning elements has been obtained through the fabrication of the coaxial diplexer (a device for GSM 1900-MHz base stations): the measured response of the fabricated device (after the best alignment) is in excellent agreement with the expected response computed through the polynomial model of the diplexer. The extension of the presented synthesis technique to triplexers and multiplexers may be possible in case of lumped junctions (structures based on manifold are then excluded).

REFERENCES [1] J. D. Rhodes, “Direct design of symmetrical interacting bandpass channel diplexer,” Inst. Elect. Eng. J.—Microw., Opt., Acoust., vol. I, no. 1, pp. 34–40, Sep. 1976. [2] J. L. Haine and J. D. Rhodes, “Direct design formulas for asymmetric bandpass channel diplexers,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 10, pp. 807–813, Oct. 1977. [3] R. Levy, “Synthesis of non-contiguous diplexers using broadband matching theory,” in IEEE MTT-S Int. Microw. Symp. Dig., 1991, pp. 543–545. [4] M. Guglielmi, “Optimum CAD procedure for manifold diplexers,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, pp. 1081–1084. [5] Y. Rong, H.-W. Yao, K. A. Zaki, and T. G. Dolan, “Millimeter-wave -band -plane diplexers and multiplexers,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2325–2330, Dec. 1999. [6] A. Morini and T. Rozzi, “Constraints to the optimum performance and bandwidth limitations of diplexers employing symmetric threeport junctions,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 2, pp. 242–248, Feb. 1996.

Ka

H

[7] L. Accattino and M. Mongiardo, “Hybrid circuit-full-wave computer-aided design of a manifold multiplexers without tuning elements,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 9, pp. 2044–2047, Sep. 2002. [8] R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, pp. 1–10, Jan. 2003. [9] G. Macchiarella and S. Tamiazzo, “Synthesis of diplexers based on the evaluation of suitable characteristic polynomials,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 111–114. [10] N. Marcuvitz, Waveguide Handbook. NewYork: Dover, 1965. [11] G. Macchiarella, “Accurate synthesis of in-line prototype filters using cascaded triplet and quadruplet sections,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 7, pp. 1779–1783, Jul. 2002. [12] S. Tamiazzo and G. Macchiarella, “An analytical technique for the synthesis of cascaded -tuplets cross-coupled resonators microwave filters using matrix rotations,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1693–1698, May 2005. [13] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 8. [14] R. Levy, “Theory of direct-coupled-cavity filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-15, no. 6, pp. 340–348, Jun. 1967. [15] A. Garcia-Lampérez, M. Salazar-Palma, and T. K. Sarkar, “Analytical synthesis of microwave multiport networks,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 455–458. [16] H.-W. Yao, J.-F. Liang, and K. A. Zaki, “Accuracy of coupling computations and its application to DR filter design,” in IEEE MTT-S Int. Microw. Symp. Dig., 1994, pp. 723–726. [17] G. Macchiarella, “An original approach to the design of bandpass cavity filters with multiple couplings,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 2, pp. 179–187, Feb. 1997.

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Giuseppe Macchiarella (M’88) was born in Milan, Italy, in 1952. He received the Laurea degree in electronic engineering from the Politecnico di Milano, Milan, Italy, in 1975. From 1977 to 1987, he was a Researcher with the National Research Council of Italy, where he was involved in studies on microwave propagation. In 1987, he became Associate Professor of microwave engineering with the Dipartimento di Elettronica e Informazione, Politecnico di Milano. His current research is in the field of microwave circuits with special emphasis on microwave filters synthesis and power amplifier linearization. He has authored or coauthored over 80 papers and conference presentations.

Stefano Tamiazzo received the Laurea degree in telecommunication engineering from the Politecnico di Milano, Milan, Italy, in 2002, and the Master degree in Information Technology from Cefriel, Milan, Italy, in 2003. He is currently with Andrew Telecommunication Products, Agrate Brianza, Italy, where he is involved in the design of microwave filters and combiners for wireless applications.

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High-Speed Digital-to-Analog Converter Using Schottky Diode Samplers Kae-Oh Sun and Daniel Warren van der Weide, Senior Member, IEEE

Abstract—A new digital-to-analog converter (DAC) structure employing Schottky diode samplers has been developed for very high-speed operation. Instead of switching used for conventional DACs, sampling of a digital bit stream is employed to retrieve the analog signals based on sampling theory. The sampled signals are added using an R-2R resistive ladder network. The samplers are designed to provide impedance matching for reflected signals. The DAC was fabricated as a hybrid circuit, and it achieved 1 Gs/s. Due to its transmission-line architecture, our design is scalable for use at much higher frequencies, as well as higher resolutions. Fig. 1. Block diagram of a typical Nyquist-rate DAC.

Index Terms—Digital–analog conversion, digtial-to-analog converter (DAC), sampler, Schottky diode.

I. INTRODUCTION IGITAL-TO-ANALOG converters (DACs) can be classified into two different categories: Nyquist-rate DACs and oversampling DACs. Usually, Nyquist-rate DACs can produce higher frequency analog outputs, but use more complicated hardware. On the other hand, oversampling DACs have simpler hardware, but frequencies of the generated analog signal are lower. One advantage of oversampling DACs is that they have a better signal-to-noise ratio. High-speed DACs have many applications in direct digital synthesis (DDS) and software-defined radio (SDR). Nyquist-rate DACs typically convert digital data into analog signals by simply switching and adding the digital data [1]. By toggling the switches according to input data, current or voltage is modulated. Conventionally, DACs have been made based on digital circuits such as decoders or flip-flops for switching. Switches used for DACs are usually made with MOSFETs or bipolar junction transistors (BJTs) with both approaches suffering from the severe switching speed limitations inherent in their intrinsic operating characteristics such as carrier recombination time or transit delay. It is well known that current mode switching is preferred for high-speed DACs. Due to the speed limit of the transistors, great effort is required to increase the operating speed even when current mode digital logic is used. Results for

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Manuscript received April 10, 2006; revised August 6, 2006. This work was supported by the Air Force Office of Scientific Research under Grant F49620-02-1-0329. K.-O. Sun was with the Department of Electrical and Computer Engineering, University of Wisconsin–Madison, Madison, WI 53706-1691 USA. He is now with the Telecommunication Research and Development Center, Samsung Electronics, Suwon 442-600, Korea (e-mail:[email protected]). D. W. van der Weide is with the Department of Electrical and Computer Engineering, University of Wisconsin–Madison, Madison, WI 53706-1691 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.883602

high-speed DACs have been reported using digital circuits [2], [3], but there are still many constraints and technical limitations of conventional approaches. Here, we have developed a structure for implementing a very high-speed DAC based on microwave circuit principles by replacing switches with Schottky diode samplers. The Schottky diode is one of the fastest switching devices available, and can be made to have a very small input capacitance and resistance. As a result, samplers having less than a 2-ps transition time have been reported [4]–[6]. Signal sampling methods using the four-diode samplers have been published as well [7]. The sampled signals are added with an R-2R [1] resistive ladder network, which was originally developed for conventional DAC circuits. The reflections from the R-2R network, due to the large impedance mismatch, are cancelled by establishing sufficient input impedance matching at the samplers, which results in a very small amount of power returning back to the R-2R network. To achieve this, a new coplanar waveguide (CPW) employing dual signal lines is proposed and analyzed using an even-mode coupled CPW analysis method. Using these circuits, we developed a 2-bit 1-Gs/s DAC as a hybrid circuit, which will be scalable to much higher frequencies and higher resolution using integrated-circuit (IC) technology. II. DESIGN CONSIDERATION Fig. 1 shows a typical DAC structure. Digital input data toggle the switches, and the signals are then added to construct analog signal representations. In this scheme, as the operating speed of the DAC becomes very high, the line length between components cannot be ignored. Generally, impedance matching between the digital data source and the sampler is poor. When the phase delay along the interconnection line is not negligible, the should be small to avoid signal shape corwave reflection ruption. Digital data contains many harmonics and impedance should be accordingly matching used for reducing ultra-broadband. However, it is not easy to construct ultra-broadband impedance-matching circuits. One simple

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Fig. 3. Data summation concept using half-sinusoidal sampling signal.

Fig. 2. Time- and frequency-domain expressions of a sampled signal. (Color version available online at http://ieeexplore.ieee.org.)

way to solve the impedance-mismatch problem is to insert buffer amplifiers whose input and output impedances are matched to the line impedances. This is difficult when the input frequency of the digital signal is very high because the bandwidth of the buffer amplifiers should cover a range from dc to several harmonic frequencies higher. Signal sampling can solve this problem as long as the sampler can be designed properly, and it confers additional advantages. For the proposed DAC design, we replaced the switch block in Fig. 1 with diode samplers to achieve high-speed operation. Fig. 2 shows the signal sampling procedure and its corresponding time- and frequency-domain expressions. can be sampled by impulses with Ideally an analog signal zero width and infinite amplitude, but practical sampling signals have a nonzero width and finite amplitude. For example, when using a series of half-sinusoidal we sample an analog signal and , signals, the sampled signal is the convolution of and appears like Fig. 2(e) in the time domain and Fig. 2(f) in the frequency domain

(1)

(2) Equations (1) and (2) show that the sampled signal contains the frequency information of at in the frequency doevery multiple time of main, as illustrated in Fig. 2(f). Therefore, if we can generate in Fig. 2(e) from digital data, it is possible to retrieve . In order to avoid aliasing, the sampling frequency should be larger than the Nyquist sampling rate. The of signal in Fig. 2(e) can be obtained by sampling each digital bit using a half-sinusoidal signal and adding the results having different magnitude scales, as shown in Fig. 3. By sampling a

Fig. 4. Schematic diagram of the sampler.

digital word using half-sinusoidal signals before all the bits are added, nonreturn to zero (NRZ) patterns are converted into return to zero (RZ) patterns. Although these sampled signals can be added using a broadband Wilkinson power combiner [10], that configuration requires more complicated hardware such as mixers and buffer amplifiers due to the bandpass characteristic of the power combiner and poor reflection performance of the circuit components. Thus, in order to simplify the hardware and to avoid any possible distortions during frequency mixing, we developed a unique sampler structure. NRZ-to-RZ conversion also provides an advantage with regard to any glitch problems arising from imperfect timing synchronization [11]. III. SAMPLER DESIGN Fig. 4 shows the schematic diagram of the sampler. The sinusoidal local oscillator (LO) signal toggles diodes D1–D4. When it is positive, all the diodes are turned on and the RF signal is transferred to the IF port. If we assume that the diodes are perfect switches, their impedance is zero when they are turned , off and infinite when they are turned on. Thus, if is . On the other hand, the input impedance when the LO signal is negative, the diodes are turned off and no signal is transferred from the RF port to IF port. The input is . The resistance is equal to , impedance and zero with the making the reflection coefficient diodes off. In Fig. 4, the RF signal originates from digital circuits and the impedance matching may not be excellent. The IF port impedance matching may not be good either because

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Fig. 5. Wave transition from unbalanced mode to balanced mode for LO signal.

that port is connected to a signal summation circuit such as an R-2R resistance ladder or a resistor string whose impedance is not matched to the DAC line impedance. A simple way to achieve a summation circuit exhibiting good input impedance matching is to use a Wilkinson power combiner. However, this needs more complicated hardware and suffers from increased and are not zero, which means there is distortion. Thus, some signal power reflected back to the sampling diodes. The reflected signal has no effect on the sampling performance as long as it arrives at the diodes when they are off. Since the impedance of the transmisis matched to the characteristic impedance sion line when the diodes are off, no signal is going back to the RF or IF ports. Therefore, the length of the CPW line should . In this case, denotes the be an odd multiple of unbalanced mode wavelength of the CPW line for the LO signal frequency used to sample the RF and IF signal. Fig. 5 describes the mode transition of the LO signal. For simplicity, the diodes, resistors, and air-bridges are not shown in this figure. The design is different from normal CPW lines in that it has dual center lines to provide good transmission with the diodes on and good impedance matching when the diodes are off. When an LO signal excites a CPW line, it propagates in an unbalanced mode (CPW mode) until it meets a CPW–slotline junction. It then propagates in a balanced mode (slotline mode). Due to the characteristics of the balanced signal, a virtual ground is made in the middle of the dual-line CPW so, ideally, the LO-RF or LO-IF isolation should be infinite. On the other hand, the balanced LO signal toggles diodes when they are positioned between center lines of the CPW (as shown in Fig. 4). The RF and IF signals only have an unbalanced mode, which is not shown in this figure because the signals propagate along the dual line CPW, as they do for normal CPW lines, and that mode in Fig. 4. determines the line length The characteristic impedance of the dual-line CPW, however, is a function of the gap between the two signal lines. It is mainly due to the fringing electric field in the gap resulting in increased of the dual-line capacitance. The characteristic impedance CPW can be calculated by considering it as a coupled CPW. is then one-half of the even-mode characteristic impedance of the coupled CPW. The phase velocity can be also obtained in the same way. The most common method employed to analyze CPW geometry is to use a conformal mapping using a Schwartz–Christoffel transformation [12], [13]. The phase velocity and wave length can be easily obtained from the effective dielectric constant. When the geometry of a coupled CPW is

Fig. 6. Characteristic impedance variation versus center gap of the dual-line CPW.

given as shown in Fig. 6(a), the even-mode effective dielectric and the characteristic impedance are constant

(3) (4)

(5)

(6) (7)

(8)

(9)

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Fig. 8. (a) Layout of the 2-bit DAC. (b) Detailed layout of the sampler.

IV. DAC DESIGN

0

Fig. 7. Measured two-tone ! ! and IM3 as a function of LO power. (a) RF power = 0 dBm. (b) RF power = 20 dBm.

0

and are the complete elliptic integrals of the first kind and they are related as follows: (10) (11) The characteristic impedance of the dual-line CPW is then half of (4), i.e., (12) Characteristic impedance variation of the dual-line CPW versus center gap is plotted in Fig. 6(b). One of the most important factor for a sampler is intermodulation product. In particular, the third-order intermodulation (IM3) products are closely related to the filtered waveform of the DAC because they can be within the passband of the low-pass filter. Thus, it and suppress is desired to increase the power level of the IM3 level when the two-tone input is considered. Fig. 7 and IM3 powers versus the input LO power level plots for different RF powers.

The layout of the 2-bit DAC is shown in Fig. 8(a). The most significant bit (MSB) and the least significant bit (LSB) are the digital signals to be sampled. The detailed schematic of the sampler is drawn in Fig. 8(b). The RF port is for the input digital signal and the IF port is for the sampled signal being added. The LO signal in Fig. 8(a) is divided by a Wilkinson power divider and drives each sampler. Digital signals are sampled and added using an R-2R resistance ladder, which is a commonly used circuit for data summation in a conventionally designed DAC. The advantage of an R-2R ladder is that it uses only two different resistance values. Thus, it is possible to minimize the errors of resistance values caused by process variations. If we assume the characteristic impedance solely of the CPW lines connected to the R-2R network equals 50 and that those lines replace 2R, as drawn in Fig. 9, resistance R should equal 25 . In this case, lumped resistors are used for R and CPW lines having are used for 2R. Fig. 9 is a genthe characteristic impedance eral schematic of an R-2R ladder circuit with -bit sampled is the output load resistance of the IF port. In input signals. this figure, bit-0 is the LSB and bit- is the MSB. The total length of the R-2R circuit is important because the reflected or transmitted waves are returned to the samplers and those waves should arrive at the samplers during the time the diodes are off to guarantee good impedance matching. Fig. 10 is an example of the -bit signal summation. In this example, the bit-0 signal is traveling along a transmission line. When the traveling wave meets the R-2R ladder network, a part of the power is reflected back to the bit-0 sampler and the rest of

SUN AND VAN DER WEIDE: HIGH-SPEED DAC USING SCHOTTKY DIODE SAMPLERS

Fig. 9. R-2R resistance ladder network with

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N -bit input data.

Fig. 10. Reflection and transmission time difference.

it is transmitted to the other samplers through the R-2R ladder. However, if every reflected and transmitted wave arrives at the , it may cause a samplers at different time problem. The waves may reflected back to the R-2R network a second time and affect the output analog signal if the samplers do not provide sufficient impedance matching at the moment the waves arrive. Fortunately, there is some margin due to the diode turn-on voltage . For GaAs Schottky diodes, is 0.7 V. Until the LO signal reaches , the diodes are off. Thus, when the LO , signal that is applied to a sampler has a peak voltage of let us assume that the phase margin is . Since the phase margin can be taken from both rising and falling edges of an LO signal, for a single cycle of the LO. Therefore, the total margin is the length margin (LM) of the R-2R circuit can be expressed as follows: (13) (14)

and in Fig. 8(a) As mentioned earlier, the length for the CPW mode and should be an odd multiple of should be quarter-wave length for the slotline mode. Since the samplers work based on different modes (CPW mode, slotline mode), the slotline mode length should be defined separately is in Fig. 8(a) and (b). Thus, for a better connectivity, , while can be . a good choice for

Fig. 11. Various waveforms generated by the DAC. (a) 15-MHz square wave. (b) 30-MHz square wave. (c) 80-MHz square wave. (d) 15-MHz sawtooth wave. (e) 30-MHz sawtooth wave. (f) 80-MHz sawtooth wave. (g) 200-MHz sine wave. (h) DC.

V. DAC TEST MEASUREMENT RESULTS The DAC was fabricated on an RO3010 board ( , in) made by the Rogers Corporation, Rogers, thickness CT. The most important parameters regarding the sampler design is the RF/IF reflection coefficient with the diodes off and the ports isolated. Isolations between the LO port and the other ports are less important because the LO frequency is filtered out at the output. However, the RF/IF isolation is critical. For a DAC test, a 17-dBm 1-GHz sinusoidal signal was applied to the LO port. To avoid aliasing, low-pass filters whose bandwidth is 300 MHz instead of sampling frequency/2 were used at the DAC output port and the RF input ports. Fig. 11 shows various waveforms generated by the DAC.

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VI. CONCLUSION We have developed a 2-bit 1-Gs/s DAC structure, which is scalable to microwave frequencies and has been fabricated as a hybrid circuit. The resolution of the proposed structure depends on the accuracy of the resistors, especially in the R-2R resistive ladder network. The physical size of the resistors should be determined by considering the power and operating frequency. The length of the resistors may be more important as the number of bits and the operating frequency increase. Although a narrower or thinner resistor has higher sheet resistance and needs shorter length for a certain resistance value, it can handle less power. Thus, a careful tradeoff must be made in such a case.

REFERENCES [1] J. W. Bruce, “Nyquist-rate digital-to-analog converter architecture,” IEEE Potentials, vol. 20, no. 3, pp. 24–28, Aug. 2001. [2] W. Cheng, W. Ali, M. Choi, K. Liu, T. Tat, D. Devendorf, L. Linder, and R. Stevens, “A 3b 40 GS/s ADC-DAC in 0.12 m SiGe,” in IEEE Int. Solid-State Circuits Conf., Feb. 2004, vol. 1, pp. 262–263. [3] P. Schvan, D. Pollex, and T. Bellingrath, “A 22 GS/s 6b DAC with integrated digital ramp generator,” in IEEE Int. Solid-State Circuits Conf., Feb. 2005, vol. 1, pp. 122–123. [4] M. J. Rodwell, M. Kamegawa, R. Yu, M. Case, E. Carman, and K. S. Giboney, “GaAs nonlinear transmission lines for picosecond pulse generation and millimeter-wave sampling,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 7, pp. 1194–1204, Jul. 1991. [5] R. Marsland, C. Madden, D. van der Weide, M. Shakouri, and D. Bloom, “Monolithic integrated circuits for mm wave instrumentation,” in Gallium Arsenide Integr. Circuit Symp., Oct. 1990, pp. 19–22. [6] D. van der Weide, J. Bostak, B. Auld, and D. Bloom, “All electronic free-space picosecond pulse generation and detection,” Electron. Lett., vol. 27, pp. 1412–1413, Aug. 1991. [7] S. H. Pepper, “Quadrature/correlating sampler and pulse generator for mmwave UWB QAM modulation and wideband signaling,” in Eur. Radar Conf., Oct. 2005, pp. 419–422. [8] S. Cohn, “A class of broadband three-port TEM-mode hybrids,” IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 2, pp. 110–116, Feb. 1968. [9] C. Q. Li, S. Li, and R. Bosisio, “CAD/CAE design of an improved wideband Wilkinson power divider,” Microw. J., pp. 125–136, Nov. 1984. [10] K. Sun and D. van der Weide, “DAC design method based on microwave circuit principles,” presented at the IEEE MTT-S Int. Microw. Symp., Jun. 2006.

[11] D. Mercey, “A 16-b D/A converter with increased spurious free dynamic range,” IEEE J. Solid-State Circuits, vol. 29, no. 10, pp. 1180–1185, Oct. 1994. [12] C. P. Wen, “Coplanar waveguide: A surface strip transmission line suitable for nonreciprocal gyromagnetic device applications,” IEEE Trans. Microw. Theory Tech., vol. MTT-17, no. 12, pp. 1087–1090, Dec. 1969. [13] R. N. Simons, Coplanar Waveguide Circuits, Components, and Systems. New York: Wiley, 2001, ch. 7, pp. 182–186. Kae-Oh Sun received the B.S. and M.S. degrees from Chonnam National University, Kwangju, Korea, in 1991 and 1994, respectively, and the Ph.D. degree in electrical engineering from the University of Wisconsin–Madison, in 2006. From 1994 to 2000, he was a Researcher with the Agency for Defense Development, Daejon, Korea, where he developed a switching-mode power supply and controller for a missile system. He is currently a Senior Research Engineer with the Telecommunication Research and Development Center, Samsung Electronics, Suwon, Korea. His research interests are passive and active RF/microwave circuits.

Daniel Warren van der Weide (S’86–M’86– SM’06) received the B.S.E.E. degree from the University of Iowa, Ames, in 1987, and the Master’s and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1989 and 1993, respectively. He has held summer positions with Lawrence-Livermore National Laboratory and the Hewlett-Packard Company, as well as full-time positions with Motorola as an Engineer and Watkins-Johnson Company as a Member of the Technical Staff. From 1993 to 1995, he was a Post-Doctoral Researcher with the Max-Planck-Institut für Festkörperforschung (Solid State Research), Stuttgart, Germany, after which he joined the Department of Electrical and Computer Engineering, University of Delaware, as an Assistant and Associate Professor and Director of the Center for Nanomachined Surfaces. In 1999, he joined the Department of Electrical and Computer Engineering at the University of Wisconsin–Madison, as an Associate Professor, becoming a Full Professor in 2004. His current research involves ultrafast electronics, low-dimensional electron systems, and the application of high-frequency techniques in biotechnology. He was the Principal Investigator on a 2003 Air Force Office of Scientific Research (AFOSR) Multiuniversity Research Initiative (MURI) entitled “Nanoprobe Tools for Molecular Spectroscopy and Control.” From 2002 to 2004, he was a University of Wisconsin Vilas Associate. Dr. van der Weide was the recipient of the 1997 National Science Foundation (NSF) CAREER Award and PECASE Award and the 1998 Office of Naval Research (ONR) Young Investigator Program award.

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Uniaxial and Radial Anisotropy Models for Finite-Volume Maxwellian Absorber Krishnaswamy Sankaran, Student Member, IEEE, Christophe Fumeaux, Member, IEEE, and Rüdiger Vahldieck, Fellow, IEEE

Abstract—The uniaxial finite-volume Maxwellian absorber used as a perfectly matched layer is extended to incorporate radial anisotropy for modeling cylindrical geometries. Theoretical background and practical applications of both uniaxial and radial absorber models are presented. Both these models employ spatially and temporally co-located electromagnetic field quantities in an unstructured mesh. The uniaxial Maxwellian absorber model is tested for a truncated waveguide problem. The influence of absorber thickness and material loss parameter on the performance of the model is analyzed. Numerical reflection coefficients down to 60 dB are achieved for fine mesh discretization with approximately 20 points per wavelength confirming the convergence of numerical results. As an extension of the technique, a radially anisotropic absorber model is tested for cylindrical mesh truncation using a representative problem involving two different test scenarios. Results are compared with an existing technique commonly used in finite-volume time-domain simulations, demonstrating substantial reduction in numerical error due to cylindrical mesh truncation. Index Terms—Computational electromagnetics (CEM), finite volume time domain (FVTD), Maxwellian absorber, perfectly matched layer (PML), radial absorber.

I. INTRODUCTION FINITE-VOLUME-BASED uniaxial Maxwellian absorber was introduced by the authors in [1] with an application to waveguide truncation problem. For scattering and antenna applications, this uniaxial model suffers from inaccuracies originating from the corner regions, which are the major sources of numerical reflections (inaccuracies) in the computed solution. Therefore, to avoid the corner regions, a radial absorber model is introduced in this paper. This radial Maxwellian absorber model uses a novel approach to achieve anisotropy in the radial direction and can be efficiently used in applications involving cylindrical or spherical geometries. The theory of the radial absorber is developed as an extension to the uniaxial model, and supporting numerical experiments are presented. The present finite-volume time-domain (FVTD) approach naturally adapts the model for application on unstructured meshes and it is based on the modified Lorentz material response of lossy dielectric media, as proposed in [2]–[4]. As compared to the convolutional perfectly matched layer (PML) discussed in [5], there is no need for performing a convolution

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Manuscript received April 6, 2006; revised August 9, 2006. This work was supported under ETH Research Grant TH-38/04-1. The authors are with the Laboratory for Electromagnetic Fields and Microwave Electronics, Swiss Federal Institute of Technology Zürich, Zürich CH-8092, Switzerland (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885577

operation during each time step. Furthermore, there is no need for unphysical field-splitting, as in the case of Bérenger’s split PMLs [6], [7] and, hence, the model satisfies Maxwell equations both inside and outside the absorber region. Unsplit-PML models have been previously studied. mainly in the framework of the spatially and temporally staggered finite-difference time-domain (FDTD) method or for the finite-element time-domain (FETD) method. The standard staircase approximation near domain boundaries impose constraints on the flexibility and accuracy of the FDTD method. This creates a strong motivation for the development of the FVTD method, which can handle unstructured meshes and additionally enables spatially and temporally co-located field storage. Using curvilinear PML models, the corner regions can be avoided in the computational domain. The curvilinear PML models reported in [8]–[11] were adapted mainly for FDTD and FETD methods, which uses update equations represented in cylindrical coordinate. The new finite-volume radial absorber model introduced in this paper is based on a different approach, which capitalizes on the capability of the FVTD method to handle unstructured mesh to its full advantage. Hence, the modeling of cylindrical geometry becomes possible without the need for coordinate transformation, as in the case of FDTD simulations. Achieving radial anisotropy using Cartesian domain formulation involves rotational transformation from locally uniaxial to globally radial behavior of the material loss parameter. This paper is organized as follows. In Section II, a brief introduction of the FVTD method is presented for modeling the modified Lorentz media. In Section III, a two-dimensional (2-D) FVTD formulation of the modified lossy Lorentz media is discussed and the relevant update equations are presented. A practical application of the uniaxial finite-volume absorber is demonstrated for the waveguide truncation problem. Some numerical implementation aspects of the uniaxial Maxwellian absorber are discussed, emphasizing the optimal choice of absorber thickness and material loss parameter. The theory of radial finite-volume Maxwellian absorber is introduced in Section IV. The concept of radial anisotropy is explained using a locally rotated uniaxial absorber model. As a validation, the radial absorber is tested for sample problems with cylindrical geometry. Finally, the performance of the radial absorber is compared with an existing mesh truncation technique. II. FVTD MODEL OF MODIFIED LORENTZ MEDIA In the context of FVTD modeling, the continuous time-dependent Maxwell equations are discretized both in space and is called a time using finite samples. Each spatial-sample corresponds control volume or cell and the temporal-sample

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to the update time step. Depending on the method of storing and updating the field quantities, different FVTD schemes are possible. For a detailed description of the FVTD method, please refer to [12]–[15]. The absorber model presented here provides simple and consistent co-located spatial and temporal field variations. In the following analysis, a 2-D transverse electric model with the electric field along the -axis and the magnetic field in the -plane ( and ) is employed. This 2-D model is tested on computational domains meshed with unstructured (conformal) triangular cells. Using the divergence theorem, the FVTD update equations inside each cell of the dielectric medium is cast in the form [14]

-axis is considered. The frequency-domain electric and magthen renetic susceptibilities of the modified Lorentz media sults in the relative permittivity and permeability tensors given by

(1)

(4)

where denotes the electromagnetic (EM) field vector with the superscript representing the matrix transpose. Each th polyhedral cell is made of faces and has a control-volume (corresponding to an area in the 2-D model). (length in the 2-D model) Each th face has an area of takes the value and a unit outward-normal . The factor and permittivity for the of free-space permeability magnetic and electric field update equations, respectively. The represents the components of vector and polarization fields inside the dielectric magnetization is called the flux function in the medium. The factor FVTD nomenclature and plays a crucial role in information exchange between adjacent cells.

III. UNIAXIAL FINITE-VOLUME MAXWELLIAN ABSORBER The polarization and magnetization field vectors of the modified lossy Lorentz media were previously used to model FDTD-based absorbing boundary conditions (ABCs) [2], [3]. These auxiliary field quantities, when included in the FVTD formulation, result in computational overhead due to additional update equations involving flux terms. In this paper, a modified approach, which reduces the computational overhead in the FVTD method, is employed to model the Maxwellian absorber model of the on a 2-D unstructured triangular grid. The modified (time-derivative) Lorentz material yields the magnetization and polarization equations as follows [4]:

(3) where the superscript denotes the modified Lorentz model due to the additional time-derivative term in (2). The frequencydomain electric and magnetic susceptibilities are directly obtained from (2) using Fourier transformation as follows:

where subscript represents the frequency-domain value with corresponding to the center frequency of the incident EM excitation. As proposed in [2], the modified Lorentz model behaves like a uniaxial absorber if it satisfies the following constraints. and : this implies that the frequency of • operation is much higher than the narrow resonance band of the material. : this avoids dispersion inside the absorber. • Under these constraints, (3) and (4) results in the modified polarization and magnetization field equations written as (5) (6) (7) The factor is the material loss parameter inside the Maxwellian . Using these constraints absorber, which is given by in (3) and (4), the modified polarization and magnetization fields are used to derive the field update equations, as given in [1] (8)

(9)

(10) (11)

additional term (2)

and where the material resonance-frequency is denoted as the resonance bandwidth is given by . The factor relates and to and , respectively. Similarly, the term couples and with time histories of or , respectively. In particplays a crucial role for numerical modeling ular, the factor and will be the subject of a detailed analysis in Section III-A. For a perfectly matched interface, a uniaxial absorber along the

where each component of explicitly depends on all the field quantities in . The factors of polarization and magnetization currents in (9) and (10) have the form of lossy conductivity terms inside the Maxwellian absorber. It can be noticed from the above system of equations that there are three standard EM field equations in (8)–(10) and an additional update , as in [16]. In contrast to [4], the equation for the scalar field is an ordinary differenupdate equation of the fourth field tial equation (ODE) in time and, hence, there is no substantial increase in the computational effort. Equations (8)–(11) constitute the final set of equations required to update the electric and

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Fig. 1. Models for calculating reflection coefficient. (top) Reference model. (bottom) Test model. From [1].

magnetic field quantities. The whole computational domain is subdivided into two parts, namely, the main computational doand the FVTD Maxwellian absorber domain . main The final update equations are similar in both domains with the inside and inside additional requirement that . This highlights an important advantage of Maxwellian absorber as compared to the split PML [6]. A parabolic profile is , increasing from 0 at chosen for the variation of inside the free-space absorber (FS-A) interface to a maximum value at the absorber truncation boundary. In numerical experiments reported before in [2] and [6], this choice of profile variation resulted in optimal performance. Furthermore, the tolerance range of the parabolic profile was found to be better compared to other options [17]. A. Practical Application: Waveguide Truncation Problem The performance of the FVTD Maxwellian absorber on unstructured mesh is tested using a 2-D parallel-plate waveguide problem. The waveguide is assumed to have infinite symmetry along the transverse -axis. The wave propagation direction is -axis. A perfect electrically conducting (PEC) towards the boundary condition (BC) is forced on the two sides of the waveguide. The proposed FVTD Maxwellian absorber is used to truncate the waveguide perpendicularly to the -axis. In order to verify the practical applicability of the FVTD Maxwellian absorber under the constraint of limited computational resource, , where the thickness of the absorber is first fixed to corresponds to the wavelength at the center frequency of the EM excitation (pulse or harmonic). A triangular spatial disis used for the cretization with cell edge dimensions of results presented here. In order to quantify the performance, the numerical reflection coefficient from the FVTD Maxwellian absorber is calculated for various angles of wave incidence. Considering the plane wave decomposition model of a waveguide mode, changing the width of the waveguide is equivalent to changing the angle of incidence with respect to the FS-A interface. For each angle of incidence, two models are built, namely, the reference and test models. The reference model is divided into two parts, one with exactly the same domain cells as in the test model, and the other , an extension, which is truncated by a first-order Silver–Mueller ABC (SM-ABC), as shown in Fig. 1. The numerical reflection is computed by subtracting the reference field values from those of the test model. The model in Fig. 1 is used to study the reflection coefficient at different angles of incidence using a first-order TE-mode excitation. The analysis is carried

Fig. 2. Angular response of the FVTD Maxwellian absorber for different material loss parameter  . From [1].

out over a range of incidence angles from near normal to 60 , which is of practical interest. The numerical reflection coefficient is calculated for different values of maximum material loss parameter and the results are shown in Fig. 2 for , , and . For lower values of , e.g., , a relatively high numerical reflection coefficient exists, which is primarily originating from the absorber truncating (PEC) BC. On the other hand, for , the numerical reflection comes higher values, i.e., from the FS-A interface. In fact, the later numerical reflection is mainly due to the spatial discretization errors. For most of the resulted in minimum numerical simulations, a value of reflection. B. Absorber Thickness Versus Performance The thickness of the absorber has a strong influence on its performance. In addition, the material loss parameter controls the damping behavior inside the absorber. In the case of split-field Bérenger PML [6], [17], for a desired (theoretical) reflection coefficient and a given thickness and loss profile inside the absorber, one could easily find the required value of maximum loss inside the PML. On the contrary, for the Maxwellian absorber model, there exists no straightforward way of deriving the maximum loss parameter required for a specified (theoretical) reflection coefficient considering the given constraints on the absorber thickness and loss profile. Hence, the study of combined effects of material loss parameter and absorber thickness on performance is a vital information for practical application of the absorber. With this objective, a model with triangular spais tested for tial discretization with edge dimension various absorber thicknesses ranging from to . The numerical reflection coefficients are computed for three difdefined as before. ferent values of material loss parameter The results of the analysis are shown in Figs. 3–5. As noticed in Fig. 3, the overall performance of the model is very low for . Especially, for absorber thickness , this results in high reflection. Therefore, for acchoice ceptable performance, a large absorber thickness is required, which increases the computational effort. The reason for this high reflection is a direct consequence of the very low damping present inside the absorber domain. Hence, in spite of damping of the wave on its forward and return paths, a significant part of the power is reflected back into the main computational domain

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Fig. 6. Graphical illustration of radial anisotropy using coordinate transformation by rotation.

Fig. 3. Effect of absorber thickness on its performance at three different angles of incidence for material loss parameter  = 1! .

of material loss parameter (e.g., as in Fig. 3), these oscillations are not observed due to the large undamped reflection originating from the truncating PEC, which is many orders higher than the reflection from the initial FS-A interface. This analysis typically in the indicates that, by choosing a large value of range of , one could opt for an absorber thickness smaller . When the value of is increased beyond a certain than , stability problems were encountered, which sets limit a maximum limit in choosing for practical applications. IV. RADIAL FINITE-VOLUME MAXWELLIAN ABSORBER

Fig. 4. Effect of absorber thickness on its performance at three different angles of incidence for material loss parameter  = 2! .

The concept of radially anisotropic cylindrical PML was reported in the framework of FDTD in [8]–[10] and for FETD applications in [11]. All these previous attempts in modeling cylindrical PML were motivated by representing Maxwell equations in the cylindrical coordinate system. Especially in the FDTD approach, in order to avoid staircasing errors at curved domain boundaries, curvilinear mesh arrangement were developed with update equations using the cylindrical coordinate system. On the contrary, within the framework of FVTD, unstructured meshing of the computational domain permits modeling of curved surfaces with a high level of accuracy and flexibility. In other words, the feature of the unstructured spatial discretization enables the FVTD method to model domain boundaries of any shape in a generalized manner. Consequently, there is no need for a special type of mesh arrangement like a curvilinear mesh and, thus, transforming the system update equations to a cylindrical coordinate system is not required. In the following, the theory of radial finite-volume absorbers is discussed in detail and a problem with two test scenarios in cylindrical geometry are simulated. A. Radial Anisotropy: Rotated Coordinate Analysis

Fig. 5. Effect of absorber thickness on its performance at three different angles of incidence for material loss parameter  = 8! .

from the truncating PEC of the absorber. When the value of is increased to and , the damping inside the absorber is substantially increased, resulting in improvement in the performance shown in Figs. 4 and 5. The oscillations noticed in the numerical reflection coefficient value in Fig. 5 correspond to constructive and destructive interferences between waves reflected at the FS-A interface and at the truncating PEC. For low values

The direction of wave attenuation inside the absorber is given by the direction of anisotropy. In the previous discussion on the uniaxial material absorber model, the anisotropy direction was chosen along the -axis. In contrast, when considering a radial absorber model described in the cylindrical coordinate , the anisotropy is defined in the radial direcsystem tion . In other words, as illustrated in Fig. 6, the local direction of anisotropy is along the -direction and the local cocan be viewed as a rotational transformaordinate through an angle in tion of the global coordinate formulation, the magnetic the -plane. For the assumed and electric field components in the rotated axes are given by

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. As clearly noticed, the rotational transformation in the -plane has no effect on the electric field comalong the -axis. The field transformation from the ponent global to the local axes is given by

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Using (21) and (22) in (18) and after some algebraic manipulations, all the field components inside the radial absorber can be expressed as follows:

(23) (12) where denotes the rotation matrix defined by the angle of rotation . The system of equations in the local coordinate is written as [1] (13) (14) (15) (16) Apart from the standard field vectors defined in , there is a , which represents the magnetic counscalar field given by terpart of polarization current, as defined in [1] and [4]. The above set of update equations differ from that of the uniaxial ab. Here, sorber (8)–(11) with respect to the fourth scalar field the update equation of the fourth field is represented as a partial differential equation (PDE) in space and time variables. In fact, one could also define the fourth field update equation as an ODE in time, as discussed in [1], but here, the usage of a PDE form of the update equation instead of an ODE ensures mathematical simplicity in modeling radial anisotropy. Numerically, once the is known, the flux function of is diflux function of with an appropriate change of rectly obtained from that of sign. In order to model the radial anisotropy using the field vecdefined in the global coordinate , all the tors and local field quantities inside each control volume must be transformed back to the global coordinate system. This reverse transformation from the local to global coordinate system is achieved using the following relation:

(24) (25) (26) Comparing (13)–(15) with (23)–(25), it is noticed that the transformation from the local coordinate to the global coordinate does not change the structure of Maxwell equations, except for the lower order terms (terms with no spatial derivatives). This is a direct consequence of rotational invariance of the Maxwell should also be split system. Logically the fourth scalar field into two components in the - and -directions. However, in the system of update (23)–(26), this fourth field can still be represented in the local coordinate system. It should be also noticed that the right-hand side of the fourth update (26) is represented in global coordinates. This mathematical manipulation is deliberate in order to use four instead of five update equations. There are clearly two extreme situations, which can be directly tested and . from the above update (23)–(26), namely, These two situations yield update equations corresponding to - and -directions, respectively. Finally, the uniaxial in the system of equations representing the radial absorber model is written using the flux-based FVTD update equations as follows:

(27)

(28) (17) (29) Similarly, the field quantities in the local coordinate should be transformed to the global coordinate as follows: (18) For complete modeling of the radial anisotropy in the global coordinate, the partial derivatives ( , ) present in (13)–(16) should be transformed back to the global coordinate using the chain rule as follows: (19) (20) Substituting (17) in (19) and (20) results in the following: (21) (22)

(30) Interestingly, the flux terms computed for (27) and (28) can be reused in (30) and this flux recycling helps in reducing computational effort. B. Numerical Experiments For testing the radial finite-volume absorber formulation, a test problem is chosen and, as before, two models (test and reference) are created (Fig. 7). For all the experiments carried out here, the thickness of the absorber is fixed to and

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Fig. 7. Model problem illustrating the test and reference domains. The test model of radius of approximately 3:33 is truncated using the finite-volume = 0:5. Maxwellian absorber of thickness d

Fig. 9. Comparison of results of numerical error using SM-ABC and finitevolume Maxwellian absorber for the centered-source scenario. Fig. 8. Different angles of incidence at the FS-A interface based on source location.

the material loss parameter is fixed to . These values are chosen from the results of the uniaxial absorber model discussed before (refer to Fig. 5). The spatial discretization employed in the following problem corresponds to triangular cells with edge . Two representative numerical experiments dimensions were carried out as illustrated in Fig. 8. In the first example, the 2-D model of the cylindrical domain is excited with an axial line source placed exactly at the center of the cylindrical domain, as depicted on the left-hand side of Fig. 8. The electric field of the line source is impressed with a time–harmonic source function. Since the location of the line source is exactly at the center, the generated cylindrical wave will impinge on the FS-A interface uniformly at all locations on the at normal incidence, i.e., FS-A interface. The numerical error due to truncation using the radial absorber is computed from the difference in field values between the test and reference model. In the second experiment, the source location is shifted towards one side, as shown on the right-hand side of Fig. 8. In this case, a large range of incidence angles will be involved. The performance of the radial absorber is compared with the first-order accurate SM-ABC commonly used in FVTD simulations. The results of the first numerical experiment is shown in Fig. 9. Theoretically, at normal incidence, the SM-ABC is a perfect ABC. Numerically, it performs at its best and its accuracy is comparable to that of the finite-volume

radial absorber. The reflection at normal incidence in the case of the radial absorber is predominantly due to discretization errors inside the absorber. When the source location is displaced away from the center, a wide range of incidence angles comes into action and the performance of the SM-ABC degrades drastically. In this case, the performance of the finite-volume radial absorber is substantially better than SM-ABC and the numerical error remains stable for any source location (Fig. 10). The numerical reflection due to the finite-volume radial absorber computed at a test point is compared with that of the SM-ABC, and the results are shown in Fig. 11. As clearly observed, the performance of the finite-volume absorber model is approximately 10 dB better than the SM-ABC. The apparent degradation in the performance compared to the uniaxial model is not unexpected because it is due to multiple reflections at grazing angles of incidence. Nevertheless, the performance of the radial absorber confirms a significant improvement compared to the existing SM-ABC. C. Outlook for Extension to Three-Dimensional (3-D) Geometries The proposed radial absorber can be generalized to 3-D geometries in two different ways. The first option is to employ a spherical absorber model with the direction of anisotropy defined along the radial direction. In order to represent the update equations only using the global field values, one has to perform a

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However, for elongated structures, employing a spherical absorber for domain truncation will drastically increase the computational volume. Hence, to avoid the computational overhead, a second option is proposed employing a cylindrical absorber model with two hemispherical absorbers appended as the top and bottom covers. Without loss of generality, if the -axis is assumed to align along the longer dimension of the elongated structure, then a cylindrical absorber can be employed with the -axis chosen as the axis of the absorber. Appending spherical absorbers on the top and bottom of the cylindrical absorber avoids corner regions and, hence, offers more accurate domain truncation. The proposed idea for 3-D extension is currently under further investigation and will be a topic of interest in the future. V. CONCLUSIONS

Fig. 10. Comparison of results of numerical error using SM-ABC and finitevolume Maxwellian absorber for the off-centered source scenario.

A new model for mesh truncation using uniaxial Maxwellian absorber in the framework of FVTD was introduced. The performance of the uniaxial absorber was tested for angular response using a coarse spatial discretization with around 12 points per wavelength. For a variation of the angle of incidence from near normal to 50 , the reflection coefficient of the FVTD Maxwellian absorber was lower than 40 dB, demonstrating the good performance achieved in practice for such coarse spatial discretization. The accuracy of the proposed model was found to further increase when employed on meshes with spatial discretization with approximately 20 points per wavelength. Numerical reflection coefficients in the range of 60 dB were achieved on fine meshes confirming convergence of numerical results. The uniaxial finite-volume Maxwellian absorber was further extended for modeling cylindrical geometries. The modified formulation of the radial absorber adapts naturally to the FVTD algorithm without any need for coordinate transformation, convolution, or curvilinear meshing. The performance of the radial absorber was compared with the existing SM-ABC. The overall performance of the radial absorber was found to be significantly better than the existing mesh truncation technique in the framework of the FVTD method. REFERENCES

Fig. 11. Comparison of numerical reflection at a test point due to the finitevolume Maxwellian absorber and SM-ABC for the example scenario shown in the inset.

inverse transformation for obtaining a locally uniaxial and globally spherical absorber behavior. Contrary to the 2-D radial absorber case, the spherical transformation will affect all the field components due to two degrees of rotation involved.

[1] K. Sankaran, C. Fumeaux, and R. Vahldieck, “Finite-volume Maxwellian absorber on unstructured grid,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 169–172. [2] R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials,” IEEE Trans. Antennas Propag., vol. 45, no. 4, pp. 656–671, Apr. 1997. [3] ——, “Time-derivative Lorentz materials and their utilization as electromagnetic absorbers,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 55, no. 6, pp. 7696–7703, Jun. 1997. [4] ——, “Time-derivative Lorentz material model-based absorbing boundary condition,” IEEE Trans. Antennas Propag., vol. 45, no. 10, pp. 1530–1535, Oct. 1997. [5] A. Roden and S. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, no. 5, pp. 334–339, 2000. [6] J.-P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, no. 2, pp. 185–200, 1994. [7] ——, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 127, no. 2, pp. 363–379, Sep. 1996.

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[8] F. Collino and P. Monk, “The perfectly matched layer in curvilinear coordinates,” SIAM J. Sci. Comput., vol. 19, pp. 2061–2090, Nov. 1998. [9] F. L. Teixeira and W. C. Chew, “Perfectly matched layer in cylindrical coordinates,” in IEEE AP-S Int. Symp., Jul. 1997, vol. 3, pp. 1908–1911. [10] P. G. Petropoulos, “Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell equations in rectilinear, cylindrical, and spherical coordinates,” SIAM J. Appl. Math., vol. 60, pp. 1037–1058, Feb.–March 2000. [11] M. Kuzuo˘glu and R. Mittra, “Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 474–486, Mar. 1997. [12] N. K. Madsen and R. W. Ziolkowski, “A three-dimensional modified finite volume technique for Maxwell’s equations,” Electromagnetics, vol. 10, pp. 147–161, 1990. [13] V. Shankar, A. H. Mohammadian, and W. F. Hall, “A time-domain, finite-volume treatment for the Maxwell equations,” Electromagnetics, vol. 10, pp. 127–145, 1990. [14] P. Bonnet, X. Ferrieres, B. Michielsen, P. Klotz, and J. Roumiguiéres, Time Domain Electromagnetics, S. M. Rao, Ed. New York: Academic, 1997, ch. 9, pp. 307–367. [15] C. Fumeaux, D. Baumann, P. Leuchtmann, and R. Vahldieck, “A generalized local time-step scheme for efficient FVTD simulations in strongly inhomogeneous meshes,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 1067–1076, Mar. 2004. [16] S. Abarbanel and D. Gottlieb, “On the construction and analysis of absorbing layers in CEM,” Appl. Numer. Math., no. 27, pp. 331–340, 1998. [17] K. Sankaran, C. Fumeaux, and R. Vahldieck, “Cell-centered finite-volume based perfectly matched layer for time domain maxwell system,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp. 1269–1276, Mar. 2006.

Krishnaswamy Sankaran (S’98) received the B.Eng. degree (with a first-class distinction) in electrical and electronics engineering from the University of Madras, Madras, India, in 2002, the M.Sc. degree in information and communication engineering from the University of Karlsruhe TH, Karlsruhe, Germany, in 2004, and is currently working toward the Ph.D. degree from the Swiss Federal Institute of Technology (ETH) Zürich, Zürich, Switzerland. From October 2003 to May 2004, he was a Research Trainee with the European Commission, Joint Research Centre, Ispra, Italy, where he was involved in the field of radar systems engineering and remote sensing. In June 2004, he joined the ETH Zürich, where he is currently with the Laboratory for Electromagnetic Field Theory and Microwave Electronics (IFH). His main research interests are numerical methods for solving EM field problems, computational physics, and applied mathematics. Mr. Sankaran is currently vice-chair of the IEEE Student Branch Zürich. He was the recipient of a full postgraduate scholarship and he was one of the recipients of the 2006 Best Student Paper Award presented at the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), San Francisco, CA.

Christophe Fumeaux (M’03) received the Diploma and Ph.D. degrees in physics from the Swiss Federal Institute of Technology (ETH) Zürich, Switzerland, in 1992 and 1997, respectively. From 1998 to 2000, he was a Post-Doctoral Researcher involved in infrared technology with the School of Optics, University of Central Florida, Orlando. In 2000, he joined the Swiss Federal Office of Metrology, Bern, Switzerland, as a Scientific Staff Member. Since 2001, he has been a Research Associate with the Laboratory for Electromagnetic Fields and Microwave Electronics (IFH), ETH Zürich, Switzerland. During Fall 2005, he was a Visiting Scientist with the Laboratory of Sciences and Materials for Electronics, and of automatic (LASMEA), University of Blaise Pascal, Clermont-Ferrand, France. His current main research interest concerns computational electromagnetics in the time domain for numerical analysis of microwave circuits and antennas. Dr. Fumeaux has been the chairman of the IEEE Swiss Joint Chapter on Microwave Theory and Techniques, Antennas and Propagation, and Electromagnetic Compatibility (EMC) since January 2006. He was the recipient of the ETH Silver Medal of Excellence for his doctoral dissertation. He was the corecipient of the 2004 Applied Computational Electromagnetics Society (ACES) Outstanding Paper Award.

Rüdiger Vahldieck (M’85–SM’86–F’99) received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from the University of Bremen, Bremen, Germany, in 1980 and 1983, respectively. From 1984 to 1986, he was a Post-Doctoral Fellow with the University of Ottawa, Ottawa, ON, Canada. In 1986, he joined the Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada, where he became a Full Professor in 1991. During the fall of 1992 and the spring of 1993, he was a Visiting Scientist with the FerdinandBraun-Institute für Hochfrequenztechnik, Berlin, Germany. In 1997, he became a Professor of EM-field theory with the Swiss Federal Institute of Technology (ETH) Zürich, Zürich, Switzerland, and Head of the Laboratory for Electromagnetic Fields and Microwave Electronics (IFH) in 2003. His research interests include computational electromagnetics in the general area of electromagnetic compatibility (EMC) and, in particular, for computer-aided design of microwave, millimeter-wave, and opto-electronic integrated circuits. Since 1981, he has authored or coauthored over 300 technical papers in books, journals, and conferences, mainly in the field of microwave computer-aided design. Prof. Vahldieck is the past president of the IEEE 2000 International Zürich Seminar on Broadband Communications (IZS2000). Since 2003, he has been president and general chairman of the International Zürich Symposium on Electromagnetic Compatibility. He is a member of the Editorial Board of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. From 2000 to 2003, he was an associate editor for the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, and from July 2003 until the end of 2005, he was the editor-in-chief. Since 1992, he has served on the Technical Program Committee (TPC) of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), the IEEE MTT-S Technical Committee on Microwave Field Theory, and in 1999, on the TPC of the European Microwave Conference. From 1998 to 2003, he was the chapter chairman of the IEEE Swiss Joint Chapter on Microwave Theory and Techniques, Antennas and Propagation, and EMC. Since 2005, he has been president of the Swiss Research Foundation on Mobile Communications. He was the recipient of the J. K. Mitra Award of the Institution of Electronics and Telecommunication Engineers (IETE) (in 1996) for the best research paper in 1995 and was corecipient of the Outstanding Publication Award of the Institution of Electronic and Radio Engineers in 1983. He was the corecipient of the 2004 Applied Computational Electromagnetic Society (ACES) Outstanding Paper Award.

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Sparse Macromodeling for Parametric Nonlinear Networks Min Ma, Student Member, IEEE, and Roni Khazaka, Member, IEEE

Abstract—Model-order reduction has proven to be an effective tool for addressing the simulation complexities of the modern microsystem such as the ones arising due to large interconnect networks. Traditional model-order reduction methods are frequencydomain methods and are, therefore, limited to linear networks. Recently, time-domain model-order reduction was developed extending this concept to nonlinear macromodels. However, the resulting reduced nonlinear macromodel is dense, which reduces the efficiency of the simulation. In this paper, a nonlinear parametric formulation suitable for sparsification is presented. This results in an efficient reduced-order nonlinear macromodel, which is sparse, and is valid over a range of parameter values, and is thus suitable for optimization and design space exploration. Numerical examples are shown to illustrate the accuracy and efficiency of the proposed method. Index Terms—Macromodels, model-order reduction, nonlinear networks, parametric networks.

I. INTRODUCTION

I

N RECENT years, the complexity of state-of-art microsystems has increased dramatically as feature sizes of integrated circuits (ICs) scale further down into nanometer range and signal frequency increases into the gigahertz range. For example, interconnects must be modeled as distributed transmission lines [1], [2]. The simulation of such distributed transmission lines in a time-domain simulator such as SPICE is prohibitively CPU expensive given the fact that interconnect networks are very large due to discretization. A promising solution to the rising complexity problem is the use of accurate and efficient reduced-order macromodels [3]–[6] to replace circuit subsections. Model-order reduction methods based on congruence transformation were developed for obtaining passive [4] efficient macromodels for linear interconnect networks [4], [7]. Such congruence transformation-based techniques have become the methods of choice for model-order reduction of the interconnect network due to their accuracy, numerical stability, and passivity [7]. These methods are, however, frequency-domain methods and are, thus, inherently limited to linear subcircuits. In [8], the concept of congruence transformation-based reduction was extended to nonlinear equations in the time domain and was shown to be stable and passive. However, while the approach in [8]

Manuscript received March 29, 2006; revised August 23, 2006. The authors are with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada H3A 2A7 (e-mail: min.ma@mail. mcgill.ca; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885578

leads to significant CPU cost savings, it is fundamentally a simulation method based on circuit reduction and it, therefore, does not produce a nonlinear macromodel, which can be reused under different input and load conditions. In [9], an singular value decomposition (SVD)-based approach was proposed for obtaining basis functions, which can be used to generate a macromodel for microelectromechanical systems. In [10], the concept in [8] was extended, and an SVD-based model reduction method was proposed, which produces a nonlinear circuit macromodel that is valid over a range of input waveforms and loading conditions. However, while this method results in an accurate and significantly smaller nonlinear macromodel, the reduced macromodel is dense, which significantly limits the CPU efficiency of the simulation. In [11], a new formulation was presented to produce a reduced-order nonlinear macromodel, which is also sparse. However, this macromodel is not parametric, and a new macromodel is required each time an internal parameter is modified. This significantly limits its effectiveness in optimization and design exploration applications. In this paper, a parametric sparse macromodeling technique for nonlinear networks is presented. This method results in a sparse reduced-order macromodel, which is also valid over a range of parameter values. This nonlinear parametric macromodel improves the simulation time for parametric nonlinear network since the macromodel only needs to be created once and can be used many times with different internal circuit parameters. In order to achieve this goal, a new formulation is proposed. The proposed formulation allows for the decoupling of both nonlinear and parametric equations by introducing constrained ports. The reduction and sparsification are performed on the linear portion of the macromodel in the space of the new formulation scheme, and the reduced macromodel is then brought back to the traditional representation by reincorporating the parametric and nonlinear equations without losing sparsity. It is to be noted that the newly introduced constrained ports have a negligible impact on the size of the reduced macromodel. This paper is organized as follows. Section II describes the system formulation for nonlinear networks. In Section III, the proposed method for obtaining sparse reduced-order nonlinear macromodels is presented. The parametric nonlinear macromodel is proposed in Section IV. Finally, numerical examples are shown in Section V and are followed by conclusions in Section VI.

II. NETWORK FORMULATION Consider a multiport interconnect network consisting of many linear and nonlinear components. The nonlinear modified

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nodal analysis [12] formulation of such a -port network with size of modified nodal analysis formulation can be written as

decoupled from the linear equations through the introduction of constrained ports. The resulting formulation is in the form of

(1a)

(3a)

(1b)

(3b)

where is a vector of node voltages appended by independent voltage source currents, linear inductor currents, nonlinear capacitor charges, and nonlinear inductor fluxes, and contain the contributions of the memoryis a vector conless and memory elements, respectively, taining algebraic functions describing the nonlinear elements of is a selector matrix that maps the port the circuit, is a sevoltages into the node space of the circuit, lector matrix that maps the port currents into the node space of is a vector containing the port the circuit, currents, and is a vector that represents independent sources inside the macromodel, e.g., the dc-bias voltage sources for inverters. The formulation in (1) can be generalized to take into account certain design parameters (interconnect geometries, resistors, capacitors, etc.). In such a case, the parametrized modified nodal analysis formulation circuit equations [12], [13] including the nonlinear and parametric components can be expressed as

(3c) and are obtained by adding the constrained ports where is obtained by to the original system in (1). The variable appending the new constrained port currents to . is essentially the same as in (1a), except for adding new rows with is a seall zero corresponding to the new constrained ports. lector matrix mapping the new constrained port voltages into is essentially the same as in (1b), except the node space. adding new rows with all zero corresponding to the new constrained ports. Equation (3c) represents the nonlinear equations of the circuit, which are expressed as nonlinear constrains on the newly introduced ports. It is to be noted that these constrains are utilized in the computation of the reduction matrix in order to ensure that the size of the reduced macromodel is not affected by the addition of the constrained ports. Having the modified formulation in (3), the reduced system is then obtained by using congruence transformation, resulting in (4a) (4b) (4c)

(2a) where (2b) where are matrices each containing the modified nodal analysis formulation stamp of a particular memoryless paare matrices each containing the modified rameter, nodal analysis formulation stamp of a particular memory paare input scalars corresponding to the varirameter, , respectively, and able parameters represented by are input scalars corresponding to the variable parameters represented by , respectively. is an algebraic function describing the contributions of the parameter to the memoryless elements. is an algebraic function deto the memory scribing the contributions of the parameter elements. III. SPARSE NONLINEAR MACROMODEL If nonlinear time-domain model-order reduction was applied directly to (1), as was outlined in [10], the resulting nonlinear macromodel would be dense. This significantly reduces the efficiency of the simulation. Here, we propose a new approach, which allows for the application of time-domain nonlinear macromodeling, as well as for the sparcification of the macromodel without any significant impact on the size of the reduced-order macromodel. A. Macromodel Formulation Suitable for Sparsification In the first step of the proposed approach, the system in (1) are is reformulated such that the nonlinear equations in

(5a) (5b)

(5c) in the The computation of the congruence transformation time domain is described in Sections III-D and III-E. The reader is referred to Section III-F for a simple illustrative example of this representation. B. Sparsification of the Reduced Macromodel The reduced macromodel in (4) is generally a dense nonlinear macromodel. However, we note that the formulation in (4a) is in the form of general linear multiport network. It is, therefore, possible to apply diagonalization techniques such as the one described in [14] to (4a). Equation (4a) can be reformulated by premultiplying (6) By applying eigendecomposition to

, we obtain (7)

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and are, in general, complex; however, a real diagonalization can be derived from (7) in the form

(8) where

is a real block diagonal matrix and (9) (10)

is defined as follows. • When the corresponding element of the diagonal matrix , is a real, the element of the matrix is . • When the corresponding elements of the diagonal matrix , and are complex conjugate, the elements of the

matrix are

.

By substituting (8) into (6), the sparse reduced system becomes (11a)

Fig. 1. Summary of the proposed algorithm.

(11b) (11c) where

is an identity matrix (12a) (12b) (12c) (12d) (12e)

Note that

and

where and represent the general port formulation of the input and output ports, is a selector matrix, represents the nonlinear elements for constrained ports, is a seand a maximum of lector matrix with elements one nonzero in each row or column that maps the vectors of port voltages and port currents entering the subsection into the is the unknown of the renode space of the network, and duced-order macromodel in (11a). The above formulation is illustrated by a simple example in Section III-F. In summary, the final reduced-order macromodel based on (13) is in the form

(12f)

(16a)

(12g)

(16b)

are sparse real reduced matrices.

where and are small and sparse matrices. Our proposed sparse nonlinear macromodeling algorithm is summarized in Fig. 1.

C. Sparse Reduced-Order Nonlinear Macromodel The final step is to reincorporate the nonlinear constrains in (11c) into the overall sparse macromodel equations in (11a). In order to achieve this, the reduced macromodel is treated as a subsection, which is represented by (11a) and (11b). The nonlinear elements, which were removed before, are then connected back to the constrained ports of the subsection to form the sparse reduced-order nonlinear macromodel

(13) where (14) (15)

D. Nonlinear Parametric Port Formulation The congruence transformation matrix used in the reduced-order macromodel must span the subspace containing over the desired range of loading conditions and input waveforms. However, it is not possible to perform a transient analysis directly on the multiport formulation in (3a). It is, in fact, necessary to take into account the condition imposed by (3b) and (3c) and obtain nonlinear parametric port formulation. For clarify of presentation, we will first consider a simple two-port network with one nonlinear element, shown in Fig. 2, then the results will be extended into general multiport nonlinear networks. Since there is one nonlinear element, a constrained port (port3) is added to the network. Here, the two ports are divided into an input port (port1) and output port (port2). The voltages across the input port, output port, and the constrained port are , , and , respectively, and the currents are , , and , respectively. If we examine the modified nodal analysis

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and the equation at port3 becomes (21) Equation (21) represents a nonlinear constraint. In this case, a simple diode model was used, where is the reverse bias saturation current of the diode and is thermal voltage. Incorporating (20) and (21) into a modified nodal analysis formulation stamp has the effect of converting the multiport network in (3a) into a parametric “single-port” network while keeping the unchanged. This is done by modifying vector of unknowns the rows corresponding to port2 and port3 equations in the modified nodal analysis formulation in (3a) as follows:

Fig. 2. Example of two-port network with one nonlinear element.

formulation equation of such a system defined in (3), we note matrix, corresponding to the that the last three rows of the port1, port2, and port3 equations in (3a) are

(22) where

(23) (17)

(24)

and

(25)

(26)

(18)

(19)

It is to be noted that there is one parameter in (22), i.e., , corresponding to the capacitive load. To extend the above method input ports, output ports network , and into constrained ports, the nonlinear parametric port formulation with capacitive loads becomes

Using this general port representation, the port equations in the last three rows are simply , , and . In other words, the port voltage can be arbitrarily set by the boundary conditions. Note that port1 is the input port and port2 is designated as output port with capacitive loads and port3 is constrained by the nonlinear element. In this case, the equation at port1 remains unchanged, but the equation at port2 becomes

(27) where is obtained by modifying rows, corresponding to the output port and constrained port equations, is a matrix with elfrom port voltages into port currents, ements containing capacitive loads parameters , is a selector matrix that maps input port voltages into and the node space of the circuit. If a resistor is connected to port2 in Fig. 2, then the port2 equation becomes

(20)

(28)

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Here we use conductance to represent the value of the resistive load. Incorporating (28) and (21) into (3a) results in

(29) The above equation is similar to that in (22), except the matrix , containing one nonzero element, i.e., . To extend the above input ports, output ports network method into , and constrained ports, the nonlinear parametric port formulation with resistive loads becomes Fig. 3. Network used for generation of subspace data.

(30) is a matrix with elements containing resistive loads where parameters . If the loads are the parallel combination of a resistor and capacitor, then the nonlinear parametric port formulation with a combination of capacitive and resistive loads becomes

(31) where and are matrices with elements containing reand capacitive paramesistive loads parameters ters , respectively [15].

Fig. 4. Input waveforms for calculation of congruence transformation.

E. Congruence Transformation Matrix Using (27), (30), or (31) according to the type of the load, the subspace is defined by performing transient responses from the initial time point up to the tersampling . This is done several times on different minal time point load conditions (for capacitive loads, , for resistive loads, ), and using a range of input waveforms , as shown in Fig. 3. Four different input waveforms are used to generate the subspace data. They are 5-V step input with fall time 50 and 500 ps and 5-V step input with a rise time of 50 and 500 ps, as shown in Figs. 4 and 5. is then defined as The subspace containing (32) Given the fact that there is typically a lot of similarities between various transient responses, the subspace typically contains a lot of redundant dimensions. In order to obtain an of this subspace, SVD [16], [17] optimal orthonormal basis is used to identify the dominant directions, which results in

(33) is a diagonal matrix with singular values and in where decreasing order. and are unitary matrices. The singular values along the diagonal of measure the relative importance

Fig. 5. Input waveforms for calculation of congruence transformation.

of the corresponding columns of . This provides a convenient way to filter out the redundant directions. Taking only the first columns of , those corresponding to the highest singular . values, produces the congruence transformation matrix is obtained from Note that although the congruence matrix (27), (30), or (31) containing the information on the output ports and constrained ports, the order reduction procedure is applied to the general port formulation in (3a) so that the reduced system is a macromodel expressed in (4a) that can be connected to the predefined range of loads.

F. Illustration Example Here, a simple example is given to illustrate the various formulations discussed thus far in Section III-E. Consider a twoport network including an nonlinear component, i.e., a diode,

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Fig. 6. Example circuit for illustration. Fig. 7. Nonlinear constrained port.

shown in Fig. 6, the modified nodal analysis formulation of the original network is as in the form of (1) as follows:

(35)

where (36) The variabl vector in (35) differs from the vector in (34) by adding a new variable, the introduced nonlinear constrained port current . Furthermore, the new current is bounded by the following nonlinear equation: (34)

where is the reverse-bias saturation current of the diode and is thermal voltage. As the nonlinear element in the above equation hinders the sparsification of the reduced system, it is decoupled from the original modified nodal analysis equation by adding a nonlinear constrained port, i.e., port3, as shown in Fig. 7. Therefore, the resulting formulation is obtained as shown in (3a)

(37)

The above equation is the nonlinear constraint on the newly introduced constrained port, as in (3c). Port3 is different from the general port in the way that the load connected to port3 is completely known. In the illustration circuit, it is a diode. This load information can be exploited in order to obtain a congruence transformation, which is not affected by the new added ports. Note that the last two rows in (35), corresponding to the port2 and port3 equations, is simply (38a) (38b) in other words, port2 and port3 can be arbitrarily set by the boundary condition. Consider that port3 is connected to the diode, port2 is designated as the output port with capacitive load. Embedding (37) and (20) into (35) without changing the

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unknown variables would result in the nonlinear parametric port formulation in (27)

Fig. 8. Reduced nonlinear sparse macromodel.

(41)

(42) IV. NONLINEAR PARAMETRIC MACROMODEL (39)

The transient responses for (39) are sampled from the initial time point to the terminal time point to form the subspace containing the system responses over the desired input waveforms and output loads. The congruence transformation matrix is then found by taking the dominant direction of this subspace by using SVD. Having the transformation matrix, the congruence transformation is applied to (35) to find the reduced system. It is to be noted that the reduced system is a three-port network with an input port, an output port connected to a capacitive load, and a constrained port connected to the nonlinear element, diode. After doing the sparsification as explained in Section III-B, the reduced sparsified macromodel is in the form of (11). The final step is to connect the diode back to the nonlinear constrained port, which results in the macromodel expressed in (13), as shown in Fig. 8, where

(40)

Consider the parametric nonlinear networks in (2) with input ports, output ports, nonlinear elements, and parametric elements. Due to the parametric terms and and the nonlinear terms , the standard sparsification process cannot be operated. They are decoupled from the original equation by adding constrained ports for the parametric terms and nonlinear terms. The resulting formula suitable for the sparsification is as follows:

(43a) (43b) (43c) (43d) Equations (43c) and (43d) represents the nonlinear elements and parametric elements, respectively, expressed as the nonlinear or parametric conditions on the newly introduced constrained ports. Therefore, in the parametric nonlinear system, we have two types of constrained ports, i.e., parametric and nonlinear ports. The nonlinear constrained ports are connected to nonlinear elements, while parametric constrained ports are connected to parametric elements. Having the formulation, the real congruence transformation is applied to the system in (43) to obtain

(44a) (44b) (44c) (44d)

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TABLE I SIZE AND CPU COST COMPARISONS

Fig. 9. Interconnect network with two inverters as example 1.

where

(45a)

(45b)

(45c) Fig. 10. Transient responses for example 1 (cases 1 and 2) from [11].

(45d) To sparsify the reduced-order model in (44a), the diagonalize process explained in Section III-B is performed, which results in

as well as the parametric information are incorporated into the formulation in (43a) and result in

(46a) (46b) (46c)

(48)

(46d) Finally, the nonlinear constrains in (46c) and parametric constrains in (46d) are reincorporated into the overall macromodel equation by taking (46a) and (46b) as a subsection. The following sparse reduced-order macromodel is obtained: (49)

(47a) (47b) are small and sparse matrices. where , , , and The congruence transformation used in model-order reduction must contain the information about the parametric elements, the nonlinear elements, and the loads. In order to do that, the load information, the nonlinear elements information,

(50) Equations (48)–(50) are a nonlinear parametric formulation with resistive loads, capacitive loads, and a combination of contains resistive and capacitive loads, respectively, where

MA AND KHAZAKA: SPARSE MACROMODELING FOR PARAMETRIC NONLINEAR NETWORKS

Fig. 11. Transient response for example 1 (case 3) from [11].

Fig. 13. Transient response for example 2 (case 1).

TABLE II THREE CASES FOR EXAMPLE 1 FROM [11]

Fig. 12. Interconnect network with two internal circuit parameters as example 2.

Fig. 14. Transient response for example 2 (case 2).

TABLE III SIZE COMPARISONS FOR EXAMPLE 2

resistive loads parameters and contains capacitive loads parameters . is obtained by rows corresponding to output ports, modifying nonlinear constrained ports, and parametric constrained ports and equations, from port voltages into port currents. contains parametric information. is a selector matrix that maps input port voltages into the node space of the circuit. In order to obtain the required subspace data, transient analyses over the predefined input waveforms, load conditions, and parametric conditions using formulation in (48), (49), or (50) are performed. The congruence transformation matrix is found by extracting the dominant subspace using SVD.

Fig. 15. Transient response for example 2 (case 3).

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TABLE IV THREE SAMPLE CASES FROM 100 TEST CASES FOR EXAMPLE 2

TABLE V CPU COMPARISONS FOR EXAMPLE 2 BASED ON 100 TEST CASES

V. NUMERICAL RESULTS Here, we present two examples. The first example considers an interconnect system containing nonlinear elements. The second example considers a nonlinear parametric interconnect system. The transient responses using the proposed method are compared to those obtained from the original system. As was expected, the results match very well. CPU comparisons for the two examples also demonstrate the efficiency of the proposed method. The proposed algorithms for all examples were implemented in MATLAB. A. Example 1 The first example is a nonlinear network containing nine coupled transmission lines, nine single transmission lines, and two inverters. The length for the coupled transmission lines is 0.1 m and the length for the single transmission lines is 0.05 m. The per unit length parameters of the nine coupled transmission lines are given in [18]. The per unit length parameters of the single m, nH/m, and transmission lines are pF/m. Inverter1 is connected between two transmission lines, while inverter2 is connected at the output of one transmission line. The output of inverter2 is considered as the output of the network, as shown in Fig. 9. After discretization of the network, the resulting size of the modified nodal analysis matrices was 3533. Four different input waveforms are used for computing the subspace data. They are 5-V step inputs with a rise time of 50 and 500 ps and 5-V step inputs with a fall time of 50 and 500 ps, as shown in Figs. 4 and 5. The load condition was set to be a capacitor with a value ranging from 0.1 to 10 pF. Using the proposed approach, the size of the reduced macromodel was 320, as shown in Table I. In order to test the proposed method, a capacitor was connected at the output of the reduced macromodel. Different cases of load capacitor values and input waveforms were considered. The transient responses for three of these cases are shown in Figs. 10 and 11. The values of the loads and input waveform for each case are given in Table II. As can be seen, the results match very well with the transient responses of the original system. The CPU cost of the reduced system for three cases in Table II range from 38 to 78 s, while the CPU cost for the original system range from 770 to 938 s. The average speed-up of 15.8 was, therefore, achieved. A summary of CPU cost comparisons for example 1 to obtain the transient responses is shown in Table I.

B. Example 2 The second example is an interconnect network with one single transmission line, nine coupled transmission lines system, and one inverter. The length for the coupled transmission lines is 0.1 m and the length for the single transmission line is 0.05 m. The per unit length parameters of the nine coupled transmission lines are given in [18]. The per unit length m, parameters of the single transmission line are nH/m, and pF/m. This system is a parametric two-port network with one resistor and one capacitor as internal circuit parameters, as shown in Fig. 12. For this network, the original modified nodal analysis matrix size is 2512. When generating the subspace data, the desired range for 100 , and the desired the parametric resistor was set to 1 range for the parametric capacitor was set to 0.1 10 pF. The load at the output port was set to be capacitive with ranging 10 pF. The input waveforms used for generating from 0.1 the subspace data were 5-V rising edge and fall edge steps with 50- and 500-ps rise/fall time, as shown in Figs. 4 and 5. Using the parametric nonlinear macromodel described in this paper, the size of the reduced model is 282, as shown in Table III. In order to test the accuracy and efficiency of the macromodel, 100 randomly chosen sample cases are tested. The parameter values, as well as the load values were chosen randomly within the acceptable range defined above. The input waveforms for testing include the step input with rise time randomly chosen between 50–500 ps, step input with fall time randomly chosen between 50–500 ps, pulse waveforms with different rise and fall times and different pulse widths, piecewise linear waveforms, and sinusoidal waveform at frequencies ranging from 1 to 4 GHz. The transient responses for three cases from 100 test cases are shown in Figs. 13–15. The values of the loads and input waveforms for the three test cases are given in Table IV. In order to calculate the CPU speed-up for the reduced-order macromodel over the original system, we include the CPU time to obtain the macromodel, which is referred to as the reduction overhead time. The overhead time consists of the time for generating the subspace data (1776.6 s) and the time for doing SVD (415.1 s). The time to do the simulation for 100 test cases using the reduced macromodel is 1883.8 s. The overall time of the 100 test cases for our proposed approach is 4075.5 s when the reduction overhead is included. On the other hand, the simulation time of the original system for 100 test cases is 46349.9 s. Therefore,

MA AND KHAZAKA: SPARSE MACROMODELING FOR PARAMETRIC NONLINEAR NETWORKS

Fig. 16. Average CPU speed-up versus number of test cases.

a CPU speed-up of 11.4 is achieved, as shown in Table V. It is to be noted that the time for generating the macromodel is a one-time cost. It is, therefore, leveraged over many simulation runs of the reduced macromodel. As can be seen from Fig. 16, the overall speed-up approaches the simulation speed-up of 24.6 when the number of test cases is large. VI. CONCLUSION In this paper, a new parametric nonlinear model-order reduction method was presented that produced reduced nonlinear macromodels, which are sparse and parametric. The macromodels are valid over a user-defined range of loading conditions, parameters, and input waveforms. As shown through numerical examples, this reduced macromodel enables significant CPU cost saving over the unreduced system.

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[7] R. Achar and M. Nakhla, “Simulation of high-speed interconnects,” Proc. IEEE, vol. 89, no. 5, pp. 693–728, May 2001. [8] P. Gunupudi and M. S. Nakhla, “Nonlinear circuit-reduction of high-speed interconnect networks using congruent transformation techniques,” IEEE Trans. Compon. Packag., Manuf. Technol. B, vol. 24, no. 3, pp. 317–325, Aug. 2001. [9] E. Hung, Y. Yang, and S. Senturia, “Low-order models for fast dynamical simulation of MEMS microstructures,” in Proc. Int. Solid-State Sens. Acuators Conf., Chicago, IL, Jun. 1997, pp. 1101–1104. [10] M. Ma and R. Khazaka, “Nonlinear macromodeling using model order reduction,” in Proc. IEEE Elect. Performance Electron. Packag. Conf., Austin, TX, Oct. 2005, pp. 131–134. [11] M. Ma and R. Khazaka, “Sparse macromodeling for nonlinear network,” presented at the IEEE MTT-S Int. Microw. Symp., San Francisco, CA, Jun. 2006. [12] C. W. Ho, A. E. Ruehli, and P. A. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst., vol. CT-22, no. 6, pp. 504–509, Jun. 1975. [13] P. Gunupudi, R. Khazaka, and M. S. Nakhla, “Analysis of transmission line circuits using multi-dimensional model reduction techniques,” IEEE Trans. Adv. Packag., vol. 25, no. 2, pp. 174–180, May 2002. [14] A. Odabasioglu, M. Celik, and L. Pileggi, “Practical considerations for passive reduction of RLC circuits,” in Proc. ACM Int. Comput.-Aided Design Conf., San Jose, CA, Nov. 1999, pp. 214–219. [15] M. Ma and R. Khazaka, “Passive model order reduction of interconnect networks with large number of ports,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1779–1782. [16] G. H. Golub and C. Van Loan, Matrix Computations. Baltimore, MD: The John Hopkins Univ. Press, 1989. [17] M. Ma and R. Khazaka, “Efficient projection based macromodel for interconnect networks,” in Proc. IEEE Signal Propag. on Interconnects Workshop , Garmisch, Germany, May 2005, pp. 181–184. [18] A. C. Cangellaris and A. E. Ruehli, “Model order reduction techniques applied to electromagnetic problems,” in Proc. IEEE Elect. Performance Electron. Packag. Conf., Oct. 2000, pp. 239–242. Min Ma (S’05) received the M.Eng degree (with honors) from McGill University, Montreal, QC, Canada, in 2004, and is currently working toward the Ph.D. degree at McGill University. Her research interests include computer-aided design of very large scale integration (VLSI) circuits and simulation and modeling of high-speed interconnects.

REFERENCES [1] C. R. Paul, Analysis of Multiconductor Transmission Lines. New York: Wiley, 1994. [2] A. Deutsch, “Electrical charactersitics of interconnections for high performance systems,” Proc. IEEE, vol. 86, no. 2, pp. 315–355, Feb. 1998. [3] I. M. Elfadel and D. D. Ling, “A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks,” in Proc. ACM Int. Comput.-Aided Design Conf., San Jose, CA, Nov. 1997, pp. 66–71. [4] A. Odabasioglu, M. Celik, and L. T. Pileggi, “PRIMA: Passive reduced-order interconnect macromodeling algorithm,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 17, no. 8, pp. 645–654, Aug. 1998. [5] R. Achar, P. Gunupudi, M. Nakhla, and E. Chiprout, “Passive interconnect reduction algorithm for distributed/measured networks,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 47, no. 4, pp. 287–301, Apr. 2000. [6] P. Gunupudi, R. Khazaka, M. Nakhla, T. Smy, and D. Celo, “Passive parametrized time-domain macromodels for high-speed transmissionline networks,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 2347–2354, Dec. 2003.

Roni Khazaka (S’92–M’03) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Carleton University, Ottawa, ON, Canada in 1995, 1998, and 2002, respectively. Since 2002, he has been Assistant Professor with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada. His current research interests include electronic design automation, numerical algorithms and techniques, and the analysis and simulation of RF ICs, high-speed interconnects, and integrated Microsystems. Dr. Khazaka has been the recipient of awards and scholarships, which include the 2002 IEEE Microwave Theory and Techniques Society (IEEE MTT–S) Microwave Prize, the Natural Sciences and Engineering Research Council (NSERC) of Canada Scholarships (at the masters and doctoral levels), Carleton University’s Senate Medal and University Medal in Engineering, the Nortel Networks Scholarship, and the IBM Cooperative Fellowship.

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Theoretical Justification of Space-Mapping-Based Modeling Utilizing a Database and On-Demand Parameter Extraction Slawomir Koziel, Member, IEEE, John W. Bandler, Fellow, IEEE, and Kaj Madsen

Abstract—We present a theoretical justification of a recently introduced surrogate modeling methodology based on space mapping (SM) that relies on an available database and on-demand parameter extraction. Fine-model data, the so-called base set, is assumed available in the region of interest. To evaluate the surrogate, we perform parameter extraction with weighting coefficients dependent on the distance between the point of interest and base points. We provide theoretical results showing that the new methodology can assure any accuracy that is required (provided the base set is dense enough), which is not the case for our benchmark SM modeling methodology. Illustrative examples emphasizing differences between modeling methodologies are provided. Index Terms—Computer-aided design (CAD), electromagnetic (EM) modeling, microwave circuits, space mapping (SM), surrogate modeling.

I. INTRODUCTION TATISTICAL analysis and yield optimization are crucial to manufacturability-driven designs in a time-to-market development environment and demand fast accurate device and component models. Full-wave electromagnetic (EM) simulations of microwave structures offer accuracy at the cost of CPU effort. High CPU cost is undesirable from the point-of-view of direct statistical analysis and design. The space mapping (SM) concept introduced by Bandler et al. [1], [2] addresses this issue. SM assumes that a high fidelity CPU-intensive “fine” model is accompanied by a low fidelity or “coarse” model. The “coarse” model can be a simplified representation such as an equivalent circuit with empirical formulas. SM modeling [3]–[8] exploits the speed of the coarse model and the accuracy of the fine model to develop fast accurate enhanced models (surrogates) valid over a wide range of parameter values. The standard SM modeling methodology [9], [10] is based on setting up the surrogate model using a small amount of fine-

S

Manuscript received April 4, 2006; revised July 6, 2006. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007239 and Grant STGP269760 and by Bandler Corporation. S. Koziel is with the Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1 (e-mail: [email protected]). J. W. Bandler is with the Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1 and also with Bandler Corporation, Dundas, ON, Canada L9H 5E7 (e-mail: [email protected]). K. Madsen is with Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby, Denmark (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.884648

points, where is the number of demodel data (usually sign variables). Extraction of the model parameters is performed over the whole set of this data. This methodology is simple and provides accuracy that is good enough for some applications. It has, however, a number of limitations, in particular, a limited capability to model nonlinearity of the fine model, limited performance for higher dimensional problems, and difficulty handling a large amount of the fine-model data. The last drawback is particularly important because in order to increase accuracy of the surrogate model over some limit, we have to provide more and more fine-model data. The only way to utilize this data in a standard SM model is to increase the number of model parameters, which makes the parameter-extraction process longer and more difficult, leaving alone the problem of model definition that would allow us to properly introduce linear and nonlinear terms to follow fine-model nonlinearity. To alleviate the foregoing difficulties, a new SM-based surrogate modeling methodology has been introduced in [11]. It requires an available database and performs on-demand parameter extraction. To evaluate the surrogate, we perform parameter extraction with weighting coefficients dependent on the distance between the point of interest and the base points. In other words, this methodology uses local fine-model information. In this study, we provide a theoretical justification of the method [11] and show that this methodology can assure any required accuracy provided that the base set is dense enough. We also give a matching error estimate for the surrogate model with respect to the fine model. II. SM MODELING WITH VARIABLE WEIGHT COEFFICIENTS [11] Here, in order to set up the notation necessary for our subsequent theoretical considerations, we briefly recall the SM modeling methodology [11]. Let : and : denote the fine and and coarse model response vectors, where are design variable domains of the fine and coarse models, and may represent the respectively. For example, chosen frequencies. We magnitude of a transfer function at the region of interest in which we want denote by enhanced matching between the surrogate and the fine model. is an -dimensional interval in with We assume that center at reference point

0018-9480/$20.00 © 2006 IEEE

(1)

KOZIEL et al.: THEORETICAL JUSTIFICATION OF SM-BASED MODELING UTILIZING DATABASE AND ON-DEMAND PARAMETER EXTRACTION

where

determines the size of . We use to denote the region of interest defined by and . Suppose we have the base set , where is the number of base points such that the . fine-model response is known at all points , We do not assume any particular location of the base points. : We define a generic surrogate model as [11] (2) , with matrices ( denotes the set of and found using the parameter extraction

, , real matrices)

(3) The flexibility of the generic model (2) can be adjusted by imposing constraints on the parameter-extraction procedure. It can also be enhanced by introducing additional parameters (see [11]). The weighting coefficients in (3) are functions of . I Coeffiare calculated according to cients

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Remark 1: It follows that the standard SM modeling technique [9], [10] is a particular case of the new technique (2)–(4), as it can be obtained from (2)–(4) by choosing a standard (i.e., and letting in (4). star-distribution-like) Remark 2: It should be emphasized that if the coarse model is continuous, then the surrogate model (2) is continuous with respect to regardless of the fact that evaluation of the surrogate requires a separate parameter extraction for every arand matrices gument. This follows from the fact that both , , , and are continuous functions of . The latter assumes that parameter extraction (3) has a unique solution for , , any values of the weighting coefficients and are continuous; the uniqueness assumption and both can be replaced by the assumption of regularity of the solution to (3) with respect to the weighting coefficients, e.g., ordinary or Lipschitz continuity. As mentioned before, one can expect that the modeling accuracy depends on the characteristic distance . In fact, it is possible to prove a rigorous result showing that the modeling error . can be arbitrarily small as For the purpose of theoretical considerations, we shall consider a slightly generalized formulation of the SM-based surrobe a generic surrogate gate model. Let model, where is the region of interest and is a parameter , the actual surrogate model domain. For any given base set is defined as response at any (6)

(4)

where is the evaluation point, and is a characteristic distance depending on the size of the region of interest and the number of base points

(5) , If the base points are uniformly distributed in is just an average distance between neighboring points. Constant determines how fast the weighting coefficients decrease with an increase of base-point distance from . Reference [11] contains a discussion on the implementation details of this method. III. MODELING ERROR VERSUS CHARACTERISTIC DISTANCE OF THE BASE SET It is intuitively obvious that modeling accuracy, according to the methodology presented in Section II, depends on the characteristic distance , in particular, that accuracy improves with decreasing . Here, we provide theoretical results showing that our methodology can assure any accuracy that is required (provided the base set is dense enough, i.e., is small enough), which is not the case for the standard methodology [9], [10]. We also give an error estimate for the surrogate model with respect to the fine model. Let us start with the following remarks.

where (7) with coefficients defined by (4) for given constant . For simplicity, we assume that no sensitivity information is used in is a compact way of writing the model. Note that the model , in which we represented all the parameters (in the case of , parameters are matrices , , , and ) by a single parameter vector . We also introduce single-point parameter extraction denoted as (8) Definition (8) should be understood in the following sense: if , then is the limit of obtained for . is uniquely defined (if are unique This means that for any nonzero ) even if problem (8) has nonunique solutions. In order to assure the existence of the limit, we need to extend and as follows: definition (4) for if and if . We also need to assume continuity of the functions involved, in particular, the continuity . of solution to (7) with respect to parameter for Assumption 1: Suppose that the following conditions hold. and are compact sets. (i) (ii) and are continuous on and , respectively.

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(iii) For any base set the problem

and any

, the solution to [see

explanation under (8)] is unique. Moreover, the solution to (8) is uniformly continuous with respect to perturbais tion in the following sense: if : the (bounded) perturbation function, then for any there is a (independent of ) such that provided that (iv) For any base set problem

and any

and are continuous on and From Assumption 1 (ii), , respectively, and because both and are compact [Assumption 1 (i)], they are, in fact, uniformly contin(independent of ) such that if uous. Thus, there is a , then (10) However, according to Assumption 1 (iv), we have

. , the solution to the is such

. that Remark 3: Assumption 1 is quite natural. First of all, is usually a multidimensional closed rectangle so it is compact. can be made compact by setting suitable bounds Similarly, for the surrogate model parameters. Continuity of the fine and coarse model [which usually implies continuity of the surrogate, e.g., as in (3)] is also typical. Assumption 1 (iii) is more complex, although it also typically follows, at least for continuous perturbation functions. Eventually, Assumption 1 (iv) is always satisfied if the surrogate model allows output SM, i.e., the transformation of the coarse model image (e.g., in the case of model (2) this can be done by either of the matrices or ). Theorem 1: Suppose that Assumption 1 is satisfied. The surrogate model (6) and (7) is then arbitrarily accurate in the fol, there is a such that for any lowing sense. For any that satisfies the condition base set (i.e., is uniform enough), we have for any , provided that the constant in (4) is sufficiently small. . We shall show that there exist Proof: Let us take and such that the assertion of the theorem holds. For any point in , any base set , and any point , we have

(9)

(11) be any base set that satisfies Let . For any , there is then an

such that (12)

We would now like to find a condition under which the term is smaller than . Due to the on , there is a (indeuniform continuity of pendent of ) such that

whenever (13) However, (14) and (15), shown at the bottom of this page, in which we have taken into consideration that the weighting coefficients are norfor any . Let us define a funcmalized, i.e., as . tion Using this function, we can write (16), shown at the bottom of as this page. Let us now define function : . Using this function, we can rewrite (16) as (17)

(15)

(16)

KOZIEL et al.: THEORETICAL JUSTIFICATION OF SM-BASED MODELING UTILIZING DATABASE AND ON-DEMAND PARAMETER EXTRACTION

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We would like to take advantage of Assumption 1 (iii). In parsuch that if ticular, there is a (18) then (19) for any that belongs to some base set. What we need to do now and constant for which is to show that there is a base set (18) holds. Let ( is well-defined because is continuous on the compact set). Let be such that for all whenever . Let be any base set such that . For such and any satisfying , , we have for all . We divide into two subsets: and . , and Obviously, we have . Let us denote by the point from that is closest to . We define (20) (21) Clearly,

. Due to our definition of , we have

(22) Let us now set the constant , we have



Fig. 1. Example 1: fine-model response ( ), standard SM surrogate model re; ; ( ), and the new SM surrogate model responses for sponses for k ( ), and k ( ). k ( ), k

=1

=124 2 =2 3 =4 +

coefficients [cf. (4)]. The only requirement is that the forwhile moving mula allows changing the decrease rate of away from the evaluation point (e.g., by proper adjustment of the control parameters). Remark 6: Good coarse models allow us to obtain very accurate surrogate models even for sparse base sets. However, it follows from Theorem 1 that even for poor coarse models, we still have the property of making the surrogate model error arbitrarily small provided that the base set is sufficiently “dense” and one can obtain perfect matching for single-point parameter extraction (this can be guaranteed by any kind of output SM). This follows from the fact that there is no assumption about “quality” of the coarse model in the Theorem: the basic analytical condition is continuity. , , and : , Example 1: Let are defined as (24) (25)

such that for any such that . For this , we have Let

(23) Let

and let be any base set for which . For this set, it follows from (22) on . At and (23) that the same time, it follows from (9), (12), (13), and (19) that, for , we have . Since the our choice of above reasoning is valid for any , this ends the proof of the theorem. Remark 4: Adjustment of the decrease rate of coefficients (by changing ) plays a crucial role in the proof of Theorem 1. In particular, it is not possible in general for the standard model to be arbitrarily accurate, regardless of the base set used (i.e., even if the characteristic distance of the base set is very small). Remark 5: Results equivalent to Theorem 1 can be proven for a different choice of the formula that determines weighting

(26) For the standard model (i.e., the one with all weighting coeffi, we have cients the same and equal to 1), for any integer , which implies that the modeling error is the same, and does not depend on the choice of in the base set (26). On the other hand, the modeling error for the new model can be reduced to zero in the limit according to Theorem 1. As an illustration, Fig. 1 shows the fine-model response, as well as the standard and the new SM and . surrogate model responses for Example 2: Consider a two-section impedance transformer example [12]. Both fine and coarse models in this problem are circuit models with design variables being the lengths of the transmission lines. The region of interest is defined (coarse model optimal solution), and size by . Fig. 2 shows a comparison of the average modeling error versus characteristic distance of the base set for

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Fig. 2. Example 2: average modeling error versus characteristic distance  of the base set for: standard SM model with input and output SM ( ), standard SM model with input, output, frequency, and implicit SM ( ), SM model with variable weight coefficients using input and output SM surrogate ( ), and SM model with variable weight coefficients using input, output, frequency, and implicit SM ( ).

2

+ 

the standard SM model with the surrogate model using input and output SM ( ), the standard SM model with the surrogate using input, output, frequency, and implicit SM ( ), and the SM model with variable weight coefficients using an input and output SM surrogate ( ), and input, output, frequency, and implicit SM ( ). The results were obtained for 100 random test points. Characteristic distances range from approximately 1.5 (which corresponds to a uniform mesh base set with 100 points) to approximately 10 (uniform mesh with four points) The results clearly show the difference between the standard and new SM modeling technique. The modeling error for the standard SM model is almost independent of the base set size. The accuracy improvement can only be observed for large values of ; after the number of base points is increased, the standard SM model is not able to exploit all available fine-model information due to the limited flexibility of the surrogate. The only way of increasing the model accuracy in a significant way is to increase the number of model parameters (in our case, by introducing additional degrees of freedom with frequency and implicit SM). In case of SM modeling with variable weight coefficients, modeling error is decreasing while characteristic distance is going down, as predicted in Theorem 1. More results can be found in [11]. Example 3: In this example, we again use the two-section transformer example in order to investigate the dependence of the modeling error on the value of the scaling factor . As before, the region of interest is defined by (coarse . Fig. 3 shows model optimal solution) and size comparison of the average modeling error versus scaling factor for four different base sets being uniform meshes with nine points ( ), 16 points ( ), 25 points ( ), and 49 points ( ). The results were obtained for 100 random test points. is, for the considered example, The results show that the optimal value of the scaling factor, which is independent of the density of the base set. This independence of the base set can be explained by the construction of (4), which is used for calculating the weight coefficients necessary to evaluate the SM surrogate model. In particular, (4) contains the square of

Fig. 3. Example 3: average modeling error versus scaling factor C for SM model with variable weight coefficients for uniform base sets with nine points ( ), 16 points ( ), 25 points ( ), and 49 points ( ).

+

2



the characteristic distance . Since is nothing else but the average distance between base points, the density of the base set is already taken into account in (4) and the distribution of the weight factors in the neighborhood of any evaluation point is invariant with respect to the base set (or, more specifically, to ). the relative distance between and base points Similar experiments performed for other examples (not shown here) indicate that the optimal value of is equal or close to 1 for most cases. The following result gives an error estimate for the surrogate model (2) and (3). and satisfy the Assumption 2: Suppose that functions following conditions: , (i) is Lipschitz continuous with respect to the first variable, i.e.,

(27)

(ii)

where , is Lipschitz continuous with respect to the second variable, i.e.,

(28) . where Theorem 2: Suppose that Assumption 2 is satisfied and is a base set. Let be such that . . Suppose Let further that the function [cf. (7)] is Lipschitz continuous, i.e., , where . We then have the following estimate for the modeling error on

(29) where

.

KOZIEL et al.: THEORETICAL JUSTIFICATION OF SM-BASED MODELING UTILIZING DATABASE AND ON-DEMAND PARAMETER EXTRACTION

Proof of Theorem 2: Let be any point in be such that . We have

, and

(30) According to Assumption 2 (i), we have (31) From the assumption of the theorem, we get (32) Finally, it follows from Assumption 2 (ii) and the assumptions of the theorem that we have

(33) Now, we have from (30)–(33) that (34) This ends the proof of the theorem. Remark 7: Theorem 2 says, in fact, that the modeling error is proportional to the characteristic distance of the base set and to the error at base points. On the other hand, for any fixed , to as small a value as desirable by proper one can reduce choice of (provided that Assumption 1 (iv) is satisfied, i.e., at the base points), although this would affect the constant (usually in an undesirable way if is too small). IV. CONCLUSION A theoretical justification of the recently published SM-based modeling methodology with variable weight coefficients has been presented. We have provided theoretical results showing that the new methodology can assure any accuracy that is required (provided that the base set is dense enough), which is not the case for the standard methodology. We have also given an error estimate for the surrogate model with respect to the fine model. Examples have demonstrated the fundamental differences between the standard and novel modeling method. REFERENCES [1] J. W. Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R. H. Hemmers, “Space mapping technique for electromagnetic optimization,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp. 2536–2544, Dec. 1994.

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[2] J. W. Bandler, R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K. Madsen, “Electromagnetic optimization exploiting aggressive space mapping,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 12, pp. 2874–2882, Dec. 1995. [3] M. H. Bakr, J. W. Bandler, and N. Georgieva, “Modeling of microwave circuits exploiting space derivative mapping,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, Jun. 1999, pp. 715–718. [4] J. W. Bandler, N. Georgieva, M. A. Ismail, J. E. Rayas-Sánchez, and Q. J. Zhang, “A generalized space mapping tableau approach to device modeling,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 1, pp. 67–79, Jan. 2001. [5] J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, and Q. J. Zhang, “Neuromodeling of microwave circuits exploiting space mapping technology,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2417–2427, Dec. 1999. [6] L. Zhang, J. J. Xu, M. Yagoub, R. T. Ding, and Q. J. Zhang, “Neuro-space mapping technique for nonlinear device modeling and large signal simulation,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 173–176. [7] V. K. Devabhaktuni, B. Chattaraj, M. C. E. Yagoub, and Q.-J. Zhang, “Advanced microwave modeling framework exploiting automatic model generation, knowledge neural networks, and space mapping,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 7, pp. 1822–1833, Jul. 2003. [8] L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, and Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2752–2767, Sep. 2005. [9] S. Koziel, J. W. Bandler, A. S. Mohamed, and K. Madsen, “Enhanced surrogate models for statistical design exploiting space mapping technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1609–1612. [10] J. W. Bandler, Q. S. Cheng, and S. Koziel, “Implementable space mapping approach to enhancement of microwave device models,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1139–1142. [11] S. Koziel and J. W. Bandler, “Space-mapping-based modeling utilizing parameter extraction with variable weight coefficients and a data base,” presented at the IEEE MTT-S Int. Microw. Symp., San Francisco, CA, Jun. 2006. [12] M. H. Bakr, J. W. Bandler, K. Madsen, and J. Søndergaard, “An introduction to the space mapping technique,” Optim. Eng., vol. 2, no. 4, pp. 369–384, Dec. 2001.

Slawomir Koziel (M’03) was born in Poland, in 1970. He received the M.Sc. and Ph.D. (with honors) degrees in electronic engineering from Gdansk University of Technology, Gdansk, Poland, in 1995 and 2000, respectively, and the M.Sc. degree in theoretical physics and mathematics and Ph.D. degree in mathematics (with honors) from the University of Gdansk, Gdansk, Poland, in 2000, 2002, and 2003, respectively. He is currently a Research Associate with the Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada. He has authored or coauthored over 90 papers. His research interests include SM-based modeling and optimization, circuit theory, analog signal processing, active filter design, evolutionary computation, and numerical analysis.

John W. Bandler (S’66–M’66–SM’74–F’78) was born in Jerusalem on November 9, 1941. He received the B.Sc. (Eng.), Ph.D., and D.Sc. (Eng.) degrees from the University of London, London, U.K., in 1963, 1967, and 1976, respectively. He joined Mullard Research Laboratories, Redhill, Surrey, U.K., in 1966. From 1967 to 1969, he was a Postdoctorate Fellow and Sessional Lecturer at the University of Manitoba, Winnipeg, Canada. He joined McMaster University, Hamilton, ON, Canada, in 1969. He was Chairman of the Department of Electrical Engineering and Dean of the Faculty of Engineering. He is currently

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Professor Emeritus in Electrical and Computer Engineering, directing research in the Simulation Optimization Systems Research Laboratory. He has authored or coauthored over 385 papers. He was a member of the Micronet Network of Centres of Excellence. He was President of Optimization Systems Associates Inc. (OSA), which he founded in 1983, until November 20, 1997, the date of acquisition of OSA by the Hewlett-Packard Company. OSA implemented a first-generation yield-driven microwave computer-aided design (CAD) capability for Raytheon in 1985, followed by further innovations in linear and nonlinear microwave CAD technology for the Raytheon/Texas Instruments Joint Venture MIMIC Program. OSA introduced the CAE systems RoMPE in 1988, HarPE in 1989, OSA90 and OSA90/hope in 1991, Empipe in 1992, and Empipe3D and EmpipeExpress in 1996. OSA created the product empath in 1996, which was marketed by Sonnet Software Inc. He is President of Bandler Corporation, Dundas, ON, Canada, which he founded in 1997. He joined the Editorial Boards of the International Journal of Numerical Modelling in 1987, the International Journal of Microwave and Millimeterwave Computer-Aided Engineering in 1989, and Optimization and Engineering in 1998. He was a Guest Editor of the International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering Special Issue on “Optimization-Oriented Microwave CAD” (1997). He was Guest Coeditor of the Optimization and Engineering Special Issue on “Surrogate Modelling and Space Mapping for Engineering Optimization” (2001). Dr. Bandler is a Fellow of the Canadian Academy of Engineering, the Royal Society of Canada, the Institution of Electrical Engineers (IEE), U.K., and the Engineering Institute of Canada. He is a member of the Association of Professional Engineers of the Province of Ontario, Canada, and the Massachusetts Institute of Technology (MIT) Electromagnetics Academy. He received the Automatic Radio Frequency Techniques Group Automated Measurements Career Award in 1994 and the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Microwave Application Award in 2004. He was an associate editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES (1969–1974) and has continued serving as a member of the Editorial Board. He was guest editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY

TECHNIQUES Special Issue on “Computer-Oriented Microwave Practices” (1974) and “Automated Circuit Design Using Electromagnetic Simulators” (1997) and guest coeditor of the Special Issue on “Process-Oriented Microwave CAD and Modeling” (1992) and “Electromagnetics-Based Optimization of Microwave Components and Circuits” (2004). He was chair of the MTT-1 Technical Committee on Computer-Aided Design. AND

Kaj Madsen was born in Denmark, in 1943. He received the cand.scient. degree in mathematics from the University of Aarhus, Aarhus, Denmark, in 1968, and the Dr.Techn. degree from the Technical University of Denmark (DTU), Lyngby, Denmark, in 1986. From 1968 to 1988, he was a Lecturer in numerical analysis, apart from the 1973–1974 academic year, when he was with AERE Harwell, Didcot, U.K. Most of his career has been spent with the Department for Numerical Analysis, DTU. From 1981 to 1983, he was with the Computer Science Department, Copenhagen University, Copenhagen, Denmark. During Summer 1978, he visited McMaster University, Hamilton, ON, Canada. In 1988, be became a Full Professor. Since the 1990s, he has arranged several international workshops on linear programming, parallel algorithms, surrogate modeling, and SM. In 1993, he joined the Department of Mathematical Modelling, DTU, and during 1995–2000 was Head of that department. In 2000, he took an active part in forming the new department Informatics and Mathematical Modelling, DTU, which includes computer science and applied mathematics. Since January 2001, he has been Head of that department. His primary fields of interest in teaching and research are nonlinear optimization, including SM techniques and global optimization, and validated computing using interval analysis.

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Dynamic Deviation Reduction-Based Volterra Behavioral Modeling of RF Power Amplifiers Anding Zhu, Member, IEEE, José C. Pedro, Senior Member, IEEE, and Thomas J. Brazil, Fellow, IEEE

Abstract—A new representation of the Volterra series is proposed, which is derived from a previously introduced modified Volterra series, but adapted to the discrete time domain and reformulated in a novel way. Based on this representation, an efficient model-pruning approach, called dynamic deviation reduction, is introduced to simplify the structure of Volterra-series-based RF power amplifier behavioral models aimed at significantly reducing the complexity of the model, but without incurring loss of model fidelity. Both static nonlinearities and different orders of dynamic behavior can be separately identified and the proposed representation retains the important property of linearity with respect to series coefficients. This model can, therefore, be easily extracted directly from the measured time domain of input and output samples of an amplifier by employing simple linear system identification algorithms. A systematic mathematical derivation is presented, together with validation of the proposed method using both computer simulation and experiment. Index Terms—Behavioral model, power amplifiers (PAs), Volterra series.

I. INTRODUCTION

I

N A wideband wireless system, the distortion induced by a power amplifier (PA) can be considered to arise from different sources or can be assigned to different physical phenomena such as: 1) static (device) nonlinearities; 2) linear memory effects, arising from time delays, or phase shifts, in the matching networks and the device/circuit elements used; and 3) nonlinear memory effects, such as those caused by trapping effects, nonideal bias networks, temperature dependence on the input power, etc. To accurately model a PA, we have to take into account both nonlinearities and memory effects. Although many behavioral models for RF PAs have been developed in recent years [1], this kind of modeling technique is still far from being mature since accurately characterizing PAs becomes more and more difficult and challenging as wireless systems migrate to higher frequencies, higher speeds, and wider bandwidths.

Manuscript received April 6, 2006; revised June 28, 2006. This work was supported by the Science Foundation Ireland under the Principal Investigator Award . This work was supported in part by the Network of Excellence TARGET under the 6th Framework Program funded by the European Commission. A. Zhu and T. J. Brazil are with the School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Dublin 4, Ireland (e-mail: [email protected]; [email protected]). J. C. Pedro is with the Institute of Telecommunications, Universidade de Aveiro, 3810-193 Aveiro, Portugal (e-mail: [email protected]). Color versions of Figs. 6–8 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.883243

The Volterra series provides a general way to model a nonlinear system with memory, and it has been used by several researchers to describe the relationship between the input and output of an amplifier [1]–[7]. However, high computational complexity continues to make methods of this kind rather impractical in some real applications because the number of parameters to be estimated increases exponentially with the degree of nonlinearity and with the memory length of the system. To overcome the high complexity of a general Volterra series, a Volterra-like approach, called the modified Volterra series, was proposed in [8] by Filicori and Vannini to model microwave transistors, and then extended to model PAs by Mirri et al. [9], [10] and Ngoya et al. [11]. This modified series has the important property that it separates the purely static effects from the dynamic ones, which are intimately mixed in the classical series. However, this modified Volterra series loses the property of linearity in model parameters, which means that the output of the model is no longer linear with respect to the coefficients [9]. This leads to the consequence that models of this kind cannot be extracted in a direct and systematic way using established linear system estimation procedures such as the least squares (LS) techniques, as is usual in the classical case. In fact, although the static part and different order dynamics can be estimated separately, extracting higher order dynamics involves complicated measurement procedures [9]–[11]. In this paper, we first extend the modified Volterra series to the discrete time domain, and rewrite it in the classical format after dynamic-order truncation. We then propose a new format of representation for the Volterra model, in which the input elements are organized according to the order of dynamics involved in the model. This is similar to the modified Volterra series, but retains the property of linearity in the parameters of the model, as for the classical Volterra series. Based on this new representation, an effective model-order reduction method is proposed, called dynamic deviation reduction [12], in which higher order dynamics are removed since the effects of nonlinear dynamics tend to fade with increasing order in many real PAs. Unlike the classical Volterra model, where the number of coefficients increases exponentially with the nonlinearity order and memory length, in the proposed reduced-order model, the number of coefficients increases almost linearly with the order of nonlinearity and memory length. Since the model complexity is significantly reduced after dynamic-order truncation, this Volterra model can be used to accurately characterize a PA with static strong nonlinearities and with long-term linear and low-order nonlinear memory effects. Furthermore, the proposed model takes advantage of the properties of the modified Volterra series so that the static nonlinearities and different order

0018-9480/$20.00 © 2006 IEEE

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dynamics can be separated after model extraction, which provides us with an effective way to derive efficient distortion compensation approaches for PA linearization. Finally, since this model is built in the discrete time domain, it can be directly embedded in system-level simulation tools and implemented in digital circuits. This paper is organized as follows. In Section II, after introducing the modified Volterra series, we present the new representation of the Volterra series. Based on this new representation, a dynamic model-order reduction is introduced in Section III. Model extraction procedures and experimental verification are given in Sections IV and V, respectively, with a conclusion in Section VI.

which represents the deviation of the delayed input signal with respect to the current input . Substituting (2) in (1), we obtain

(3) II. VOLTERRA SERIES A Volterra series is a combination of linear convolution and a nonlinear power series so that it can be used to describe the input/output relationship of a general nonlinear, causal, and time-invariant system with fading memory. In the discrete time domain, a Volterra series can be written as (1) where and represents the input and output, respecis called the th-order Volterra kernel. tively, and In real applications, and assumed in (1), the Volterra series is normally truncated to finite nonlinear order and finite memory length [2]. Unlike neural networks or other nonlinear functions, the output of the Volterra model is linear with respect to its coefficients. Under the assumption of stationarity, if we solve for the coefficients with respect to a minimum mean or least square error criterion, we will have a single global minimum. Therefore, it is possible to extract the nonlinear Volterra model in a direct way by using linear system identification algorithms. The Volterra series has been successfully used to solve many problems in science and engineering [2]–[4]. However, since all nonlinearities and memory effects are treated in the same way, the number of coefficients to be estimated increases exponentially with the degree of nonlinearity and with the memory length of the system. It is very difficult to identify a practically convenient experimental procedure for the measurement of kernels of order greater than five so that the described classical Volterra-series formulation can only be practically used for the characterization of weakly nonlinear systems. A. Modified Volterra series To overcome the limitation of the classical Volterra series, a Volterra-like approach, called a modified Volterra series [8]–[10], or dynamic Volterra series [11], was proposed, in which the input/output relationship for a nonlinear system with memory is described as a memoryless nonlinear term plus a purely dynamic contribution. This was based on introducing the dynamic deviation function (2)

After regrouping the coefficients, it is immediately apparent that the output signal in (1) can be expressed through the following dynamic-deviation-based Volterra-like series: (4) and represents the static and dynamic charwhere acteristics of the system, respectively. can be expressed as a power series of the current input signal (5) where

is the coefficient of the polynomial function, while is the purely dynamic part

(6) 1 represents the th-order dynamic kernel of the where th-order nonlinearity. The relationship between the coefficients of the classical Volterra formulation and and is presented in the those of the dynamic series Appendix. In this model, the static nonlinearities and the dynamic part are separated. Furthermore, controlling the value of , i.e., the order of the dynamics, allows us to truncate the model to a simpler version. For instance, in [8]–[11], (6) was truncated to first order. In that case, the modified Volterra model would have the form

(7) in which only the static and first-order dynamic behavior are retained. 1Note that here we use w (1) instead of g [x(n); . . .], which was used in [10], to represent the dynamic coefficients. g [x(n); . . .] is the combination of w (1) and x (n), which depends nonlinearly on x(n), while w (. . .) is independent from x(n).

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However, the static part and the different order dynamics have to be extracted separately in this model, which involves very complicated measurement procedures [10], [11], especially when higher order dynamics are included. B. New Representation of Volterra Series In order to take advantage of the modified Volterra series, but also keep the model extraction as simple as possible, we derive a new representation of the Volterra series here. Let us start from the first-order truncated modified Volterra series in (7). At first sight, this modified Volterra model seems to be fundamentally different from the classical Volterra series. However, if we re-substitute (2) in (7), we obtain

(11) Regrouping the coefficients write (11) as

,

, and

, we can

(12)

(8)

Following the same procedures of (8)–(12), we can rewrite the classical Volterra series in (1) as

After some rearrangements, it can be shown that

(9) Now, we truncate (6) to second order, and the model becomes (13)

(10) In the same way, re-substituting (2) in (10), we obtain

which leads to a new representation of Volterra series, where represents the th-order Volterra indices are “0,” corresponding to kernel where the first . Compared the input item to (1), we can see that the coefficients in (13) are the same as in the classical expression, but the sequence of the input product items in the input vector has been changed. In this new representation, represents the possible number of product terms of the delayed inputs in the input items. For means only one delayed input is included in the instance, . On the other hand, compared product, i.e., to the dynamic-deviation based series in (6), we see that can also be interpreted as the order of the dynamics involved in the , will model since it decides how many deviations, i.e., be included in the input vector. To make this clear, we now further demonstrate the properties of the new Volterra representation by using kernels indices with their corresponding input items, as shown in Table I, where a and a “0” corresponds to the current instantaneous input non-“0”, i.e., an “ ,” corresponds to the delayed input .

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TABLE I INDICES OF COEFFICIENTS

In Table I, each row includes kernels from the same order of nonlinearity, while the columns are divided by the order of the dynamics involved in the model. We can easily see that the value of directly indicates how many non-“0” indices are in the kernel and, thus, find out how many delayed inputs are involved in the means that all its input prodinput products. For instance, ucts have two components from delayed inputs, e.g., “012” cor. In the classical Volterra series responds to of (1), the coefficients are gathered by rows in Table I, which is based on the orders of nonlinearity, while in the new representation of (13), the coefficients are organized by columns, i.e., the corresponds to orders of the dynamics involved, where the first term in (13), then the second column, and so on. This makes the new Volterra model have the same advantages as the modified Volterra series. However, at the same time, the property of linearity in the coefficients is also kept from the classical Volterra series. Thus, this new representation makes possible an effective model-order reduction method and a systematic distortion evaluation approach, while keeping the conventional linear procedures for the model extraction, as will be discussed in Sections III and IV.

III. DYNAMIC DEVIATION REDUCTION In most real PAs, the distortions mainly arise from the static nonlinearities, and the effects of nonlinear dynamics in the PA fade with increasing order. This means that the static nonlinearities and low-order dynamics are the dominant sources of the distortions induced by the PA. Therefore, it is reasonable to remove higher order dynamics in the model to reduce the model complexity. In [8]–[11], the modified Volterra series was truncated to the first order, in which only first-order dynamics are accounted for in the model. However, as discussed in [13], while this firstorder truncation permits accurate modeling of highly nonlinear systems, its effectiveness tends to be limited to those systems where the nonlinear dynamics are sufficiently small so that they can be omitted. Unfortunately, it is found in practice that many solid-state amplifiers exhibit nonnegligible nonlinear dynamics, especially due to thermal and bias circuit modulation effects, which implies that nonlinear memory effects become apparent. In that situation, a first-order truncation is insufficient. Higher order dynamics must also be accounted for, and more terms need to be added to improve the accuracy of the model. However, we

cannot simply add higher order terms to the dynamic model because increasing the order of dynamics in (6) results in a rapid growth of model extraction effort, requiring complicated multidimensional measurements. Fortunately, the new Volterra representation in (13) provides us with a very flexible way to prune the Volterra model efficiently, keeping, at the same time, the model extraction complexity to an acceptable level, as is explained below. Since in (13) represents the order of the dynamics of the input products, we can easily control the order of dynamic be, havior by limiting the value of , i.e., setting where is a small number, thus pruning the model, as in the modified Volterra series. For instance, it is easy to see that the second-order truncated modified Volterra model in (10) is equivalent to the truncation of the new Volterra model in (13) by lim, which leads to (12). iting The key difference between (10) and (12) is that they require different model extraction procedures. Extracting the model in (10) requires difficult experimental measurements, as described in [10] and [11], while the coefficients in (12) can be extracted in a direct way since the output of this model is still linear with respect to all coefficients. This can be done by using LS algorithms to estimate the Volterra kernels from measured arbitrary input and output data of the PA in the discrete time domain, as presented in Section IV. The decision on how to select the truncation order depends on the practical characteristics of PAs and the model fidelity required. We refer to this model reduction approach as “dynamic deviation reduction” since represents the order of the dynamic deviation in the model. Note that this dynamic-order truncation does not affect the nonlinearity or memory truncation in the same way as in the classical series. In other words, it only removes higher order dynamics, preserving the static nonlinearities and low-order dynamics. For example, in (12), we removed the higher order dynamics, whose order is over two—i.e., all kernels in column 3 and beyond in Table I were omitted—but we are still able to characterize high-order static nonlinearities by increasing , or to model longer-term linear and first/second-order nonlinear dynamics by increasing . In conclusion, we have three truncation parameters, i.e., , , and , to choose from in this dynamic model-order reduction, which renders the application of the Volterra model much more flexible. In the classical Volterra series, we only truncate the model by limiting the order of nonlinearity and memory length so

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Fig. 2. Functional block diagram for dynamic distortion evaluation.

Fig. 1. Truncated Volterra model structure.

that the number of the th-order coefficients is .2 However, after dynamic deviation reduction, the number of coefficients will only be .3 When has a small value, the total number of kernels can be kept reasonably small even with large values of and . This significantly simplifies the model structure and reduces the model extraction effort. However, model fidelity can still be acceptable since higher order dynamics do not significantly impact on the output of the PA. Model implementation also becomes much simpler since only a limited number of multiplier products are needed, as shown in Fig. 1. There, a polynomial series is used to construct the instantaneous transfer function, while transversal finite impulse response (FIR) filters are used to implement the time shifts and convolutions [1], [3]. Note that, in this figure, the even-order nonlinear terms were omitted since only odd-order nonlinearities affect the first-zone output, i.e., the one where the information is transmitted. Also, only real RF signals were considered. For handling carrier-modulated signals, a low-pass equivalent Volterra model was developed in [12], where complex envelope signals were assumed. Furthermore, as discussed in Section II, the new representation of the Volterra series in (13) is equivalent to the modified Volterra series of (4). This means that the coefficients of the modified Volterra series can be directly calculated from the coefficients extracted for (13) or vice versa. Therefore, when the Volterra kernels in (13) are extracted, the modified series in 2For formulation simplicity, this number includes all kernels. If kernel symmetry is considered and omitting even-order kernels that do not contribute to the PA’s first zone output, the total number of coefficients can be further reduced, but it still increases exponentially with P . 3This number can also be decreased if kernel symmetry is again considered and even orders are omitted.

(4) can be easily constructed. The purely static effects and different orders of dynamics can then be separated. As illustrated in Fig. 2, this provides us with an effective way to investigate the origins of different kinds of distortion and to evaluate their effects on the output of the PA. As the functional block diagram shows, the nonlinear static and different dynamic characteristics are built into several sub-blocks according to their orders. Hence, by switching on branches containing these blocks, we can observe how the distortion changes in the output, and can thereby evaluate the effects induced by the static or dynamic nonlinearities. Of course, similar blocks could be used upstream of the PA to operate as pre-distorters so as to cancel the distortions induced by the PA, although that is not detailed in this study. IV. MODEL EXTRACTION A. Excitation Signals In this study, we use arbitrary signals as the excitation. To make sure the excitation source is sufficiently rich to excite all important properties of the system, most of the techniques used for the extraction of the Volterra model to date are formulated through a system approach, using the correlation properties of Gaussian white noise [2]–[4]. However, it is not convenient to use these approaches with contemporary commercial circuit simulators or experimental measurements. This is because most commercial simulators cannot handle a general Gaussian white noise source, and also practical PAs are not excited by Gaussian noise signals. Thus, here, we use a combination of several time-domain wideband code division multiple access (W-CDMA) user signals to extract the Volterra kernels. W-CDMA is a popular air interface technology for third-generation RF cellular communication systems, which supports wide RF bandwidths, typically from 5 to 20 MHz. It is based on the direct-sequence code division multiple access (DS-CDMA) technique, i.e., user information bits are spread over a wide bandwidth by multiplying the user data with quasi-random bits (called chips) derived from code division multiple access

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(CDMA) uncorrelated spreading codes. It is well known that a general model of a DS-CDMA system with spread-spectrum (SS) signals is described as [15]

signal to the PA, i.e., our device-under-test (DUT). The output of the DUT is then down-converted and sampled by the vector signal analyzer (VSA). The sampled input and output data are captured and finally used to extract behavioral models for the PA. From the point-of-view of system identification, we can consider that the coefficients appearing in (13) are a generalization defining a linear of the impulse response coefficients model. Consequently, one possible approach to the problem of the Volterra model parameter estimation is to treat it as a large, but standard, linear regression problem. In particular, we could form a single large parameter vector containing all of the unand define the matrix including known coefficients appearing in all of the product terms , where is the total length the model for of the available data record. If we assume the presence of an un, the Volterra model modeled error can be written as

(14)

(15)

Fig. 3. Experimental test bench.

where baseband quadrature or binary phase-shift keying modulated signal and pseudonoise binary code with a bandwidth of . is the carrier frequency and is the phase of the carrier associated with the th SS signal. According to the law of large numbers and the central limit theorem in statistics, no matter what the distribution of each SS signal is, will tend towards as becomes large, the CDMA signal a (band-limited) zero-mean Gaussian stochastic process [15]. Therefore, a composite baseband CDMA or W-CDMA excitation signal can be utilized as an equivalent band-limited white Gaussian process to estimate the Volterra transfer function of a PA. Furthermore, a W-CDMA signal has much higher peak-to-average power ratio and much wider modulation frequency components than the sometimes used two-tone signal, which means that it can drive the PA through a wider nonlinearity and dynamics region. W-CDMA signal sources are currently available in most commercial computer-aided design (CAD) software, e.g., Agilent ADS, MATLAB/Simulink, etc. It is also a built-in feature of most of the latest signal generators. B. Extraction Methodology As mentioned earlier, the output of the new Volterra model is linear with respect to its coefficients. It is, therefore, possible to extract the nonlinear Volterra model in a direct way by using arbitrary sampled input and output signals. Recently, a time-domain stimulus-response measurement solution has been proposed by Agilent Technologies [16] (shown in Fig. 3), which uses arbitrary waveforms, e.g., complex W-CDMA envelopes, as the input excitation. Similar configurations are also used by many other companies and researchers. In this test system, the modulated data files are first created at baseband, downloaded to the arbitrary waveform generator, as complex in-phase (I) and quadrature (Q) signals, which are then fed to an IQ modulator present in the electronic signal generator (ESG). The signal generator produces the test

where . A popular solution to this problem is the LS method, in which is estimated as the value that minimizes the model error criterion (16) where represents the transpose.4 A standard result states that such an estimate can be given by (17) This result has the advantage of notational simplicity and general applicability. Obviously, other linear adaptive techniques, such as the recursive least squares (RLS) and the least mean squares (LMS) algorithms, could also be here employed to estimate the model parameters. C. Model Fidelity Evaluation The PA behavioral model presented in this study operates on baseband time-domain waveforms. To directly assess the predictive accuracy of the model, a very useful time-domain waveform metric, termed the normalized mean square error (NMSE) [17], can be employed. This verification metric is the total power of the error vector between the measured and modeled waveforms, normalized to the measured signal power, given explicitly by

(18) 4For the low-pass equivalent model, this transpose becomes the Hermitian transpose.

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Fig. 4. Simplified schematic diagram of the simulated PA.

where the measured and modeled in-phase and quadrature waveforms have sample points. It is assumed that the “true” waveform is much closer to the measured waveform than the modeled waveform. Thus, the NMSE is indeed a metric of model fidelity. However, many other system-level performance evaluation figures, e.g., adjacent channel power ratio (ACPR), error vector magnitude (EVM) and bit error ratio (BER), etc., could also be employed to evaluate the model fidelity. V. MODEL VALIDATION Here, we verify the new behavioral model through both computer simulations and experimental tests. The first example is intended to test the model ability in capturing the various nonlinear and dynamic effects of microwave PA circuits. Thus, we used a PA equivalent circuit in a standard microwave simulation software package to have easy control on the nonlinearity and memory effects. This also allowed us to eliminate noises and measurement errors in computer simulation, putting in evidence the actual model deficiencies. The disadvantage associated to such a test is that the validity of the behavioral model becomes obviously conditioned by the accuracy of the equivalent-circuit model used. To make this modeling technique closer to the “real” world, we then also tested a commercial heterojunction bipolar transistor (HBT) PA in our laboratory. By using the Agilent connected-solution test bench shown in Fig. 3 [16], we captured the complex envelope data from the measured input and output of the PA, and then used them to extract and validate the behavioral model proposed. Since only the envelopes carry useful information in these systems, all behavioral models herein extracted belong to the low-pass equivalent format [12]. A. Computer Simulations In this test, we designed an equivalent-circuit PA model and simulated it with the Agilent ADS microwave simulation software package. This is a GaAs MESFET class-A PA operating at with distributed matching 2 GHz under a bias of 88% of networks. The block diagram is shown in Fig. 4. We used a W-CDMA signal as the excitation, and captured the simulated input and output data of the PA. These data were then used for model extraction and model validation. To show the memory effects presented by the PA, we first simulated the circuit under a simple quadrature amplitude modulation (QAM) signal for various information bandwidths and for two different bias impedances. The resulting dynamic AM/AM

Fig. 5. Sample AM/AM diagrams indicate the memory effects presented in the PA. (a) 1-MHz envelope with ideal bias networks. (b) 10-MHz envelope with ideal bias networks. (c) 1-MHz envelope with nonideal bias networks. (d) 10-MHz envelope with nonideal bias networks.

plots are shown in Fig. 5 (the AM/PM plots have similar aspects, which are not shown here).

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Fig. 6. Sample time-domain waveforms of predicted and simulated behavioral for the case (b) PA.

As shown in case (a), the PA is almost static when operated with a narrow band of 1 MHz and with ideal bias networks. Thus, in this case, a memoryless representation, such as the AM/AM and AM/PM model, could be used. However, when the bandwidth increases from 1 to 10 MHz, some memory effects become apparent (the AM/AM plot presents hysteresis), as shown in case (b). These memory effects are mainly due to the PA’s matching networks, and they are mostly linear since they manifest themselves even in the PA small-signal region. Another widely known way to create memory effects for narrow bandwidths is to increase the reactance presented by the bias networks. That is shown in case (c), where now most of the effects are nonlinear, as can be seen from the fact that they only appear beyond the PA’s onset of gain compression. Finally, in case (d) we have both linear and nonlinear memory effects (10-MHz bandwidth and for the increased bias impedance), something that could be expected from a real PA subject to wide bandwidth signals. Since we want to evaluate the model’s ability in treating various orders of system dynamics, we extracted a model for the PA as shown in case (b)—only first-order dynamics—and for the PA as shown in case (d)—first-order and higher order dynamics. In case (b), considering that the memory effects mainly emerged from linear and low-order nonlinear dynamics, we truncated the dynamic model to the first order, i.e., with nonlinearity order and memory length . The model was extracted via the LS estimation process proposed in Section IV. The average NMSE was 41 dB, a relative error less than 0.01%, which indicates that the first-order model predicted the PA output waveform quite well in this situation. We also calculated the coefficients for the equivalent modified Volterra model, and then the static and dynamic parts were separated. A sample of time-domain waveforms is shown in Fig. 6, where we can see that the model that includes only the static part is less accurate than the one including the dynamics. In truncated model performed quite case (d), a first-order poorly as the NMSE could not get below 36 dB. However, when we added the second-order dynamics into the model, i.e., , the NMSE was improved to 42 dB. Again, set the time-domain waveforms are shown in Fig. 7. These results

Fig. 7. Sample time-domain waveforms of predicted and simulated behavioral for the case (d) PA.

TABLE II MODEL PERFORMANCE IN THE TIME DOMAIN

clearly show that different orders of dynamic truncation have to be employed under different conditions, depending on the system characteristics and the desired model fidelity. B. Experimental Tests In order to validate the proposed behavioral modeling technique in a real system, a commercial HBT class-AB PA was tested. This PA was operated at 2.14 GHz and excited by downlink 3GPP W-CDMA signals of 3.84-Mc/s chip rate and peak-to-average power ratio equal to 8.2 [email protected]% probability on complementary cumulative distribution function (CCDF). The test bench setup used the ADS–ESG–VSA connected solution shown in Fig. 3. Around 12 000 sampling data points, with a sampling rate of 15.36 MHz, were captured from the PA input and output envelope signals. In this test, the nonlinearity of the model was truncated to and order 5, and the memory length was set to 3, i.e., . For comparison, we also truncated the order of the dynamics, i.e., set the value of , from 1 to 5, which means that we extracted five different models from the first-order dynamic truncation to the full model. To evaluate the model’s fidelity in the time domain, the NMSEs for each partial model were calculated. These results are shown in Table II, where we can see that the performance of the first-order model is quite poor. When the second-order dynamics were added in, the accuracy of the model was significantly improved. Nevertheless, increasing further the order of the dynamics only achieved minor improvements. The performance of the full model, in the case of max, was even worse than the truncated ones. This is imum common in nonorthogonal Volterra models, and is due to the fact that, when too many coefficients are involved, more uncertainties are brought into the model extraction process.

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APPENDIX The relationship between the classical Volterra formulation and the dynamic Volterra series can be developed as follows. coincides with the mulIn the static part, each coefficient tiple summation of the corresponding Volterra kernels of the same dimension (A.1) In the dynamic part, the coefficients of the first-order dynamics are (A.2) (A.3)

Fig. 8. Measured and modeled spectra of the PA first zone output.

The frequency-domain spectra of the outputs are shown in Fig. 8. From these results, we can see that the first-order dynamic model predicted the spectrum quite well in the in-band part, but some offsets appeared in the adjacent channels. The second-order model did better, but no obvious improvement was achieved after further increasing the order of the dynamics, which reflects what was already observed with the time-domain metric. From these measurement results, we can conclude that static nonlinearities and low-order nonlinear dynamics do dominate nonlinear distortions caused by the tested PA. Therefore, it is indeed reasonable to remove higher order dynamics in the model, to reduce the model complexity, since their effects quickly fade with increasing order. Since the model structure becomes much simpler after model reduction, we gain room to increase the maximum order of nonlinearity to cover higher order nonlinear effects, enabling in this way the application of the Volterra model to strongly nonlinear systems. In addition, we may increase the memory length to characterize a wider range of long-term linear and low-order nonlinear memory effects if needed. VI. CONCLUSION A new format of Volterra series has been introduced in this paper, which consisted of regrouping the Volterra coefficients so that different dynamic orders can be controlled and separated, but keeping the easiness of the model extraction process. Based on this new representation, we proposed a “dynamic deviation reduction,” which greatly simplified the model structure and, therefore, significantly reduced the complexity of Volterra-series-based behavioral models. Using this model reduction approach, we can effectively trade off between model simplicity and model fidelity, in a judicious manner, making the application of the Volterra model more flexible in practical applications. A model of this kind was shown to be easily extracted from time-domain measurements or simulations and simply implemented in system-level simulators.

.. .

(A.4)

is the original th-order Volterra Thus, we can see that plus the sum of kernels of the kernel with the index same dimension with different indices, but in which one of them equals . The second-order coefficients are (A.5) (A.6)

.. .

(A.7)

The coefficients for higher order dynamics can be derived in the same way. REFERENCES [1] J. C. Pedro and S. A. Maas, “A comparative overview of microwave and wireless power-amplifier behavioral modeling approaches,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1150–1163, Apr. 2005. [2] M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, reprint ed. Melbourne, FL: Krieger, 1989. [3] V. J. Mathews and G. L. Sicuranza, Polynomial Signal Processing. New York: Wiley, 2000. [4] V. Z. Marmarelis, Nonlinear Dynamic Modeling of Physiological Systems. New York: Wiley, 2004. [5] A. Zhu, M. Wren, and T. J. Brazil, “An efficient Volterra-based behavioral model for wideband RF power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., 2003, pp. 787–790.

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[6] A. Zhu and T. J. Brazil, “Behavioral modeling of RF power amplifiers based on pruned Volterra series,” IEEE Microw. Wireless Compon. Lett., vol. 14, pp. 563–565, Dec. 2004. [7] ——, “RF power amplifiers behavioral modeling using Volterra expansion with Laguerre functions,” in IEEE MTT-S Int. Microw. Symp. Dig., 2005, WE4D-1. [8] F. Filicori and G. Vannini, “Mathematical approach to large-signal modeling of electron devices,” Electron. Lett., vol. 27, no. 4, pp. 357–359, 1991. [9] D. Mirri et al., “A modified Volterra series approach for nonlinear dynamic systems modeling,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 8, pp. 1118–1128, Aug. 2002. [10] D. Mirri, F. Filicori, G. Iuculano, and G. Pasini, “A nonlinear dynamic model for performance analysis of large-signal amplifiers in communication systems,” IEEE Trans. Instrum. Meas., vol. 53, no. 4, pp. 341–350, Apr. 2004. [11] E. Ngoya et al., “Accurate RF and microwave system level modeling of wideband nonlinear circuits,” in IEEE MTT-S Int. Microw. Symp. Dig., 2000, vol. 1, pp. 79–82. [12] A. Zhu, J. Dooley, and T. J. Brazil, “Simplified Volterra series based behavioral modeling of RF power amplifiers using deviation-reduction,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, WEPG-03. [13] N. Le Gallou et al., “Analysis of low frequency memory and influence on solid state HPA intermodulation characteristics,” in IEEE MTT-S Int. Microw. Symp. Dig., 2001, vol. 2, pp. 979–982. [14] M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems, 2nd ed. Norwell, MA: Kluwer, 2000. [15] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication. Reading, MA: Addison-Wesley, 1995. [16] “Connected simulation and test solutions using the Advanced Design System” Agilent Technol., Palo Alto, CA, Applicat. Notes 1394, 2000. [17] M. S. Muha, C. J. Clark, A. A. Moulthrop, and C. P. Silva, “Validation of power amplifier nonlinear block models,” in IEEE MTT-S Int. Microw. Symp. Dig., 1999, vol. 2, pp. 759–762.

Anding Zhu (S’00–M’04) received the B.E. degree in telecommunication engineering from North China Electric Power University, Baoding, China, in 1997, the M.E. degree in computer applications from Beijing University of Posts and Telecommunications, Beijing, China, in 2000, and the Ph.D. degree in electronic engineering from University College Dublin (UCD), Dublin, Ireland, in 2004. He is currently a Lecturer with the School of Electrical, Electronic and Mechanical Engineering, UCD. His research interests include high-frequency nonlinear system modeling and device characterization techniques with a particular emphasis on Volterra-series-based behavioral modeling for RF PAs. He is also interested in wireless and RF system design, digital signal processing, and nonlinear system identification algorithms.

José C. Pedro (S’90–M’95–SM’99) was born in Espinho, Portugal, in 1962. He received the Diploma and Doctoral degrees in electronics and telecommunications engineering from the Universidade de Aveiro, Aveiro, Portugal, in 1985 and 1993, respectively. From 1985 to 1993, he was an Assistant Lecturer with the Universidade de Aveiro, and a Professor since 1993. He is currently a Senior Research Scientist with the Instituto de Telecomunicações, Universidade de Aveiro, as well as a Full Professor. He has authored or coauthored several papers appearing in international journals and symposia. He coauthored Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2003). His main scientific interests include active device modeling and the analysis and design of various nonlinear microwave and opto-electronics circuits, in particular, the design of highly linear multicarrier PAs and mixers. Dr. Pedro is an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and is also a reviewer for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He was the recipient of the 1993 Marconi Young Scientist Award and the 2000 Institution of Electrical Engineers (IEE) Measurement Prize.

Thomas J. Brazil (M’86–SM’02–F’04) was born in County Offaly, Ireland. He received the B.E. degree in electrical engineering from University College Dublin (UCD), Dublin, Ireland, in 1973 and the Ph.D. degree from the National University of Ireland, Dublin, Ireland, in 1977. He subsequently worked on microwave subsystem development with Plessey Research (Caswell), U.K., from 1977 to 1979. After a year as a Lecturer with the Department of Electronic Engineering, University of Birmingham, Birmingham, U.K., he returned to UCD in 1980, where he is currently a Professor with the School of Electrical, Electronic and Mechanical Engineering and holds the Chair of Electronic Engineering. He has worked in several areas of science policy, both nationally and on behalf of the European Union. From 1996 to 1998, he was Coordinator of the European EDGE project, which was the major European Union (EU) Framework IV (ESPRIT) project in the area of high-frequency CAD. His research interests are in the fields of nonlinear modeling and device characterization techniques with particular emphasis on applications to microwave transistor devices such as GaAs field-effect transistors (FETs), high electron-mobility transistors (HEMTs), bipolar junction transistors (BJTs), and HBTs. He also has interests in convolution-based CAD simulation techniques and microwave subsystem design. Prof. Brazil is a Fellow of Engineers Ireland. He is a member of the Royal Irish Academy. From 1998 to 2001, he was an IEEE Microwave Theory and Techniques Society (MTT-S) worldwide Distinguished Lecturer in high-frequency applied to wireless systems. He is currently a member of the IEEE MTT-1 Technical Committee on CAD.

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Low-Loss Differential Semicoaxial Interconnects in CMOS Process Jun-De Jin, Shawn S. H. Hsu, Member, IEEE, Ming-Ta Yang, Associate Member, IEEE, and Sally Liu

Abstract—Design, characterization, and modeling of differential semicoaxial interconnects based on a standard 0.18- m CMOS process are presented for the first time. The differential semicoaxial line shows a low differential-mode attenuation constant of 1.00 dB/mm at 50 GHz and a slow-wave factor above 3.1 over a wide frequency range. The characteristics of differential semicoaxial lines for differential mode, common mode, slow-wave effect, and coupling effect are also investigated in details based on the measured mixed-mode -parameters. The lumped circuit is adopted to model the CMOS differential semicoaxial lines. An excellent agreement between the measured and modeled results is obtained up to 50 GHz. Index Terms—CMOS, differential line, lumped mode -parameters, semicoaxial interconnects.

, mixed-

I. INTRODUCTION

T

HE ADVANCED CMOS technologies have dramatically increased the operation frequency of Si-based differential monolithic microwave integrated circuits (MMICs) [1], [2]. In the scope of circuit design, the differential topology features advantages of low common-mode noise, large output power, and small even-order harmonics. However, without careful design, the differential interconnects in the circuit can degrade the overall circuit performance, especially at high frequencies. The commonly used interconnect structures for microwave circuits are the microstrip line [3], [4] and coplanar waveguide (CPW) [4]–[6]. For Si-based integrated circuits (ICs), however, they may not be the best candidates due to the crosstalk and loss of the lines [7]. In this study, low-loss differential interconnects with a semicoaxial structure are realized by utilizing the multiple metal layers in modern CMOS process. With a semirounded ground plane, the differential semicoaxial line structure can be expected to reduce the crosstalk from the adjacent interconnects and the loss introduced by the lossy Si substrate. The concept of semicoaxial structure has been reported in [8], but only with simulated results for single semicoaxial lines Manuscript received April 9, 2006; revised September 7, 2006. This work was supported in part by the National Tsing Hua University–Taiwan Semiconductor Manufacturing Company Joint-Development Project and by the National Science Council under Contract NSC 94-2215-E-007-005 and Contract NSC 95-2752-E-007-002-PAE. J.-D. Jin and S. S. H. Hsu are with the Department of Electrical Engineering and Institute of Electronics Engineering, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C. (e-mail: [email protected]; [email protected]). M.-T. Yang and S. Liu are with the Taiwan Semiconductor Manufacturing Company, Hsinchu, Taiwan 300-77, R.O.C. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.886000

in the silicon-on-insulator (SOI) process. For differential semicoaxial lines in standard CMOS technologies, a preliminary investigation has been reported by the authors [9]. In this study, a more detailed analysis on the slow-wave effect, coupling effect, and modeling of the differential semicoaxial lines will be presented. These topics have not been analyzed and discussed for CMOS-based differential lines, which also provide useful information for the interconnect design and optimization for Si-based differential ICs. Section II compares various interconnect structures and describes the design of differential semicoaxial lines. Section III presents and discusses the measured characteristics of differential semicoaxial lines for both the differential and common modes. In addition, slow-wave and coupling effects are investigated in details based on the mixed-mode -parameters [10], [11]. Section IV focuses on the modeling of differential equivalent cirsemicoaxial lines by utilizing the lumped cuit, and Section V concludes this study. II. ANALYSIS AND DESIGN OF DIFFERENTIAL SEMICOAXIAL INTERCONNECTS Three differential-interconnect structures in the CMOS process are shown in Fig. 1, and the pros and cons are summarized in Table I. For the differential microstrip and differential semicoaxial lines, the lossy Si substrate is shielded by the bottom metal layer. On the other hand, the differential CPW suffers more from the loss introduced by the lossy Si substrate, which is referred to as substrate skin effect [7]. Regarding the crosstalk reduction, the differential microstrip line is relatively poor due to no ground planes existed between the signal lines for coupling isolation, while that of the differential semicoaxial line is excellent since the sidewall and bottom ground planes significantly alleviate the crosstalk through the SiO layer and Si substrate, respectively. The crosstalk of the differential CPW is between the other two structures due to the presence of substrate coupling. The above qualitative analysis suggests that the differential semicoaxial line is the best structure among the three interconnects. These trends have also been verified by electromagnetic (EM) simulations. The designed differential semicoaxial lines were fabricated in a standard one-poly and six-metal layers (1P6M) 0.18- m CMOS process. The signal line was realized by the top-metal layer (M6) with a thickness of 2.34 m, while the semirounded ground planes were designed by the multiple metal layers from M2 to M6, as shown in Fig. 1(c). The geometries, except the of the top ground plane, were designed by the emwidth [12] with pirical equations for characteristic impedance three different of 33, 50, and 75 , as summarized in Table II. was designed the same as signal width . The The

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Fig. 2. Micrograph of line D-SC4. The area of each probing pads is 50 50 m .

2

Fig. 1. Microwave interconnect structures for: (a) differential microstrip line, (b) differential CPW, and (c) differential semicoaxial line in a standard 1P6M 0.18-m CMOS process. (Color version available online at http://ieeexplore. ieee.org.)

TABLE I COMPARISON OF VARIOUS CMOS MICROWAVE INTERCONNECT STRUCTURES Fig. 3. Lumped-element RLGC circuit model with one section for a symmetric differential line. (a) Four-port model. (b) Differential mode. (c) Common mode. From [9].

and the pads area was minimized to 50 50 m both to improve the deembedding accuracy. Fig. 2 shows the micrograph of line D-SC4. TABLE II GEOMETRIES OF DESIGNED DIFFERENTIAL SEMICOAXIAL LINES (H = 6:52 m, l = 400 m. FROM [9]

length of all differential semicoaxial lines is 400 m due to the limited chip area.

III. MEASUREMENT RESULTS AND DISCUSSION The differential semicoaxial lines were measured on-wafer with Cascade coplanar ground–signal–ground–signal–ground (GSGSG) infinity probes and an Agilent E8364A four-port PNA network analyzer from 0.2 to 50 GHz. For the Si-based interconnect measurements, deembedding becomes a critical issue due to the low signal level and the lossy Si substrate. In this study, the ground shielded test structure was employed [13]

A. Four-Port Circuit Model The four-port lumped-element circuit model of a symmetric differential line is depicted in Fig. 3(a), which includes the coupling effects between the two signal lines. The mutual inductance and capacitance per unit length describe the current and voltage coupling, respectively. , , , and describe the series resistance, series inductance, shunt conductance, and shunt capacitance per unit length, respectively. The four-port differential line model can be converted to one differential-mode and one common-mode two-port circuit models, as shown in Fig. 3(b) and (c), respectively. The relation between the four- and two-port circuits are also indicated. Note that is the coupling coefficient of a transformer, and can be calculated . This model will be used for both interconnect analby ysis and modeling below. B. Mixed-Mode -Parameters Since a four-port differential semicoaxial line is driven by the differential- and common-mode signals, the high-frequency characteristics can be described by the mixed-mode -parameters. Four 2 2 matrices are included, and referred , differento as the -parameters of differential-mode , common-to-differential-mode tial-to-common-mode , and common-mode . The measured four-port

JIN et al.: LOW-LOSS DIFFERENTIAL SEMICOAXIAL INTERCONNECTS IN CMOS PROCESS

Fig. 4. Differential-mode Z (Z ential semicoaxial lines from [9].

) and common-mode

Z (Z

) for differ-

-parameters of differential semicoaxial lines are converted to the mixed-mode -parameters by the following equation [14]:

(1)

Fig. 5. Differential-mode ( ) and common-mode ( ) for differential semicoaxial lines ( is from [9]).

. The line D-SC2 follows the relation of due to a large spacing of 79.5 m that is employed, while the other three differential semicoaxial lines have smaller than 4 resulting from the small used. in both differential-mode The attenuation constants and common-mode are shown in Fig. 5. As can be seen, the losses of all D-SC lines are less than 3.5 dB/mm at 50 GHz, which can be attributed to the perfectly shielded lossy Si substrate and the wave propagation close to an ideal TEM mode with the semicoaxial structure. For a low-loss and weakly coucan be approximated to , as can be pled differential line, derived from the model in Fig. 3 as follows: it also decreases

where

(5) (6)

(2)

For a symmetric differential line, as studied here, and are nonexistent, therefore, only and are analyzed. C. Mixed-Mode

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and

The measured differential-mode and commonmode can be obtained from and , respectively of each differential semicoaxial [15]. As shown in Fig. 4, , which can be understood by the line is larger than equations derived from Fig. 3 (3) (4) As observed from (4), is independent of a coupling effect due to the fact that in-phase common-mode signals are not inter, ), acting. For a weakly coupled differential line ( and should be and , respectively. Note that the coupling effect is affected mainly by , while the metal spacing ( ). A small increases and

and represent the differential- and commonwhere mode resistances, respectively. The line D-SC2 shows a trend due to a large that is employed. Since the large of , for the rest of the differencoupling effect decreases tial semicoaxial lines are all larger than . In addition, from a , a larger comparison between the lines with the same results in a smaller . The trend of in Fig. 5 is consisof tent with (5). Note that the line D-SC2 shows the lowest 1.00 dB/mm at 50 GHz compared with the other geometries, of 15 m and a large of which can be attributed to a wide 79.5 m adopted in the design. A further analysis of different origins of the loss in D-SC lines will be carried out in Section IV.

D. Slow-Wave Effect The slow-wave factor is the ratio of the wave velocity in vacuum to that in dielectric . An increased slow-wave factor results in a reduced , leading to a smaller effective wavelength, which can be very useful for the passive microwave component design such as couplers and dividers [16]. With a large slow-wave factor, the component size, as well as the signal loss can be effectively reduced.

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Fig. 6. Differential-mode slow-wave factor ( = ) and common-mode slow-wave factor ( = ) for differential semicoaxial lines.

Fig. 8. Common-mode RLGC for differential semicoaxial lines from [9].

proximity effect. In addition, the observed is higher than , instead of being equal in an ideal case. This can be attributed to the fact that the common-mode signal currents repel each other at the edges of the signal lines, while the differential-mode both attract each other due to proximity effect. Both effects reduce the current cross section, but the repelled condiand tion results in a relatively smaller area. The increased with frequency can be attributed to the dielectric conductivity, which is proportional to frequency. From Figs. 7(b) and and present an obvious reduction at 1 GHz be8(b), cause the current loop area is reduced by the skin effect and proximity effect. In addition, the almost frequency-independent and suggest that the dispersion effect of the SiO layer is relatively weak. Fig. 7. Differential-mode RLGC for differential semicoaxial lines from [9].

From the phase constant in the vacuum and the measured , the obtained slow-wave factor in differenphase constant and common-mode are shown in tial-mode Fig. 6. The observed slow-wave factors are all higher than the square root of the dielectric constant (3.9) of SiO due to the is reduced by the fact that the wave velocity large and . The large can be mainly attributed to a large current loop area resulting from the semicoaxial structure [17]. The large is due to the increased ground-plane area and the coupling effect between the signal lines. For example, a high of 3.1 is observed in D-SC3. With this structure, the physical size of an interconnect for a certain electrical length can be effectively reduced by a factor of approximately 3 compared to that in vacuum. E. Mixed-Mode

Components

and , the extracted components for both From differential- and common-mode circuit models are illustrated in Figs. 7 and 8, respectively. As shown in Figs. 7(a) and 8(a), and increase with frequency due to the skin effect and

F. Coupling Effects From the differential- and common-mode circuit models, as shown in Fig. 3, the and can be derived as (7) (8) As depicted in Fig. 9, the measured and both present a low-frequency dependence. Moreover, both the current and voltage coupling increase when decreases. For example, a of 0.4 and 75 fF/mm are observed for D-SC3, high and respectively. are the critical parameters for the Note that the and design, as described in (3). With a low coupling effect, the empirical equations for single lines can be employed directly for differential lines, which provide a simple design approach for differential lines. On the other hand, the required chip area can be reduced with high of interconnects designed for low in (3) can sigcoupling effect. The presence of a high and nificantly reduce the required large and small . As a result, differential interconnect can be achieved by small a low signal linewidth.

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TABLE III DESCRIPTION FOR GEOMETRICAL AND PHYSICAL PARAMETERS

Fig. 9.

k and C

for differential semicoaxial lines.

where IV. MODELING OF DIFFERENTIAL SEMICOAXIAL LINES Lack of an accurate differential lines model greatly handicaps the differential-type Si-based MMIC design. For CMOS differential lines, an accurate equivalent-circuit model with a wide frequency range is still not available. In this study, a systematic approach is developed to model the differential semicoaxial circuit model with seclines by the lumped-element tions. Physical-based semiempirical equations are employed, and the model is verified up to 50 GHz. Each identical section of the model has been shown in Fig. 3(a). The sufficient section number for accurate modeling can be estimated by the following equation: (9) where is the maximum operation frequency, is the wave velocity, and is the length of the interconnect. The derivation of an interof (9) is under the assumption that if a section , a lumped-circuit model connect is smaller than or equal to can be employed to describe the characteristics accurately. In contrast to the modeling of a single line, additional efforts were made to include the coupling effects in the differential line. , , , and are calculated first by neglecting one of the signal lines in the differential interconnect, while both signal lines are . The semirounded structure is taken into account for and simplified by adopting a parallel-plate structure with additional fitting parameters to describe the sidewall effect from the ground plane. For a grounded interconnect with a lossless substrate, mainly originates from both the signal and ground metal lines. is dominated The ac resistance of the signal line by the skin effect resulting from the finite metal width and is based on the thickness [15], while the dc part simple resistivity equation. On the other hand, the dc resistance of the ground line is negligible due to an overall large metal can be cross-sectional area, while the ac resistance modeled by the skin effect with an area parameter. Therefore, can be represented as (10)

(11) (12) (13) accounts for the effective ground metal The fitting parameter cross section. The descriptions for the geometrical and physical parameters are tabulated in Table III. The inductance mainly relates to the current loop area enclosed by the signal and ground lines. Regarding the parallelplate structure, the concept of geometric-mean-distance (g.m.d.) is utilized to describe the frequency-independent loop induc[18]. Since both skin and proximity effects retance duce the effective metal width and thickness, an additional freis introduced quency-dependent internal inductance [19]. The total inductance is a sum of and , and each component can be written as (14) (15) where (16) (17) (18) is the g.m.d. between the top and bottom metal and where layers, is a geometry-dependent factor, and and are the g.m.d. of the signal and bottom ground lines, respectively. The fitting parameter in (15) is adopted to model the g.m.d. of the sidewall ground plane. By considering the frequency-dependent dielectric conducand can tivity, the modeled is proportional to frequency be written as (19)

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Fig. 10. Measured and modeled mixed-mode S -parameters for line D-SC1. (a) Differential-mode S in phase. (c) Common-mode S and S in magnitude. (d) Common-mode S and S in phase.

The first term on the right-hand side of (19) accounts for the accounts for conductance of the parallel-plate structure, and the sidewall of the ground plane. The capacitance can be calculated by the microstrip line approximation with a geometry-dependent due to the electric field exists in both air and the SiO layer [15]. The additional capacitance introduced by the sidewall is included by . The overall can be written as

(20) where

(21) As observed from (20), the modeled is frequency independent, which agrees well with the measured results since the frequency dependence of the dielectric material is negligible in the measured frequency range. can be calculated by . between two signal lines is simplified to a frequency-independent parameter since the mea-

and S

in magnitude. (b) Differential-mode S

and S

sured results show a low-frequency dependency. Therefore, can be represented as [18]

(22) where (23) The first term on the right-hand side of (22) is derived based on an infinite current loop area, which differs from the confined is loop area in the real case. Therefore, a fitting parameter introduced to compensate for the overestimated mutual inductance. consists of a parallel-plate capacitance between two The signal lines and a fringing capacitance in the air and SiO layer. The fringing part is represented by a fitting parameter to simis frequency independent. plify the model. The modeled Based on the developed modeling methodology, an excellent agreement between the measured and modeled mixed-mode -parameters for differential semicoaxial lines is obtained up to 50 GHz. Fig. 10 shows the results for line D-SC1 as an example. Note that the estimated is two from (9), while a section number of four was employed here for an improved modeling accuracy.

JIN et al.: LOW-LOSS DIFFERENTIAL SEMICOAXIAL INTERCONNECTS IN CMOS PROCESS

From the above analysis, the different loss origins in a low-loss D-SC line can be investigated quantitatively. At high frequencies, the dominant differential-mode losses are and the dielectric the conductor loss . For line D-SC2 with the lowest loss at 50 GHz, the high-frequency conductor loss is mainly due to skin effect. By using (11) and and are 0.7 and 4.1 mm, (12), the resistance is 0.46 dB/mm, assuming respectively. The calculated is negligible. On the other hand, the conductance is negligible, and is 0.6 mS/mm from (19), assuming the estimated is 0.47 dB/mm. As a result, the overall calculated loss from both the conductor and dielectric layers is 0.93 dB/mm, which is close to the measured result of 1.00 dB/mm at 50 GHz. V. CONCLUSION In this paper, the low-loss differential semicoaxial lines in a standard CMOS process have been investigated in detail. The mixed-mode -parameters were adopted to characterize , , slow-wave factor, components, , and the of four-port differential semicoaxial lines. A low of 1.00 dB/mm at 50 GHz was obtained for a differential semicoaxial line with a particular geometry. A large slow-wave factor above 3.1 was observed for differential semicoaxial lines due to the semirounded ground plane. Measured and showed small frequency dependence. For a differential semicoaxial line with a metal spacing of 2.4 m, high coupling coefficients of 0.4 and 75 fF/mm were observed. The impacts design were also discussed. In of coupling effects on addition, the differential semicoaxial lines were modeled by circuit model with an excellent the lumped-element accuracy up to 50 GHz. ACKNOWLEDGMENT The authors would like to thank S.-Y. Cho, Taiwan Semiconductor Manufacturing Company, Hsinchu, Taiwan, R.O.C., and C.-Y. Chan, National Tsing Hua University, Hsinchu, Taiwan, R.O.C., and the Chip Implementation Center (CIC), Hsinchu, Taiwan, R.O.C., for the chip measurement. REFERENCES [1] L. M. Franca-Neto, R. E. Bishop, and B. A. Bloechel, “64 GHz and 100 GHz VCOs in 90 nm CMOS using optimum pumping method,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2004, pp. 444–445. [2] P.-C. Huang, M.-D. Tsai, H. Wang, C.-H. Chen, and C.-S. Chang, “A 114 GHz VCO in 0.13 m CMOS technology,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2005, pp. 404–405. [3] B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, “SiGe bipolar transceiver circuits operating at 60 GHz,” IEEE J. Solid-State Circuits, vol. 40, no. 1, pp. 156–167, Jan. 2005. [4] M. T. Yang, P. P. C. Ho, T. J. Yeh, Y. J. Wang, and D. C. W. Kuo et al., “On the millimeter-wave characteristics and model of on-chip interconnect transmission lines up to 110 GHz,” in IEEE MTT-S Int. Microw. Symp. Dig., June 2005, pp. 1819–1822. [5] C. H. Doan, S. Emami, A. M. Niknejad, and R. W. Brodersen, “Millimeter-wave CMOS design,” IEEE J. Solid-State Circuits, vol. 40, no. 1, pp. 144–155, Jan. 2005.

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[6] B. Kleveland, T. H. Lee, and S. S. Wong, “50-GHz interconnect design in standard silicon technology,” in IEEE MTT-S Int. Microw. Symp. Dig., June 1998, vol. 3, pp. 1913–1916. [7] H. Ymeri, B. Nauwelaers, K. Maex, D. D. Roest, and S. Vandenberghe, “Accurate analytic expressions for frequency-dependent inductance and resistance of single on-chip interconnects on conductive silicon substrate,” Phys. Lett. A, vol. 28, pp. 195–198, Jan. 2002. [8] J. Kim, B. Jung, P. Cheung, and R. Harjani, “Novel CMOS low-loss transmission line structure,” in IEEE Radio Wireless Conf., Sep. 2004, pp. 235–238. [9] J.-D. Jin, S. S. H. Hsu, M.-T. Yang, and S. Liu, “Low-loss single and differential semi-coaxial interconnects in standard CMOS process,” presented at the IEEE MTT-S Int. Microw. Symp., 2006. [10] D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: Theory and simulation,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 7, pp. 1530–1539, Jul. 1995. [11] A. Ferrero and M. Pirola, “Generalized mixed-mode S -parameters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 458–463, Jan. 2006. [12] G. Ghione and C. Naldi, “Parameters of coplanar waveguides with lower ground plane,” Electron. Lett., vol. 19, no. 18, pp. 734–735, Sep. 1983. [13] T. E. Kolding, “Shield-based microwave on-wafer device measurements,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 6, pp. 1039–1044, Jun. 2001. [14] S. Baek, S. Ahn, J. Park, J. Kim, J. Kim, and J.-H. Cho, “Accurate high frequency lossy model of differential signal line including mode-conversion and common-mode propagation effect,” in Int. Electromagn. Compat. Symp., Aug. 2004, vol. 2, pp. 562–566. [15] Y. Eo and R. Eisenstadt, “High-speed VLSI interconnect modeling based on S -parameter measurements,” IEEE Trans. Compon., Hybrids, Manuf. Technol., vol. 16, no. 5, pp. 555–562, Aug. 1993. [16] T. S. D. Cheung, J. R. Long, K. Vaed, R. Volant, and A. Chinthakindi et al., “On-chip interconnect for mm-wave applications using an allcopper technology and wavelength reduction,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2003, pp. 396–397. [17] A. Komijani, A. Natarajan, and A. Hajimiri, “A 24-GHz, 14.5-dBm fully integrated power amplifier in 0.18-m CMOS,” IEEE J. SolidState Circuits, vol. 40, no. 9, pp. 1901–1908, Sep. 2005. [18] F. W. Grover, Inductance Calculations: Working Formulas and Tables. New York: Van Nostrand, 1946. [19] X. Qi, B. Kleveland, Z. Yu, S. Wong, R. Dutton, and T. Young, “Onchip inductance modeling of VLSI interconnect,” in IEEE Int. SolidState Circuits Conf. Tech. Dig., Feb. 2000, pp. 172–173.

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Jun-De Jin was born in Taipei, Taiwan, R.O.C., in 1979. He received the M.S. degree in electronics engineering from National Tsing Hua University, Hsinchu, Taiwan, R.O.C., in 2003, and is currently working toward the Ph.D. degree in electronics engineering at National Tsing Hua University. His research involves the designation of Si-based RF devices and circuits. In the summer of 2004, he was an Intern with the Taiwan Semiconductor Manufacturing Company (TSMC), Hsinchu, Taiwan, R.O.C., where he studied the characteristics of Si-based interconnects. Mr. Jin was a recipient of the Gold Medal of the 2001 ELAN Microcontroller Competition, the Silver Medal of the 2002 National Semiconductor Temperature Sensor Competition, and the Bronze Medal of the 2006 TSMC Outstanding Student Research Award.

Shawn S. H. Hsu (M’04) was born in Tainan, Taiwan, R.O.C. He received the B.S. degree in electrical engineering from National Tsing Hua University, Taiwan, R.O.C., in 1992, the M.S. degree in electrical engineering and computer science from The University of Michigan at Ann Arbor, in 1997, and the Ph.D. degree from National Chiao Tung University, Taiwan, R.O.C., in 2003. From 1992 to 1994, he was a lieutenant in the R.O.C. Army. From 1994 to 1995, he was a Research Assistant with National Chiao Tung University. In

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1997, he joined the III–V Integrated Devices and Circuits Group, National Chiao Tung University. He is currently an Assistant Professor with the Department of Electrical Engineering, National Tsing Hua University. His current research interests include the analytical and empirical large-signal and noise modeling of Si/III-V based devices for RFIC/MMIC design applications, the implementation and development of various measurement techniques to extract parameters for equivalent-circuit models, and the design of MMICs and RFICs using Si/III-V based devices for low-noise, high-linearity, and high-efficiency system-on-chip (SOC) applications.

technologies. He is currently the Manager of the Device (MOS, HBT and passive) Modeling, and Characterization Service Team, where he is responsible for mixed-signal/RF device modeling. He has authored or coauthored over 30 technical papers in international journals and conferences in the area of RF device characterization and modeling covering the fields of III–V AlGaAs/InGaAs HEMTs, Si/SiGe BiCMOS, and mostly in the RF CMOS. Dr. Yang served on the Advisory Workshop Committees of Compact Modeling for RF/Microwave Applications (CMRF) (2004–2006) and as a committee member on “Device and Modeling” of the SiRF in 2007.

Ming-Ta Yang (S’93–A’06) was born in Tainan, Taiwan, R.O.C., in 1966. He received the B.S and M.S. degrees in physics and applied physics from ChungYuan University, Chung -Li, Taiwan, R.O.C., in 1989 and 1992, and the Ph.D. degree in electrical engineering from National Central University, Chung-Li, Taiwan, R.O.C., in 1995. His doctoral dissertation was focused on the characterization and model of AlGaAs/InGaAs doped-channel heterostructure field-effect transistors (FETs) and its application in MMICs. During the 1989 academic year, he joined the Department of Physics, ChungYuan University, as a member of the faculty. In 1995, he joined Mosel Vitelic Inc., Hsin-Chu, Taiwan, R.O.C., where he was involved with very large scale integration (VLSI) advanced technology development. In 1998, he then joined the Taiwan Semiconductor Manufacture Company Ltd. (TSMC), Hsinchu, Taiwan, R.O.C., where he set up the High-Frequency Characterization Laboratory and organized a team to response for the development of characterization and SPICE model both in mixed-signal and RF applications. His current research interests include the development of advanced high-frequency characterization and modeling of devices both in RF CMOS and high-speed SiGe HBT BiCMOS

Sally Liu received the B.S. and M.S. degrees in physics and applied physics from National Tsing-Hua University, Hsinchu Taiwan, R.O.C., in in 1972 and 1974, respectively, and the Ph.D. degree in electrical engineering and computer science from University of California at Berkeley, in 1981. Since 2004, she has been Director of the Advanced Technology Modeling Division, Taiwan Semiconductor Manufacturing Company (TSMC), Hsinchu, Taiwan, R.O.C. Prior to this, she spent 15 years with AT&T Bell Laboratories, six years with Conexant/Rockwell Semiconductors, and two years with RFIC. She has been engaged in the research and development of device modeling and simulation, circuit simulation and optimization, statistical modeling and design centering, circuit verification, intellectual property (IP) characterization, and electrical design automation (EDA) framework.

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An Empirical Bipolar Device Nonlinear Noise Modeling Approach for Large-Signal Microwave Circuit Analysis Pier Andrea Traverso, Member, IEEE, Corrado Florian, Member, IEEE, Mattia Borgarino, and Fabio Filicori Abstract—An empirical bipolar transistor nonlinear noise model for the large-signal (LS) noise analysis of microwave circuits is described. The model is derived according to the charge-controlled nonlinear noise behavioral modeling approach, and includes nonlinearly controlled equivalent noise (EN) generators describing the low-frequency (LF) noise up-conversion encountered in LS RF operation. LS-modulated shot-noise sources and parametric LF noise in parasitic resistors are also taken into account for improved model accuracy. Details for the implementation of the proposed cyclostationary EN generators in the framework of a computer-aided design tool are presented. As an application example, a simplified version of the proposed nonlinear noise model for two GaInP–GaAs HBTs has been formulated and empirically characterized on the basis of both bias-dependent LF noise and phase-noise measurements. Measured and simulated noise performance of a monolithic voltage-controlled oscillator over a set of different operating conditions is shown for the validation of the proposed approach. Index Terms—Cyclostationary noise, low-frequency (LF) noise, low phase noise (LPN), noise up-conversion, nonlinear noise model.

I. INTRODUCTION N MANY microwave applications, such as the design of mixers and low phase-noise (LPN) oscillators, accurate noise models of the electron devices involved are needed. The problem of describing the effects of noise phenomena under nonlinear operation has been intensively dealt with by numerous authors, both in terms of analysis at circuit/system level [1]–[5] and from a fundamental/physics-based standpoint [6]–[11]. As far as circuit-oriented empirical device models are concerned, along with the characterization of the broadband noise (e.g., thermal- and shot-noise), any noise modeling approach should also take into account the nonlinear mechanisms that are responsible for the up-conversion to RF of low-frequency (LF)1 noise phenomena perturbing the behavior of both field-effect and bipolar devices.

I

Manuscript received March 31, 2006; revised September 14, 2006. This work was supported in part by the Italian Ministry of Instruction, University and Research. P. A. Traverso, C. Florian, and F. Filicori are with the Department of Electronics, Computer Science, and Systems, University of Bologna, 40136 Bologna, Italy and also with MEC s.r.l., 40123 Bologna, Italy (e-mail: [email protected]). M. Borgarino is with the Department of Information Engineering, University of Modena and Reggio Emilia, 41100 Modena, Italy (e-mail: borgarino. [email protected]). Color versions of Figs. 7 and 10–15 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/TMTT.2006.885991 1In this study, the term “low-frequency” refers to the bandwidth from tens of hertz up to a few megahertz, in which the spectral density functions of shortcircuit noise currents (measured under quiescent operation of the device) contain nonuniform (i.e., “colored”) contributions that are relevant with respect to the white noise levels.

A circuit-oriented noise model for computer-aided design (CAD) large-signal (LS) analyses of microwave nonlinear circuits is usually defined by inserting suitable lumped equivalent noise (EN) sources within an otherwise noiseless description of the device. In most practical cases, the experimental characterization of these EN generators is carried out starting from LF noise measurements at different bias conditions. Such an empirical investigation provides accurate information on auto- and cross-spectral densities in the LF bandwidth of the electrical quantities (usually short-circuit noise currents) at the ports of the device under quiescent operation. Linear circuit transformations enable the extraction from empirical data of the unknown parameters, which characterize the EN generator spectral densities, whose dependence on the device operation is inherently defined in terms of bias values. However, the correct strategy for dealing with and controlling these EN sources under the nonlinear LS operating conditions encountered in microwave mixers and oscillators is still under investigation. Moreover, additional noise sources, which only marginally affect the LF noise at the ports under quiescent operation, but become important when the device is operated under microwave LS operating conditions, may be needed in order to correctly take into account the perturbation due to low-frequency-generated (LFG) stochastic phenomena on the high-frequency charge-storage and carrier-transit dynamics of the device. Recently, more refined modeling approaches have been proposed [12], [13] in order to describe the noise up-conversion by means of cyclostationary EN generators. In some empirical studies [13]–[15], quite sophisticated setups have also been exploited, which are capable of measuring the sideband noise at the output of the device driven into LS high-frequency operation. In this way, additional information is achieved on the EN sources under conditions that are more similar to the actual noise-perturbed LS regime to be predicted. The charge-controlled nonlinear noise (CCNN) model [16], [17] has been proposed for the circuit-oriented prediction of nonlinear noise effects in electron devices under LS operation. This technology-independent empirical approach is potentially capable not only of reproducing the LF noise behavior of the device under bias-varying quiescent condition, but also providing accurate noise conversion predictions by adequately describing the time-varying instantaneous modulation laws of the EN sources under device LS operation. On the basis of this approach, preliminary results for a nonlinear noise model of microwave bipolar devices have been recently presented [18] in the framework of phase-noise (PN) predictions in oscillator circuits. In this paper, the overall approach is outlined in detail. In Section II, the formulation and the topology of the EN generators, which account for the LF noise

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generated in the intrinsic device and converted by the LS operation, are discussed. Parametric instantaneously modulated LF noise in the parasitic resistors is also included in the proposed approach, along with the modulation of shot-noise sources. In Section III, the experimental procedures for model extraction are described, while Section IV provides details concerning the implementation of all the EN generators in the framework of Agilent’s Advanced Design System (ADS). Section V deals with model validation, which has been carried out by applying the proposed approach to two different GaInP–GaAs HBTs and comparing the results of LS noise analyses to measurements under several different LS operating conditions. II. NONLINEAR MODELING APPROACH TO NOISE PHENOMENA IN BIPOLAR DEVICES In this section, the analytical formulation and the circuit-oriented topology of the complete nonlinear noise model for bipolar devices will be discussed by separately classifying and dealing with the different noise phenomena, whose statistical moments (i.e., auto- and cross-spectral densities) are inherently distributed over very different frequency bandwidths, when the device is operated under either quiescent or small-signal (SS) operation. A further differentiation will be introduced when dealing with intrinsic and extrinsic device networks. More precisely, the propagation of LFG noise (flicker or noise, trap-assisted generation–recombination (G–R) noise, etc.) at the device intrinsic ports under LS operation will be described by means of a simplified (though still sufficiently accurate for the purpose of EN generator modeling) nonlinear charge-controlled description for the bipolar transistor, which is perturbed by a suitably defined set of behavioral noise sources. This method leads to the definition of circuit-oriented EN generators, which are nonlinearly controlled by the instantaneous values of LS electrical quantities at the intrinsic ports. A similar approach will also be followed for the modeling of noise within the device series parasitic resistors. In particular, it will be shown that an LFG, but LS-modulated contribution must also be considered in the noisy current flowing through the parasitic resistors. Finally, the presence of broadband noise phenomena (i.e., shot-noise) arising directly at RF frequencies and their modulation under LS operation will be taken into account.

at the intrinsic ports and perturbed by the fluctuations . The conductive term in (1) is also explicitly perturbed by the set . Each of the processes , which are assumed to be stationary and mutually independent, is defined with one of the possible auto-spectral density “shapes” (represented by for index ) which are typical of LF noise contributions ( for G–R noise with a given frequency flicker, corner , etc.). Index is exploited for differentiating noise processes having the same spectral shape (i.e., the same ), but a different influence on the electric quantities when propagated up to the intrinsic ports. This can be interpreted by saying that two or more processes with identical “color” are the macroscopic lumped (still internal) representation of LF physical microscopic noise phenomena of the same nature, but with different locations within the device structure. It is worth noticing that the lumped sources introduced in (1) only account for (according to an equivalent behavioral standpoint) distributed microscopic LF noise phenomena, i.e., noise characterized by slow dynamics with respect to the operation of the device. This enables the description of the perturbations due to in terms of algebraic functions. Broadband noise is not included2 in (1) and will be dealt with separately in Section II-C. By means of simple manipulations [16], [17] of (1) (based on the hypothesis that set linearly perturbs the LS deterministic operation of the device), the random processes can be propagated up to the intrinsic terminals and the analytical equations of four EN generators can be obtained, which represent the CCNN model formulation. Different topologies for the set of four external noise sources are possible [17], all being fully equivalent from a theoretical standpoint. However, the best topology can be chosen according to the device technology (field effect or bipolar) and the schematic features of the noiseless device model to which the four noise generators will be applied. In particular, in this study, the solution of Fig. 1 will be considered, which involves a couple of EN voltage sources and a couple of EN current sources expressed as

(2)

A. LF Noise and Up-Conversion Within the Intrinsic Device According to the technology-independent general approach outlined in [16] and [17], LF physical microscopic noise phenomena distributed within the intrinsic bipolar device can be adequately taken into account by introducing a set of elementary colored stochastic processes into the otherwise conventional quasi-static charge-controlled description of the intrinsic for vector transposition) transistor (notation

(1) is the vector of the noisy ( ) where equivalent charges, which are nonlinearly controlled by the inapplied stantaneous value of the voltages

1) Features and Applications of the CCNN Generators: The EN generators in (2) are nonlinearly controlled by the instantaneous value of the voltages applied at the intrinsic terminals. These sources depend on the bias levels under quiescent or SS conditions, while they are modulated by the (quasi-)periodic steady-state operation when the model is used for LS noise analyses of microwave circuits. Since EN generators (2) derive from an inherently nonlinear approach, they can be exploited both under linear and nonlinear operation, according to a coherent and unified methodology. 2The inclusion of broadband noise in those microscopic phenomena, which are behaviorally accounted for by processes x, would be possible, but at the cost of replacing the quasi-static equation (1) with finite-memory functional relationships between instantaneous currents and past evolution of x along the memory time.

TRAVERSO et al.: EMPIRICAL BIPOLAR DEVICE NONLINEAR NOISE MODELING APPROACH FOR LS MICROWAVE CIRCUIT ANALYSIS

Fig. 1. Topology of the EN generators accounting for LF noise in the intrinsic device, chosen among those identified with the CCNN approach.

Fig. 2. Circuital topology of the four EN generators accounting for LF noise generated within the intrinsic bipolar device (from Fig. 1 after equivalent transformation).

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is strongly reduced if compared to the modulation laws associ. This property is confirmed by emated with the original pirical experience, and can be intuitively explained by considering that short-circuit LF “excess” noise currents must become vanishingly small when the device is driven into the “off” state, where no bias power is provided. Instead, in the case of series EN voltage generators, an analogous property is directly guaranteed by the inherent nonlinearity of the deterministic part of the model, even when the bias dependence of EN voltage generators is neglected. Therefore, this transformation simplifies the procedures for model extraction and implementation. Moreover, since the main nonlinearity in bipolar devices derives from the exponential dependence of currents and diffused charges on the operating voltages, in order to achieve a further reduction in the nonlinearity of the EN generator modulation in (2) laws, the voltage-controlled functions can be algebraically transformed by considering the nonlinear relationships

(3) This feature of the proposed model should be compared with many conventional approaches, which are based on the definition of EN generators that are experimentally obtained exclusively by means of LF noise investigation under bias-varying quiescent operation. In these cases, in which the dependence of EN generators on the electron device operation is intrinsically reduced to the quiescent point (i.e., voltage and/or current bias values), ambiguities arise on the way the EN sources should be dealt with when they are used for nonlinear LS noise analyses. For example, simply using the voltage and/or current values at which the device is biased as the controlling variables of the EN generators under LS operation would totally neglect any possible direct modulation (thus, cyclostationarity) of the latter by the LS regime. Instead, the CCNN generators (2) not only allow for the accurate fitting of the measured bias-dependent LF noise behavior under linear operation, but are also associated with uniand vocal and unambiguous nonlinear modulation laws they can be exploited in LS analyses coherently with a nonlinear dynamic model of the deterministic device. It should also be noted that the quasi-static representation (1) is only aimed at the EN generator analytical formulation and topological identification: once the EN generators have been experimentally extracted, they might also be applied at the intrinsic ports of a more refined nonquasi-static nonlinear dynamic noiseless model of the device. 2) EN Generator and Controlling Variable Transformations: The EN generator topology proposed in this study for a bipolar device is shown in Fig. 2, where a common-base scheme is used for the deterministic model. It derives from the topology of Fig. 1, which has been modified by referring at the emitter by means of an EN port the EN current generator voltage generator , whose analytical formulation can be directly obtained from (2) through the SS conductance matrix of the device model resistive network. This modification makes it possible to consider a noise genwhose nonlinearity with respect to the LS regime erator

are the total LS conductive currents flowing where through the emitter and collector equivalent diodes, respectively, within the intrinsic bipolar device model. Thus, the final operative expressions for the CCNN approach-based cyclostationary EN generators become

(4) In this formulation, the current-control, besides preserving the generality of the approach, allows for a much simpler extraction for the modulation laws in (4) of the four EN generators and a more reliable implementation within numerical environments. Expression (4) can be rewritten in the compact form (5) where , while vector conhaving the th spectral shape (i.e., tains all the processes the th “color”). The associated th matrix in (5) is the set of nonlinear functions that establish the laws of propagation of up to the EN generators and the device ports. In many applications, the active devices are usually operated in classes A, AB, and B (or C), which involve operation only either in the normal active region or in the “off” state, where is practically zero. Under such conditions, all the current modulation laws associated with the EN generators in Fig. 2 (i.e., the conductive become simpler to deal with since

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Fig. 3. Proposed nonlinear noise model for bipolar devices.

Fig. 4. Noise model for each of the parasitic resistors.

current flowing into the base terminal of the resistive network) remains the only LS controlling variable. This simplified modulation strategy will be exploited for the four CCNN generators in all the experimental examples of Section V.

a complementary standpoint, all the elements of vector associated with processes accounting for thermal noise must also be null since thermal noise is not modulated by the current in the resistor. Thus, the LFG EN voltage source is obtained. By manipulating (7) as

B. Noise in Parasitic Resistors Fig. 3 shows the location of the EN generators (4) proposed in this study for the prediction of LFG (in the intrinsic device) noise nonlinear conversion. A Gummel–Poon-like nonlinear model is considered for the description of the noiseless intrinsic device. A basic set of resistive, capacitive, and inductive parasitics is also included. As far as noise generation in the series parasitic resistors is concerned, these introduce both LFG [6] and broadband noise within the device behavior. In order to model these overall noise effects arising from the resistors, a perturbation approach will be followed, which is similar to the CCNN approach adopted for the intrinsic device. More in detail, the “noisy” memoryless relationship between the current flowing into a given parasitic resistor and the applied voltage can be written as (6) with the random process vector having the same nature and interpretation of that perturbing (1), but now including elements that also account for broadband white noise. This is possible since the behavior of the resistor can be considered to be memoryless even in the presence of perturbations with very high dynamics. By assuming (6) to be linear with respect to the variables and , a McLaurin series expansion truncated at the second-order cross-term gives (7) in (7), which is fully indepenThe noise contribution dent of the regime since the elements of vector are constants, must clearly coincide with the classical equivalent thermal noise . In fact, the resistor cannot genopen-circuit voltage erate any noise other than thermal noise under zero-current operation. Thus, all the elements of associated with random processes accounting for colored G–R and flicker noise in the resistor must be null due to energy conservation constraints. From

(8) G–R and noise effects in the parasitic resistor can be dealt with according to a parametric method, consisting in the introduction of time-varying additive fluctuations , which perturb the otherwise deterministic resistance value. This behavioral parametric interpretation is confirmed by other fundamental studies [6], [19]. By introducing the Norton equivalent of (8), the overall noise model (Fig. 4) for the parasitic resistors is obtained, which consists of a conventional EN curand an rent generator for thermal noise EN current generator (9) accounting for LFG parametric noise. The latter is linearly modulated by the instantaneous LS current flowing through the resistor and leads to LFG noise up-conversion. The two EN generators in Fig. 4, to be associated with each series parasitic resistor , have been depicted as an overall EN in Fig. 3. current source C. Shot-Noise Modulation As discussed in Section II-A, the broadband noise affecting the intrinsic device is not taken into account by the CCNN approach (1). However, diffusion noise through bipolar junctions cannot be neglected since it gives important contributions to the RF noise spectra at the device ports. Considering LS nonlinear operating conditions, a shot-noise current source can be described with very good approximation [20]–[22] by its time-varying spectral density (10) which is dependent on the instantaneous current flowing throughout the junction. The spectral property (10) is justified

TRAVERSO et al.: EMPIRICAL BIPOLAR DEVICE NONLINEAR NOISE MODELING APPROACH FOR LS MICROWAVE CIRCUIT ANALYSIS

by the fact that the correlation times of shot-noise phenomena are very short with respect to the typical period of operation. Starting from this property of shot-noise modulation, which is well accepted in the recent literature (e.g., [12] and [22]), a suitable time-domain analytical definition of the stochastic process(es) fulfilling (10) is now needed in order to allow for a simple, but accurate inclusion of cyclostationary shot-noise in the overall nonlinear noise model proposed. In particular, the behavioral EN generator can be written as

low-noise transimpedance amplifier-based system. Taking into account that the noise processes together with the thermaland shot-noise sources are mutually independent, the measured bias-dependent LF noise data can be expressed as

(12)

(11) where is a white normalized random process. , Thus, two EN current generators defined in (11), have been considered in this study, which are controlled by the instantaneous intrinsic base and collector conductive current, respectively, and account for the modulation of shot-noise phenomena by the LS regime. These two independent [23] EN generators complete the nonlinear noise model proposed for microwave bipolar devices: their location within the intrinsic network is straightforward, thus they are not shown in Fig. 3. III. EXPERIMENTAL EXTRACTION OF THE EN GENERATORS In the following, the criteria and experimental procedures for the characterization of the EN generators in Fig. 3, which account for LFG noise both in the intrinsic device and parasitic resistors, will be described. It will be shown that both LF noise measurements under bias-varying quiescent operation and noise data obtained by operating the device under LS RF oscillating conditions are exploited to this purpose. Although the discussion will be provided as far as possible from a general standpoint, several operative assumptions/approximations will be made in order to reduce the complexity of the extraction task. These hypotheses have been exploited in the practice to obtain the nonlinear noise models whose prediction accuracy is discussed in Section V. However, the generality of the approach proposed in Section II could also suggest different practical solutions, possibly required by other device processes and/or circuit applications. A. LF Noise Measurements: Identification of the Stochastic Process Structure The first step toward the characterization of the CCNN apconsists proach-based generators of the identification of the most suitable set of normalized random processes perturbing the intrinsic device, as in (1). As far as the spectral density “shapes” are concerned, which characterize the th color of each , these may include both a flicker noise term and an adequate number of G–R-like contributions (i.e., Lorentzian spectral shapes) having different corner frequencies . The unknown set of ’s is identified on the basis of LF noise data obtained at the ports of the device under quiescent operation. In this study, the experimental setup described in [24] and [25] has been exploited, which provides the accurate direct measurement of bias-dependent base and collector short-circuit noise currents (auto- and cross-spectral densities , and in the (100 Hz–100 kHz) bandwidth) through a

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in terms of the thermaland shot-noise contributions (which are known a priori), the shapes flicker and the values of bias-dependent empirical functions . Only the dependence on the base current has been considered in (12) since, under quiescent bias conditions in the active forward region, the dependence of noise is normally almost negligible in bipolar parameters on , the unknown values of ’s and transistors. For any bias the corner frequencies of the Lorentzian spectral shapes can be easily computed by numerical fitting of (12) to the measured LF data. Once a suitable minimal set of spectral density “shapes” have been empirically idenand the weighting functions of independent noise processes tified, the number must also be chosen for each th color. This is necessary in order to establish a general scheme (according to the noise modeling approach (1)) of full, partial, or zero correlation for each given couple of EN generators out of the set of four in (4) and (5). By considering quiescent or SS operation in the active forward region only, (5) can be rewritten as follows: (13) flicker

(14)

where is the vector containing the contributions to the EN -dimengenerators due to the th color processes (i.e., the sional ) and -matrices are now controlled by the base current bias value. By remembering again that the ’s are mutually independent stochastic processes, (13) and (14) allow for the straightforward computation of the spectral structure (under quiescent operation) of the four EN generators with respect to any given set of bias-dependent values . for the elements of the matrices From a general standpoint, it can be shown that a common value of for the whole set of colors guarantees the possibility of matching any choice of the -shaped four autospectral and six cross-spectral densities associated with the stochastic processes within each provided that the 16 elements of are considered as unknowns of the th problem. However, the problem can be strongly simplified by considering that, in practical cases, some of the CCNN approach-based EN generators in (13) may have a clearly dominating effect on the circuit performance, while some cross-correlation terms can be neglected without significant loss of accuracy. This means that, in practical applications, a number of elements of ’s can be set to zero, and the matrices become strongly sparse.

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Fig. 6. SS equivalent circuit for the bipolar transistor in which the k th “color” LFG noise is separately taken into account.

Fig. 5. Influence of the k th “color” processes on the corresponding EN generator contributions through the modulation laws in (15).

This was the choice adopted in the HBT noise model extraction examples discussed in this study. In particular, only the statistical correlation between the elements of the and that between the elements of couple have been considered as nonnegligible for the device noise behavior within the application circuit. This operative hypothesis is equivalent to splitting the vector into two nonoverlapping subsets and of random processes, which perturb in an exclusive way the charge and the conductive current (1), respectively (i.e., independent microscopic noise phenomena are supposed to have a dominating effect either on the charge or the conductive current component operation) [16]. Thus, (14) can be expressed, for each given color , in the following simplified form:

The SS equivalent circuit for the bipolar device under quiescent operation is shown in Fig. 6, in which the th color conis separately dealt with. An overall EN generator tribution , which also includes the th color parametric noise contributions due to emitter and base extrinsic resistors, has been taken into account since, under the quiescent regime, the single LF noise contributions to this voltage EN generator cannot be separately meaand the noisy collector resistor do not sured. Both contribute to measured LF noise in the active region operation and, consequently, have been neglected. The spectral structure of EN generators in Fig. 6 is expressed in terms of LF noise data and differential parameters as

(16)

(17)

(18)

(15)

, , where and are the th terms in the summations of (12). By considering (15), (17) becomes

(19) Fig. 5 schematically summarizes the effects of the four th color processes on the contribution , through the six nonzero coefficients in (15) according to the above-mentioned hypotheses.

which provides the estimation of modulation law contributions at each value by choosing, without any loss of generality,3 the positive root of (19). Analogously, (18) yields

B. EN Generator Modulation Function Identification From LF-Quiescent and RF-LS Noise Data The bias-dependent LF noise data exploited for the identification of the suitable set of spectral shapes can be used along with the relationships in (15) to derive a system of equations in terms of the unknowns (i.e., the EN generator modulation laws in (4) evaluated over a discrete grid of bias values).

(20)

W

processes x are all independent, an arbitrary change of sign of each (or, equivalently, of each column of ) does not alter the results of noise ’s analyses. Consequently, a positive sign for all the diagonal elements of can be assumed.

x

3Since

W

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which provides the values of . As far as (16) is considered, by recalling (15) again and exploiting the result for resistor , the following equation for color is obtained:

. Equation (25) is obcan be introduced with tained by algebraically canceling the shape in the ratio . From (24) and (25), the following two expressions:

(21)

(26) (27)

where the unknown functions and and the paramand have been evidenced on the left-hand side. eters includes measured data and the values for Function . According to the equivalent circuit in Fig. 6, the preliminary considerations in Section I and (21), quiescent-bias LF noise measurements do not provide enough information for the univocal characterization of the cyclostationary EN generators to be used for LS noise analyses. This can be intuitively understood by considering that the parallel capacitive network in Fig. 2, which clearly has an important role under LS RF operation, and is practically negligible, owing to its high-impedance response in LF noise measurements. To overcome this problem, (21) must be dealt with by for introducing suitable additional parameters (i.e., a set each color), which can be characterized only when RF LS and noise data are available. The constant coefficients in (21), which describe the modulation of the th color parametric noise in and , respectively, represent an of intuitive choice for the first two elements of the set LS-identified parameters. In addition, an adequately approximate independence of bias currents can be reasonably assumed . This operative hypothesis, for the ratio which is somehow supported by the fact that (owing to energy conservation constraints) both spectral densities must show a common “turn-off” behavior as the bias currents tend to zero, (the third allows for the definition of a constant parameter element in ) from (21) as follows:

(22) with (22) as

. The expression for

directly derives from

(23) with and being chosen as the positive root of (22) and (23), respectively. In analogy with (22), also in the case of the couple , a simplifying assumption can be reasonably made, which involves the ratio between the th color spectral densities under quiescent operation. More precisely, (24) defines the parameter (to be included into ), which can be assumed as scarcely dependent on the bias values. In addition, the frequency-domain coherence parameter [26] (25)

and . are obtained, which define the values of Equations (19), (20), (22), (23), (26), and (27) along with a suitable choice for

flicker

(28)

allow for the characterization of the EN generators in Fig. 3 and the parametric . noise in Clearly, empirical data consisting only of bias-dependent LF noise spectral density measurements lead to a family of noise models for the device whose elements (each derived by a dif’s) are all equivalent as far as LF ferent arbitrary choice for noise analyses under linear operation are considered. Fig. 7 shows the comparison between LF noise measurements on a GaInP–GaAs two-finger 2 30 m HBT and simulations, which have been carried out according to the proposed approach of Fig. 3, in which EN generators are characterized on the basis of LF noise data exclusively. Both base and collector short-circuit noise currents (LF auto-spectral densities) measured for different bias conditions are depicted along with the predictions provided by any of the possible LF noise models belonging to the family. By giving different arbitrary values to the parameters , it is possible to switch among the elements of the family, obtaining the same identical accurate LF predictions, but with very different results in terms of LS noise performance. ’s are the overall sets of parameters to In conclusion, the be characterized by means of additional noise data, which can be measured under LS RF operating conditions, as described below. In order to obtain experimental information on the device noise behavior at its ports under operating conditions in which the nonlinear mechanisms of noise conversion and modulation are activated, a special-purpose laboratory setup has been implemented. The device is driven into autonomous LS oscillations through a parallel feedback oscillator loop so that the additional noise behavior information is obtained in terms of PN data. The setup architecture4 schematic can be found in [18]: it has been implemented by exploiting conventional components and can be easily replicated and characterized in any microwave laboratory. This oscillating structure drives the device into an LS regime with different possible operating frequencies, loop amplitudes, bias, and LF impedances at the device ports. Although closed-form relationships linking measured PN data and pacannot easily be derived, the fitting of PN data rameters and the univocal characterization of the modulation laws in (4) and (5) can be effected by means of numerical optimization. Bias-, LF impedance-, and compression level-dependent PN 4This laboratory setup is similar to those used by other authors [27], aimed at device selection for LPN oscillator design.

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Fig. 8. CAD implementation of one of the EN generators, which account for LFG noise in the intrinsic bipolar device.

TABLE I MODEL PARAMETERS (r = 1) FOR THE BASE-EMITTER EN CURRENT GENERATOR EXTRACTED FOR THE SIX-FINGER HBT NONLINEAR NOISE MODEL Fig. 7. LF noise at different bias values for a GaInP–GaAs two-finger (2 30 m) HBT (measurements versus model predictions).

2

measurements have been exploited in Section V for the optimization of parameters by comparing empirical data with LS noise simulations of the laboratory setup carried out in the framework of the CAD package in which the nonlinear noise model has been implemented. Since the obtained functions showed, as expected, a mild nonlinearity with respect to the controlling current, polynomial expansions truncated to low orders or simple linear combinations of powers can be used to represent their analytical expressions, in order to transform the lookup-tablebased extraction into a closed form with a finite relatively small number of model parameters. IV. EN GENERATOR IMPLEMENTATION In this section, detailed information will be provided about the implementation of all the EN generators (including shotnoise sources), which form the proposed nonlinear noise model for bipolar devices. This task was carried out in the framework of Agilent’s ADS 2005A by exploiting standard user-interface components. In particular, the CAD features adopted are as follows. 1) Current or voltage colored noise generators used to imple. ment the elementary colored processes 2) Symbolically defined devices (SDDs), which make it posin sible to implement the nonlinear modulation laws (5) that multiply the colored noise processes. The use of SDDs for cyclostationary noise generator implementation can also be found in [16] and [28].

3) Current-controlled voltage sources adopted to sense the instantaneous LS conductive currents of the device that non. linearly control the laws As an example, in Fig. 8, a functional scheme of the EN generator from (4) and Fig. 3 is illustrated. As observed in Section II-A, and considering device operation only in the normal active or off-state region, the EN generator is simply , thus, controlled by the base conductive LS current (29)

where the ’s from notation (4) coincide with in the compact equivalent notation (5). The nonlinear modulation laws have been implemented con. sidering a dependence of the kind The values of the multiplicative and exponential parameters of the EN generator extracted in the case of the HBT noise model discussed in Section V are reported in Table I, as regards (the values are consisthe contribution corresponding to with normalized auto-spectral tent with processes density). As far as LFG and thermal noise in the parasitic resistors are concerned, the CAD implementation of the proposed model is described in Fig. 9. For the sake of simplicity, only the base resistor noise model is depicted. In fact, in the examples given in Section V, this resistor has the most relevant contribution to

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Fig. 9. CAD implementation of the EN generator that accounts for LFG noise in the base parasitic resistor (only fundamental flicker is considered here).

up-converted PN in LS operation. As can be seen in this figure, the LFG noise generator is modulated by the overall base current (conductive plus capacitive), which is sensed at the intrinsic base terminal and fed to the SDD. The SDD device performs the modulation of the LFG EN generator by multiplying the sensed instantaneous current by the elementary colored process. Generally speaking, there is one process for each color: however, in Section V, only the flicker noise normalized process was implemented since, during the model identification via fitting of PN measurements of the test bench described in [18], the G–R noise contributions of the parasitic resistors were found to be negligible. In Fig. 10, the implementation of the shot-noise generator is described using the same operative approach and CAD components. In this case, a capture of the actual implementation on Agilent’s ADS schematic is also shown, where the normalized white noise generator, SDD component, and current-controlled voltage-source device for the base conductive current sensing are shown. V. EXPERIMENTAL RESULTS In this section, the prediction capabilities of the nonlinear noise modeling approach proposed will be shown, by discussing examples of LS noise analyses in which the performance in terms of LFG noise conversion and shot-noise modulation can be evaluated. The modeling approach of Fig. 3 has been applied to a 30 m HBT. Three different GaInP–GaAs six-finger 2 “colors” have been chosen for the definition of set in (1): kHz and GR2 with fundamental flicker, GR1 with kHz. As far as the correlation scheme among the EN generators (4) is concerned, only the correlation between the elements of the couple and that between the elements of have been supposed to be different . from zero, with the choice Thus, the EN generators (4) have been preliminarily characterized on the basis of LF noise data: an example of the accuracy achievable in LF SS noise analyses by exploiting any of the models of the obtained family is shown in [18]. The complete extraction of the EN generators has been carried out by fitting

Fig. 10. CAD implementation of the EN generator that accounts for base current shot-noise in the intrinsic bipolar device.

the PN data obtained through the RF oscillating structure under different LS conditions, as described in Section III-B. All the EN generators have been implemented in ADS, including modulated shot-noise and noisy parasitic resistors. More precisely, of the base reonly the parametric flicker perturbation sistor has been considered. A 4.2-4.5-GHz monolithic microwave integrated circuit (MMIC) voltage-controlled oscillator (VCO) has been designed using the GaInP–GaAs HBT process according to the series feedback topology shown in [18]: only the forward active and off-state regions of the device are involved in the instantaneous operation of this circuit. In Fig. 11, a very good agreement between measured and simulated PN performance is shown. All the PN analysis results given here have been obtained through standard numerical resources (namely, the .PNMX simulation component) available in ADS2005A, with default values for simulation parameters. In order to point out the influence on LS noise analysis predictions of the modulation strategy adopted for the EN generators, two additional versions of the noise model have been implemented: namely, the “bias-controlled” model, in which the EN generators (4) are controlled simply by the quiescent bias value of the base current, and the “mean value-controlled” model, in which the harmonic-balance mean value of the base current is instead used as the controlling quantity. The less accurate PN simulation results obtained with these two test-aimed models can be found in [18].

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Fig. 11. Measured and predicted SSB PN for a GaInP–GaAs HBT-based VCO (V = 6 V). It is also shown that neglecting LS instantaneous modulation of LFG noise in parasitic resistors degrades the model accuracy.

0

Fig. 12. Measured and predicted SSB PN at 10 kHz from the carrier versus VCO tuning voltage.

In Fig. 12, the comparison between measured and simulated PN at 10 kHz for different values of the tuning voltage is shown. Similarly accurate results at 1 kHz can be found in [18]. The HBT-based VCO has been intentionally designed and implemented with external resistive bias networks: the base, collector, and emitter device contacts are directly available offchip, exploiting only a decoupling from the RF signal by means of LC networks (Fig. 13). This setup has been used to characterize the VCO PN in correspondence with different bias values and different LF impedances imposed by the off-chip bias networks. In Fig. 14, the PN measured at 10 kHz versus LF base impedance level is compared with the predictions obtained by means of the proposed nonlinear noise model. The accuracy shown by the model is clearly a very important feature to exploit during the design of an MMIC oscillator, when integrated bias networks have to be designed. Another important validation test has been performed by comparing the measured VCO PN performance with the model predictions obtained by neglecting the instantaneous

Fig. 13. Designed VCO and external base bias network with variable LF loading impedance (other bias networks omitted).

Fig. 14. VCO PN measured and predicted at 10 kHz from the carrier versus LF base impedance values.

modulation by the LS regime in the implementation of the EN generator, which accounts for LFG noise in the parasitic base resistor. As shown in Fig. 11, the analysis accuracy is strongly reduced when the EN generator is controlled simply through the current bias value, especially for lower values of the frequency offset. A similar validation test has also been carried out in order to show the effectiveness of the modulation strategy for shot-noise generators, as discussed in Section II-C. In Fig. 15, the measured VCO PN performance is compared with the complete model predictions, and the predictions obtained by neglecting the instantaneous modulation of the shot-noise generators, and considering only the mean currents flowing through the device junctions. Clearly the complete model offers a better prediction of PN performance. In Fig. 15, only the frequency window (10 kHz–1 MHz) is reported to highlight the prediction differences, while, as expected, the two versions of the model gave identical accurate results at lower offsets from the carrier, where

TRAVERSO et al.: EMPIRICAL BIPOLAR DEVICE NONLINEAR NOISE MODELING APPROACH FOR LS MICROWAVE CIRCUIT ANALYSIS

Fig. 15. VCO PN performance: neglecting LS instantaneous modulation of shot-noise generators degrades the model accuracy.

the shot-noise converted contribution is masked by the “colored” source ones. VI. CONCLUSION The general formulation of an empirical nonlinear noise modeling approach for microwave bipolar devices has been described. The cyclostationary EN generators proposed, which are controlled by the instantaneous values of currents involved in the transistor LS RF operation, allow for the prediction of the nonlinear conversion of LFG noise (both within the intrinsic device and parasitic resistors) and shot-noise. The model has been experimentally extracted for a GaInP–GaAs HBT technology on the basis of SS LF noise data and LS PN measurements. Examples of comparison between PN performance predictions and measurements for a 4.2–4.5-GHz MMIC VCO under different operating conditions have been provided in order to validate the proposed approach. Detailed information on the implementation of the EN generators in the framework of Agilent’s ADS has also been given. Current activity is devoted to the validation of the modeling approach when exploited for nonlinear noise analyses of nonautonomous circuits under forced LS operation such as mixers used for synchronous demodulation. REFERENCES [1] F. X. Kaertner, “Determination of the correlation spectrum of oscillators with low noise,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 1, pp. 90–101, Jan. 1989. [2] U. L. Rohde, C. Chao-Ren, and J. Gerber, “Design and optimization of low-noise oscillators using nonlinear CAD tools,” in Proc. 48th IEEE Int. Freq. Contr. Symp., Jun. 1994, pp. 548–554. [3] V. Rizzoli, F. Mastri, and D. Masotti, “General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 5, pp. 807–819, May 1994. [4] A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: A unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 5, pp. 655–674, May 2000. [5] U. L. Rohde and A. K. Poddar, “A unified method of designing low noise microwave oscillator,” in Proc. Int. SBMO/IEEE MTT-S Conf., Jul. 2005, pp. 38–41.

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[6] A. van der Ziel, “Unified presentation of 1=f noise in electronic devices: Fundamental 1=f sources,” Proc. IEEE, vol. 76, no. 3, pp. 233–258, Mar. 1988. [7] F. N. Hooge, “ 1=f noise sources,” IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 1926–1935, Nov. 1994. [8] P. H. Handel, “Fundamental quantum 1=f noise in semiconductor devices,” IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 2023–2033, Nov. 1994. [9] C. M. Van Vliet, “Macroscopic and microscopic methods for noise in devices,” IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 1902–1915, Nov. 1994. [10] F. Bonani and G. Ghione, Noise in Semiconductor Devices, Modeling and Simulation. New York: Springer-Verlag, 2001. [11] F. Bonani, S. Donati Guerrieri, and G. Ghione, “Noise source modeling for cyclostationary noise analysis in large-signal device operation,” IEEE Trans. Electron Devices, vol. 49, no. 9, pp. 1640–1647, Sep. 2002. [12] J.-C. Nallatamby, M. Prigent, M. Camiade, A. Sion, C. Gourdon, and J. J. Obregon, “An advanced low-frequency noise model of GaInP–GaAs HBT for accurate prediction of phase noise in oscillators,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1601–1612, May 2005. [13] M. Rudolph, F. Lenk, O. Llopis, and W. Heinrich, “On the simulation of low-frequency noise upconversion in InGaP/GaAs HBTs,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 7, pp. 2954–2961, Jul. 2006. [14] O. Llopis, J. B. Juraver, M. Regis, M. Chaubet, and J. Graffeuil, “Evaluation of two non-standard techniques for the phase noise characterization at microwave frequencies,” in Proc. IEEE/EIA Int. Freq. Contr. Symp., Kansas City, MO, 2000, pp. 511–515. [15] O. Llopis, J. B. Juraver, B. Tamen, F. Danneville, M. Chaubet, A. Cappy, and J. Graffeuil, “Nonlinear noise modeling of a PHEMT device through residual phase noise and low frequency noise measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, 2001, pp. 831–834. [16] F. Filicori, P. A. Traverso, and C. Florian, “Non-linear modeling of low-to-high-frequency noise up-conversion in microwave electron devices,” in Proc. 1st Int. Fluctuations and Noise—Noise in Devices and Circuits Symp., Santa Fe, NM, Jun. 2003, pp. 192–203. [17] F. Filicori, P. A. Traverso, C. Florian, and M. Borgarino, “Identification procedures for the charge-controlled non-linear noise model of microwave electron devices,” in Proc. 2nd Int. Fluctuations and Noise—Noise in Devices and Circuits II Symp., Maspalomas, Spain, May 2004, pp. 337–348. [18] C. Florian, P. A. Traverso, M. Borgarino, and F. Filicori, “A nonlinear noise model of bipolar transistors for the phase-noise performance analysis of microwave oscillators,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, 2006, pp. 659–662. [19] S. Perez, T. Gonzalez, S. L. Delage, and J. Obregon, “Microscopic analysis of generation–recombination noise in semiconductors under DC and time-varying electric fields,” J. Appl. Phys., vol. 88, pp. 800–807, 2000. [20] C. Dragone, “Analysis of thermal and shot noise in pumped resistive diodes,” Bell Syst. Tech. J., vol. 47, pp. 1883–1902, 1968. [21] J. E. Sanchez, G. Bosman, and M. E. Law, “Two-dimensional semiconductor device simulation of trap-assisted generation–recombination noise under periodic large-signal conditions and its use for developing cyclostationary circuit simulation models,” IEEE Trans. Electron Devices, vol. 50, no. 5, pp. 1353–1362, May 2003. [22] G. Niu, “Noise in SiGe HBT RF technology: Physics, modeling, and circuit implications,” Proc. IEEE, vol. 93, no. 9, pp. 1583–1597, Sep. 2005. [23] H. Fukui, “The noise performance of microwave transistors,” IEEE Trans. Electron Devices, vol. ED-13, no. 3, pp. 329–341, Mar. 1966. [24] M. Borgarino, “Full direct low frequency noise characterization of GaAs heterojunction bipolar transistors,” Solid State Electron., vol. 49, pp. 1361–1369, 2005. [25] L. Bary, M. Borgarino, R. Plana, T. Parra, S. J. Kovacic, H. Lafontaine, and J. Graffeuil, “Transimpedance amplifier-based full low-frequency noise characterization setup for Si/SiGe HBTs,” IEEE Trans. Electron Devices, vol. 48, no. 4, pp. 767–773, Apr. 2001. [26] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures. New-York: Wiley, 2000. [27] O. Llopis, “Oscillator basics and guidelines for low noise design dielectric resonator oscillators (DRO),” presented at the Low Phase Noise Oscillators, Eur. Gallium Arsenide Semiconduct. Applicat. Symp. Workshop, Munich, Germany, 1999, short course. [28] C. Gourdon, J. C. Nallatamby, D. Baglieri, M. Prigent, M. Camiade, and J. Obregon, “Accurate design of HBT VCOs with flicker noise up-conversion minimization using an advanced low-frequency cyclostationary noise model,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1519–1522.

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Pier Andrea Traverso (M’03) was born in Modena, Italy, in 1969. He received the M.S. degree in electronic engineering and Ph.D. degree in electronic and computer science engineering from the University of Bologna, Bologna, Italy, in 1996 and 2000, respectively. He is currently a Research Associate with the Department of Electronics, Computer Science and Systems, University of Bologna. His main research activity is in the areas of nonlinear dynamic system characterization and modeling, microwave and millimeter-wave device characterization and modeling, and sampling instrumentation and techniques. Dr. Traverso is a member of the Italian Association of Electrical and Electronic Measurements.

Corrado Florian (S’02–M’04) was born in Forlì, Italy, in 1975. He received the M.S. degree in electronic engineering from the University of Ferrara, Ferrara, Italy, in 2000, and the Ph.D. degree in electronic and computer science engineering from the University of Bologna, Bologna, Italy, in 2004. He is currently a Research Associate with the Department of Electronics, Computer Science and Systems, University of Bologna. His main research activity is in the areas of microwave monolithic circuit design, hybrid RF circuit design, nonlinear dynamic system characterization and modeling, microwave and millimeter-wave device characterization and modeling. Dr. Florian was the recipient of the Best Paper Prize presented at the 2001 European Gallium Arsenide and Other Compound Semiconductors Application Symposium. He was also the recipient of the Student Paper Prize presented at the 2002 European Gallium Arsenide and Other Compound Semiconductors Application Symposium.

Mattia Borgarino was born in Parma, Italy, in 1968. He received the Laurea degree in electronic engineering and Ph.D. degree in information technology from the University of Parma, Parma, Italy, in 1993 and 1999, respectively. From 1999 to 2000, he was with the Laboratoire d’Analyse et d’Architecture des Systems, Centre National de la Recherche Scientifique (LAAS-CNRS), Toulouse, France, as a Post-Doctoral Fellow. In 2000, he joined the University of Modena and Reggio Emilia, Modena, Italy, where he is currently an Associate Professor. His current main research interests cover the LF noise characterization and modeling of microwave transistors and the design of Si-based RFICs. Dr. Borgarino is a member of Istituto Nazionale di Fisica della Materia (INFM) and the Institute of Physics (IOP).

Fabio Filicori was born in Imola, Italy, in 1949. He received the M.S. degree in electronic engineering from the University of Bologna, Bologna, Italy, in 1974. In 1974, he joined the Department of Electronics, Computer Science and Systems, University of Bologna, initially as Research Associate, and then becoming an Associate Professor of applied electronics. In 1990, he became a Full Professor of applied electronics with the University of Perugia. In 1991, he joined the Faculty of Engineering of the University of Ferrara, where he was a Full Professor responsible for the degree course in electronic engineering. He is currently a Full Professor of electronics with the Faculty of Engineering of the University of Bologna, where he is also responsible for the Ph.D. course in electronic, computer science and communications engineering. During his academic career, he has held courses on computer-aided circuit design, electron devices and circuits, and power electronics. His main research activities are in the areas of CAD techniques for nonlinear microwave circuits, electron device nonlinear modeling, sampling instrumentation, and power electronics. Dr. Filicori is a member of the Editorial Board of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He is a member of the Technical Program Committee of the GaAs Symposium.

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Multiport-Amplifier-Based Architecture Versus Classical Architecture for Space Telecommunication Payloads Alain Mallet, Aitziber Anakabe, Jacques Sombrin, Member, IEEE, and Raquel Rodriguez Abstract—This paper discusses the suitability of using a multiport amplifier (MPA) for a power section of space telecommunication payloads with power flexibility requirements. The performances of an MPA-based architecture are compared to those of a classical amplification architecture having one power amplifier 4 -band MPA comper beam. This study is based on a 4 posed of four paralleled traveling-wave tube amplifiers (TWTAs). First, a static model of the MPA has been extracted from conventional characterizations. Second, the MPA has been characterized in a realistic environment for telecommunication operation. The good agreement between measured and simulated data serves to validate the MPA model. Once the model has been validated, exhaustive simulations are performed to compare the performances of the MPA-based and classical architectures in terms of power consumption and the TWTA’s saturation power. As a result, the MPA approach proves to be an interesting solution because of its greater flexibility, lower power consumption, and lower saturation power required by the TWTAs. Index Terms—Communication systems, multiport circuits, power amplifiers (PAs), satellite communication, traveling-wave amplifiers, traveling-wave tubes (TWTs).

I. INTRODUCTION

I

N ORDER to efficiently meet the evolution of the market over the large lifetime of satellites and minimize businessplan risks, the increase of flexibility is demanded by operators for multimedia telecommunication payloads [1]. This flexibility can be expressed in terms of antenna coverage, power allocation on the coverage, or global satellite flexibility to manage in orbit a fleet of satellites. Phased-array antenna-based payload is the most flexible solution since it offers a high level of in-orbit reconfigurability [2]–[4]. In spite of its great flexibility, this approach is not generally implemented in current space telecommunication missions, which are not yet so demanding. Today, although technologically possible,1 2 phased-array antenna-based payload is not

Manuscript received April 7, 2006; revised July 10, 2006. The work of A. Anakabe was supported by the Spanish Commission of Science and Technology under Grant TIC2003-004453. A. Mallet, J. Sombrin, and R. Rodriguez are with the Centre National d’Etudes Spatiales, 31401 Toulouse, France (e-mail: [email protected]; [email protected]; [email protected]). A. Anakabe is with the Electricity and Electronics Department, University of the Basque Country, 48080 Bilbao, Spain (e-mail: [email protected]). Color versions of Figs. 1, 2, and 4–20 and Tables III and V are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.885904 1Spaceway

mission at Boeing home page. [Online]. Available: http://www. boeing.com/defense-space/space/bss/factsheets/702/spaceway/spaceway.html 2Winds mission at Nasda home page. [Online.] Available: http://www. nasda.go.jp/projects/sat/winds/index_e.html

- and -band. often economically viable, especially in the Nevertheless, it will probably play a leading role in the evolution of future telecommunication space missions that involve a large number of beams with great flexibility requirements. Alternatively, using multiport amplifiers (MPAs) can be an attractive solution to respond to flexibility requirements in terms of power allocation switching since an MPA can intrinsically handle unbalanced traffic among beams and traffic variation over the time [5], [6]. In order to optimize the limited dc power available in the spacecraft, a very precise analysis is necessary. Furthermore, the saturation power required for the traveling-wave tube amplifiers (TWTAs) can be very close to the technological limits. Therefore, the adequate sizing of the payload must be accurately calculated in order to ensure the required transmission quality. That is to say, the saturation power of power amplifiers (PAs) and their associated operating point in terms of output backoff (OBO) must be carefully chosen in order to minimize either the dc power consumption or the saturation power for a given transmission quality. Other factors that have already been discussed in the literature must also be considered, e.g., the port-signal assignments [7], [8] and reliability [9], [10]. The aim of this paper is to demonstrate, through simulation and measurement results, the advantage of an MPA solution with respect to classical amplification architectures (with one PA per beam) provided that the operating point is carefully chosen in both cases. For that, the operation principle of MPAs and the main performances of the particular MPA characterized in this study are presented in Section II. The methodology proposed to select the optimum operating point, both from simulation and measurement results, is described step by step in Section III. This methodology is applied in Section IV to the analysis of a single TWTA under multicarrier excitation. Section V details the MPA model extraction and validation in the context of a representative multicarrier application. Finally, in Section VI, the performances of the MPA-based architecture and the classical architecture are compared for a TV direct video broadcasting application involving one single modulated carrier per channel. II.

-BAND MPA

A. MPA Operation Principle An MPA is composed of an array of PAs in parallel and a Butler matrix networks that consist pair of complementary of 90 hybrid networks [11]. A 4 4 MPA is shown in Fig. 1. The signal at each input in the MPA is divided into signals

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Fig. 3. Simplified transmission diagram.

2

Fig. 1. 4 4 MPA operation principle. Combination/cancellation principle for one input/output pair.

tube (TWT) from Thales Electron Devices, Velizy, France, an electronic power conditioner (EPC) from ETCA, Charleroi, Belgium, and a linearizer from Alcatel Alenia Space. Butler matrices have been developed by TILAB, Turin, Italy, and they are implemented in waveguide to minimize losses. The performances of the presented MPA are the following. W. • Output power per channel GHz. • Overall bandwidth • Instantaneous bandwidth MHz. • Frequency range: 19.7–20.2 GHz. dB at 4-dB OBO. • III. METHODOLOGY AND TOOLS Fig. 2.

Ka-band MPA.

with particular phase relationships. These signals are amplified separately in each PA and are recombined in the output Butler matrix. In this way, the signal at each input is amplified by all the PAs, but assembled at the corresponding output. The main advantage of this amplification architecture is that it provides intrinsic power flexibility since power is shared between the channels. The combined power of all the PAs is available for any channel, provided that the other channels do not require power at the same time. This power flexibility is obtained without necessarily increasing the power consumption. In contrast, an important drawback of the MPA is related to isolation losses between channels due to different electrical characteristics of each path. Besides, since all input signals are amplified at each PA, multicarrier operation is reached even when a single carrier is introduced at each input. In conclusion, the MPA is adapted to missions that require flexibility in terms of power reallocation and will be especially advantageous if input signals are already multicarrier. Therefore, the advantage of an MPA-based architecture can only be evaluated from realistic measurements or from simulations with accurate models and realistic signals. B. 4

4

-Band MPA

The studied MPA has been developed by Alcatel Alenia Space, Toulouse, France, under a European Space Agency contract. As is shown in Fig. 2, the MPA is composed of four -band paralleled TWTAs. Each TWTA is composed of a 120 continuous wave (CW) saturation power traveling wave

A. Optimization Criteria The overall performance of the transmission link is imposed by the required bit error rate (BER). For a given demodulator, this BER can be converted into a useful signal to parasitic signal . This ratio can be obtained from reratio quirements, the bit rate and the symbol rate as in the following: (1) The parasitic signal has different origins: intermodulation caused by nonlinear elements, interferences, and added noise. As schematically shown in the simplified transmission diagram of Fig. 3, the final goal is to ensure the BER while minimizing either the dc power consumption on the payload or the saturation power of the TWTAs. In order to compare the performances of different configura[12] and ratios. For tions, we make use of the a nonlinear PA family, these criteria allow the determination of the optimum operating point of the TWTAs in terms of OBO whatever the link budget, i.e., for any . These optimization criteria can be extracted from simulations or measurement results, as explained hereafter. The overall principle consists of ensuring the transmission quality for all users while minimizing the selected criterion ( or ). In principle, this fact imposes the rigorous study of each user case (each modulated carrier) one by one. However, in practice, the analysis will be focused on the most obviously deteriorated modulated carriers. and is detailed The procedure for determining in the following paragraphs.

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In this paper, the dissipated power, which can also be a limiting parameter, is not taken into account. Nevertheless it could be easily analyzed in an analogous way by extracting as follows: (6) denotes the transmitted intermodulation signal (the where part reflected by the filters is dissipated in the payload). B. Simulation Methodology and Associated Software

Fig. 4. Illustration of the determination of optimum OBO from P =N and P =N curves.

Initially, the following parameters have to be obtained either from simulation or measurement results, as described in Sections III-B and C, respectively. • Input backoff (IBO): always referring to CW input saturation power (the sweep parameter). • OBO: referring to CW output saturation power. : total dc power consumption. • : useful signal power for the reference modulated carrier. • : signal-to-interference ratio for the reference modu• lated carrier. specification (given by (1) and associFrom the ratio as ated to the demodulator), we can deduce the (2)

All the simulations in this work have been carried out by means of Communication Library (COMLIB) software (a CNES internal simulation development), based on FORTRAN libraries. For that end, it has been specifically adapted to simulate the MPA’s behavior. COMLIB is based on a complex envelop simulation and it is used to simulate transmission chains taking into account linear and nonlinear distortions. Signal sample vectors are transformed alternately into time and frequency domains according to the description of the different elements. The MPA is modeled from the Butler matrices characterizachartion and the measured AM/AM, AM/PM curves and acteristics of TWTAs [13]. ratio is calculated from the equivalent gain method The [14]. The equivalent gain value, given in (7) as follows, is defined as the ratio between the portion of the output signal correlated with the input signal and the input signal itself: (7) with denoting the signal sample element (voltage value). Thus, the noise of the signal not correlated with the input is (8)

and can then be easily calculated, as in (3) and (4), respectively,

and the useful signal (9)

(3)

can then be computed as

(4) where (5) is the dc power corresponding to the reference modulated carrier with denoting the bandwidth of this reference modulated denoting the total bandwidth. carrier and and Once these parameters are obtained, curves can be plotted versus OBO. An illustrative example is given in Fig. 4. It can be seen that the minima of those curves correspond, respectively, to the optimal operating point in terms of dc consumption or in terms of saturation power. It is important to note that the minimum values of those two different criteria cannot be directly compared. Eventually, the saturation power and the operating point are chosen according to the absolute dimensioning parameter of the specific mission (dc power or TWTA’s saturation power).

(10) Finally, the parameters related with the two optimization criteria ( and ) can be calculated from these values following the procedure detailed in Section III-A. C. Measurement Methodology and Tools The measurements have been carried out in a transmission system bench (BST) developed at CNES under an internal advanced telecommunication program (ATF) program for test -band multimedia satellite systems. This and analysis of easily reconfigurable facility has been used to test the MPA in representative payload architectures with realistic signals. A photograph of the MPA characterization under the transmission system bench is shown in Fig. 5. Unlike simulation procedures, directly extracting the intermodulation signal from the overall interferences (intermodulation and noise) is not straightforward in the case of modulated

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Fig. 5. MPA characterization under BST test-bench.

Fig. 7. P =N versus OBO for a single TWTA loaded with one, two, three, and six modulated carriers.

Fig. 6. (a) Demodulator “calibration” procedure. (b) Configuration example: TWTA with three modulated carriers.

multicarrier measurements. Therefore, we propose an indirect method consisting of the following two steps. Step 1) Determine the signal to interference ratio corresponding to the BER specification for a single modulated carrier [see Fig. 6(a)]. Step 2) Determine the amount of added noise needed to obtain the same BER for any configuration [see Fig. 6(b)]. and For a given BER, the signal to interference ratio can be extracted because the the signal to noise ratio demodulator is receiving the same useful signal to noise intermodulation ratio in both Steps 1) and 2).

Fig. 8. P =N versus OBO for a single TWTA loaded with one, two, three, and six modulated carriers.

TABLE I OPTIMUM OPERATING POINTS IN TERMS OF P AND ASSOCIATED P =N AND P =N FOR A TWTA LOADED WITH ONE, TWO, THREE, AND SIX MODULATED CARRIERS

IV. SINGLE TWTA OPERATION The determination of the optimum operating point in terms of OBO and the choice of the saturation power of PAs are illustrated here by their application to a single TWTA loaded with a different number of modulated carriers with an equal bit rate. curves for a TWTA loaded with one, two, three, The and six modulated carriers have been obtained from measurement results, as described in Sections III-A and C and are plotted in Fig. 7. It can be seen that the optimum OBO moves from 0.6 to 2.4 dB when changing from a single modulated carrier to multicarrier operation. curves for a TWTA with one, two, Similarly, the three, and six modulated carriers have been obtained from measurement results and are depicted in Fig. 8. In this case, the optimum OBO moves from 0.5 to 1.8 dB when changing from a single modulated carrier to multicarrier operation. As expected, when increasing the number of modulated carriers, the optimum operating point of the TWTA is obtained for a greater OBO since intermodulation caused by nonlinear elements increases with the number of modulated carriers. More-

over, we can state that the case of three modulated carriers can be considered almost as a multicarrier operation. Numerical results for the optimum operating point in terms of and are summarized in Tables I and II, respectively. It per carrier significantly increases (1.5 dB) can be seen that from 1–6 modulated carriers, in addition to a drastic increase in the required TWTA saturation power. Note that the optimum operating point depends on the chosen optimization criterion or . V. MPA CHARACTERIZATION FOR MODEL EXTRACTION AND VALIDATION A. MPA Modeling The following two types of characterizations have been performed in order to extract the MPA model.

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TABLE II OPTIMUM OPERATING POINTS IN TERMS OF P AND ASSOCIATED P =N AND P =N FOR A TWTA LOADED WITH ONE, TWO, THREE, AND SIX MODULATED CARRIERS

Fig. 10. (a) Four beams of a typical Ka-band telecommunication multimedia system coverage. (b) Reference scenario.

Fig. 9. Comparison between measured and simulated P for the MPA.

=P characteristic Fig. 11. MPA-based architecture that fulfills the requirements.

• Nonlinear characterizations: AM/AM, AM/PM, and dc power consumption, as a function of input power, of each amplifying branch (mainly composed of a linearizer, TWTA, and phase and magnitude adjustment components). • Linear characterizations: -parameters of Butler matrices. In order to validate this nonlinear static model, measured and curves are superposed in Fig. 9. It can be simulated seen that a very good agreement has been obtained. B. MPA Model Validation on Realistic Instance In order to thoroughly validate the model for our specific use, a representative case of multicarrier operation for space telecommunication applications has been studied. The MPA has been characterized using the BST test-bench shown in Section III-C and the measurement results have been compared with simulations. This example has been presented in detail in [15]. Only a brief summary is given here, where illustrative comparisons between simulations and measurement results are provided. -band telecommunication Four beams of a typical multimedia system coverage with two frequencies and two polarizations are considered in this instance [see Fig. 10(a)]. 12 quadrature phase-shift keying (QPSK) modulated carriers are allocated in these four beams. During the mission, channel reallocation possibility is required. The 12 modulated carriers can be switched between the four beams. A frequency plan that satisfies the required mission and defines the chosen reference scenario is depicted in Fig. 10(b). The defined mission can be directly carried out using a 4 4 MPA, as shown in Fig. 11. The operating point of the MPA has been optimized using the methodology described in Section III.

Fig. 12. P =N and P

=N versus OBO for the MPA-based architecture.

Fig. 12 shows the and ratios as a function of the OBO (referring to the MPA CW saturation power) obtained from both simulation and measurement results. The optimum operating point varies from 1.1 to 1.6 dB depending on the criterion that we consider. Note that there is a very good agreement between measurements and simulated data. In addition to validating the accuracy of the MPA model, this application was used in [15] to compare MPA performances with classical amplification architecture performances, evidencing the advantage of the MPA for a multicarrier application with flexibility requirements. This cumbersome measurement campaign and the corresponding simulations confirmed the accuracy of the extracted MPA model. This model will be used in Section VI to evaluate, exclusively from simulation results, the advantage of an MPA for a power flexible application with a single modulated carrier, of variable symbol rate, per channel.

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Fig. 13. Flexible bandwidth allocation illustration.

TABLE III DESCRIPTION OF THE THREE CONFIGURATIONS

VI. COMPARISON BETWEEN CLASSICAL AND MPA-BASED AMPLIFICATION ARCHITECTURES

Fig. 14. P =N curves for the determination of optimum OBO for the MPAbased architecture.

Fig. 15. P =N curves for the determination of optimum OBO for the MPAbased architecture. Level of carrier 1 from unbalanced configuration increased 0.5 dB.

A. Reference Scenario This second example concerns an application where a bandis allocated for the TV direct video broadcasting on width four beams with four antennas. Two polarizations are used: horizontal ( ) and vertical ( ). The bandwidth is considered to be shared between two beams in any desired configuration. As depicted in Fig. 13, is shared by beams 1 and 2 on polarization and reutilized in polarization for beams 3 and 4. Three representative configurations of this mission will be considered, which are: 1) balanced; 2) unbalanced; and 3) limit (see Table III). The “limit configuration” corresponds to the extreme case where only two beams among the four are used. In order to perform realistic simulations, actual values from the demodulator of the measurement BST test-bench are conis fixed to 3.25 dB, as it sidered in all cases. Thus, corresponds to this demodulator with the given BER specification (10 without coding). B. MPA-Based Architecture The defined mission can be directly carried out using a 4 4 MPA. The operating point of the MPA has been optimized using the methodology described in Section III in order to minimize (fixed to dc power consumption for the given curves are initially plotted 3.25 dB). For that, in Fig. 14, versus OBO for the three different configurations. The two curves traced in solid line correspond, respectively, to the two

modulated carriers of different rate involved in the “unbalanced configuration.” The lower rate modulated carrier (triangles) is the most degraded and represents the dimensioning case value, around because it corresponds to the higher 8.4 dB for 1.9-dB OBO. A solution to reduce the dc consumption consists of increasing the relative power level of this carrier. A parametric study has been performed on this relative level and an optimum over level of 0.5 dB has been obtained. The modified curves for the unbalanced scenario are updated in Fig. 15. This example illustrates the capability for compensating, at least partially, the pumping effect of the smallest carriers in the nonlinearities by increasing their relative level at the input. An optimum OBO of 1.8 dB is determined from Fig. 15 for optimizing . Fig. 16 shows the versus OBO curves for the four configurations. The optimum operating point is approximately 1.5 dB for this parameter. It is important to note that these optimum operating points are independent of the noise power density. The dimensioning configuration is now the limit configuraand . We will tion since it corresponds to higher now consider the noise power , extracted from the link budget, in order to determine the evolution, versus the OBO, of the required saturation power of the TWTAs and the associated dc power consumption of the MPA.

MALLET et al.: MPA-BASED ARCHITECTURE VERSUS CLASSICAL ARCHITECTURE FOR SPACE TELECOMMUNICATION PAYLOADS

Fig. 16. P =N curves for the determination of optimum OBO for the MPAbased architecture. Level of carrier 1 from unbalanced configuration increased 0.5 dB.

Fig. 17. P and P curves for the determination of optimum OBO for the MPA-based architecture corresponding to the limit case.

and

can be calculated as (11) (12)

where denotes the sum of the symbol rates of the different signals and “4” corresponds to the number of paralleled TWTAs in the MPA under study. In the configuration under study, Ms/s Besides, a noise density dBm/Hz W/Hz has been extracted from the considered link budget. The saturation power and dc power consumption computed from (11) and (12) are plotted in Fig. 17. The horizontal straight line corresponds to the maximum allowed saturation power of TWTAs (120 W). Thus, 1.8-dB OBO has been finally chosen as optimum operating point since the dc consumption is minimized and the saturation power of TWTAs is within the fixed limit. This leads to the following values: • optimum operating point: 1.8-dB OBO; • saturation power of TWTAs: 120 W; • dc power consumption: 830 W.

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Fig. 18. P =N and P =N curves for the determination of optimum OBO for the architecture without MPA.

C. Architecture Without MPA The architecture that fulfills the defined mission is very simple. It is composed of four independent TWTAs. Nevertheless, since each of the TWTA must be capable of amplifying a modulated carrier up to 35 Ms/s, all of them must have the same saturation power, fixed by this maximum symbol rate. According to the previously presented methodology, and curves are plotted in Fig. 18 versus OBO for the . given curve is flatter than It can be seen in Fig. 18 that the the one. Besides, the saturation power of TWTAs is the dimensioning parameter, because we have stated that it must remain below 120 W. Consequently, the optimum operating point dB in order to minimize . For the is chosen 0.55-dB optimum OBO, dB is obtained. In the configuration under study, with four TWTAs that must is be able to amplify a modulated carrier up to 35 Ms/s, given by (13) Ms/s and dBm/Hz W/Hz with (extracted from the link budget). W. Note that this saturation power This leads to required for the TWTAs is far beyond the limit that we have imposed (120 W). In order to calculate the dc power consumption, the optimal ratio is first operating point that ensures the required deduced in Fig. 19 for the three lower rate modulated carriers. This optimum operating point corresponds to the intersection versus OBO curve and the reference between each level (in this example, fixed to 3.25 dB). The corresponding degradation of the power-added efficiency (PAE) with increasing OBO appears in Fig. 20. Under fullcharge operation (35-Ms/s modulated carrier), the TWTAs operate at the modulated signal saturation power with maximum PAE. As the rate decreases (29, 16, and 3 Ms/s), the OBO increases and TWTAs operate with lower PAE. Table IV summarizes the operating points and the associated dc power deduced for the four modulated carriers. In the last column, the dc power consumption is normalized to the symbol rate in order to illustrate the overconsumption of the smaller modulated carriers.

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TABLE V DC CONSUMPTION CALCULATION FOR THE THREE CONFIGURATIONS

Fig. 19.

C (N + I ) curves for the different symbol rates.

TABLE VI MAIN CHARACTERISTICS AND PERFORMANCES FOR THE TWO DIFFERENT ARCHITECTURES

Fig. 20. PAE versus OBO.

TABLE IV OPERATING POINT AND ASSOCIATED DC POWER FOR THE DIFFERENT SYMBOL RATES

The associated dc power for the three configurations can be calculated. The results are summarized in Table V.

creased due to the smaller PAE of the four TWTAs that operate with 4.2-dB OBO. In conclusion, MPA-based architecture leads, on average, to a lower dc power consumption because the limit case will rarely occur. Above all, using an MPA, the mission can be satisfied with TWTAs with appreciably lower saturation power. Flexible TWTAs could be an interesting solution to reduce dc power consumption because of the lower degradation of the PAE when operating with backoff. However, it should be noted that the TWTA’s saturation power requirement for this architecture could not be lowered using flexible TWTAs. The MPA has demonstrated its advantage even if it does not seem, at first sight, well suited to this configuration with one modulated carrier per beam. VII. CONCLUSION

D. Performances Comparison Table VI summarizes the dc power needed for the three configurations and the two different architectures with and without an MPA. In a classical amplification architecture, without an MPA, criterion has been used to determine the saturation the power of the TWTAs. The corresponding dimensioning input signal is one 35-Ms/s QPSK modulated carrier. For the limit case, a classical amplification architecture is less consuming than the MPA one (635 W against 831 W), as shown in Table VI. Nevertheless, since power flexibility requirement has been immust be evaluated for the dimensioning case, i.e., for posed, the balanced configuration. The solution with the MPA is, in this case, favorable in terms of dc power consumption (890–830 W). Indeed, dc consumption of the classical solution is highly in-

Flexibility is certainly a key factor in the next generation of telecommunication multimedia payloads. MPA is an attractive solution to partially answer the increasing flexibility requirements demanded by operators. However, the evaluation of the benefits associated to an MPA-based architecture must rely on representative measurements or on simulations performed with accurate models and realistic signals. In order to avoid laborious and time-consuming measurement campaigns required for each particular application, a model of the MPA has been extracted from a complete characterization process. This model has been validated through both CW signals and signals from a representative multicarrier application. A comparison of performances between the MPA-based and classical power amplification architectures has then been carried out for a power flexible application that involves a single modulated carrier per channel. MPA

MALLET et al.: MPA-BASED ARCHITECTURE VERSUS CLASSICAL ARCHITECTURE FOR SPACE TELECOMMUNICATION PAYLOADS

solution has been proven to be very attractive, as it leads to lower dc power consumption with lower saturation power TWTAs.

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[15] A. Mallet, A. Anakabe, J. Sombrin, R. Rodriguez, and F. Coromina, “Multi-port amplifier operation for -band space telecommunication applications,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1518–1521.

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ACKNOWLEDGMENT The authors acknowledge the helpful collaboration of F. Coromina, European Space Agency (ESA), Noordwijk, The Netherlands, who participated in the definition and analysis of the tests. The authors wish to further acknowledge the assistance of F. Gizard, C. Laporte, T. Robert and J.P. Taisant, all of the BST/ATF Team, Centre National d’Etudes Spatiales (CNES), Toulouse, France. The authors further wish to thank L. Lapierre, CNES, P. Baretto-Da-Rocha and P. Frichot, both with Alcatel Alenia Space, Toulouse, France, and H. Fenech, Eutelsat, Paris, France, for helpful discussions. REFERENCES [1] V. Marziale, A. Pisano, and G. Di Paole, “Flexible payload technologies to enable multi mission satellite communication systems,” presented at the 24th AIAA Int. Commun. Satellite Syst. Conf. and Exhibit. San Diego, CA, Jun. 2006. -band satellite active [2] N. Seong, C. Pyo, J. Chae, and C. Kim, “ phased array multi-beam antenna,” in IEEE 59th Veh. Technol. Conf., May 2004, vol. 5, pp. 2807–2810. [3] A. Jacomb-Hood and E. Leir, “Multibeam active phased arrays for communications satellites,” IEEE Micro, vol. 1, no. 4, pp. 40–47, Dec. 2000. [4] S. Egami and M. Kawai, “A power-sharing multiple-beam mobile satellite in band,” IEEE J. Sel. Areas Commun., vol. 17, no. 2, pp. 145–152, Feb. 1999. [5] S. Egami and M. Kawai, “An adaptative multiple beam system concept,” IEEE J. Sel. Areas Commun., vol. SAC-5, no. 4, pp. 630–636, May 1987. [6] F. Andre, “Multiport power amplifier: A flexible architecture for multichannel amplification on board satellites,” in 5th IEEE Int. Vac. Electron. Conf., 2004, p. 268. [7] W. A. Sandrin, “The Butler matrix transponder,” COMSAT Tech. Rev., vol. 4, no. 2, pp. 319–345, Fall 1974. [8] M. Tanaka and Y. Suzuki, “Nonlinear distortion analysis of multiport amplifier,” presented at the 22nd AIAA Int. Commun. Satellite Syst. Conf. and Exhibit., Monterey, CA, 2004. [9] M. Tanaka and S. Egami, “Reconfigurable multiport amplifiers for in-orbit use,” IEEE Trans. Aerosp. Electron. Syst., vol. 42, no. 1, pp. 228–236, Jan. 2006. [10] F. Coromina and A. Martin Polegre, “Failure robust transmit RF front end for focal array fed reflector antennas,” presented at the 22nd AIAA Int. Commun. Satellite Syst. Conf. and Exhibit., Monterey, CA, 2004. [11] B. Piovano, L. Accatino, A. Angelucci, T. Jones, P. Capece, and M. Butler matrices Votta, “Design and breadboarding of wideband for multiport amplifiers,” in SBMO Int. Microw. Conf., Aug. 1993, vol. 1, pp. 175–180. [12] J. Sombrin, “A new criterion for the comparison of TWT and linearized TWT and for the optimization of linearizers used in transmission systems,” presented at the ESA/NATO Microw. Tubes for Space, Military, and Commercial Applicat. Workshop, Noordwijk, The Netherlands, Apr. 7–10, 1997. [13] C. Laporte, L. Lapierre, A. Mallet, and A. Anakabe, “Behaviour of a TWTA with a single or multicarrier input signal for telecommunication applications,” in 35th Eur. Microw. Conf., Paris, France, Oct. 4–6, 2005, pp. 1651–1653. [14] J. Lajoinie, E. Ngoya, D. Barataud, J. M. Nebus, J. Sombrin, and B. Riviere, “Efficient simulation of NPR for the optimum design of satellite transponders SSPAs,” in IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, Jun. 1998, vol. 2, pp. 741–744.

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Alain Mallet was born in Limoges, France, on November 24, 1971. He received the Ph.D. degree in microwave communications from the Microwave and Optical Communications Research Institute (IRCOM), Brive, France, in 1996. In 1993, he joined IRCOM, where he was involved with high-efficiency amplifier design methods. In 1999, he joined the Microwave and Time Frequency Department, Centre National d’Etudes Spatiales (CNES), Toulouse, France, where he is currently a Research Engineer involved in topics related to active components (characterization, modelization, simulation, and design).

Aitziber Anakabe was born in Barakaldo, Spain, in 1976. She received the Electronic Physics and Electronic Engineering degrees and Ph.D. degree in electronics from the University of the Basque Country, Bilbao, Spain, in 1999, 2000, and 2004, respectively. In 1999, she joined the Electricity and Electronics Department, University of the Basque Country, where she was involved with the stability analysis of nonlinear microwave circuits. In 2004, she joined Centre National d’Etudes Spatiales (CNES), Toulouse, France, as a Post-Doctoral Researcher. In 2005, she rejoined the Electricity and Electronics Department, University of the Basque Country. Her research deals with nonlinear analysis and modeling of microwave circuits and measurement techniques.

Jacques Sombrin (M’88), was born in Lons, France, in 1949. He received the Engineer degree from the École Polytechnique, Paris, France, in 1969, and the Engineer degree from the École Nationale Supérieure des Télécommunications (ENST), Paris, France, in 1974. In 1974, he joined the Centre National d’Etudes Spatiales (CNES), Toulouse, France, as a Microwave Engineer. He was involved with the modelization and simulation of the nonlinearities of TWTAs used in communication satellite payloads and on the design of elliptic filters. He is currently a Senior Expert and Assistant Director for Radio Frequency with CNES, where he is in charge of research and technology within this domain. His research interests include the increase of TWT efficiency and linearity, system simulation of nonlinearities and power consumption, and the global optimization of satellite payloads and communication systems. Dr. Sombrin is a Senior Member of the French Society of Electrical and Electronics Engineers (SEE).

Raquel Rodriguez was born in Barcelone, Spain, in 1979. She received the Telecommunications Engineering degree from the Universitat Politènica de Catalunya, Barcelona, Spain, in 2004. In 2004, she joined the Centre National d’Etudes Spatiales (CNES), Toulouse, France, as a Microwave Engineer. Her research interests are related to microwave circuits and technologies.

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Monolithic Broadband Gilbert Micromixer With an Integrated Marchand Balun Using Standard Silicon IC Process Sheng-Che Tseng, Student Member, IEEE, Chinchun Meng, Member, IEEE, Chia-Hung Chang, Chih-Kai Wu, and Guo-Wei Huang

Abstract—A single-ended wideband downconversion Gilbert micromixer is demonstrated in this paper using 0.35- m SiGe BiCMOS technology. A transimpedance amplifier with resistive feedback is utilized in the IF stage while a broadband Marchand balun is employed to generate wideband differential local oscillator signals. The planar Marchand balun topology employed in this paper can generate truly balanced signals even in the presence of the lossy low-resistivity ( 10 cm) silicon substrate. A systematic approach to measure the frequency response of each individual stage in a Gilbert mixer is developed in this paper. This single-ended wideband mixer has the conversion gain of 15 dB, 1dB of 19 dBm, 3 of 7 dBm, and the noise figure of 13 dB. The mixer works from 3.5 to 14.5 GHz.



IP

IIP

Index Terms—Downconverter, Marchand balun, micromixer, SiGe BiCMOS, silicon substrate, transimpedance amplifier (TIA), wideband.

I. INTRODUCTION

T

HE ERA of the wireless applications with high data-rate transmission and multiple functions is coming, e.g., the IEEE 802.11a/b/g combo system [1], ultra-wideband (UWB) system [2], and WiMAX system [3]. The range of carrier frequencies and their bandwidth constantly increase. The obligation of the complicated data processing belongs to the baseband design, while the RF integrated circuit (IC) design takes responsibility for the wide range frequency and broad bandwidth operation. Nevertheless, the design of the high-frequency and wideband RF circuits is a big challenge in the overall solution implementation. For an active mixer, the transistors have natural instinct to perform wide range and broad bandwidth frequency translation. Due to the input/output matching networks, narrowband passive components, and loading effects, the mixer’s wideband ability is restricted. Manuscript received March 31, 2006; revised July 25, 2006. This work was supported by the National Science Council of Taiwan, R.O.C., under Contract NSC 95-2752-E-009-001-PAE and Contract NSC 95-2221-E-009-043-MY3, by the Ministry of Economic Affairs of Taiwan under Contract 94-EC-17-A-05-S1020, by the Ministry of Education Aim for Top University Program under Contract 95W803, and by the National Chip Implementation Center. S.-C. Tseng, C. Meng, and C.-H. Chang are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: [email protected]). C.-K. Wu was with the Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. He is now with Agilent Technologies, Tao-Yuan 324, Taiwan, R.O.C. G.-W. Huang is with National Nano Device Laboratories, Hsinchu, 300 Taiwan, R.O.C. Digital Object Identifier 10.1109/TMTT.2006.884690

For the wideband circuit design, the wideband matching of the input/output ports is a significant issue. The common implemented active mixer is a Gilbert mixer using the emitter-coupled differential input stage. Owing to the high input impedance of the common-emitter-configured transistors, the reactive or resistive matching is needed at the input port. For the reactive matching, the matching bandwidth relates to the orders of the passive matching network. Increasing the order of the matching network can expand the operation bandwidth, but also takes more area. Although the resistive matching can perform wideband matching, it also introduces loss. The variant of the Gilbert mixer, the so-called micromixer, which is defined as a microwave mixer in [4], has the properties of the wideband input matching and single-ended input. Those properties facilitate the realization of the wideband and single-ended mixer. In this paper, the input stage of the mixer is made up of the micromixer. For the balanced mixers, the Gilbert switch quad demands differential local oscillator (LO) signals. It is cumbersome to use an off-chip balun for the wideband balanced LO signal generation because the differential signals experience the different delay paths on the circuit board, especially at high frequencies. Hence, a single-to-differential LO balun is integrated in the IC process to form a single-ended mixer. Since it is difficult to achieve truly differential signals with equal magnitude and opposite phase by an active balun in addition to more power consumption at high frequencies, a passive balun is taken into consideration. The Marchand balun is a very wideband passive balun and is popularly used for broadband applications such as a double-balanced diode mixer [5] and a frequency doubler [6]. However, most Marchand baluns are realized on a semi-insulating or high-resistivity substrate. The proper Marchand balun topology suitable for a standard silicon IC process is identified in this paper to maintain the truly balanced signals regardless of the substrate loss. High impedance resistors or active pMOS loads are usually employed to obtain high conversion gain. In addition, the pMOS current mirror is used to effectively combine the differential IF output current signals of the mixer and establish a singleended output. However, the high impedance causes a low-frequency pole at the output stage, which slows down the IF response. The transimpedance amplifier (TIA) with resistive feedback is, hence, utilized at the output stage to reduce the output impedance and extend the bandwidth in this paper [7], [8]. A single-ended wideband Gilbert downconverter is fabricated in the 0.35- m SiGe BiCMOS technology and demonstrated in

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TSENG et al.: MONOLITHIC BROADBAND GILBERT MICROMIXER WITH INTEGRATED MARCHAND BALUN

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Fig. 1. Planar Marchand balun with =4 coupled lines.

this paper. It is composed of a micromixer, an integrated LO Marchand balun, and a TIA output amplifier. In this paper, a technique to measure the RF, LO, and IF stages of a Gilbert mixer is developed. This mixer has 15-dB conversion gain, 13-dB noise figure, and 400-MHz IF bandwidth and works from 3.5 to 14.5 GHz. The Marchand balun design concept and the measured results of a monolithic planar Marchand balun are represented in Section II, and Section III depicts the entire circuits of the micromixer with an integrated Marchand balun. Section IV then shows the experimented results, including the performances of an individual micromixer and an overall micromixer with an integrated Marchand balun. Finally, Section V gives a conclusion with a brief summary of the mixer’s performances.

II. ANALYSIS AND IMPLEMENTATION OF THE PLANAR MARCHAND BALUN ON SILICON IC PROCESS

A. Analysis The Marchand balun, a very broadband passive balun, was proposed in 1944 and has one unbalanced input and two balanced outputs [9]. The compensated Marchand balun can perform impedance transformation from the balanced port to the unbalanced port. The load at the balanced port is shunted with a quarter-wavelength short stub and in series with a quarter-wavelength open stub [10], [11]. Nevertheless, this type is not easily realized in the IC process, especially in the silicon IC process, and thus is not commonly used in ICs. The planar Marchand balun is composed of two back-to-back quarter-wavelength coupled lines, as shown in Fig. 1. Each coupled line has four ports—input, direct, coupled, and isolated ports. Two coupled ports of coupled lines are connected with short ends; the direct ports are tied together. One of the input ports is connected with an open end and the other is the unbalanced input of the Marchand balun, while the balanced outputs of the Marchand balun are from the isolation ports. This configuration is the most popular one, and other topologies of the Marchand balun had been developed in [12]. The transmission and reflection properties of the Marchand balun can be analyzed easily by the properties of the coupler

Fig. 2. S -parameter derivation of the planar Marchand balun with =4 coupled lines. (a) S . (b) S .

and open and short terminals [13]. The quarter-wavelength coupled line has the scattering parameters for the coupled and transmitted ports and , which are derived in Appendix. The relation between and of the coupled line is written as no loss with loss.

(1)

The short terminal results in an antiphase total reflection, whereas the open terminal causes an in-phase total reflection. When a signal inputs at port 1, one part of the input signal, the solid line signal, shown in Fig. 2(a), couples to the short terminal, then reflects totally in an antiphase fashion, and finally voltage wave transmits to port 2. This causes the transmitting to port 2. The other part, the dotted line signal, is analyzed more complicatedly, as shown in the following steps. Step 1) The dotted line signal transmits to the open terminal and reflects totally. Step 2) Some reflected power directly transmits to the middle and then couples to port 2; the rest power couples to the short terminal . Step 3) A proportion of power reflected from the short terminal , couples to the open terminal, , and then reflects totally. Finally, the reflected signal progresses repeatedly from Step 2). Consequently, the transmission coefficient form ports 1 to 2 . Therefore, caused by the dotted line signal is the total transmission coefficient from ports 1 to 2 is (2) With the same analysis approach, the total transmission coefficient form ports 1 to 3 is (3) as shown in Fig. 2(b). Based on the calculations of and , this balun performs single-to-differential conversion perfectly, regardless of the silicon substrate loss and metal loss, thanks

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

S -parameter derivation of the planar Marchand balun. The nodes (1–3) of the tree denote ports 1–3. The others nodes are denoted in Fig. 1.

B. Implementation

Fig. 4. Magnitude of the transmission and reflection at the input port of the planar Marchand balun with respect to coupling coefficients k for the cases of no loss.

to the symmetric signal delivery, as shown in Fig. 2(a) and (b). This procedure to figure out the scattering parameters can be portrayed in the tree formation, as shown in Fig. 3. The tree and , in Fig. 3, symbolize ports 1–3, nodes open end, and short terminal, respectively, as shown in Fig. 1. As a result, the -parameter matrix of the planar coupled-line Marchand balun can be expressed as

(4) Fig. 4 displays the magnitude of the transmission and reflection at the input port of two configurations with respect to different coupling coefficients , as defined in the Appendix with the assumption of no loss. The coupling coefficient is designed as the value of 1 3 or 4.8 dB, for a good input matching, , and the maximum transmission [14]. The optimal i.e., Marchand balun is practically implemented on account of the low optimal coupling coefficient.

The coupled-line Marchand balun can be realized by Lange couplers [15], [16], broadside coupled lines [12], [17], [18], and spiral transmission lines [12], [17], [19]–[21]. In order to shrink the size of the balun, an interleave transformer is employed as a quarter-wavelength coupled line in our study, as shown in Fig. 1. The transformer-type coupled lines, namely, spiral transmission lines, can achieve the desired coupling coefficient. The coupledline Marchand balun with two short terminals and one open end is applied and the two ac ground terminals tied together can provide a dc bias for the mixer’s switch quad. For the balanced mixers, the LO switch quad is driven by the differential signals. A wideband single-to-differential Marchand balun is demanded in order to offer differential LO signals and to reserve the mixer wideband operation. Given that the input is not matched to the source impedance of the Gilbert cell impedance , the -parameters of Marchand balun are modified as shown in (5) at the bottom of the following page [14]. However, the balance of the two outputs is independent of the coupling coefficient and the load impedance . Even if the load impedance of the Marchand balun is not matched, the outputs also have equal magnitude and opposite phase. Most monolithic Marchand baluns are fabricated on the semi-insulating GaAs substrate. A Marchand balun on the cm) silicon substrate had also been high-resistivity ( 4000 demonstrated [22]. Recently, the Marchand balun was practiced using standard silicon processing with a shielding ground plane [23]. However, the shielding ground plane limits the even-mode characteristic impedance and then reduces the balun bandwidth [21]. The operating bandwidth of the Marchand balun increases monotonically when the ratio of the even-mode characteristic impedance to the odd-mode characteristic impedance of the coupled line increases. A high even-mode characteristic impedance is preferred for a wideband Marchand balun. Thus, the high even-mode characteristic impedance of coupled lines can be achieved in our Marchand balun topology to obtain wide bandwidth. Besides, the higher effective dielectric constant for the balun without the shielding ground plane is good for size reduction. In this paper, the planar Marchand balun, as shown in Fig. 5, is implemented directly on the low-resistivity ( 10 cm) silicon

TSENG et al.: MONOLITHIC BROADBAND GILBERT MICROMIXER WITH INTEGRATED MARCHAND BALUN

Fig. 5. Die photograph of a monolithic Marchand balun. The connecting line is approximately 180 m and is restricted by the GSGSG probe. From simulation, the coupling coefficient of the coupled line is approximately 0.5 at 12 GHz. (Color version available online at http://ieeexplore.ieee.org.)

substrate with the high even-mode characteristic impedance to hold broadband operation. This Marchand balun is formed by two-section transformer-type coupled lines and is designed at the center frequency of 12 GHz. The size of Marchand balun is approximately 660 m 250 m. It is very compact thanks to the size advantage of the transformer-type coupled lines. The coupled lines are made of the top metal with the thickness of 0.93 m, the spacing of 5 m, and the width of 5 m. The interleave transformer has approximately 3 : 3 turns. The substrate thickness is approximately 350 m and the distance between the top metal and the substrate is approximately 6.2 m. From simulation, the coupling coefficient of the coupled line is approximately 0.5 at 12 GHz. The experimental measured data, IE3D simulation results, and the calculated data from (4) based on IE3D simulated and of the Marchand balun in Fig. 5 are displayed in Figs. 6 and 7. The delta plots of the phase and amplitude errors are presented in Fig. 8. The magnitude imbalance in output ports is approximately 2 dB. This magnitude imbalance results from the loss of the connecting line between two transformer-type coupled lines, as shown in Fig. 5. The length of the connecting line is approximately 180 m. The inevitable finite connecting line in the Marchand balun test pattern is constrained by the ground–signal–ground–signal–ground

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Fig. 6. Input return loss of the planar Marchand balun.

Fig. 7. Transmission coefficients of the planar Marchand balun.

(GSGSG) pad employed for the measurement purpose. The finite connecting line can be minimized in the final fabricated circuit. On the low-resistivity silicon substrate, the signal transmission of the balun is dominated by the first component, i.e., the of (2) and (3). However, the voltage direct coupled term

(5)

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Fig. 8. Phase error and magnitude error of the planar Marchand balun.

Fig. 10. Schematic of the micromixer with an LO Marchand balun and a TIA output buffer.

III. CIRCUIT DESIGN

Fig. 9. Dissipated loss of the Marchand balun.

wave directly coupled to port 3 experiences the connecting-line loss. Thus, the transmission magnitude is lower than . This phenomenon corresponds to the measured results. The outputs are more balanced in magnitude when the connecting line is removed in the IE3D simulation, as shown in Fig. 7, but the phase balance is almost unaffected by the connecting line. In other words, the connecting line has high associated loss than phase delay. The dissipated loss of a Marchand balun is defined as Loss

(6)

and is approximately 6 dB, as shown in Fig. 9. In our study, the Gilbert mixer with the integrated Marchand balun has a short connecting line to provide balanced outputs. The usable bandwidth is more than 10 GHz. The mixer conversion gain is insensitive to the LO power provided that the phase is balanced and the LO power is large enough to commutate the RF current. The reason will explained by the measured results in Section V. The magnitude imbalance resulting from the small connecting line loss is, hence, not a matter of mixer’s operation. This balun is appropriately utilized as a single-to-differential balun at the LO port in this mixer even though the magnitude imbalance occurs.

The entire schematic of the single-ended wideband downconverter is shown in Fig. 10. This downconverter is formed by the micromixer, the Marchand balun, and the TIA output buffer. Each element has the broadband property. The micromixer can be considered as the combination of two single-balanced mixers. One mixer is formed by the common; the other is composed of emitter-configured RF amplifier . The LO switch the common-base-configured RF amplifier , and . The curquad is made up of the transistors , rent mirror pair and provides the balance dc currents in the RF input stage and then these two RF amplifiers have equal magnitude and opposite phase transconductance gain to obtain regood mixer balance. Moreover, the diode-type transistor duces the input impedance of and enhances the speed of the common-emitter-configured input stage. The input impedance and and the resistors is controlled by the transistors and . It is easy to achieve wideband matching so this micromixer can act as a wideband mixer [24]. To establish a single-ended output, the pMOS current mirror is applied to combine the differential output current signals of the mixer. Furthermore, a TIA amplifier is used in the output stage of this mixer. The frequency response of the input stage . is dominated by the common-emitter-configured transistor As shown in Fig. 11, in the critical path, the RF input stage is viewed as a transconductance amplifier (TCA), the IF output stage is a TIA, while the LO switch quad is inserted in the middle and performs the frequency translation. The topology is very similar to the well-known Cherry–Hooper amplifier—a TCA stage in cascade with a TIA stage [7]. The LO current commutation quad Gilbert mixer cell is used to switch the connecting current between the TCA and TIA stages. Thus, the conversion gain and frequency response can be analyzed as a TCA for the RF stage and a TIA for the IF stage. The TIA output buffer employs a resistive feedback to enlarge the output bandwidth. In addition, a Darlington pair is also utilized to enhance the speed of transistors. Therefore, this output stage of the mixer

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Fig. 11. Cherry–Hooper technique employed in the micromixer.

Fig. 13. Die photographs of the micromixers: (a) without a Marchand balun and (b) with a Marchand balun designed at the center frequency of 9 GHz.

are the resistances looking into the base–emitter terminals of and in Fig. 12, respectively [25]. As a result of a resistive feedback, the poles are extended by the feedback factor of . The overall voltage gain can be calculated as (13) Fig. 12. Small-signal models of the: (a) TCA and (b) TIA.

has single-ended and wideband properties. To analyze the frequency response, the small-signal model is split into two parts, as shown in Fig. 12. For simplicity, the base–emitter resistance and base–collector capacitance are neglected in the frequency response analysis. The complete transfer functions of the TCA and TIA stages from exact circuit analysis are denoted as (7) where

(8)

From the open-circuit time-constant analysis, the poles of the TCA and TIA stages in Fig. 12 are (9) and (10) where

These three components (the micromixer, TIA amplifier, and Marchand balun) construct a single-ended wideband downconverter. Due to the single-ended and wideband matching properties, this Marchand micromixer with the integrated Marchand balun has a wide range of usage. IV. MEASUREMENT RESULTS The Gilbert mixer along with a compensated Marchand balun was demonstrated on a semi-insulating GaAs substrate by Hamed et al. [26]. In this paper, the coupled-line planar Marchand balun is implemented on a low-resistivity standard silicon substrate and, to the best of our knowledge, combined with a micromixer for the first time. Two wideband micromixers were fabricated using 0.35- m SiGe BiCMOS technology [27]. Both mixers have identical active circuitry, except the LO Marchand balun. Fig. 13 illustrates two die photographs of the implemented mixers. The left-hand-side photograph is a micromixer without a Marchand balun and its chip size is 0.75 mm. The chip size of the to approximately 0.75 mm right-hand-side chip with an integrated Marchand balun is approximately 1 mm 1 mm. This integrated Marchand balun is redesigned by taking away the connecting line described in Fig. 5 in order to obtain more balanced outputs. The Marchand 700 m and is balun only occupies the area of 300 m designed at the center frequency of 9 GHz. The measurement results of the micromixer without the Marchand balun give excellent agreement with the wideband operation of the micromixer. The Marchand mixer then also performs wideband mixing.

(11) A. Micromixer Without a Marchand Balun

and (12)

The mixer without the Marchand balun has the broad band property and works up to 15 GHz. The conversion gain is ap-

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Fig. 14. Conversion gain of the micromixer without Marchand balun with respect to LO power.

proximately 15 dB and the 3-dB IF bandwidth is approximately 400 MHz [27]. Fig. 14 illustrates that the effect of the LO power on the conversion gain is measured with the fixed IF frequency of 100 MHz, but different LO frequencies by Agilent’s E4448A power spectrum analyzer (PSA). The current commutation in the Gilbert cell is responsible for the frequency translation. The differential pair of the bipolar Gilbert cell only needs a small twist voltage (approximately 0.1 V) to perform the near-perfect current commutation. Once the LO power is large enough to drive the switch quad of the Gilbert mixer, the conversion gain keeps constant and is insensitive to the LO power. If the LO power is too large, the quad switch SiGe HBT transistors enter the saturation region and then the mixer gain degrades. However, there is more power to drive the switch quad at higher frequencies. With the LO frequency increase, the LO power range for the flat constant conversion gain region decreases. The IF and RF bandwidth experiments in [27] give the direct measurement of the IF and RF stage frequency response of the mixer, while the frequency response of the LO Gilbert cell is examined in Fig. 14. The higher the LO frequency, the narrow the flat gain region becomes. The flat gain region still exists for LO frequencies up to 18 GHz. According to the measured results, the maximum operating frequency of the mixer is approximately 15 GHz and is limited by the RF input stage. B. Micromixer with an Integrated Marchand Balun To form a single-ended mixer, a Marchand balun is utilized at the LO port. This Marchand balun has more than 10-GHz bandwidth and is compatible with the wideband property of the micromixer. The measured return loss at the RF, LO, and IF ports is represented in Fig. 15. The return-loss performance of the RF input and IF output keeps the same as that of the previous active mixer, while the return loss of the LO input is improved by the Marchand balun. The return loss of the RF, LO, and IF ports is below 14, 6, and 10 dB, respectively. The conversion gain of the micromixer with the LO Marchand balun is

Fig. 15. Return loss of the micromixer with the integrated planar Marchand balun.

Fig. 16. Conversion gain of the micromixer with the integrated planar Marchand balun.

measured with a fixed 100-MHz IF when the LO power equals to 6 dB. Fig. 16 displays the experiment result. This mixer with the integrated Marchand balun can operate from 3.5 to 14.5 GHz with 11-GHz 3-dB bandwidth. The conversion gain in the 3-dB bandwidth is approximately 15 dB and is the same as that of the mixer without the Marchand balun. The low-resistivity substrate of standard silicon IC process introduces the connecting line loss. Even if this loss causes the output magnitude imbalance of the Marchand balun, the magnitude imbalance can be tolerable when a Marchand balun is employed at the LO part of mixer as a single-to-different balun because LO power does not affect the conversion gain at the flat region, as shown in Fig. 14. The switch quad SiGe HBT transistors especially only demand small power to steer the RF current totally from one side to the other side of the differential pair. In other words, there is a wide range of the constant conversion gain region in terms of the LO power. Thus, the wideband Marchand balun is properly used to preserve the wideband mixing even if there is magnitude imbalance. The 3.5-GHz lower bound and 14.5-GHz upper bound of the mixer’s frequency response

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Fig. 17. Port-to-port isolations of the micromixer with the integrated planar Marchand balun.

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Fig. 19. Noise figure of the micromixer with the integrated planar Marchand balun.

mixer operates at 6 and 10 GHz, the conversion gain is higher and the noise figure is lower simultaneously. The lowest noise figure is approximately 13 dB. Both mixers work with a 5-V supply and have the same core power consumption of approximately 60 mW. The additional Marchand balun does not consume any dc power. This wideband Marchand micromixer not only maintains the performances of the original micromixer without an integrated balun, but also provides a single-ended input and output solution. V. CONCLUSION

Fig. 18. IP hand balun.

and IIP of the micromixer with the integrated planar Marc-

are restricted by the Marchand balun and RF input stage, respectively, according to the measured results of the individual components (the Marchand balun and Gilbert mixer without balun) and the experimental outcome in Fig. 16. The port-to-port isolations of the Marchand mixer are presented in Fig. 17. During the operating frequencies of the Marchand balun, the mixer has the higher LO-to-IF isolation of approximately 35 dB. In addition, the reverse isolation of the transistors at the input stage provides the higher LO-to-RF isolation, especially at low frequencies. The RF-to-IF isolation is below 20 dB. and the input The input 1-dB gain compression point third-order intercept point of the micromixer with the integrated Marchand balun as a function of frequency are measured, is approximately 19 dBm, while as shown in Fig. 18. is approximately 7 dBm. The input signal with the frequency below 7 GHz has harmonics located in the operating frequency range. Hence, the in-band harmonic is measured when is approximately 12 dBm. the input frequency is 5 GHz and The noise figure of the Marchand mixer is measured at each frequency of 2, 6, 10, and 14 GHz, as shown in Fig. 19. When the

In this paper, a heuristic approach to derive the three-port scattering parameters of the lossy Marchand balun has been introduced. The appropriate Marchand balun topology with the capability of resisting the loss in the standard silicon IC process has been identified. A systematic approach to measure the frequency response of the RF, IF, and LO stages of a Gilbert mixer has been developed. Thus, a single-ended wideband Gilbert mixer with the integrated planar Marchand balun has been demonstrated using 0.35- m SiGe BiCMOS technology. This single-ended wideband mixer with the integrated Marchand of 19 dBm, balun has the conversion gain of 15 dB, of 7 dBm, of 12 dBm, a minimum noise figure of 13 dB, and works from 3.5 to 14.5 GHz with 400-MHz IF bandwidth. The developed frequency response measurement technique can be employed to identify the frequency-limiting mechanism. The lower bound of 3.5 GHz is limited by the LO stage, while the upper bound of 14.5 GHz is limited by the RF stage.

APPENDIX DERIVATION OF COUPLED AND TRANSMISSION SCATTERING PARAMETERS OF A LOSSY COUPLED LINE The even- and odd-mode matrix method is employed to analyze the lossy coupled line, as shown in Fig. 20. Half of the coupled line can be considered as a lossy transmission line. matrices are denoted as Then, the even- and odd-mode

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with frequencies in the presence of loss and the coupled line is dispersive. In our analysis of the Marchand balun formula on a standard lossy silicon substrate in Section II, the values of and can be substituted by (A5) and (A6). The matching condition is designed at the center frequency. Thus, the of heuristic analysis, as shown in Figs. 2 and 3, is valid at the center frequency for a Marchand balun on a lossy substrate. Under the lossless condition, the complex characteristic impedances and become real numbers and , respectively. can be designed for all The matching condition frequencies and, thus, the analysis in Figs. 2 and 3 is valid for all , (A5) and (A6) frequencies. At the frequency where become well-known formulas as

Fig. 20. Four-port network of coupled lines.

Fig. 21. Electric circuit model of a transmission line for the even mode.

(A7) (A1) and

and (A8) where the coupling coefficient

is equal to

(A2) (A9) respectively. A lossy transmission line for the even mode is shown in Fig. 21 and the even-mode characteristic impedance is expressed as (A3) with the per-unit-length resistance , inductance , con, and capacitance , [28]. is the odd-mode ductance characteristic impedance and can be defined similarly to with its associated and . The even- and odd-mode propagation constants are assumed to be equal for simplicity and and are complex numare defined as . In other words, bers for the lossy transmission line. Under the matching con, where is the terminal impedance, dition of the coupled line has perfect matching and excellent isolation. Therefore, the scattering parameter matrix for a lossy coupled line is derived as

(A4)

where the scattering parameters for the coupled and transmitted ports and are (A5)

and

(A6)

respectively [29]. The Marchand balun analysis in Section II-A is developed based on this scattering matrix (A4). As shown and vary in (A3), the lossy characteristic impedances

REFERENCES [1] K. R. Rao, J. Wilson, and M. Ismail, “A CMOS RF front-end for a multistandard WLAN receiver,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 5, pp. 321–323, May 2005. [2] P. Heydari, “A study of low-power ultra wideband radio transceiver architectures,” in IEEE Wireless Commun. Networking Conf., Mar. 2005, vol. 2, pp. 758–763. [3] A. Ghosh, D. R. Wolter, J. G. Andrews, and R. Chen, “Broadband wireless access with WiMax/802.16: Current performance benchmarks and future potential,” IEEE Commun. Mag., vol. 43, no. 2, pp. 129–136, Feb. 2005. [4] B. Gilbert, “The MICROMIXER: A highly linear variant of the Gilbert mixer using a bisymmetric class-AB input stage,” IEEE J. Solid-State Circuits, vol. 32, no. 9, pp. 1412–1423, Sep. 1997. [5] W. R. Brinlee, A. M. Pavio, and K. R. Varian, “A novel planar doublebalanced 6–18 GHz MMIC mixer,” in IEEE MTT-S Int. Microw. Symp. Dig., San Diego, CA, May 1994, pp. 9–12. [6] S. A. Maas and Y. Ryu, “A broadband, planar, monolithic resistive frequency doubler,” in IEEE MTT-S Int. Microw. Symp. Dig., San Diego, CA, May 1994, vol. 1, pp. 443–446. [7] E. M. Cherry and D. E. Hooper, “The design of wideband transistor feedback amplifiers,” Proc. IEE, vol. 110, no. 2, pp. 375–389, Feb. 1963. [8] B. Razavi, Design of Integrated Circuits for Optical Communications. New York: McGraw-Hill, 2003, ch. 5, sec. 5.2.3, pp. 136–140. [9] N. Marchand, “Transmission-line conversion transformers,” Electronics, vol. 17, no. 12, pp. 142–145, 1944. [10] G. Oltman, “The compensated balun,” IEEE Trans. Microw. Theory Tech., vol. 14, no. 3, pp. 112–119, Mar. 1966. [11] A. M. Pavio and A. Kikel, “A monolithic or hybrid broadband compensated balun,” in IEEE MTT-S Int. Microw. Symp. Dig., May 1990, vol. 1, pp. 483–486. [12] T. Gokdemir, S. B. Economides, A. Khalid, A. A. Rezazadeh, and I. D. Robertson, “Design and performance of GaAs MMIC CPW baluns using overlaid and spiral couplers,” in IEEE MTT-S Int. Microw. Symp. Dig., Denver, CO, Jun. 1997, pp. 401–404. [13] R. Mongia, I. Bahl, and P. Bhartia, RF and Microwave Coupled-Line Circuits. Norwood, MA: Artech House, 1999, pp. 411–438. [14] K. S. Ang and I. D. Robertson, “Analysis and design of impedancetransforming planar Marchand baluns,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 2, pp. 402–406, Feb. 2001. [15] C. Nguyen and D. Smith, “Novel miniaturised wideband baluns for MIC and MMIC applications,” Electron. Lett., vol. 29, no. 12, pp. 1060–1061, Jun. 1993.

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[16] M. C. Tsai, “A new compact wideband balun,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1993, vol. 1, pp. 141–143. [17] T.-H. Chen, K. W. Chang, S. B. Bui, H. Wang, G. S. Dow, L. C. T. Liu, T. S. Lin, and W. S. Titus, “Broadband monolithic passive baluns and monolithic double-balanced mixer,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 1980–1986, Dec. 1991. [18] K. Nishikawa, I. Toyoda, and T. Tokumitsu, “Compact and broadband three-dimensional MMIC balun,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 1, pp. 96–98, Jan. 1999. [19] Y. J. Yoon, Y. Lu, R. C. Frye, and P. R. Smith, “A silicon monolithic spiral transmission line balun with symmetrical design,” IEEE Electron Device Lett., vol. 20, no. 4, pp. 182–184, Apr. 1999. [20] K. S. Ang, S. B. Economides, S. Nam, and I. D. Robertson, “A compact MMIC balun using spiral transformers,” in Asia–Pacific Microw. Conf., Singapore, Nov. 1999, pp. 655–658. [21] M. Shimozawa, K. Itoh, Y. Sasaki, H. Kawano, Y. Isota, and O. Ishida, “A parallel connected Marchand balun using spiral shaped equal length coupled lines,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, Jun. 1999, pp. 1737–1740. [22] Y. J. Yoon, Y. Lu, R. C. Frye, M. Y. Lau, P. R. Smith, L. Ahlquist, and D. P. Kossives, “Design and characterization of multilayer spiral transmission-line baluns,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp. 1841–1847, Sep. 1999. [23] H.-Y. Chang, P.-S. Wu, T.-W. Huang, H. Wang, C.-L. Chang, and J. G. J. Chern, “Design and analysis of CMOS broadband compact highlinearity modulators for gigabit microwave/millimeter-wave applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 20–30, Jan. 2006. [24] C. C. Meng, T. H. Wu, T. H. Wu, and G. W. Huang, “A 5.2 GHz 16 dB gain CMFB Gilbert downconversion mixer using 0.35 m deep trench isolation SiGe BiCMOS technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, Jun. 2004, pp. 975–978. [25] A. S. Sedra and K. C. Smith, Microelectronic Circuits, 5th ed. New York: Oxford Univ. Press, 2004, pp. 637–638. [26] K. W. Hamed, A. P. Freundorfer, and Y. M. M. Antar, “A monolithic double-balanced direct conversion mixer with an integrated wideband passive balun,” IEEE J. Solid-State Circuits, vol. 40, no. 3, pp. 622–629, Mar. 2005. [27] S.-C. Tseng, C. C. Meng, C.-H. Chang, C.-K. Wu, and G.-W. Hung, “Broadband Gilbert micromixer with an LO Marchand balun and a TIA output buffer,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1509–1512. [28] D. K. Cheng, Field and Wave Electromagnetics, 2nd ed. Reading, MA: Addison-Wesley, 1989, pp. 437–444. [29] R. Mongia, I. Bahl, and P. Bhartia, RF and Microwave Coupled-Line Circuits. Norwood, MA: Artech House, 1999, pp. 136–137.

Chinchun Meng (M’02) received the B.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 1985, and the Ph.D. degree in electrical engineering from the University of California at Los Angeles (UCLA), in 1992. He demonstrated the first continuous wave (CW) operation of a multiquantum well IMPATT oscillator at 100 GHz during his doctoral research. He is currently an Associate Professor with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. His current research interests are in the areas of RF ICs, high-frequency circuits, and highspeed devices.

Sheng-Che Tseng (S’05) received the B.S. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2003, and is currently working toward the Ph.D. degree in communication engineering from National Chiao Tung University. His current research focuses on RF ICs and highfrequency circuitry.

Guo-Wei Huang was born in Taipei, Taiwan, R.O.C., in 1969. He received the B.S. degree in electronics engineering and Ph.D. degree from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1991 and 1997, respectively. In 1997, he joined National Nano Device Laboratories, Hsinchu, Taiwan, R.O.C., where he is currently a Researcher. His current research interests focus on microwave device design, characterization, and modeling.

Chia-Hung Chang was born in Taipei, Taiwan, R.O.C., in 1982. He received the B.S. degree in electrical engineering from Yuan Ze University, Taiwan, R.O.C., in 2004, and the M.S. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2006. He was involved with pseudomorphic high electron-mobility transistor (pHEMT) monolithic-microwave integrated-circuit (MMIC) amplifiers and SiGe RF mixers during his master’s research.

Chih-Kai Wu received the B.S. and M.S. degrees in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2003 and 2005, respectively. From 2003 to 2005, he was with the Research Laboratory, National Chiao Tung University, where he implemented RF front-ends and 60-GHz microwave circuit design. He also focused on RF testing and on-wafer measurement with the National Nano-device Laboratory (NDL). Upon completion of the M.S. degree, he joined the Electronic Measurement Group, Agilent Technologies, Tao-Yuan, Taiwan, R.O.C., as an Application Engineer, where he supports and delivers training with wireless and mobile instruments in customer sites.

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Silicon-Integrated Differential Bandpass Filters Based on Recursive and Channelized Principles and Methodology to Compute Their Exact Noise Figure Sébastien Darfeuille, Julien Lintignat, Roberto Gómez-García, Member, IEEE, Zoheir Sassi, Bruno Barelaud, Laurent Billonnet, Bernard Jarry, Senior Member, IEEE, Hervé Marie, and Patrice Gamand, Senior Member, IEEE

Abstract—In this paper, two silicon-integrated differential active bandpass filters are presented. The first one is a recursive filter based on a cellular approach. This circuit is independently tunable in terms of power transmission gain, center frequency, and bandwidth. The chip surface is less than 1.4 mm2 . For this prototype, measurements demonstrate a 1.9–2.4-GHz center-frequency tuning range with a typical gain of 15 dB and a 3-dB bandwidth of 60 MHz. Gains of up to 40 dB and bandwidths as low as 20 MHz are also achievable in the 2.05–2.38-GHz range. Subsequently, the design of an integrated three-branch channelized bandpass filter is addressed. The proposed filter uses an active power splitter at its input. Moreover, the channels are based on elementary first-order tunable recursive stages derived from the previously described topology, thus making the overall filter fully reconfigurable. This second circuit, whose layout size is smaller than 3 mm2 , can exhibit 3-dB bandwidths of 90 MHz and gains of up to 20 dB within a 1.95–2.23-GHz tuning range. Controllable high selectivity for each rejected band can be obtained through the generation of adjustable out-of-band transmission zeros. Furthermore, a dual-band behavior is also feasible through this filter. To conclude, an original method to extract the exact noise figure of differential circuits is reported, and applied to the filter prototypes developed in this study. The Philips QUBIC4 0.25- m silicon BiCMOS process has been used for the design of the two circuits presented. Index Terms—Active filters, channelized filters, differential circuits, mixed modes, monolithic microwave integrated circuit (MMIC), noise figure, noise waves, recursive filters, silicon BiCMOS integrated circuits (ICs), tunable filters.

I. INTRODUCTION ODAY, off-chip passive filters can be found in a vast majority of RF front-ends [1]. In their design, the achievement of low insertion-loss and high-selectivity performances has become a major issue. Thus, suitable band selections, by efficiently rejecting spurious signals and out-of-band noise, can

T

Manuscript received March 31, 2006; revised August 22, 2006. S. Darfeuille, H. Marie, and P. Gamand are with the Innovation Center RF, NXP, 14079 Caen, France (e-mail: [email protected]; [email protected]; [email protected]). J. Lintignat, Z. Sassi, B. Barelaud, L. Billonnet, and B. Jarry are with the XLIM Research Institute, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 6172, University of Limoges, 87060 Limoges, France (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). R. Gómez-García is with the Department of Signal Theory and Communications, University of Alcalá, Alcalá de Henares, 28871 Madrid, Spain (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885906

be carried out with these filters. Nevertheless, they are often expensive, space consuming, and cannot easily be tuned. Active filters are an interesting alternative to counteract the aforementioned limitations [2]. Since they can simultaneously perform the filtering and low-noise amplifying functions, more compact and lower cost circuit implementations are feasible. Furthermore, the integration of these filters with the other basic modules of the transceivers (e.g., oscillators and mixers for up/down frequency signal conversions) in one single manufacturing process becomes insignificant as they share the same technology. Another key advantage is tunability, easily affordable with this class of filters. Thus, the design of flexible transceiver architectures supporting multiple modern standards (e.g., global system for mobile communications (GSM), Universal Mobile Telecommunications System (UMTS), or Bluetooth) at the same time could be greatly simplified in terms of space and circuit complexity. However, as a difference regarding passive filters, factors such as nonlinear distortion, noise performance, power transmission gain, and power-handling capabilities must be considered in their design. Unfortunately, to date, there is not an abundance of integrated active filter solutions appropriate for the RF and microwave bands. This is a result, in part, of the impossibility of extrapolating classic low-frequency active filter arrangements based on operational amplifiers to these frequency ranges. Furthermore, the low quality factors of the passive elements implemented in monolithic microwave integrated circuits (MMICs) makes things more difficult when a high selectivity is required. The aforementioned limitation leaves only the following two possibilities for the MMIC active filter designer. • The compensation for the passive losses by using negative resistors or active circuits directly emulating the passiveelement function, but with low loss or even gain: here, the main drawbacks are the high noise and current-consumption levels, and the poor power-handling ability caused by the large number of active devices needed in high-order filter synthesis. • The development of novel active filter arrangements, decorrelating the lossy passive components and the filtering action as much as possible: this is the case of microwave filters based on signal-interference techniques, such as transversal, recursive and channelized filters. In this paper, two original topologies of microwave active bandpass filters integrated on silicon are reported. The first

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Fig. 1. Block diagram of the cascaded two-stage recursive filter. Fig. 2. Principle scheme of the proposed elementary recursive stage.

one is a fully differential two-stage recursive filter. Regarding past studies dealing with microwave recursive filter design, this structure is independently tunable in terms of center frequency, bandwidth, and power transmission gain. The second one is a three-branch channelized bandpass filter. It is based on an active power divider at its input, and branches reusing a single-stage version of the previously described tunable recursive filter. This makes the channelized filter fully reconfigurable, not only in frequency, but also in filtering response shape. Moreover, measurements and simulations are provided to validate the proposed active filter configurations. To conclude, a method for extracting the exact noise figure of differential circuits is explained, and subsequently applied to the MMIC recursive and channelized filter prototypes of this study. These two circuits, implemented with the Philips QUBIC4 0.25- m silicon BiCMOS process [3], have been designed in the Cadence environment. This paper is organized as follows. The design of the twostage fully differential integrated recursive filter is approached in Section II. Section III deals with the MMIC reconfigurable three-branch channelized filter. The results corresponding to the exact noise figure of differential circuits, and its application to the developed recursive and channelized filters, are described in Section IV. Finally, the most relevant conclusions of this study are set out in Section V. II. MMIC TUNABLE TWO-STAGE RECURSIVE FILTER Over the years, recursive filters have been mainly developed for low-frequency digital filtering applications. However, these structures can also be extrapolated to the analog domain to implement high-performance RF and microwave analog filters, in both hybrid and MMIC technologies [4]–[7]. The block diagram of the recursive filter topology to be designed here is detailed in Fig. 1. As shown, it corresponds to a simple two-stage recursive filter based on a cellular approach [8]. This means that the elementary first-order recursive stages are cascaded instead of being arranged in a more classic ladder configuration. The main advantage of this configuration is that, depending on the selection of the values for the delay factors of the recursive branches, filtering responses with different degrees of selectivity can be obtained. Indeed, the resulting overall transfer function corresponding , is given by to Fig. 1, i.e.,

(1)

where is an input weight factor and , and , refer to the weight and delay factors of the first and second feedback loops, respectively. Thus, from (1), the following applies. , a second-order response is achieved as • For follows:

(2) , the following third-order response • For is derived by using only two first-order recursive stages:

(3) , should be Note that, for both cases, the condition fulfilled to assure the electrical stability of the filter [9] ( is the absolute value of a complex number). Other benefits of this recursive topology to be highlighted are the ease of preservation of the aforementioned stability (with a separate control of the stability of each cell) and its good technological reproducibility (it is shaped by the cascade of same-type elements) [8]. Moreover, as an added value, an independent tuning in terms of power transmission gain, center frequency, and bandwidth can be obtained with this structure. As demonstrated below, regarding past studies, this is the key feature of the recursive filter reported in this paper [10]. A. MMIC Implementation The topology selected to implement the differential first-order recursive filter stages is obtained from [6], although a choice was made here to place the delay cell into the feedback branch (Fig. 2). The use of a lumped passive delay section has been preferred instead of an active solution, even taking into account the large size of the inductors (Fig. 3). Indeed, this choice permits the power consumption to be limited and ensures electrical stability robustness. Varactor diodes controlled by two independent voltages (one for each recursive cell) have been included in order to separately adjust the intended delay in each filter section. Thus, the tunability of the transfer function is added as a feature of the overall recursive topology. The circuit carrying out the amplification and summation, derived from the topologies proposed in [6] and [11], is shown in

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Fig. 3. Electrical scheme of the proposed tunable passive delay section. Fig. 6. Simulated frequency and differential-mode power transmission gain j) tuning of the open loop feedback branch. (jS

Fig. 4. Simplified electrical scheme of the proposed amplifier/adder.

Fig. 5. Simulated power transmission gain of the direct-input amplifier for differential-mode (jS j) and common-mode (jS j) signals.

Fig. 4. As can bee seen, this adder provides two differential inin Fig. 4), the puts: one for the direct input of the filter ( in Fig. 4). The use of a casother for the feedback loop ( code topology for the direct input ensures better noise performance than a common-base one. The feedback input is designed through a conventional differential amplifier configuration including a gain control by means of a current-mirror source [12]. These two amplifiers share their load resistors, thus exhibiting a common differential output. Note that all the information reported in this paper concerning the -parameters is based on the mixed-mode formalism [13]. This enables the characterization of a differential device in its two possible operating modes and the conversions between them: differential and common modes, and common-to-differential and differential-to-common mode conversions. Fig. 5 shows the simulated power transmission gain of the direct-input amplifier for both differential and common-mode signals. The simulations have been carried out using the commercial integrated circuit (IC) design software Cadence. As shown, a differential gain close to 9.5 dB is obtained around 2 GHz,

Fig. 7. Simplified electrical scheme of the buffer stage (VGLNA).

whereas the common-mode gain is less than 7 dB. The noise figure, simulated making use of ideal baluns, is around 2.3 dB at 2 GHz, while the current consumption is less than 8 mA. In Fig. 6, several plots corresponding to the simulated differential-mode power transmission response of the feedback branch in open-loop configuration (i.e., the delay cell cascaded with the feedback amplifier) are shown. Specifically, they include the following. • On the left-hand side, the center-frequency tuning ability of the circuit loop, for a bandwidth around 300 MHz, is proven. Note that the bandpass filtering shape of the response is a direct result of the inherent bandpass nature of the delay element. However, the interest in this structure is that the delay value varies as a function of the center-frein Fig. 3), thus leading to a center-frequency setting ( quency control of the whole recursive filter. Here, the gain in Fig. 4) has been used to control of the amplifier ( adjust the maximum values of the open loop gain close to 0 dB for electrical stability reasons. • On the right-hand side, the differential-mode gain tuning capability of the open loop feedback branch is demonstrated. In particular, a narrower bandwidth for the recursive filter is achieved by increasing the feedback gain. Finally, a simple CMOS-controlled variable-gain low-noise amplifier (VGLNA) acting as an output buffer is cascaded at the output of the recursive filter. Indeed, a pMOS transistor operating as a variable resistance has been inserted between and the cascode transistors base (see Fig. 7). Thus, by tuning the gate voltage of the pMOS transistor in Fig. 7), the differential-mode gain of this ampli( fier stage, and as a consequence that of the whole filter, are set. This is illustrated in the left-hand portion of Fig. 8, where a

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Fig. 8. Simulated variations of the jS j- and jS output buffer as a function of the pMOS gate biasing.

j

-parameters of the

Fig. 10. Simulated and measured center-frequency tuning performance of the constructed recursive filter prototype for a differential-mode signal (BW = 60 MHz). f and BW denote the tuned center frequency and 3-dB bandwidth of the filter, respectively.

Fig. 9. Recursive filter chip micrograph.

8-dB variation for the maximum power transmission gain of the output buffer is obtained at around 2 GHz, without significant changes in its output matching (see the right-hand portion of Fig. 8). The great response-shape flexibility of the overall recursive filter, feasible through the use of tunable structures in each firstorder stage, must be emphasized. In practice, it is possible to control independently the center frequency (by acting on the delay elements), the bandwidth (with the gain in the feedback input of the adders), and the overall gain (through the output buffer). This will be experimentally demonstrated below. Fig. 9 is a micrograph of the constructed chip. The circuit dimensions are 1.05 1.3 mm . Inductors have been designed with Momentum software. B. Measurement Results The results obtained in the characterization of the constructed recursive filter prototype are now reported. The measurements have been carried out with an Agilent ENA Series E5071B network analyzer that, with four independent accesses, allows the direct mixed-mode -parameter characterization of the device being tested [14]. The simulated and measured center-frequency tuning performance of the filter prototype for a differential-mode signal is shown in Fig. 10. As can be seen, this filter can be tuned within the 1.90–2.38-GHz range while maintaining constant values for both the maximum power transmission gain and the 3-dB bandwidth: 15 dB and 60 MHz in this case, respectively. Note that

Fig. 11. Simulated and measured differential-mode power transmission gain j) and bandwidth tuning performance of the constructed recursive filter (jS prototype (f = 2:16 GHz).

the measured responses are in good agreement with those simulated thanks to the tuning capabilities of the circuit. The measured full center-frequency tuning range of the filter is 1.73–2.38 GHz, i.e., of 32% (1.7–2.4-GHz simulated, i.e., of 35%). However, as proven in Fig. 10, it is not possible to obtain constant and acceptable differential-mode power transmission gain and bandwidth below 1.9 GHz simultaneously. The adjusted values for gain and selectivity of Fig. 10 are not the best achievable: the differential-mode power transmission gain can be up to 40 dB and the 3-dB bandwidth can be decreased to 20 MHz throughout the entire 2.05–2.38-GHz range, while preserving the electrical stability (see the left-hand portion of Fig. 11). Moreover, as illustrated in the right-hand portion of Fig. 11 for a center frequency of 2.16 GHz, it is possible to obtain wider and flatter bandpass responses throughout the whole measured tuning range, by setting nonequal, but very close delay values in each recursive stage. Depending on the tuned center frequency, and for the typical 15-dB differential-mode power transmission gain and 60-MHz 3-dB bandwidth, as shown in Fig. 10, the output-referred 1-dB compression point is from 25 to 21 dBm. This is a result of the large number of active cascaded sub-cells making up the overall filter. Under the same conditions, the power consumption of the filter varies between 45–63 mW for a biasing voltage of 2.7 V.

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Fig. 12. Typical simulated and measured differential-mode S -parameters (jS j) of the constructed recursive filter prototype for a broader frequency = 40 MHz). range (f = 1:87 GHz, BW

taken into account: the generation of parasitic electromagnetic couplings, not only between the inductors, but also between the transmission-line segments connecting the active blocks making up the recursive filter, and the presence of ground loops. The circuit layout has been designed in order to avoid such effects to occur, thus their impact should be strongly limited. The inaccurate modeling of the transistors at high frequencies might also have an influence on this deviation: unexpected power gain increases (or decreases) at such frequencies can then occur. However, this problem is nearly impossible to demonstrate in our particular case. Finally, note that this prototype has been tested without being embedded in any package. Indeed, this filter is not intended to be used as an isolated chip (in that case, it would be obligatory to first characterize the empty package in order to remove its effect from the measured filter chip response [16], or to take its presence into account during the design of the circuit), but rather to be integrated in a whole transceiver.

Thanks to the presence of the amplifier at the input and of and responses the buffer at the circuit output, the are quasi-independent of the different tuning parameters states. In any case, within the 1.73–2.38-GHz measured tuning range, they are less than 9.5 and 14.5 dB, respectively. This value -parameter can be explained by the fact that, for of the the chosen inductorless adder topology, it is not possible to achieve noise and power matching simultaneously over a wide frequency band [15]. Here, a compromise has thus been made between these two parameters, leading to a noise figure within the 3.7–5.7-dB range depending on the tuning settings. Con-parameter, its magnitude is directly driven by cerning the the values of the buffer cascode collectors resistors. Finally, for completeness, typical simulated and measured differential-mode -parameters of the constructed recursive filter prototype are drawn for a broader frequency range in Fig. 12. This has been done for a tuned center frequency equal to 1.87 GHz and a 3-dB bandwidth of 40 MHz. Here, the following points must be commented upon. • The disagreement seen between the simulated and mea-parameter (upper right portion of Fig. 12) is a sured result of the network analyzer “noise floor,” through which power levels lower than 60 dB can hardly be measured. In any case, the great reverse-isolation performance of the constructed filter is experimentally demonstrated. • A noticeable discrepancy between the simulated and mea-parameter (lower left portion of Fig. 12) can sured be observed in the higher than passband rejected frequencies. Since the electrical stability of the circuit was verified, this might be caused in part by the narrowband models of the inductors used during the design of the recursive filter.1 Regarding this phenomenon, some other effects have to be 1This is a well-known problem for MMIC silicon designers, related with the incorrect handling of S -parameter files in Cadence. Thus, when custom integrated components are designed through an electromagnetic simulator (e.g., Momentum), equivalent-circuit models based on lumped elements must be derived from the computed S -parameter results. In particular, for the recursive filter proposed in this paper, equivalent models made up of nine lumped elements for each of its inductors designed with Momentum have been used. The complexity of these models remains affordable, as the time needed to compute their element values is reasonable.

III. MMIC RECONFIGURABLE THREE-BRANCH CHANNELIZED FILTER Microwave channelized filters were first introduced by Rauscher in 1994 [17]. These filters, based on feedforward signal-interference principles, have a primary importance because they perform highly selective filtering actions obtained from the transversal combination of low-order responses. Indeed, in bandpass-filtering cases, transfer functions with sharp cutoff slopes and deep-rejection stopbands can be achieved through the generation of out-of-band transmission zeros. Several design solutions for channelized filters in hybrid technology have been proposed in the past using a reduced number of branches, two [18], [19] or even three [20]–[23], for high-pass, low-pass, bandpass, and notch-rejection applications. When three channels are used, a higher selectivity can be obtained, but at the expense of increasing the design complexity. The block diagram of a classic three-branch channelized bandpass filter in hybrid technology is detailed in Fig. 13. Its operating principle is also shown. As can be seen, the overall filter consists of a power divider and combiner at the input and output ports, and three branches shaped by the cascade connection of an amplifier, a passive filter, and a delay element. Here, note that a distinction is made between one channel, called “the main channel,” and the other two, called “the auxiliary channels.” In each branch, the passive filter provides the required low-order filtering profile and the amplifier gives power transmission gain, reverse isolation, and inter-stage matching. The delay element, usually built with a transmission line, achieves suitable phase conditions leading to destructive interferences of the output signals at the passband edges and in-band signal enhancements. The power divider and combiner splits or recombines the signals going to or issuing from the three channels. One of the main drawbacks of the three-branch channelized filter implemented in hybrid technology is its high sensitivity to undesired deviations in the partial responses of the branches. Also, since the inter-channel phase conditions are achieved

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Fig. 14. Block diagram of the proposed MMIC three-branch channelized bandpass filter.

assured. The output recombination is carried out through a direct reconnection of the channels outputs. Moreover, in each channel, the set shaped by the low-order passive filter and the amplifier (hybrid solution) has been replaced by an elementary tunable first-order recursive stage. From Fig. 14, it is obvious that the transfer function of the is as follows: MMIC three-branch channelized filter

Fig. 13. Three-branch channelized bandpass filter in hybrid technology. (a) Classic block diagram. (b) Operating principle.

through linear frequency-dependent transmission-line segments, destructive signal interferences cannot be preserved throughout the entire attenuated bands. Hence, as a consequence, the out-of-band rejection levels are not maximized. The aforementioned difficulties make the three-branch channelized arrangement more suitable for integration, where the channel responses can easily be adjusted through tuning elements. This avoids any sensitivity problem, adding the reconfigurability of the transfer function as a new feature. Moreover, as proven below, constant phase differences between signals can be generated on MMICs. Thus, filtering responses with optimum out-of-band rejection levels become feasible A. Silicon Integration When silicon integration is addressed, two major issues must be solved, which are: 1) the low quality factor of the passive components and 2) the impossibility of using distributed elements, such as planar power couplers and filters or transmission-line-based delay networks. Therefore, the structure shown in Fig. 13 is not suitable for a MMIC design. As a consequence, alternative efficient solutions compatible with integration must be suggested here for all the functional blocks making up the channelized filter. The block diagram of the proposed MMIC three-branch channelized bandpass filter topology is detailed in Fig. 14. As can be seen, the input division is achieved by means of an active power divider, also providing the required constant phase differences between the filter branches. Thus, the achievement of filtering responses with maximally attenuated stopbands is

(4) where , , , , , , and , , are the design parameters of the recursive filter stages inserted in the main channel, lower auxiliary channel, and upper auxiliary channel, , , and denote the firstrespectively ( order recursive transfer functions of these branches). Obviously, to assure the electrical stability of the channelized filter, the , , and should be fulfilled. The requisite coefficient represents the loss of the signal-division process. and are the constant phase differences generated by the active divider between the auxiliary channels and the main , channel. Note that, for a suitable operation, the condition must be met. A deeper insight into the different blocks making up the MMIC channelized filter is provided below. 1) Active Power Divider: The circuit scheme for the divider is derived from a typical cascode low-noise amplifier (LNA) design (Fig. 15) [12], where the common-base stage has been doubled to provide four different outputs. When one of these outputs is left unused, three signals of equal amplitude are achieved, two of them being 180 -phase-shifted relative to the third one. The power transmission gains of the divider obtained at each output for differential- and common-mode input signals are plotted in Fig. 16. These results have been obtained by using the mixed-mode -parameter formalism, particularized for the case of a device with one differential port (written as “1” in Fig. 15) and three single-ended ports (designated as “2,”

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Fig. 17. Phase differences between the differential-mode power transmission parameters of the divider outputs “3” and “4” and the divider output “2” (left), and phase imbalance between the divider outputs “3” and “4” (right).

Fig. 15. Electrical scheme of the proposed active divider.

Fig. 18. Functional block diagram of the proposed recursive cell.

Fig. 16. Mixed-mode power transmission gains of the active divider at each output for: (left) differential and (right) common-mode input signals.

“3,” and “4”, the port “2” corresponding to the main channel output and the others to the auxiliary channel outputs). The method used to compute these parameters is very similar to the generalized mixed-mode -parameter approach reported in and refer to the gains obtained [24]. In Fig. 16, , as between the differential input and the single output “2” and common-mode shown in Fig. 15, for differential input signals. In the same way, and ( and ) denote, respectively, the gains at the outputs “3” and “4” for a differential-mode (common-mode) input signal. As can be seen in Fig. 16, for a differential-mode input signal, the gains at the single outputs “3” and “4” are equal, and only 0.3 dB higher than the gain at the single output “2.” This small discrepancy is a result of the imperfect circuit symmetry of the divider, caused by the different impedance values loading the unused cascode branch (open circuit) and the single outputs “2,” “3,” and “4” (50 ). However, this is not a critical issue since it can be easily compensated in the low-order filters of the channels by setting the gain levels of the recursive cells appropriately. On the other hand, the common-mode gain is less than 15 dB for all the outputs. This high common-mode rejection is a mandatory feature of the divider for a correct channelized filter operation since it ensures the achievement of the required phase opposition between the signals to be inserted in the filter branches.

Finally, Fig. 17 draws the phase differences between the differential-mode power transmission parameters associated to the divider outputs “3” and “4” and the divider output “2.” As expected, a nearly perfect phase opposition between the divider outputs of the auxiliary channels and that of the main channel is obtained (see left portion of Fig. 17). Here, note also the slight deviation with regard to the 180 exact value (less than 0.5 within the 1–3-GHz band) caused by the aforementioned divider circuit asymmetry. Nevertheless, as proven in the right portion of Fig. 17, a perfect phase balance between the outputs of the two auxiliary channels is achieved. 2) First-Order Recursive Cells: The chosen topology for the first-order recursive stages to be inserted in filter channels is derived from the recursive arrangements described in Section II. As detailed in Fig. 18, it consists of an active adder, a passive delay cell, and an output buffer. Compared to the previously presented recursive topology, the buffer output is matched here to a 150- impedance to ensure the standard 50- output matching for the overall filter. Moreover, one of the inputs of the adder cascode amplifier has been connected to ground in order to provide a single-ended input (see Fig. 18). 3) Channelized Filter: The layout of the designed filter is drawn in Fig. 19. Its dimensions are 2.03 1.40 mm , but the upper right-hand quarter of the chip is not used. Thus, the effective surface required to design the circuit is 2.15 mm . B. Simulation Results The results obtained in the simulation of the designed channelized filter prototype are described below. As demonstrated here, thanks to the different adjustment points of the first-order recursive filters placed in the overall filter channels, a large variety of bandpass filtering profiles can be obtained.

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TABLE I DESIGN PARAMETER VALUES FOR THE THEORETICAL FILTERING RESPONSES

Fig. 19. Three-branch channelized filter layout.

Fig. 20. Simulated and theoretical differential-mode (jS j) power transmission response of the designed channelized filter prototype and single branches (two transmission zeros).

Fig. 20 shows a simulated bandpass differential-mode power transmission response of the designed channelized filter prototype with two transmission zeros, together with those of the single branches. The theoretical responses associated with the overall filter and the unitary channels, as described in (4), are also provided for comparison. The design parameter values for these theoretical responses are summarized in Table I, and have been computed as detailed in the Appendix. For this example, the maximum overall differential-mode power transmission gain is 13.2 dB, and the 3-dB bandwidth is 85 MHz. The out-of-band rejection level is higher than 28 dB for frequencies whose separation from the 1.97-GHz center frequency is more than 100 MHz. For illustration, Fig. 21 compares the theoretical differential-mode power transmission responses, for this example, corresponding to the MMIC solution [constant phase differences between channels (Fig. 14)] and a computed ideal channelized filter in hybrid technology [linear frequency-dependent phase differences between channels (Fig. 13)]. As previously pointed out and proven here, the MMIC topology leads to those filtering responses with higher out-of-band rejection levels. Moreover, as the recursive filters embodied in the branches are frequency tunable, the overall response can also be tuned within the 1.95–2.23-GHz band. This is shown in Fig. 22. Filtering profiles with one transmission zero and, thus, with different selectivity for each rejected band, are also feasible through the designed channelized filter prototype. This is

Fig. 21. Theoretical differential-mode (jS j) power transmission response of the channelized filter with constant phase differences [MMIC solution (Fig. 14)] and linear frequency-dependant phase differences [hybrid solution (Fig. 13)].

demonstrated in Fig. 23. Note that this feature makes this filter very useful for the design of the transmit/receive diplexers directed to base stations and mobile communications systems, where the filter specifications tends to be asymmetric. In this case, only one transmission zero is generated, whereas the second auxiliary channel is used for improving the filter in-band flatness. Furthermore, as a goal towards the multifunctionality pointed out by recent studies [25], [26], this transmission zero can be shifted as desired, below [see Fig. 23(a)] or above [see Fig. 23(b)] the main passband, by acting on the filter tuning points. This feature leads to a fully reconfigurable transfer function throughout the 1.95–2.23-GHz tuning range. As can be seen in Fig. 24, a third shape of filter response, exhibiting a dual-bandpass behavior, can also be obtained. Here,

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Fig. 22. Simulated center-frequency tunability of the designed channelized filter prototype (two transmission zeros).

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j) power transFig. 24. Simulated and theoretical differential-mode (jS mission response of the designed channelized filter prototype (dual-bandpass behavior).

For all the depicted transfer functions, the input power matching is better than 10 dB up to 2.1 GHz, and the output power matching is higher than 15 dB up to more than 2.5 GHz. The power consumption of the whole circuit is always less than 28 mA for a voltage supply of 2.7 V. The common-mode is less than 18 dB, and all power transmission gain the mode conversion parameters are below 20 dB, except that corresponding to the common-to-differential mode conversion (between 5–10 dB, depending on the channel’s recursive cell gain). This behavior is caused by the use of single-ended connections between the divider outputs and the recursive stage inputs. Here, a fully differential design could allow this figure-of-merit to be reduced to very small values if required. C. Sensitivity Analysis

Fig. 23. Simulated and theoretical differential-mode (jS j) power transmission response of the designed channelized filter prototype (one transmission zero). (a) Response with a lower-than-passband transmission zero. (b) Response with a higher-than-passband transmission zero.

a single transmission zero is generated between the two passbands in order to produce a high inter-band rejection level. In this example, the transmission zero is located at 2.013 GHz, the lower and upper passbands are centered at 1.93 and 2.10 GHz, and the 3-dB bandwidths are equal to 24 and 22 MHz, respectively. The maximum differential-mode power transmission gains of the two resonant frequencies have been fine tuned to make them equal at 19 dB. Furthermore, it should be highlighted that the inter-band transmission zero can also be shifted by acting on the filter settings. This leads, as an advantage with regard to most research dealing with dual-band filter design [27], [28], to a full control of the two resonant frequencies and their associated amplitudes and bandwidths as well.

Sensitivity in channelized filters to mismatch,2 process3 and temperature variations is a critical issue, more still for MMIC designs. Indeed, a suitable channelized filter operation needs highly precise amplitude and phase relations between the transfer functions of their branches. Thus, if these relations are not met, destructive and constructive signal-interferences could not be generated, hence, distorting the overall filter response. In the case of differential circuits, mismatch becomes a major problem since branches are differently affected by it. Specifically, for the channelized filter reported here, the input divider is the most sensitive element related to this issue, as it sets the required constant phase differences between channels. The mismatch effect on the phase differences between the differential-mode power transmission parameters associated to the divider outputs of the auxiliary channels (ports “3” and “4” in Fig. 15) and the main channel (port “2”), for a 50-run simulation, 2Mismatch refers to different causes (e.g., fluctuations in dimensions, doping, and oxide thickness) leading to component-to-component variations in the same circuit [29], [30]. 3Process variations are batch-to-batch variations, making circuits (that are affected as a whole) issued from two different wafers to exhibit different performances [29], [30].

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Fig. 25. Mismatch effect on the phase differences between the differentialmode power transmission parameters of the divider outputs of the auxiliary channels (ports “3” and “4” in Fig. 15) and the main channel (port “2”).

Fig. 26. Mismatch effect on the phase imbalance between the divider outputs of the auxiliary channels (ports “3” and “4” in Fig. 15).

Fig. 27. Monte Carlo analysis for the differential-mode (jS j) and common-mode (jS j) power transmission responses of the designed channelized filter prototype.

is represented in Fig. 25. For these curves, the phase imbalances between the divider outputs of the auxiliary channels are shown in Fig. 26. As mentioned above and proven here, the mismatch influence differs from one branch to the others. Note also that, in any case, the phase imbalance between the divider outputs of the auxiliary channels is lower than 0.4 . This deviation is small enough to hardly distort the channelized filter behavior. Moreover, in practice, some rules can be used to minimize the mismatch between critical elements, such as positioning the components to be matched as close as possible (e.g., transistors of the differential pairs), and use of particular placement patterns of these components (e.g., “interleaving,” “common-centroid,” and “rotational-symmetry” layout procedures) [29], [30]. On the other hand, as process variations affect the whole circuit in an identical way, it is not possible to reduce their influence by means of specific layout techniques. In Fig. 27, the effects of these variations on the differential- and common-mode power transmission gains of the channelized filter, through a 50-run Monte Carlo simulation, are presented. As can be seen, the common-mode gain is not significantly affected, as its value is always lower than 15 dB. On the other hand, the differential-mode gain, which benefits from

the interferences between channels, is strongly dependent on the process: in most cases, the resulting response is worse than the designed ideal one (in certain situations, the circuit can even become unstable). However, this is not an unaffordable problem since the independent tuning capabilities of the branches making up the channelized filter (in center frequency, bandwidth, and gain) allow not only a fully reconfigurable transfer function to be achieved, but also to compensate the unpredictable effects caused by these process variations. Furthermore, this can easily be done by combining the channelized filter with an automatic control system [31], thus ensuring the intended overall filter performances independently of the nonideal factors affecting the circuit. Finally, the last possible source of variations to be taken into account is the temperature dependency of every electrical component of the filter, whether it be passive or active. Here, the best solution is to use robust biasing circuitry like bandgap voltage references and proportional-to-absolute temperature (PTAT) current sources [12]. Although they have not been used in this study to limit the circuit complexity, for a mass-production-oriented commercial design, they would be mandatory to achieve a temperature-independent filter chip. In Section IV, a method to determine the exact noise figure value, applicable to the two previously reported differential filters, is described. To date, the noise figure of differential circuits has been simulated using baluns. Here, it will be demonstrated that this can lead to significant errors when conversion-mode gains are not negligible, which is the case of the channelized filter developed in this study. IV. EXACT NOISE FIGURE COMPUTATION FOR DIFFERENTIAL CIRCUITS According to the IEEE definition, the noise figure of a twoport network at a given frequency is the ratio of the overall output noise power per bandwidth unit to the portion of that output noise power caused by the input noise, where the input K . Equivalently, it is noise power is given by “one” plus the ratio of the output noise caused by the two-port network to the output noise originated from the input noise. However, no IEEE definition for the noise figure of multiport networks, presenting more than one output nodes, has been provided. In the case of differential amplifiers, two physical output ports must be considered. This means two kinds of output corresponding to the different operating modes of the amplifier to be taken into account: the differential-mode output and the common-mode output. Consequently, two noise figures can be defined, one for each mode. To simplify the analysis, and as a logic assumption for well-designed differential circuits, the common mode will be considered to be highly rejected. Hence, the derivation of the differential-mode noise figure must only be approached. In [32], a methodology to generalize the noise-wave formalism to devices exhibiting more than one output port was proposed. From this study, the definitions of the aforementioned noise figures for differential devices can be established. Specifically, the differential-mode noise figure is defined here as the ratio of the overall output noise power in the differential mode to the portion of that noise power caused by the input noise in

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Fig. 28. Noise-wave formalism of a four-port circuit. Fig. 29. Differential network with matched sources.

both the differential and common modes. In other words, it is “one” plus the ratio of the output noise in the differential mode coming from the device to the output noise in the differential mode resulting from the input noise. In Section IV-A, the mixed-mode formulation is applied to the noise-wave formalism [33] to derive an analytical expression for the exact differential-mode noise figure of a differential network. Furthermore, it is proven that this true noise figure can be extracted directly from the simulated differential noise figure calculated via the classic “balun method.” The obtained results are also applied to the computation of the exact differential noise figures of the previously reported recursive and three-branch channelized filter prototypes.

available 1-Hz bandwidth noise power at the input and output ports. The off-diagonal terms correspond to the correlation products

(6)

The differential-mode noise figure of the four-port network can be defined as follows: (Fig. 28) (7)

A. Exact Differential Noise Figure In order to obtain an equation representing the exact differential-mode noise figure of a differential network, the noise-wave formalism must be applied together with the mixed-mode -parameter formulation. For differential circuits, the noise-wave formalism consists of modeling the noise of a four-port device with appropriate , , , and internal noise-wave generators, referred to as in Fig. 28. , and , are, respectively, the differentialHere, and common-mode noise waves at the input and output differential and common ports. Moreover, these noise waves are assumed to be time-varying complex-correlated random variables characterizable through an Hermitian matrix. The contribution of the aforementioned noise waves to the reflected differential- and common-mode signal waves at the , and , in Fig. 28, corresponding ports, designed as respectively, can be expressed as follows:

is the differential noise power at the output of the where denotes differential device coming from the generator, and the differential noise power at the output of the differential device caused by the device itself. and using the noise-wave formalism, To calculate the differential network is assumed to be embedded within matched sources, as shown in Fig. 29. The incident noise waves are also assumed to be uncorrelated in this scheme [32]. This implies that the incident differand the incident common-mode ential-mode noise wave noise wave are uncorrelated as well. Furthermore, it can be proven that the noise powers applied to the differential- and common-mode ports become equal, i.e., (8) Under these conditions, the noise correlation matrix of the can be evaluated. Specifically, overall network (Fig. 29) by using Wedge’s embedding method [33] in the mixed-mode formalism, the following is derived:

(5)

where is the differential-mode two-port -parameter matrix, is the two-port common-mode -parameter matrix, , are the two-port -parameter matrixes representing , and , denote conversion between modes, and incident differential- and common-mode signal waves. The noise correlation matrix of the differential network is then given by (6), where the diagonal terms represent the

(9) Here, the following results must be commented upon.

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Fig. 30. Differential network embedded between two baluns.

Fig. 31. Passive subcircuit.

• The differential noise power at the output of the differential device caused by itself is driven by the noise correlation matrix of the aforementioned device, i.e., (10)

The overall two-port network made up of the differential circuit itself and the two baluns is then connected to its 50- source impedance. Thus, the classic two-port method can be used to derive the formula for the noise figure of the differential network calculated via the “balun method”

• The first term of the noise correlation matrix , represents the overall differential-mode noise power at the output as follows:

(14) In most cases, under device-matching conditions, the conversion term is highly rejected and, therefore, its contribution can be ignored. Hence, (14) becomes

(11) Thus, by introducing (10) and (11) in (7), the following formula for the exact differential-mode noise figure is derived:

(12) As can be seen, the exact differential-mode noise figure depends not only on the differential-mode noise, but also on the common-mode noise via the common-to-differential mode-con. Note that this expression can only be evalversion gain uated from the corresponding mixed-mode -parameters and signal and noise waves computed via simulation or measurement procedures. In the following step, it is shown how the exact differentialmode noise figure can be obtained directly from the simulated noise figure computed via the classic “two-port balun-method.” B. Simulated Noise Figure With the “Balun Method” It is well known that the only way to simulate the noise figure of a differential network properly is the “two-port balun-method.” As can be seen in Fig. 30, it consists of embedding the differential network under test between two baluns. In this figure, ideal baluns such as those found in most parts of CAD tools have been considered. They are described by the : following mixed-mode -parameter matrix

(13)

To evaluate the noise figure of the network detailed in Fig. 30, the latter is first divided into two subcircuits: an active subcircuit (the differential device itself) and a passive subcircuit shaped by the two baluns, as shown in Fig. 31.

(15) By assuming that corresponds to the noise power ), the coming from the source impedance (i.e., exact differential-mode noise figure of the network [ (12)] can be expressed in terms of the simulated one [ (15)] as follows: (16) Note that this expression provides an efficient solution to compute the exact differential-mode noise figure of a differential network straightforwardly from that simulated via the “two-port balun-method.” Furthermore, it proves that the accuracy of the “balun-simulated” noise figure value depends . on the common-to-differential mode conversion gain C. Application Examples The previous results are applied here to compute the exact differential-mode noise figure of the MMIC active filters described in Sections II and III. The recursive filter is first considered. Fig. 32 plots the simulated and measured differential and common-to-differential mode-conversion power transmission responses of the constructed recursive filter. As can be seen in Fig. 32, the mode conversion of the recursive filter is highly rejected. Thus, the “balun-simulated” noise figure will be in very close agreement with the exact differential noise figure. This is shown in Fig. 33, demonstrating that, in this case, the classic simulation method using baluns gives an accurate representation of the differential noise figure. Subsequently, the three-branch channelized filter is addressed. As explained in Section III, the chosen nonfully

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Fig. 32. Simulated and measured differential (jS j) and common-to-differj) power transmission response of the recursive ential mode-conversion (jS filter.

j) and common-to-differential mode Fig. 34. Simulated differential (jS conversion (jS j) power transmission response of the channelized filter.

Fig. 33. Exact and two-port simulated (“balun method”) differential noise figure of the recursive filter.

differential arrangement to implement the filter (connections between the active divider outputs and the first-order recursive filters inputs of branches are of the single type) leads to a mode conversion, which gain cannot be neglected compared to the differential mode gain (Fig. 34). Moreover, as the result of the large number of active elements needed in the design, this filter was mainly optimized in terms of power consumption at the expense of not maximizing the mode-conversion rejection. The “balun-simulated” and the exact differential-mode noise figure curves for the channelized filter are shown in Fig. 35. As expected, in this case, the “balun-simulated” noise figure is not accurate. This is a result of the great influence of the channelized filter mode-conversion gain on the noise figure formulas given by (12) and (15). Specifically, the error between the exact noise figure and that obtained via the “balun-method” is approximately 8% at the center frequency and 12%–17% at the upper and the lower edges of the filter passband, respectively.

Fig. 35. Exact and two-port simulated (“balun method”) differential noise figure of the channelized filter.

V. CONCLUSION In this paper, a novel integrated microwave two-stage recursive bandpass filter has been first proposed. This is a very flexible circuit, independently tunable in terms of center frequency, bandwidth, and power transmission gain. To validate this recursive filter topology experimentally, measurements and simulations results of a 2-GHz prototype constructed in silicon technology have also been provided. Subsequently, a MMIC reconfigurable three-branch channelized bandpass filter has been presented. It is based on an original active divider arrangement, and three channels based on elementary stages of the previously reported recursive filter structure. Moreover, theoretical and simulated results have been given to demonstrate the reconfigurability potentiality of this filter: frequency-tunable responses exhibiting one or two transmission zeros with a single or dual-bandpass behavior can be achieved. Finally, an original methodology to extract the exact noise figure of differential devices has been described. This method has been applied to the

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Step 2) The values for the constant phase differences beare comtween auxiliary and main channels puted by forcing the generation of a transmission in the theoretical zero at the frequency value overall transfer function. This is done through the following two steps: Step a)Computation of the frequency value , as a solution to the following equation: (20) Fig. 36. First-order recursive filtering response.

two integrated filter prototypes developed in this study. The obtained results have been satisfactory, also proving the inaccuracy on the classic “two-port balun method” for computing the noise figure of differential circuits with nonnegligible mode-conversion gain. Here, it should be pointed out that this noise analysis only deals with the simulation of the exact differential-mode noise figure for differential networks. The measurement technique to retrieve this true noise figure, which cannot be carried out directly with currently available noise-test equipment, is an ongoing research topic.

Note that, for bandpass filtering profiles with two transmission zeros (Fig. 20), two solutions can be obtained from (20). Specifically, in Table I, the solution corresponding to the lower transmission zero was chosen. Step b)Application of the following relationships: (21) (22) where is the phase of a complex number. Step 3) The value for the loss factor of the signal-division is calculated as process

APPENDIX This appendix describes how the values for the theoretical design parameters of the channelized filter and branches, as detailed in (4), can be derived from their simulated responses. , , , and will Here, refer, respectively, to the simulated transfer functions of the channelized filter, main, lower, and upper auxiliary channels. The procedure, programmed in MATLAB, consists of the following steps. Step 1) The values for the design parameters of the firstare oborder recursive filters of branches tained from the center frequency , -dB relative , and maximum power transmisbandwidth of their simsion gain ulated transfer functions as follows (Fig. 36): (17)

(18) (19) . Obviously, a better where value in-band reconstruction is achieved as a closer to one is selected. In particular, in Table I, relative bandwidths referred to 3-dB have been used.

(23) where

is the maximum-value function.

ACKNOWLEDGMENT The authors would like to thank the Innovation Center RF, Philips Semiconductors, Caen, France, for their assistance in the construction of the recursive filter prototype. REFERENCES [1] I. C. Hunter, L. Billonnet, B. Jarry, and P. Guillon, “Microwave filters—Applications and technology,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 794–805, Mar. 2002. [2] L. Billonnet, B. Jarry, S. E. Sussman-Fort, E. Rius, G. Tanné, C. Person, and S. Toutain, “Recent advances in microwave active filter design. Part I and II,” Int. J. RF Microw. Comput.-Aided Design Eng., pp. 159–189, Mar. 2002. [3] D. Szmyd, R. Brock, N. Bell, S. Harker, G. Patrizi, J. Fraser, and R. Dondero, “QUBIC4: A silicon RF-BiCMOS technology for wireless communication ICs,” in Proc. Bipolar/BiCMOS Circuits and Technol. Meeting, Dec. 5–9, 2001, pp. 60–63. [4] C. Rauscher, “Microwave active filter based on transversal and recursive principles,” IEEE Trans. Microw. Theory Tech., vol. MTT-33, no. 12, pp. 1350–1360, Dec. 1985. [5] W. Mouzannar, L. Billonnet, B. Jarry, and P. Guillon, “A new design concept for wideband frequency-tunable and high-order MMIC microwave active recursive filters,” Microw. Opt. Technol. Lett., vol. 24, no. 6, pp. 380–385, Mar. 2000. [6] S. Andersson, P. Caputa, and C. Svensson, “A tuned, inductorless, recursive filter LNA in CMOS,” in Proc. ESSCIRC Conf., Florence, Italy, Sep. 24–26, 2002, pp. 351–354.

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[7] S. Darfeuille, B. Barelaud, L. Billonnet, B. Jarry, H. Marie, A. de la Torre, N. T. Luan Le, and P. Gamand, “A differential-based singleended 2 GHz low-noise recursive filter on silicon,” in 34th Eur. Microw. Conf., Amsterdam, The Netherlands, Oct. 11–15, 2004, pp. 49–52. [8] M. Delmond, L. Billonnet, B. Jarry, and P. Guillon, “High-order monolithic active recursive filter based upon multicellular approach,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 17–21, 1996, pp. 623–626. [9] A. W. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1999. [10] S. Darfeuille, R. Gómez-García, J. Lintignat, Z. Sassi, B. Barelaud, L. Billonnet, B. Jarry, H. Marie, and P. Gamand, “Silicon-integrated 2-GHz fully differential tunable recursive filter for MMIC three-branch channelized bandpass filter design,” presented at the IEEE MTT-S Int. Microw. Symp., San Francisco, CA, 2006. [11] R. Tao and M. Berroth, “Monolithically integrated 5 Gb/s CMOS duobinary transmitter for optical communication systems,” in IEEE Radio Freq. Integrated Circuits Symp., Fort Worth, TX, Jun. 6–8, 2004, pp. 21–24. [12] P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits. New York: Wiley, 1993. [13] D. Bockelman and W. Eisenstadt, “Combined differential and common-mode scattering parameters: Theory and simulation,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 7, pp. 1530–1539, Jul. 1995. [14] Agilent Technol., Palo Alto, CA, “ENA 2, 3 and 4 port RF network analysers data sheet,” 2005. [Online]. Available: http://cp.literature.agilent.com/litweb/pdf/5988-3780EN.pdf [15] T. K. Nguyen, C. H. Kim, G. J. Ihm, M. S. Yang, and S. G. Lee, “CMOS low-noise amplifier design optimization techniques,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 1433–1441, May 2004. [16] Y. L. Chow, G. E. Howard, and M. G. Stubbs, “On the interaction of the MMIC and its packaging,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 8, pp. 1716–1719, Aug. 1992. [17] C. Rauscher, “A new class of microwave active filters,” in IEEE MTT-S Int. Microw. Symp. Dig., May 1994, pp. 605–608. [18] ——, “Two-branch microwave channelized active bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 3, pp. 437–444, Mar. 2000. [19] R. Gómez-García, J. I. Alonso, and C. Briso-Rodríguez, “On the design of high-linear and low-noise two-branch channelized active bandpass filters,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 50, no. 10, pp. 695–704, Oct. 2003. [20] C. Rauscher, “Microwave channelized active filters—A new modular approach to achieving compactness and high selectivity,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 1, pp. 122–132, Jan. 1996. [21] B. Kapilevich, “Understand the operation of channelized active filters,” Microw. RF, pp. 89–92, Jan. 1997. [22] C. Rauscher, “Varactor-tuned active notch filter with low passband noise and signal distortion,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 8, pp. 1431–1437, Aug. 2001. [23] R. Gómez-García and J. Alonso, “A design technique for three branch channelized bandpass filters,” in 33rd Eur. Microw. Conf., Munich, Germany, Oct. 7–9, 2003, pp. 215–218. [24] A. Ferrero and M. Pirola, “Generalized mixed-mode S -parameters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 458–463, Jan. 2006. [25] W. M. Fathelbab and M. B. Steer, “A reconfigurable bandpass filter for RF/microwave multifunctional systems,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1111–1116, Mar. 2005. [26] H. Zhang and K. J. Chen, “A microstrip bandpass filter with an electronically reconfigurable transmission zero,” presented at the 36th Eur. Microw. Conf., Manchester, U.K., Sep. 10–15, 2006. [27] L. C. Tsai and C. W. Hsue, “Dual-band bandpass filters using equallength coupled-serial-shunted lines and Z -transform technique,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1111–1117, Apr. 2004. [28] K. C. Lin, C. F. Chang, M. C. Wu, and S. J. Chung, “Dual-bandpass filters with serial configuration using LTCC technology,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2321–2328, Jun. 2006. [29] M. Dessouky and M. M. Louerat, “A layout approach for electrical and physical design integration of high-performance analog circuits,” in 1st Int. Quality Electron. Design Symp., 2000, pp. 291–298. [30] A. Hastings, The Art of Analog Layout, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2002. [31] E. Neber, S. Quintanel, L. Billonnet, B. Jarry, and M. H. W. Hoffmann, “Analysis of an automatically tuned filter and its application at microwave frequencies,” in 33rd Eur. Microw. Conf., Munich, Germany, Oct. 7–9, 2003, vol. 3, pp. 915–918.

[32] J. Randa, “Noise characterization of multiport amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 10, pp. 1757–1763, Oct. 2001. [33] S. Wedge and D. Rutledge, “Wave techniques for noise modeling and measurement,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 11, pp. 2004–2012, Nov. 1992.

Sébastien Darfeuille was born in Limoges, France, in 1979. He received the Master and Ph.D. degrees in high-frequencies and optical telecommunications from the University of Limoges, Limoges, France, in 2002 and 2006, respectively. During his doctoral studies, he was with the XLIM Research Institute [formerly the Institut de Recherche en Communications Optiques et Microondes (IRCOM)], where he was with the C2S2 Department involved with the integration of original topologies of active filters on silicon. In 2006, he joined Philips Semiconductors (now NXP), Caen, France, where he is currently an RF Designer involved in the design of low-power functions for automotive applications.

Julien Lintignat was born in Saint Maurice, France, on July 3, 1979. He received the Master degree in high-frequencies and optical telecommunications from the University of Limoges, Limoges, France, in 2003, and is currently working towards the Ph.D. degree at the XLIM Research Institute, University of Limoges. He is currently with the C2S2 Department, XLIM Research Institute, University of Limoges. His research interests are the analysis, design, development, and measurement of RF and microwave differential devices, circuits, and systems.

Roberto Gómez-García (S’02–M’06) was born in Madrid, Spain, in 1977. He received the Telecommunication Engineer and Ph.D. degrees from the Polytechnic University of Madrid, Madrid, Spain, in 2001 and 2006, respectively. His Telecommunication Engineer thesis concerned the design of microwave channelized active bandpass filters. His doctoral dissertation concerned the analysis, design, and development of high-selective and tunable microwave bandpass filters based on signal-interference techniques. During Fall 2004, he was with the C2S2 Department, XLIM Research Institute (formerly IRCOM), University of Limoges, Limoges, France. Since April 2006, he has been an Associate Professor with the Department of Signal Theory and Communications, University of Alcalá, Alcalá de Henares, Madrid, Spain. His current research interests are the pursuit of new concepts to design both fixed and tunable advanced high-frequency filters. He is a reviewer for Electronic Letters in the field of microwave filters. Dr. Gómez-García is a reviewer for the IEEE MICROWAVE AND WIRELESS LETTERS.

Zoheir Sassi received the Engineer in Electronics degree from the INELEC Institute, Boumerdes, Algeria, in 1999, the Master degree in high-frequencies and optical telecommunications from the University of Limoges, Limoges, France, in 2002, and is currently working toward the Ph.D. degree at the XLIM Research Institute, University of Limoges. He is currently with the C2S2 Department, XLIM Research Institute, University of Limoges, in collaboration with the Innovation Center RF of Philips Semiconductors (now NXP), Caen, France. His research interests are the design of CMOS and BiCMOS analog active filter topologies for new generation mobile-communications standards.

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Bruno Barelaud received the Ph.D. degree from the University of Limoges, Limoges, France, in 1989. He is currently an Associate Professor with the XLIM Research Institute, University of Limoges. His main field of interest is low-noise active microwave and RF functions. He is currently involved in the study of new methods for low-noise microwave amplifier and active filter design, frequency-control techniques, and low-noise integrated differential circuits. His research also focuses on modeling of injection and susceptibility of electronic functions and simulation of their interactions in RF and mixed-signal ICs.

Laurent Billonnet received the Ph.D. degree from the University of Limoges, Limoges, France, in 1993. He is currently an Associate Professor with the XLIM Research Institute, University of Limoges. His main field of interest is low-noise active microwave functions. He is currently involved in the study of novel techniques for low-noise microwave amplifier design, low-noise active filter design, frequency-control techniques, and low-noise integrated differential circuits. His research also focuses on new analysis, design, and measurement methods for differential devices, circuits, and systems.

Bernard Jarry (M’93–SM’97) received the Ph.D. and HDR degrees from the University of Limoges, Limoges, France, in 1985 and 1994, respectively. In 1986, he joined Thomsom-CSF, Orsay, France. Since 1987, he has been with the XLIM Research Institute, Unité Mixte de Recherche (UMR), Centre National de la Recherche Scientifique (CNRS) 6172, University of Limoges, where he is currently a Full Professor. His main field of interest are low-noise RF and microwave MMICs, including single-ended and differential LNA design and characterization, active filter design, and frequency-control techniques.

Hervé Marie received the Electrical Engineer degree from Ecole Nationale Supérieure d’Ingénieurs (ENSI) Caen, Caen, France, in 1988. In 1988, he joined Philips Semiconductors, Caen, France, where he designed analog-to-digital converters. From 1990 to 1994, he was with Ion Beam Applications (IBA), Louvain-la-Neuve, Belgium, where he designed particle accelerators for medical/industrial applications. In 1994, he rejoined Philips Semiconductors (now NXP), where he developed mixed-signals circuits such as video modulators. He curfilters, high-speed front-ends, and continuous-time rently designs multimode transmitters and frequency synthesizers for wireless applications. He also teaches IC design at ENSI Caen. He holds 14 patents.

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Patrice Gamand (SM’06) was born in France, in March 1959. He received the Ph.D. degree in microelectronics from the University of Lille, Lille, France, in 1984. In 1984, he joined Philips Research Laboratories, where he was involved with microwave and millimeter waves ICs. In 1993, he joined Philips Semiconductors (now NXP), Caen, France, to develop read/write amplifiers for hard disk drives (HDDs). In 1998, he became involved with telecommunication activity by managing the cellular RF application-specific integrated circuit (ASIC) development. In 2001, he joined the Competence Centre RF, Philips Semiconductor, as Development Services Manager then as Technology Manager. Since 2006, he became the General Manager of the RF Innovation Center, Philips Semiconductor. He has authored or coauthored over 20 technical papers. He holds over 20 patents.

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Full-Wave Analysis of Inhomogeneous Deep-Trench Isolation Patterning for Substrate Coupling Reduction and Q-Factor Improvement Sidina Wane, Member, IEEE, and Damienne Bajon, Member, IEEE

Abstract—Full-wave analysis of deep-trench isolation patterning (DTP) is presented for substrate coupling reduction and -factor improvement. Effects of the buried layer (BL) doping level and grounding mechanisms on substrate coupling are analyzed. Influences of induced depletion regions on substrate coupling are investigated. -factor improvement of on-chip RF inductors resulting from the interruption of BLs and part of the lossy substrate by DTP to limit electric and magnetic energy dissipation is studied. The combination of DTP with topological optimization demonstrates high -factor enhancement. Distributed capacitances and resistances resulting from the BL and substrate grating are evaluated. Coupling between inductors and limits of representations by lumped-element equivalent circuits to account for distributed effects are discussed. Comparison of obtained results with two-and-one-half- and three-dimensional-based commercial electromagnetic tools and with measurement data for reference structures are presented. Index Terms—Deep-trench isolation patterning (DTP), depletion regions, eddy current, floating ground plane, local and global ground reference, factor, RF inductors, seal ring, substrate coupling, transverse wave formulation (TWF).

I. INTRODUCTION

M

AJOR limitations of silicon-based RF integrated circuits to meet the high-performance requirements of present and next-generation communication systems principally concern parasitic couplings between sensitive function blocks and the low factor achievable for on-chip spiral inductors and transmission line interconnects. In order to reduce electromagnetic (EM) parasitic couplings and improve the factor of on-chip spiral inductors, different methodologies classified in [1] into three categories have been proposed and investigated in recent research. These three categories are, respectively, related to the optimization of inductor intrinsic parameters (thick metal interconnects [2]–[5]), architecture-based techniques (differentially driven inductors [6], [7]), and substrate stack-modification-based techniques (proton implants [8], patterned ground shields [9]–[11], micromachining substrate Manuscript received March 30, 2006; revised July 11, 2006. S. Wane is with Philips Semiconductors, 14000 Caen, France (e-mail: sidina. [email protected]). D. Bajon is with the Ecole Nationale Supérieure de l’Aéronautique et de l’Espace, 31055 Toulouse, France (e-mail: [email protected]). Color versions of Figs. 1–4, 7, 8(b), 9, 10, 12(a), 12(b), 13, 15, 18, 20–24(a), 25, and 27 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.885579

cavities [12], trench isolation [13], [14]). All these techniques aim at reducing various energy dissipation origins involving complex physical mechanisms that include skin effect, eddy currents, and polarization/dielectric/radiation losses. To analyze energy dissipation and coupling causes in order to select or innovate appropriate isolation strategies, EM simfactor of on-chip ulation tools are required. While the spiral inductor enhancement techniques associated with inductor intrinsic parameter optimization and architecture-related approaches can be accurately analyzed using standard EM simulators, techniques and methodologies associated to substrate stack modifications remain very challenging for numerical EM methods. Accurate incorporation in EM simulations of substrate features as depletion regions, PWells, NWells, or insulating deep-trenches, as shown in Fig. 1, necessitates the modeling of stacks of inhomogeneous layers with arbitrary doping profiles. Two-and-one-half-dimensional (2.5-D) numerical integral methods well known to provide reliable results are still limited, to the authors’ best knowledge, to multilayered structures with homogeneously doped layers [15]. Three-dimensional (3-D) numerical methods, suitable for the analysis of multilayered structures with arbitrarily doped layers, are penalized by extremely implosive computation complexity resulting from the high discrepancy between the substrate features scale, on the one hand, and the layout geometrical dimensions on the other. Small geometrical details impose, for an accurate discretization, space step size often a lot smaller than what can be dictated by the smallest wavelength enclosed in the simulation-domain limits. This leads to important memory requirement and CPU computation delays even if adaptive meshing procedures are associated to frequency or time interpolations. Design rules usually elaborated from experimental studies, generally based on costly trial-and-error procedures, are highly dependent on signal frequencies, as well as on substrate stack doping profiles and, therefore, must be adapted to each new technologies. In this paper, an original EM analysis of inhomogeneous deep-trench isolation patterning (DTP) is presented for -factor improvement and substrate coupling reduction. Section II discusses effects of the buried layer (BL) doping level on substrate coupling. Different grounding configurations for the BLs are considered, to estimate the impact of spatial distribution of the ground contacts on the global isolation performances between sensitive blocks. In addition, the influences of induced depletion

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Fig. 2. Methodology replacing a function block (e.g., block 1) by a pad of similar dimension for substrate coupling analysis.

Fig. 1. Cross section of a typical RF integrated circuit showing substrate features (deep-trench isolation, PWell, NWell, depletion regions) of disparate scales and doping profiles. Fig. 3. View of the test structure for investigation of BLs conductivity and grounding configuration.

regions on substrate coupling are investigated. Section III discusses -factor improvement of on-chip RF inductors resulting from the interruption of BLs, and part of the lossy substrate by deep-trench patterning to limit electric and magnetic energies dissipation. The EM analysis is carried out using the hybrid transverse wave formulation (TWF) method [15] that associates the advantages of integral methods to the benefits and flexibility of differential approaches. Impacts of different deep-trench patterning options, as well as the influence of BL grounding on -factor enhancement are presented. The tradeoff between reduction of magnetic or electric energy dissipation is analyzed through the effects of deep-trench patterning penetration inside the substrate. The distributed capacitances resulting from the BLs and substrate grating are evaluated using a general methodology for extraction of circuits compact models. Comparisons of obtained results with 2.5-D- and 3-D-based commercial EM tools and with measurement data for reference structures show satisfactory agreement.

II. EFFECTS ON SUBSTRATE COUPLING OF BURIED LAYER CONDUCTIVITY AND GROUNDING: MODELING OF DEPLETION REGIONS A. Influence of the BLs Doping Level Since complete full-chip EM analysis including couplings between integrated components and sub-block and block functions is difficult to achieve with today’s available EM design tools, a methodology to simplify circuit complexity should be considered. A simple methodology, commonly used in substrate coupling analysis, consists of replacing sensitive blocks or components by pads (p or n implants, as shown in Fig. 2) of equivalent shape and geometric dimensions. For instance, at the component level p plugs can represent source/drain regions and n buried diffusions can correspond to collectors of NPN transistors. Fig. 3 shows a test structure for the investigation of substrate coupling dependence on the BL doping level. The signal

WANE AND BAJON: FULL-WAVE ANALYSIS OF INHOMOGENEOUS DTP

Fig. 4. Cross-sectional view of the reference structures with: (a) BL grounded and (b) BL floating by insertion of deep-trench isolation. (a) Configuration with BL grounded. (b) Configuration with BL floating.

Fig. 5. Effects of the BL conductivity  at 2 GHz for the test structure in Fig. 3.

and grounding on substrate coupling

pads (S) are connected to plug 1 and plug 2 representing the aggressor (injector) and victim (receiver), respectively, illustrated in Fig. 4. The test structure is composed of a 500- m-thick lossy silcm and a 2- m-thick icon substrate with a resistivity of 20 BL of conductivity in siemens per meter, taken as a variable in Fig. 5, covered with an insulating silicon dioxide layer. The ground seal ring on the metal 6 level is connected to the BL by four substrate contacts through via-holes, as shown in between the Figs. 3 and 4. The evolution of the coupling at 2 GHz for the two p plugs against the BL conductivity different grounding configurations in Fig. 4(a) and (b) is presented in Fig. 5.

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Fig. 6. Top view of the BL: (a) grounded and (b) floating configurations. (a) Configuration with continuous path between p plugs and ground contacts; (b) Configuration without continuous path between p plugs and ground contacts.

+

+

The floating configuration of the BL Fig. 4(b) is obtained by introducing a 1.5- m-thick trench isolation ring to isolate, from the ground contacts, the portion of the BL where the p plugs are diffused. This floating configuration poses some difficulties to standard 2.5-D EM design tools. The principal difficulties concern the accurate simulation of the boundary conditions at the limits of the BL domain bounded by the isolation trench ring [see Fig. 4(b) or Fig. 6(b)]. Table I shows the comparisons between different EM approaches [TWF, Sonnet Software, Momentum, High Frequency Structure Simulator (HFSS)] and measurement. The measurements are reported for S/m. In Table I, the symbol “ ” corresponds to situations not being properly simulated using the associate EM tool (according to the current versions). In Sonnet Software, the grounded option can be easily simulated, although the floating option is difficult to analyze because of the presence of the box imposing electric wall boundary conditions at the limits of the stack of layers. In Momentum software, as the layer stack is assumed to have and in Fig. 6(a)], infinite space extension [ the grounded option is difficult to simulate; while using HFSS, particular attention has to be paid to the definition of radiating or absorbing boundary conditions matching with surrounding free space. Issues on the convergence of the simulation results against the meshing procedure also have to be considered. increases, in Fig. 5, the BL becomes more conductive As and the two p plugs are more and more sensitive to grounding configuration of the BL. This sensitivity of the BL to the spatial distribution of grounding contacts [16] can give rise to very different isolation performances, in particular for high values of

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TABLE I COMPARISON BETWEEN DIFFERENT EM TOOLS FOR THE SIMULATION OF THE TEST STRUCTURES IN FIG. 4. AT 1 GHz

. Since the ground ring and the BL cannot be rigorously assimilated to a single node despite their small dimensions (see Fig. 3), static (electrostatic or magnetostatic) approaches do not lead to accurate results [17] and full-wave attributes of the coupling have to be considered. In Fig. 5, the grounded and floating configurations for the BL exhibit roughly the same behavior for values less than or equal to 100 S/m [17]. Howagainst ever, for greater than this limit, the two configurations lead to very different results. The floating configuration shows a saturated, but monotoagainst : as nous variation of the coupling parameter increases, the impedance between the two p plugs decreases and the coupling becomes more and more significant. The grounded configuration leads to very low coupling for very due to the short circuit impressed between high values of the ground and signal contacts in Fig. 4(a). The observed low coupling in this case has to be considered as virtual since the associated insertion losses are dominant. Table I illustrates the . virtual coupling observed for high-conductivity values of S/m, in Table I, dB and With dB are obtained for the grounded configuration, while for dB and dB. Even the floating option, for moderate values of the BL conductivity ( S/m in Table I), noticeable differences can be observed between the grounded and floating options. given in (1), acA normalized coupling parameter counting for both the insertion and coupling parameters, has to be considered for optimum power transfer evaluation (1) High absolute values of in decibels lead to a poor insertion parameter, while lower absolute values result in weak isolation S/m gives performance. Applying (1) for dB and dB, respectively, for the floating and grounded options.

Fig. 7. Cross-sectional view of a typical CMOS structure with depletion regions NWell/p-BL and DNWell/substrate.

B. Influence of Depletion Regions Depletions layers contribute to the frequency response of the substrate and may have significant influence on the coupling paths. The depletion regions shown in Fig. 7 result from the difference in doping level between the NWell region and the buried p-layer, on the one hand, and the deep NWell (DNWell) and the Si substrate, on the other. NW-BL designates the depletion region between the NWell region and the BL, and DNW-BL represents the depletion region between the DNWell region and Si . The NWell and substrate. The depletion region width is DNWell thickness and resistivity are taken, respectively, equal cm. In Fig. 7, the PWell region to 0.75 m and 4 10 has the same conductivity and thickness as the BL. Fig. 8(a) compares the insertion and coupling parameters against frequency of the structure in Fig. 7 with and without ( : reference structure) including depletion regions. Comparison between EM-simulation results with the TWF method and an equivalent-circuit model built on frequency independent (resistance), (inductance), (capacitance), and (conductance) elements in Fig. 8(b) shows satisfactory agreement for signal frequencies up to 40 GHz. The general RLCG equivalent-circuit model of the structure without depletion layers, composed of frequency-independent lumped elements, which constitutes the “intrinsic part” in Fig. 8(b), does not result from any estimation or fitting procedure, but from exact identification between EM simulation and equivalent network responses. , , and , respectively, represent the capacitance, resistance, and inductance values associated to the electrical behavior of is the substrate conductance the BL. and represents the substrate capacitance. Table II

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Fig. 9. Effects of the depletion region capacitance CNW-BL on the coupling parameter S against frequency: comparison between the RLCG model and = 0:8 m) results. EM simulation (for 

Fig. 8. S - and S -parameters against frequency of the structure in Fig. 7: Comparison between: (a) EM simulation results and general RLCG model. (b) Asymmetric RLCG equivalent network including depletion region capacitances.

Fig. 9 presents the evolution against the frequency of deduced from the RLCG model for coupling parameter different values of the depletion layer peripheral capacitance ( and fF). The EM simulation results for a depletion region width m are in good agreement, particularly at low frequency, with the RLCG model fF. results for a peripheral capacitance C. Effects of Local and Global Ground References

TABLE II RLCG EXTRACTED VALUES FOR THE ELECTRICAL EQUIVALENT CIRCUIT IN FIG. 8(b)

gives the nominal values extracted from EM simulations for the intrinsic part of the equivalent circuit in Fig. 8(b). The depletion region NW-BL is represented by the ver. The depletion region tical (peripheral) capacitance DNW-BL is approximated by the horizontal capacitance . Both and are inserted in the equivalent network as lumped elements between parallel and serial coupling branches without modifying the obtained values of the elements extracted from the EM simulation of the structure without depletion layers. The equivalent network obtained in this way demonstrates in Fig. 9 its capability to predict the results obtained with the EM simulation including the depletion layers. In Fig. 8(b), the two-ports are related to the parasitics resulting from the numerical EM exciting sources or measurement probing. Fig. 8(a) shows that the effects of the depletion regions become transparency at high frequency, around 20 GHz for the considered nominal values.

The analysis of RF or microwave circuits generally refers to specified input and output ports for the determination of their parameters (scattering, impedance, or admittance parameters). In nodal analysis, a port is reduced to a node (with zero spatial extension) defined as a two-terminal element: one terminal corresponding to the signal and the other representing the common “global” ground reference. However, in EM analysis, a port has a nonzero spatial extension (assumed to be small in regard to the wavelength for an univocal definition of voltages and currents) and cannot always be referred to as a “global” ground. To accurately account, in EM analysis, for real measurement conditions, the probing pattern used in the measurement setup protocol must be included in the simulation. Fig. 10 shows a coplanar waveguide (CPW) pattern used for the analysis of a device-under-test (DUT). The finite extension of the floating lossy ground plane renders the definition of a common ground reference difficult because of the resulting attenuation and delay in the ground return current. Moreover, as EM excitation sources most often assume uniform distribution of EM fields [see Fig. 11(a) and (b)], the port discontinuities are represented in Fig. 10 by the two-port identified to the , , and elements, which may corrupt the interpretation of the numerical simulation results. To investigate the impact on EM couplings of “local” and “global” ground references illustrated in Fig. 12(c), the two grounding options shown in Fig. 12(a) and (b) are considered. Fig. 12(a) corresponds to a floating lossy ground seal ring and Fig. 12(b) represents a numerically auto-grounded microstrip (MST)-like configuration. The MST-like configuration could also be considered with a floating ground option (by toggling the auto-ground reference). The seal ring configuration could

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Fig. 10. CPW GSG pattern for the analysis/measurement of a DUT and illustration of current density and electric field, respectively, in MST and CPW numerical EM excitations.

Fig. 12. (a) Two-port with floating ground reference. (b) Two-port with numerically auto-grounded reference. (c) Multiport with local and global ground references.

Fig. 11. (a) Nonuniform (real excitations) field distribution and (b) uniform field (numerical excitations) distribution on the exciting port regions.

be associated to the auto-grounded option (by connecting autoground reference) as well. These two complementary combinations are not represented in Fig. 12 due to space restrictions. and serial resistances The wiring inductances of the feeding interconnections contacting the signal pads to the DUT and the seal ring electrical lumped elements and representation are rigorously deduced from EM simulations results of Fig. 13 with an original deembedding procedure for floating ground references. Fig. 13 shows the simulated -parameters of the seal ground ring without a DUT or interconnect [see Fig. 12(a)] and with a 400- m-long transmission line (as shown in the inset) in the floating ground reference option. In Fig. 14, the floating ground reference configuration in Fig. 12(a) is referred to as CPW configuration and compared to the auto-ground configurations in Fig. 12(b) for the computation of the coupling parameter against frequency of the test structures in Fig. 6. Significant differences can be observed between the floating ground reference and the auto-grounded options. The auto-grounded option is investigated for both

Fig. 13. S and S against frequency of a coplanar transmission line with floating seal ground ring: characterization of the seal ground ring.

MST and CPW excitations illustrated in the inset of Fig. 10; noticeably different behavior has to be underlined. It is essential to notice that the -parameters in Fig. 14 include the effects ) and of the numerical source discontinuities (two-port

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Fig. 14. Comparison between the floating ground reference option and the auto-ground configuration for the computation of the coupling parameter S against frequency of the structures in Fig. 6.

the parasitics , , , and resulting from the inductances and resistances of the feeding interconnects and seal ground ring. The coupling parameter exhibits a nonmonotonous behavior against frequency for the floating CPW configurations. At low frequency (less than 5 GHz in Fig. 14), a coupling decreasing in magnitude as the frequency increases is observed due to the presence of the floating seal ground ring. However, at high frequency, coupling increasing in magnitude as the frequency increases is observed. Both for the MST option and CPW configuration, floating BLs lead to greater coupling.

Fig. 15. Reference structures with floating ring loops for: (a) high- and (b) low-impedance configurations for investigation of metal topology effects on the efficiency of deep trench patterning (DTP-X and DTP-Y).

III. INTERRUPTION OF BLS BY DTP A. Effects of DTP on EM Coupling Between Interconnects: Influence of Floating Ring Loops To investigate the effects of the metal topology on the deeptrench isolation performances to reduce EM coupling, the two test case structures shown in Fig. 15 are simulated using the TWF method. In the first test case structure of Fig. 15(a), the two ground–signal–ground (GSG) probes, with the associated feeding lines, represent the aggressor (noise source or excitation) and the victim separated by concentric floating ring loops. The second test case in Fig. 15(b) represents two coupled interconnect lines separated by the concentric rings, as in Fig. 15(a). Couplings dependence against the number of ring loops (turns) for the test case structure in Fig. 15(a) is investigated in Fig. 16: as the number of ring loops decreases, isolation performances decreases at low and moderate frequencies. This is not true at high frequency, above 20 GHz, because of various higher order effects. The influence of different options of deep trench patterning on EM coupling is shown in Fig. 17(a). The options without DTP and without floating ring loops correspond to the reference structures with the BL [assuming the nominal values for the conductivity (1000 S/m) and thickness (2 m)]. It is observed, but not reported here for conciseness reasons, that floating ring loops can significantly corrupt isolation performances in presence of low-resistivity BLs in both test-

Fig. 16. Coupling against the frequency for different number of ring loops.

case structures. However, introducing DTP leads to important reduction of coupling effects. In the case of the test-case structure with interconnect lines, the existence of privileged directions for the DTP has to be observed [18]. In Fig. 17(a), DTP-X and DTP-Y, respectively, represent deep trench patterning in the - and -directions, namely perpendicular or parallel directions to the interconnect lines in Fig. 15(b). The interruption of the BL and part of the silicon substrate by DPT-X leads, in Fig. 17(a), to better isolation performances

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Fig. 18. Eddy current induced by spiral inductor magnetic field on semiconducting layers: insertion of trench isolation to increase impedance path of eddy current.

Fig. 19. Influence of a BL (BP-Layer) on the Q factor against frequency. Fig. 17. (a) Isolation and coupling parameters against frequency for various options of deep trench patterning (DTP-X, DTP-Y). (b) Impacts of BL grounding on coupling with floating ring loops. The parameters are L = 300 m, L = 430 m, the separation distance between ring loops s = 18:75 m, w = = 600 m, the spacing 37:5 m, the length of the interconnect lines L between lines is d = 470 m.

(increased absolute value of - and -parameters) up to 50 GHz. Fig. 17(b) compares isolation performances in the presence of floating ring loops for grounded and floating BL. For the grounded configuration of the BL, comparison of the obtained simulation results with Sonnet Software simulations shows satisfactory agreement (for reference structures without DTP). B. Effects of DTP on the

Factor of Spiral Inductors

The penetration of the magnetic field into the substrate stack causes magnetic energy losses that result in low- factor and substrate coupling problems. In order to increase the impedance paths of undesirable eddy currents induced by the magnetic field in the substrate stack, DTP is introduced underneath the inductor to interrupt the lossy BL and part of the lossy silicon substrate, as illustrated in Fig. 18. Fig. 19 shows the effect against frequency of low-resistivity BL (BP layer) beneath the inductor on the factor.

Removing the BL increases both the factor and the vertical electric field penetrating into the substrate. A tradeoff between reduced eddy currents and limited penetration of vertical electric field can be obtained in breaking the underlying BL and Si substrate by the deep trench patterning. In fact, the deep trench patterning acts as blocking p-n-p junctions perpendicularly to the spiral inductor traces. As the blocking deep trench patterning imposes local high-impedance boundary conditions, it must be narrow enough to limit losses resulting from the penetration of vertical electric field into the substrate stack. The impact of a deep trench patterning on the factor against frequency is presented in Fig. 20(a) in reference to deep trench patterning options shown in Fig. 21, and in comparison with a reference structure without deep trench patterning. The option BP designates the case where deep trench patterning is limited to the BP layer. Option BP-Si represents the case where the deep trench patterning penetrates both the BP and Si substrate. Options BP-G and BP-F, respectively, refer to configurations where the BP is grounded and floating. It is seen that the deep trench patterning leads to a higher factor when the BL is floating. In addition to interrupting the BL, penetration of the deep trench patterning inside the Si substrate improves the factor in the BP-Si-G case.

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Fig. 21. View of different deep trench patterning options and zoom on the interrupted BL according option IV from [1].

Q

Fig. 20. Effects of the DTP on the factor versus frequency: (a) impact of ) into the substrate and of BL BP grounding. the penetration depth ( (b) View of deep trench patterning interrupting the BL and part of the substrate, distributed capacitances from [1].

h

The factor is computed using the following conventional definition (2), directly drawn from energy dissipation considerdesignates the short-circuit input admittance ations, where of the spiral inductor

This shows that the deep trench patterning considerably reduces the capacitance to substrate. The per square sheet resisin Fig. 20(b)] tance of the BP fragments [real part of at 0.1 GHz. is Comparative analysis in terms of the maximum factor of the four options for the deep trench patterning in Fig. 21 leads denotes poto the following design rule where the symbol tentially greater than

(3) (2) In (2), designates the dissipated power, denotes the period, and is the pulsation. The approximation of the total stored energy represents the difference between the average stored magnetic and electric energies. Such approximation in terms of admittance parameters (for a two-port model) is much greater than as the prois only valid when posed definition for the factor drops to zero at the resonant frequency. Other definitions for the factor can be considered and compared [19]. In this study, we restrict ourselves to the conventional definition in (2). The interruption of the BL and a part of the Si substrate results in floating BL and Si fragments. This introduces distributed with capacitances with the traces of the spiral inductor and with other the noninterrupted part of the Si substrate surrounding fragments , as illustrated in Fig. 20(b). Average extracted values of 0.30 and 0.13 fF m are obtained for , respectively, without and with deep trench patterning at 0.1 GHz.

Such a design rule has to be carefully understood as strongly dependant on the relative values of the substrate and BL resistivities, on one hand, and on the considered frequency range, on the other. C. Comparison With Measurement Results and With Other Relevant EM Methods A 4.5-turn on-chip square inductor is considered as a reference structure for comparison with published measurement data [13] and with simulation results from commercial EM tools. The outermost strip of the inductor (on metals 5 and 4) is 200 m with a strip width of 14 m and a turn-to-turn m. Metal 5 is separated from the substrate by spacing a 7.1- m-thick silicon dioxide. The first five rows of Table III present comparisons between our simulation results using the TWF method and measurement data with and without deep m . Comparison with simutrench patterning lation results from the method-of-moments-based commercial EM tools without deep trench patterning is also reported in

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TABLE III COMPARISON WITH MEASUREMENT DATA [13] AND COMMERCIAL EM SOFTWARE FOR THE REFERENCE STRUCTURE IN PART FROM [1]

Q

-factor enhancement resulting from DTP isolation in conjunction Fig. 23. with topology optimization from [1].

the outer turns reduces ohmic losses, predominant in the external turns, while narrow width is considered for the inner turns, where the magnetic field is maximum. Fig. 23 shows the factor of the improved structure against the frequency in comparison with the reference structure, demonstrating a significant enhancement of approximately 400% for the maximum factor. In Fig. 24(b), the influence against frequency of the BL grounding on the coupling between the two square inductors shown in Fig. 24(a) is presented. Each inductor has the geometric properties of the reference structure in Table III. It is observed that a floating BL induces more coupling than a grounded BL, particularly at high frequencies. Fig. 25(a) and (b) shows the distribution of the current density magnitude on the interface between the BL and Si substrate, respectively, with and without deep trench patterning (option IV of Fig. 21). Reduced dissipated power can be observed when deep trench patterning is interrupted by the BL.

Fig. 22. Simple Pi-equivalent-circuit model of the inductor from [1].

Table III. The columns of Table III, respectively, refer to , the resonant frequency the -factor maximum value —at which the factor drops to zero—and, considering the Pi-equivalent circuit model in Fig. 22 for the reference , the parallel capacitance structure, the inductor value , the serial resistance and the homogenous substrate elements and . The last row of Table III presents improved performances of the on-chip inductor resulting from a combination of deep trench patterning and topological optimization. Although the concept of layout optimization for inductors has already been mentioned in previous studies [20], its application in conjunction with DTP is original and has never been proposed, to the authors’ best knowledge. The idea of topological optimization consists of choosing a different strip width for each inductor turn. Wider width for

D. Extraction of Compact Circuit Model Parameters for Back Annotation of Parasitic Elements Methodology for Compact Circuit Model Parameters Extraction: Starting from EM analysis results, the methodology for model parameter extraction uses a rational function representation of transfer functions to approximate impedance or admittance parameters as a ratio of polynomials [21]–[23]. Casting impedance or admittance matrix elements in a pole-residue form gives a straightforward way to determine compact equivalentcircuit models composed of frequency-independent elements. This allows for the derivation of a general wideband N-Pi equivalent-circuit representation shown in Fig. 26 that properly accounts for the different behaviors resulting from skin effect, eddy-current losses, and semiconductor doping profiles space variation. Limits of single Pi-network representations are discussed in [24] and [25]. The extraction procedure first determines the unknown complex coefficients of the numerator and denominator polynomials in (4) for a given function representing the series

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Fig. 25. Current density distribution at 2 GHz on the interface between the BL and the Si substrate: (a) without and (b) with deep trench patterning (option IV of Fig. 21). From [1]. (a) BL level without DTP (Option I). (b) BL level with DTP (Option IV).

Fig. 24. (a) View of two coupled on-chip inductors. (b) Evolution of the coupling S 21-parameter against frequency for the reference structure: effects of the BL grounding from [1].

impedance in Fig. 26

or the shunt (parallel) admittance

(4)

where and are, respectively, the real and imaginary with , with denoting parts of the rational function the pulsation and assuming a normalization to unity with and . Taking an odd integer without loss of generality, the expansion of (4) gives

(5)

Fig. 26. (a) Single Pi-equivalent circuit. (b) Generalized N-Pi-equivalent-circuit representations.

(6)

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TABLE IV EXTRACTED SUBSTRATE ELEMENTS IN FIG. 3(b)

Fig. 27. Electrical equivalent-circuit representation of the two-coupled inductors.

for the real and imaginary parts, respectively. From (5) and (6), a linear set of algebraic equations (7) is built where the vector collects the unknown coefficients , , , and of the polynomials in the numerator and denominator of (4) (7) The rectangular matrix and the vector both depend on the frequency and on the real and imaginary parts of the rational . Once the vector of the unknown coefficients is function determined using an appropriate numerical technique (enhanced factorization optimal for ill-conditioned large matrix sysis factored to obtain the stable tems), the denominator of poles (8) is the direct term and is the pole of order In (8), with a multiplicity . designates the residue of order , with being the total number of poles. Extraction of Spiral Inductor Models: The extraction of a general and compact model of two coupled on-chip inductors in Fig. 27 uses a symmetric single pi equivalent-circuit rep, resentation shown in Fig. 26(a) for each inductor. , and , respectively, designate the series inductance, series resistance, and series feed-forward capaciand parasitic capacitance tance. The BL conductance in series with the substrate conductance and parasitic capacitance and the inter-metal capacrepresent the shunt element of the inductor itance equivalent circuit. In Table IV, the nominal values of , , , , and extracted from EM simulations for the reference inductor structure of Table I are reported. are Since for design reasons the inductance value not really tunable, only effects of the element parameters , , , , and on the factor will be studied.

Fig. 28. Insertion of a parasitic transformers in the equivalent-circuit representation of a single inductor to account for magnetic losses: (a) in single  -network and (b) in generalized N-Pi-network.

Closed-form expressions of the real and imaginary parts of for a single spiral inductor the short-circuit input admittance in the inset of Fig. 23 are given by (9) and (10) (9)

(10)

where

,

, and

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Fig. 29. Effects of BL grounding on the magnitude of Y - and Y -parameters against frequency for the two square coupled inductors.

Fig. 31. Evolution of the conventional Q factor against frequency: (a) for different values of R and (b) for different values of C .

Fig. 30. Evolution of the conventional Q factor against the inductor series resistance at different frequencies.

The closed-form expressions split the real and imaginary into separate contributions of the intrinsic inductor parts of contribution and the intrinsic substrate stack contribution. Thus, (9) and (10) inspired by the equivalent-circuit representation in Fig. 22 do not show coupling through magnetic losses between , , and ) and the the intrinsic inductor elements ( substrate stack parameters ( , , , , and ). Such magnetic coupling can be accounted for by adding to the equivalent circuit a parasitic transformer with a secondary winding connected to representing the equivalent resistance of the BL and Si substrate, as illustrated in Fig. 28. The parasitic adds the terms and transformer , respectively, to the real and imagiin (9) and (10). Theses two terms will account nary parts of

for the coupling between the intrinsic inductor contribution and the intrinsic substrate stack contribution. This coupling is one of the main reasons why general conclusions on deep trench efficiency are closely related to the involved resistivities and frequency ranges. In the general pole-residue form of (8), the series impedance in the N-pi equivalent-circuit representation can be modeled using the following relation: (11) where and , respectively, represent the dc resistance denoting a mutual and dc inductance with inductance contribution in Fig. 28. in Fig. 28(b) is The shunt (or parallel) admittance given by the following relation: -

(12)

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Fig. 31(a) and (b) shows the variation against the frequency of the factor, respectively, for different values of the BL resisand parasitic capacitance tance ( and fF). It is seen that the maximum factor increases as the BL resistance and capacitance increase. The dependence of the factor on the substrate parasitic conductance and capacitance is presented in Fig. 32(a) and (b), respectively, at 3 GHz. The variation presents a minimum value of the factor against inaround 0.01 S. Lower substrate conductance creases the maximum value of the factor. Lower can be achieved by introducing between the BL and substrate a polysilicon patterned ground shield [9], [10], [26] or by inserting a local semi-insulating region in the silicon substrate obtained with proton implants. IV. CONCLUSION

Fig. 32. Evolution of the conventional at 3 GHz. (b) against G

Q

factor: (a) against

C

and

where - represents the parallel impedance formed by the substrate stack, except oxide layers

(13) The quality factor of the inductor can be deduced using (2) from (9) and (10). Although magnetic losses can be accounted for in the electrical equivalent circuit, effects related to the electrical state of the BL (grounded or floating) remain difficult to represent by lumped elements. Fig. 29 shows the effects against the freand of the two quency on the admittance parameters spiral inductors in Fig. 27 of the grounded and floating BL. In Fig. 30, the variation of the factor against the inductor seis presented for different frequencies ries resistance lead to greater fac(1–4 GHz). Lower values of tors at low frequency. Lower values for are achievable by increasing the inductor metal thickness (use of copper metallization) [2]–[4] or by means of geometry and topology optimization.

EM analysis of patterned deep-trench isolation for substrate coupling reduction and -factor enhancement, using the TWFmethod, has been presented. Dependence of substrate coupling on the BL doping level and grounding configuration has been discussed. Influences of induced depletion regions on substrate coupling have been investigated. Evaluation, from EM simulations, of depletion regions capacitances has been proposed. Interruption of BLs and part of the silicon substrate by DTP to improve on-chip spiral inductor factors have been studied. The effects of the DTP penetration inside the substrate on the quality factor have been investigated. Distributed capacitances resulting from the BL grating have been evaluated. It has been observed that DTP considerably reduces the capacitances to substrate by a factor exceeding 50%. Combination of DTP with layout topological optimization has demonstrated high -factor improvement exceeding 4 enhancement. It has been shown that introduction of DTP can be more efficient in term of coupling reduction than completely removing the BL because of Si substrate screening provided by the remaining BL fragment. Limits of electrical lumped-element representation to account for distributed effects and magnetic losses are discussed. A general methodology for systematic extraction of compact equivalentcircuit models including mutual coupling terms has been proposed. The evolutions of the factor against extracted compact equivalent-circuit parameters have been presented allowing for direct optimization in common circuit simulators. The simulation results obtained with the TWF approach have been successfully validated by comparison with other relevant EM methods (2.5-D and 3-D approaches) and with published measurement data for reference structures. ACKNOWLEDGMENT The authors would like to thank the reviewers for their suggestions concerning the final form of this paper. REFERENCES [1] S. Wane and D. Bajon, “Electromagnetic investigation on RF spiral inductors with inhomogeneous patterned deep-trench isolation,” presented at the IEEE MTT-S Int. Microw. Symp. San Francisco, CA, 2006.

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[2] J. N. Burghartz, D. C. Edelstein, K. A. Jenkins, and Y. H. Kwark, “Spiral inductors and transmission lines in silicon technology using copper-damascene interconnects and low-loss substrates,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 10, pp. 1961–1967, Oct. 1997. [3] Y.-S. Choi and J.-B. Yoon, “Experimental analysis of the effect of metal thickness on the quality factor in integrated spiral inductors for RF ICs,” IEEE Electron Device Lett., vol. 25, no. 2, pp. 76–78, Feb. 2004. [4] W. B. Kuhn and N. M. Ibrahim, “Analysis of current crowding effects in multiturn spiral inductors,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 1, pp. 31–38, Jan. 2001. [5] W. B. Kuhn, A. W. Orsborn, M. C. Peterson, S. R. Kythakyapuzha, A. I. Hussien, J. Zhang, J. Li, E. A. Shumaker, and N. C. Nair, “Spiral inductor performance in deep-submicron bulk-CMOS with copper interconnects,” in IEEE MTT-S Int. Microw. Symp. Dig, 2002, pp. 301–304. [6] M. Danesh and J. R. Long, “Differentially driven symmetric microstrip inductors,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 1, pp. 332–340, Jan. 2002. [7] C.-C. Tang, C.-H. Wu, and S.-I. Liu, “Miniature 3-D inductors in standard CMOS process,” IEEE J. Solid-State Circuits, vol. 37, no. 4, pp. 471–480, Apr. 2002. [8] T.-S. Chen, J. D.-S. Deng, C.-Y. Lee, and C.-H. Kao, “Improved performance of Si-based spiral inductors,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 10, pp. 466–468, Oct. 2004. [9] C. P. Yue and S. S. Wong, “On-chip spiral inductors with patterned ground shields for Si-based RF ICs,” IEEE J. Solid-State Circuits, vol. 33, no. 5, pp. 743–752, May 1998. [10] S. Akatimagool, D. Bajon, and H. Baudrand, “Analysis of multi-layer integrated inductors with wave concept iterative procedure (WCIP),” in IEEE MTT-S Int. Microw. Symp. Dig., May 2001, vol. 3, pp. 1941–1944. [11] J.-H. Chang, Y.-S. Youn, H.-K. Yu, and C.-K. Kim, “Effects of dummy patterns and substrate on spiral inductors for sub-micron RF ICs,” in IEEE MTT-S Int. Microw. Symp. Dig., 2002, pp. 529–532. [12] J. B. Yoon, B. K. Kim, C. H. Han, E. Yoon, and C. K. Kim, “Surface micromachined solenoid on-Si and on-glass inductors for RF applications,” IEEE Electron Device Lett., vol. 20, no. 9, pp. 487–489, Sep. 1999. [13] C. A. Chang, S. Tseng, J. Y. Chuang, S. Jiang, and J. A. Yeh, “Characterization of spiral inductors with patterned floating structures,” IEEE J. Solid-State Circuits, vol. 52, no. 5, pp. 1375–1380, May 2004. [14] C. S. Kim, P. Park, J.-W. Park, N. Hwang, and H. K. Yu, “Deep trench guard technology to suppress coupling between inductors in silicon RFIC,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2001, vol. 3, pp. 1873–1876. [15] S. Wane, D. Bajon, H. Baudrand, and P. Gamand, “A new full-wave hybrid differential-integral approach for the investigation of multilayer structures including non-uniformly doped diffusions,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 200–215, Jan. 2005. [16] M. B. Steer, J. F. Harvey, J. W. Mink, M. N. Abdulla, C. E. Christoffersen, H. M. Gutierrez, P. L. Heron, C. W. Hicks, A. I. Khalil, U. A. Mughal, S. B. Nakazawa, T. W. Nuteson, J. Patwardhan, S. G. Skaggs, M. A. Summers, S. Wang, and A. B. Yakovlev, “Global modeling of spatially distributed microwave and millimeter-wave systems,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 830–837, Jun. 1999. [17] S. Wane, D. Bajon, H. Baudrand, C. Biard, J. Langanay, and P. Gamand, “Effects of buried layers doping rate on substrate noise coupling: Efficiency of deep trench techniques to improve isolation capability,” in IEEE RFIC Symp. Dig., Jun. 2004, pp. 179–182. [18] S. Wane and D. Bajon, “Influence of interrupting buried layers and ringloops on electromagnetic coupling in RFIC’s,” in IEEE AP-S Symp. Dig., Jul. 2006, pp. 4349–4352. [19] H. Jiang, Y. W. , J. A. Yeh, and N. C. Tien, “On-chip spiral inductors suspended over deep copper-lined cavities,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2415–2422, Dec. 2000. [20] J. M. López-Villegas, J. Samitier, C. Cané, P. Losantos, and J. Bausells, “Improvement of the quality factor of RF integrated inductors by layout optimization,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 1, pp. 76–82, Jan. 2000. [21] M. Elzinga, K. Virga, L. Zhao, and J. L. Prince, “Pole-residue formulation for transient simulation of high-frequency interconnects using householder LS curve-fitting techniques,” IEEE Trans. Adv. Packag., vol. 25, no. 2, pp. 142–147, May 2000. [22] T. Mangold and P. Russer, “Full-wave modeling and automatic equivalent-circuit generation of millimeter wave planar and multilayer structures,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 851–858, Jun. 1999.

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[23] P. Russer and A. C. Cangellaris, “Network oriented modeling, complexity reduction and system identification techniques for electromagnetic systems,” in Proc. 4th Int. Comput. Electromagn. in Time-Domain: TLM/FDTD and Relat. Tech. Workshop, Nottingham, U.K., Sep. 17–19, 2001, pp. 105–122. [24] Y. Cao, R. A. Groves, X. Huang, N. D. Zamdmer, J.-O. Plouchart, R. A. Wachnik, T.-J. King, and C. Hu, “Frequency-independent equivalent circuit model for on-chip spiral inductors,” IEEE J. Solid-State Circuits, vol. 38, no. 3, pp. 419–426, Mar. 2003. [25] A. C. Watson, D. Melendy, P. Francis, K. Hwang, and A. Weisshaar, “A comprehensive compact-modeling methodology for spiral inductors in silicon-based RFICs,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 849–857, Mar. 2004. [26] S. Wane, D. Bajon, H. Baudrand, and P. Gamand, “Multilevel approach for the investigation of substrate parasitic in mixed-signal IC’s from full-wave analysis,” in IEEE RFIC Symp. Dig., Jun. 2003, pp. 263–266.

Sidina Wane (M’98) was born in Kaedi, Mauritania, in 1972. He received the Eng.-Dipl. degree in electrical engineering (with high honors) and D.E.A. degree in optics and microwave communication systems (with high honors), from the Ecole Nationale d’Ingénieurs de Tunis (ENIT), Tunis, Tunisia, in 1998 and 1999, respectively, and the Ph.D. degree in microwaves and electronics (with high honors) from the Institut National Polytechnique of Toulouse (INPT), Toulouse, France, in 2002. From 2002 to 2003, he was a Post-Doctoral Research Associate with the Electromagnetic Research Group, Ecole Nationale Supérieure de l’Electronique, l’Electrotechnique, d’Informatique, d’Hydraulique et des Télécommunications (ENSEEIHT), Toulouse, France. He is currently a Senior System-in-Package (SiP) Engineer with Philips Semiconductors, Caen, France, where he is involved in the standardization of design tools and methodologies for multitechnology design flows for quality and productivity enhancement. His research interests include signal processing and digital engineering, modern numerical techniques for modeling EM fields and waves, and computer-aided design of millimeter-wave, microwave circuits and optical applications. Dr. Wane was the recipient of the 1998 Optics and Microwave Communication Systems Prize for his engineering dissertation. He was the recipient of the Genie Electrique, Electronique, Télécommunications (GEET) Award and Leopold Escande Award in 2002 for his doctoral dissertation. In 2003, his research on the development of EM tools, conducted from INPT and SUPAERO, received the Agence Nationale de Valorisation de la Recherche (ANVAR) Award presented by the French Ministry of Research.

Damienne Bajon (M’88) received the B.Sc. and M.Sc. degrees in electrical engineering from the Université Paul Sabatier, Toulouse, France, in 1981, and the Ph.D. degree in microwaves and electronics (with high honors) from the Institut National Polytechnique of Toulouse (INPT), Toulouse, France, in 1985. Since 1985, she had been actively involved in the research activities of the Groupe de Recherche en Electromagnetisme (GRE), Laboratoire de Microondes, Ecole Nationale Supérieure de l’Electronique, l’Electrotechnique, d’Informatique, d’Hydraulique et des Télécommunications (ENSEEIHT), Toulouse, France. In 1989, she joined the Ecole Nationale Supérieure de l’Aéronautique et de l’Espace (SUPAERO), Toulouse, France, where, since 2004, she has been a Full Professor in charge of EM research activities and teaching of numerical EM methods and microwave theory and techniques. Her research interests include EM field and computational electromagnetics and modeling techniques for integrated microwave and millimeter-waves circuits. She has been involved in the organization of several international conferences and symposia and serves as a reviewer for several journals. Dr. Bajon was the secretary of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) French Chapter from 2004 to 2005 and is currently the vice chairman since 2005.

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Design and Analysis of Low Flicker-Noise CMOS Mixers for Direct-Conversion Receivers Jinsung Park, Student Member, IEEE, Chang-Ho Lee, Member, IEEE, Byung-Sung Kim, Member, IEEE, and Joy Laskar, Fellow, IEEE

Abstract—This paper presents the design and analysis of low flicker-noise RF mixers in a 0.18- m CMOS process for -band direct-conversion receivers. The low flicker-noise mixers are implemented by incorporating a double-balanced Gilbert-type configuration, the RF leakageless current bleeding technique, and the resonating technique for the tail capacitance. First, a double-balanced Gilbert-type mixer using the current bleeding technique has been fabricated and measured for lowering flicker corner frequency. Second, a double-balanced Gilbert-type mixer using the current bleeding technique with one resonating inductor has been designed to improve conversion gain and flicker-noise performance. Third, by using two separate inductors at the node between the current bleeding device and local oscillator switches, conversion gain and flicker-noise performance are significantly improved. A conventional Gilbert-type mixer without any technique has also been fabricated and measured for comparative purposes. The Gilbert-type mixer using the current bleeding technique with two resonating inductors has a measured conversion gain of 16.1 dB, a measured input third-order intercept point of 5 dBm, a measured noise figure of 9.8 dB at 1 MHz, and a flicker corner frequency of 125 kHz while consuming only 7 mW of dc power. To the best of our knowledge, the proposed mixer shows the lowest flicker corner frequency (125 kHz) with more than 15 dB of conversion gain in the CMOS process. Index Terms—CMOS mixer, current bleeding, direct-conversion receiver, flicker noise, Gilbert-type mixer.

I. INTRODUCTION

I

N A direct-conversion receiver, flicker noise degrades the signal-to-noise ratio (SNR) and total noise figure (NF), which results in the degradation of receiver sensitivity. In narrowband RF systems, bandwidth utilization is a critical issue and it can be maximized by using a reduced flicker-noise receiver system because we can utilize more channels around the dc area. In a multicarrier modulation system like orthogonal frequency division multiplexing (OFDM), spectral efficiency can also be improved by using a reduced flicker-noise receiver system. CMOS transistors suffer from high intrinsic flicker noise, which is inversely proportional to the device area [1]. Therefore, minimum length of the device increases flicker noise.

In general, passive CMOS mixers are considered as the appropriate choice for direct-conversion receivers because they do not contribute to flicker noise. However, due to conversion loss, a higher gain of a low-noise amplifier (LNA) is required to minimize baseband noise contribution. In order to decrease flicker noise in CMOS active mixers, the bias current of the local oscillator (LO) switches should be small enough to lower the height of noise pulses. The static current bleeding technique was proposed to reduce the bias current of the LO switches [2]. However, the impedance of the LO switches as seen from the RF stage is increased as we reduce the bias current of the LO switches. In addition, RF leakage current flows into the bleeding circuit, which decreases conversion gain and also allows more RF current to be shunted by the tail capacitance ( ) at the node between the LO switches and RF transconductance stage. The tail capacitance should be minimized to decrease the indirectly translated flicker noise [3]. To minimize the tail capacitance, a smaller device size is appropriate for the LO switches, which increases the intrinsic flicker noises. The dynamic current bleeding technique has also been proposed to improve the flicker-noise performance [4]. It injects a dynamic current totally equal to the bias current of the LO switches at only the LO switching event. In this paper, we have designed and analyzed three low flicker-noise CMOS mixers, which are: 1) a Gilbert-type mixer based on the current bleeding technique; 2) a Gilbert-type mixer based on the current bleeding technique with one resonating inductor; and 3) a Gilbert-type mixer based on the current bleeding technique with two resonating inductors. First of all, a Gilbert-type mixer with only the current bleeding circuit has been designed and analyzed for comparative purposes. Second, a Gilbert-type mixer with one inductor has been designed to overcome some drawbacks of the static bleeding technique. Finally, a new double-balanced Gilbert-type mixer using the static current bleeding circuit and two resonating inductors is proposed to reduce flicker noise without sacrificing NF, conversion gain, and linearity performance. II. THEORY A. Device Model

Manuscript received March 30, 2006; revised August 11, 2006. J. Park, C.-H. Lee, and J. Laskar are with the Georgia Electronic Design Center, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]; [email protected]; [email protected]). B.-S. Kim is with the RF Microelectronic Design Laboratory, School of Information and Communication Engineering, Sungkyunkwan University, Suwon 440-746, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885582

There are two different theories that can explain the physical origins of flicker noise. In the carrier density fluctuation model, originally proposed by McWorther [5], the noise is explained by the fluctuation of channel-free carriers due to the random capture and emission by the Si–SiO interface traps known as slow rates. Using this model, the input referred noise is independent of the gate bias voltage and the magnitude of the noise

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PARK et al.: DESIGN AND ANALYSIS OF LOW FLICKER-NOISE CMOS MIXERS FOR DIRECT-CONVERSION RECEIVERS

Fig. 1. Measured current noise spectrum for nMOS devices with 0:18 m, W = 98 m, and W = 196 m.

L =

spectra is proportional to the density of the interface trap. On the other hand, the mobility fluctuation model, first proposed by Hooge et al. [6], suggests the gate voltage dependence in the input referred noise. The model is based on the empirical experimental observation of the noise in the homogeneous samples, and the input referred noise shows strong gate-bias dependence. In the -channel transistors, the input referred noise shows no gate-bias dependence when the gate bias is varied from subthreshold to strong inversion. This suggests that flicker noise in -channel devices follows carrier density fluctuation. In the -channel devices, strong gate-bias dependence in the input referred noise is observed. Mobility fluctuation seems to be able to explain the -channel noise behavior. The unified model with a functional form resembling the number fluctuation model at low bias and the mobility fluctuation model at high bias has been proposed and this unified noise model is often used as the basis for circuit simulations, like BSIM3. This model describes the flicker noise of - and -type MOSFETs in all operating regimes. Details on the BSIM3v3 model can be found in [7]. The simplified level-3 HSPICE model is (1) where is a process parameter, and are the effective width and length, and is the oxide capacitance. This model is not as accurate as the BSIM3v3 model, but serves as a guiding empirical formulation and has been used extensively to model flicker noise for first-order approximate solutions. Fig. 1 shows the measured noise spectral density of -channel devices with m, m, and m. This measurement was done by using the Agilent 35670A dynamic signal analyzer. As seen from Fig. 1, the intrinsic flicker noise is inversely proportional to the device area. The device sizes shown in Fig. 1 were used for designing mixers in Section III. B. Switching Mixer Fundamentals Fig. 2(a) shows a conventional double-balanced Gilbert-type mixer. The mixer comprises an RF input transconductance stage, LO switches, and output loads.

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Fig. 2. (a) Double-balanced Gilbert-type mixer. (b) Equivalent model of the single-balanced mixer.

The output current of the single-balanced mixer of Fig. 2(b) , , and [8] is a function of (2) is the instantaneous LO voltage, is the bias where is the small-signal current for the RF transconductor, and current for the RF transconductor. By using a first-order Taylor expansion [8]

(3) or (4) where and are periodic waveforms and is the small-signal current at the output of the RF transconductor. As shown in Fig. 2(b), by current division, (5) where and are the transconductances of is eliminated in a double-balanced switching stages [8]. mixer with perfect device matching. The conversion gain of the mixer then becomes [8] (6) where is the LO frequency and switching times for the LO signal.

is the ON-and-OFF

C. Flicker-Noise Mechanism We can separately consider flicker-noise contribution depending on the output stage, RF input stage, and LO switching pair stage. The output stage can be realized by means of polysilicon resistors that do not generate flicker noise. The RF input stage does not produce, to the first order, flicker noise at the output in the frequency band of signal. In fact, flicker noise from the RF input stage is up-converted to LO frequency and does not appear at baseband [3]. Therefore, the flicker-noise

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Fig. 5. Double-balanced Gilbert-type mixer with current bleeding circuit and one resonating inductor.

Fig. 3. Double-balanced Gilbert-type mixer with current bleeding circuit.

Fig. 4. Equivalent model of the double-balanced Gilbert-type mixer with current bleeding circuit.

Fig. 6. Equivalent model of the double-balanced Gilbert-type mixer with current bleeding circuit and one resonating inductor.

performances of the mixer are primarily determined by LO switching pair devices. There are two major mechanisms that generate the flicker noise of the switching pair devices. The first one is the direct mechanism, due to the finite slope of the switching pair transitions. The LO switches generate noise pulse trains by the direct mechanism and the dc average of noise pulse trains is the output flicker-noise current as follows [3]: (7) (8)

Fig. 7. Simplified model of the double-balanced Gilbert-type mixer with current bleeding circuit and one resonating inductor.

where is the bias current for the RF transconductance stage, is the LO period, is the equivalent flicker noise of the switching pair, and is the slope of the LO signal. and are also the effective width and length, is the oxide is a process parameter [3]. capacitance, is frequency, and From (7), it is worth noticing that low-frequency noise at the appears at the output directly, and the output gate of switch flicker-noise current is decreased if the product of the slope of the LO signal at zero-crossing and its period [3]. According to is inversely proportional to the device area. (8),

In order to decrease flicker noise in the direct mechanism, a popular method is to reduce the width of the noise pulses, which can be implemented by reducing the value of . To reduce the value of , the size of the switching pairs needs to be increased, and large switching devices increase the parasitic capacitance of the switching pairs, resulting in the flicker noise indirectly translating to the output. This is the indirect mechanism, the second mechanism that generates flicker noise. In the indirect mechanism, flicker noise mainly depends on the tail capacitance of the node between the LO switches and RF transconductance

PARK et al.: DESIGN AND ANALYSIS OF LOW FLICKER-NOISE CMOS MIXERS FOR DIRECT-CONVERSION RECEIVERS

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Fig. 10. Simplified parallel RLC resonator model of the double-balanced Gilbert-type mixer with current bleeding circuit and two resonating inductors.

Fig. 8. Double-balanced Gilbert-type mixer with current bleeding circuit and two resonating inductors.

Fig. 9. Equivalent model of the double-balanced Gilbert-type mixer with current bleeding circuit and two resonating inductors.

Fig. 11. Microphotograph of CMOS mixers. (a) Conventional Gilbert-type mixer without current bleeding. (b) Mixer with current bleeding.

stage [3]. When a sine-wave LO is applied to the mixer, the average of the output noise current generated by the indirect mechanism is [3] (9) where is the tail capacitance of the node between the LO switches and the RF transconductance stage, is the LO peis the transconductance of the LO switches, and is riod, the equivalent flicker noise of the switching pair. According to (9), the tail capacitance should be small enough to decrease the effect of the indirect mechanism. III. CIRCUIT DESIGN AND ANALYSIS A. Gilbert-Type Mixer With Bleeding Technique

Fig. 12. Microphotograph of CMOS mixers. (a) Mixer with current bleeding and one resonating inductor. (b) Mixer with current bleeding and two resonating inductors.

In general, increasing the bias current of the RF transconductance stage makes higher gain and better linearity possible, but a larger LO switching current causes voltage headroom issue. Therefore, as shown in Fig. 3, the static current bleeding technique is implemented by using two PMOSFETs to reduce the bias current of the LO switches [4]. From (7), if the bias current of the LO switches is decreased, the output flicker-noise

current generated by the direct mechanism can be minimized. Fig. 3 shows a double-balanced Gilbert-type mixer with current bleeding circuits. The mixer comprises an RF input transconductance stage, LO switches, output loads, and pMOS current bleeding circuits.

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TABLE I MEASURED RESULTS OF FOUR MIXERS

Fig. 14. Simulated and measured conversion gain variation with RF frequency (LO power = 0 dBm).

Fig. 13. Simulated and measured conversion gain variation with LO power (RF frequency = 5:2 GHz, LO frequency = 5:2 GHz). Fig. 15. Simulated and measured NFs of the three mixers.

As shown in Fig. 4, from (4) and (5), by current division,

(10) As can be seen from (10), some RF current flows into the bleeding circuit by current division and it decreases conversion gain. On the other hand, the output noise current of LO switches is decreased as the bleeding current is increased. If the amount of the bleeding current is increased, the bias current of the LO switches is decreased. As we can see from (7), the noise current by the direct mechanism is then decreased. However, there are a few drawbacks with the conventional current bleeding technique. As the bias current of the LO switches is reduced, the impedance of the LO switches as seen from the RF stage is increased. Therefore, as shown in Fig. 4, more RF leakage current flows into the bleeding circuit, which decreases conversion gain. It also allows more RF current to be shunted by the tail capacitance. To solve this drawback, the dynamic current injection method has been proposed [4]. The main idea of the dy-

namic current injection method is to inject current at only the switching event by using a control circuit [4]. Even though the dynamic injection is a good method to replace the conventional current bleeding technique, there are a few drawbacks. It shows a very low conversion gain, which is similar to passive mixers, and it may also require high LO voltage swing to turn on and off the pMOS control circuit. The main ideas in this paper to design low flicker-noise CMOS mixers are related to the following: how to reduce the bias current of LO switches, and how to reduce the tail capacitance, which makes it possible to reduce flicker noise generated by the indirect mechanism. Both ideas should be considered simultaneously without sacrificing mixer bandwidth and linearity performance. First of all, the static current bleeding technique, as shown in Fig. 3, has been used to reduce the bias current of the LO switches. B. Gilbert-Type Mixer With Bleeding Technique and One Resonating Inductor Even if the current bleeding technique can reduce the bias current of the LO switches, flicker noises are still generated by

PARK et al.: DESIGN AND ANALYSIS OF LOW FLICKER-NOISE CMOS MIXERS FOR DIRECT-CONVERSION RECEIVERS

Fig. 16. Measured input 1-dB compression point of the mixer with two resonating inductors.

Fig. 17. Measured IIP3 of the mixer with two resonating inductors.

the indirect mechanism. The tail capacitance is still needed to be reduced. The best way to reduce the tail capacitance is to minimize the size of the LO switches and RF transcondutance stages. However, CMOS transistors suffer from high intrinsic flicker noise, which is inversely proportional to the device area. Therefore, one inductor ( ) is connected between the common source node of the LO switches, as shown in Fig. 5, to resonate the tail capacitance out, and the conversion gain and flickernoise performance are improved simultaneously under resonant condition. As shown in Fig. 6, by resonating the tail capacitance can be high with , the impedance at node A looking into enough to protect some RF current from being shunted by the tail capacitance. We have improved the conversion gain ranging from 2 to 3 dB in simulation by using one inductor. However, there are still two shunted paths for RF current leakage. One is the current bleeding circuit, and the other one is the shunted is the shunted impedance of inductor. As shown in Fig. 7, one inductor . The portion of RF current that is not shunted by current division. For by the tail capacitance flows into example, is 750 ( nH with and at 5.2 GHz) and is approximately 1 k ( of the bleeding PMOS).

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Fig. 18. Measured flicker corner frequency of the mixer with two resonating inductors.

Fig. 19. Measured NF of the mixer with two resonating inductors.

TABLE II MEASURED RESULTS OF FLICKER CORNER FREQUENCY WITH BLEEDING CURRENT VARIATIONS

C. Gilbert-Type Mixer With Bleeding Technique and Two Resonating Inductors Our final approach is to use the current bleeding technique with two inductors connected between the common source node of the LO switches and the pMOS, as shown in Fig. 8. Therefore, two inductors (3.3 nH each) are connected to the pMOS device to resonate the tail capacitance out, and the conversion gain and flicker-noise performance are improved simultaneously under resonant condition.

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TABLE III COMPARISON OF MIXERS

Another important role of these two inductors is to protect RF current flowing into the current bleeding circuit. This helps RF current flow into the mixer output directly. Therefore, we can achieve more conversion gain than the conventional current bleeding technique. As can be seen from Fig. 9, LO drives nodes A and B in phase and a common mode equivalent circuit has been used for analyzing the circuit. If the RF transconductance stage works and is virtually short, as differentially, the node between shown in Fig. 9. Fig. 10 shows the simplified small-signal model of Fig. 8 for half of the double-balanced mixer, and the same analytical method can be applied to the other half. The input impedance in the parallel RLC resonant circuit, shown in Fig. 10, is (11)

is the resonant frequency. From (16), the input where is a purely real impedance. impedance at resonant frequency By using two resonating inductors, we have decreased the . Therefore, we have improved effect of the tail capacitance conversion gain by 6 dB and flicker-noise corner frequency by kHz kHz kHz at the expense of an 425 kHz increase in the silicon area due to inductors in comparison to the Gilbert-type mixer based on the current bleeding technique. Also, as can be seen from Figs. 7 and 9, the mixer with one inductor has one more shunted resistance path for RF leakage current than the mixer with two inductors. It is the reason why we can achieve more conversion gain by using two inductors than the mixer with one inductor. At resonance, the impedance of two resonating inductors is 550 ( nH with and at 5.2 GHz) and because and is virtually shorted. the node between

(12)

IV. SIMULATION AND MEASUREMENT RESULTS

and the power delivered to the resonator is (13) (14) The power dissipated by the resistors

and

is (15)

At resonance, (16) (17) (18)

The chip microphotographs of the three mixers are shown in Figs. 11 and 12. For comparative purposes, a conventional Gilbert-type mixer has also been fabricated, as shown in Fig. 11(a). The conventional Gilbert-type mixer was designed exactly the same as the mixer with the current bleeding technique, which is shown in Fig. 11(b), except the current bleeding circuit. Fig. 12(a) presents a die photograph of the Gilbert-type mixer with one resonating inductor, and Fig. 12(b) shows the die photograph of the mixer with two resonating inductors. All measurements were performed using an on-wafer probe station. Two off-chip baluns were used to generate differential signals for RF stages and LO stages, respectively. For 50matching at the mixer output, on-chip output buffers were fabricated with the mixers. Table I summarizes the measured results for the four fabricated mixers and shows that the proposed two mixers using the resonating technique outperform the conventional current bleeding mixer on conversion gain and flicker corner frequency. It also shows that the proposed mixer based on the current bleeding technique with two resonating inductors

PARK et al.: DESIGN AND ANALYSIS OF LOW FLICKER-NOISE CMOS MIXERS FOR DIRECT-CONVERSION RECEIVERS

has the best performance on conversion gain and flicker corner frequency. The variations of conversion gain with LO power for all three mixers were simulated and measured in Fig. 13. In Fig. 14, conversion gain is decreased as the resonating frequency is changed, especially for two mixers: the mixer with one resonating inductor and the mixer with two resonating inductors. This means that conversion gain is maximized under resonant condition for these two mixers, as analyzed in Section III. Fig. 15 shows the simulated and measured NFs for three mixers. The mixer with two resonating inductors has a measured conversion gain of 16.2 dB with an LO power of 0 dBm. The mixer also has a measured input 1-dB compression point of 14 dBm and an input third-order intercept point (IIP3) of 5 dBm, as shown in Figs. 16 and 17, respectively. The LO to RF isolation is 36.3 dB. Fig. 18 shows output noise power spectral density, which was measured on both an HP 4395A low-frequency spectrum analyzer and Agilent 35670A dynamic signal analyzer for more accurate measurement. The measured flicker-noise corner frequency is 125 kHz, which is the lowest corner frequency ever reported using a CMOS active mixer with a more than 15 dB of conversion gain based on experimental results. Fig. 19 shows the measured NF for the mixer with two resonating inductors and it is found to be 9.8 dB at 1 MHz and above. Table II also shows the measured results of the flicker corner frequency with different bleeding currents for the mixer with one inductor and two inductors, respectively. As we increase the bleeding current, the bias current of the LO switches is decreased and the noise current generated by the direct mechanism is also simultaneously decreased. Therefore, as we analyzed in Section III, the flicker corner frequency is decreased. This is shown in Table II. More detailed results of three fabricated mixers are summarized and compared in Table III. V. CONCLUSION Three double-balanced Gilbert-type down conversion mixers, i.e., a Gilbert-type mixer based on the current bleeding technique, a Gilbert-type mixer based on the current bleeding technique with one resonating inductor, and a Gilbert-type mixer based on the current bleeding technique with two resonating inductors, have been designed and analyzed to improve flickernoise performance without sacrificing conversion gain, NF, and linearity performance for direct-conversion receivers. The proposed mixers, fabricated in a 0.18- m CMOS process, show significantly improved performances on flicker noise and conversion gain. The main ideas of the proposed mixers are to reduce the bias current of LO switches, to resonate the tail capacitance ( ), and to minimize the amount of RF current flowing into the current bleeding circuit. Among the three CMOS mixers, the Gilbert-type mixer based on the current bleeding technique with two resonating inductors shows the best performance on flicker noise and conversion gain. In this mixer, two inductors are separately connected to each node between the current bleeding pMOS device and LO switching devices in order to resonate the tail capacitance out. In addition, the inductors protect RF current flowing into the current bleeding circuit, which results in improvements of conversion gain. By using two inductors, conversion gain is increased by 6 dB in comparison to the Gilbert-type mixer based on the current bleeding technique, and the flicker

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corner frequency is decreased from 550 to 125 kHz. By using one resonating inductor, conversion gain is increased by 3 dB in comparison to the mixer based on the current bleeding technique, and the flicker corner frequency is decreased from 550 to 180 kHz. In conclusion, the Gilbert-type mixer based on the current bleeding technique with two resonating inductors shows better results on flicker noise and conversion gain performance than the other two mixers. Measurements on the Gilbert-type mixer based on the current bleeding technique with two resonating inductors give an NF of 9.8 dB at 1 MHz, a conversion gain of 16 dB, an IIP3 of 5 dBm, and a flicker corner frequency of 125 kHz. The circuit consumes 3.9 mA from a 1.8-V supply. The overall performance of the fabricated mixers shows good agreement with the proposed design ideas. ACKNOWLEDGMENT The authors thank P. O’Farrell, National Semiconductor, Atlanta, GA, and A. J. Aude, Samsung Advanced Institute of Technology (SAIT), Yongin, Korea, for their technical support and chip fabrication. REFERENCES [1] J. Chang, A. A. Abidi, and C. R. Viswanathan, “Flicker noise in CMOS transistors from subthreshold to strong inversion at various temperatures,” IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 1965–1971, Nov. 1994. [2] Z. Zhang, Z. Chen, and J. Lau, “A 900 MHz CMOS balanced harmonic mixer for direct conversion receivers,” in IEEE Radio Wireless Conf., Sep. 2000, pp. 219–222. [3] H. Darabi and A. A. Abidi, “Noise in RF-CMOS mixers: A simple physical model,” IEEE J. Solid-State Circuits, vol. 35, no. 1, pp. 15–25, Jan. 2000. [4] H. Darabi and J. Chiu, “A noise cancellation technique in active-RF CMOS mixers,” in Int. Solid-State Circuits Conf., 2005, pp. 544–545, Session 29. [5] A. L. McWorther, “1=f noise and germanium surface properties,” in Semiconductor Surface Physics. Philadelphia, PA: Univ. Pennsylvania Press, 1957, p. 207. [6] F. N. Hooge, T. G. M. Kleinpenning, and L. K. J. Vandamme, “Experimental studies on 1=f noise,” Rep. Progr. Phys., vol. 44, pp. 497–532, 1981. [7] K. W. Chew, K. S. Yeo, and S.-F. Chu, “Effect of technology scaling on the 1=f noise of deep submicron pMOS transistors,” Solid State Electron., vol. 48, no. 7, pp. 1101–1109, Jul. 2004. [8] M. T. Terrovits and R. G. Meyer, “Noise in current-commutating CMOS mixers,” IEEE J. Solid-State Circuits, vol. 34, no. 6, pp. 772–783, Jun. 1999. [9] D. Manstretta, R. Castello, F. Gatta, P. Rossi, and F. Svelto, “A 0.18 m CMOS direct-conversion receiver front-end for UMTS,” in Int. SolidState Circuits Conf. Tech. Dig., 2002, pp. 240–241. [10] G. Montagna, R. Castello, R. Tonietto, M. Valla, and I. Bietti, “A 72 mW CMOS 802.11a direct conversion receiver with 3.5 dB NF and 200 kHz 1=f noise corner,” in VLSI Circuits Tech. Symp. Dig., 2004, pp. 16–19. [11] C. D. Hull and R. G. Meyer, “A systematic approach to the analysis of noise in mixers,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 12, pp. 909–919, Dec. 1993. [12] A. Abidi, “Direct-conversion radio transceivers for digital communications,” IEEE J. Solid-State Circuits, vol. 30, no. 12, pp. 1399–1410, Dec. 1995. [13] E. E. Bautista et al., “A high IIP2 downconversion mixer using dynamic matching,” IEEE J. Solid-State Circuits, vol. 35, no. 12, pp. 1934–1941, Dec. 2000. [14] S.-G. Lee et al., “Current-reuse bleeding mixer,” Electron. Lett., vol. 36, no. 8, pp. 696–697, Apr. 2000. [15] H. Darabi and J. Chiu, “A noise cancellation technique in active-RF CMOS mixers,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2628–2632, Dec. 2005.

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[16] E. A. M. Klumperink, S. M. Louwsma, G. J. M. Wienk, and B. Nauta, “A CMOS switched transconductor mixer,” IEEE J. Solid-State Circuits, vol. 39, no. 8, pp. 1231–1240, Aug. 2004. [17] D. Manstretta, M. Brandolini, and F. Svelto, “Second-order intermodulation mechanisms in CMOS downconverters,” IEEE J. Solid-State Circuits, vol. 38, no. 3, pp. 394–406, Mar. 2003. [18] D. Manstretta, R. Castello, and F. Svelto, “Low 1=f noise CMOS active mixers for direct conversion,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 48, no. 9, pp. 846–850, Sep. 2001. [19] B. Razavi, “Design considerations for direct-conversion receivers,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44, no. 6, pp. 428–435, Jun. 1997. [20] J. Park, C.-H. Lee, B. Kim, and J. Laskar, “A low flicker noise CMOS mixer for direct conversion receivers,” presented at the IEEE MTT-S Int. Microw. Symp., Jun. 2006.

Jinsung Park (S’04) was born in Seoul, Korea, in 1971. He received the B.S. degree (with second highest honor) from Myongji University, Yongin, Korea, in 1994, the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 1998, and is working toward the Ph.D. degree in electrical and computer engineering at the Georgia Institute of Technology. From 2000 to 2001, he was with Summit Microelectronics, San Jose, CA, where he was an Analog and Mixed-Signal Integrated Circuit (IC) Design Engineer involved with power management ICs for network backbone application. His current research interests includes CMOS direct-conversion receiver design, low flicker-noise receiver design, receiver architecture for multiple-input–multiple-output (MIMO) application, highly linear receiver design, and CMOS power-amplifier design by using distributed active transformers for global system for mobile communications (GSM) application.

Chang-Ho Lee (M’01) received the B.S. and M.S. degrees in electrical engineering from Korea University, Seoul, Korea, in 1989 and 1991, respectively, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 1999 and 2001, respectively. From 1994 to 1996, he was a Research Engineer with Dacom Corporations, Seoul, Korea. In 2000, he joined RF Solutions Inc. Norcross, GA, where he was a Staff Engineer. Since 2003, he has been a member of the research faculty with the Georgia

Institute of Technology. His research interest includes satellite/wireless communication system design, and design/characterization of the transceiver RF integrated circuits (RFICs) in GaAs devices and Si-based CMOS/SiGe HBT processes, as well as low-temperature co-fired ceramic (LTCC)/multilayer organic (MLO)-based multilayer multichip modules development for wireless communication applications. His current research is related to low-power reconfigurable front-end design for cognitive radio applications.

Byung-Sung Kim (S’96–A’98–M’03) was born in Seoul, Korea, in 1965. He received the Ph.D. degree in electronic engineering from Seoul National University, Seoul, Korea, in 1997. In 1997, he joined the School of Electrical and Computer Engineering, Sungkyunkwan University, Suwon, Korea, where he is currently an Associate Professor. His main research interests are RF CMOS IC and system-on-package (SOP) design.

Joy Laskar (S’84–M’85–SM’02–F’05) received the B.S. degree in computer engineering with math/physics minors (with highest honors) from Clemson University, Clemson, SC, in 1985, and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 1989 and 1991, respectively. Prior to joining the Georgia Institute of Technology in 1995, he held faculty positions with the University of Illinois at Urbana-Champaign and the University of Hawaii. With the Georgia Institute of Technology, he holds the Joseph M. Pettit Professorship of Electronics and is currently the Chair for the Electronic Design and Applications Technical Interest Group. He is also the Director of the Electronic Design Center, Georgia Institute of Technology. and the System Research Leader for the NSF Packaging Research Center. His research has produced numerous patents and transfer of technology to industry. Most recently, his research has resulted in the formation of two companies. In 1998, he cofounded the advanced wireless local area network (WLAN) IC Company RF Solutions, which is now part of Anadgics (Nasdaq: Anad). In 2001, he cofounded the next-generation interconnect company Quellan Inc., Atlanta, GA, which develops collaborative signal-processing solutions for enterprise applications. Prof. Laskar has been appointed an IEEE Distinguished Microwave Lecturer for the 2004–2006 term for “Recent Advances in High Performance Communication Modules and Circuits” seminar.

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A Broadband Single-Stage Equivalent Circuit for Modeling LTCC Bandpass Filters Yu-Shun Tsai and Tzyy-Sheng Horng, Senior Member, IEEE

Abstract—A single-stage equivalent circuit is proposed to model microwave bandpass filters (BPFs) fabricated in low-temperature co-fired ceramic (LTCC) technology up to several times its passband frequency. The equivalent circuit adopts a modified T topology with the expandable multilayer resonators to achieve an extremely large bandwidth. It can be efficiently established from the measured -parameters using direct extraction or rational approximation. As a result, the modeled -parameters for a 2.45-GHz wideband local area network (WLAN) LTCC BPF show good agreement with the measured results over a wide frequency range up to 8.5 GHz. Such a broadband model can be used to accurately predict the suppression of harmonics and interferences in system simulation of the WLAN front-end modules. Index Terms—Equivalent-circuit model, low-temperature co-fired ceramic (LTCC) bandpass filter (BPF), wideband local area network (WLAN) BPF.

Fig. 1. Microwave BPFs causing the termination effects on the active components in the transmitter and receiver of a wireless front-end module.

I. INTRODUCTION

I

N WIRELESS front-end applications, microwave bandpass filters (BPFs) are crucial components to suppressing the output harmonics in the transmitter and the input interferences in the receiver, as illustrated in Fig. 1. When connected with the power amplifiers or low-noise amplifiers, they possibly vary the load or source termination impedances at harmonic frequencies, which has an impact on linearity and efficiency of the amplifiers. However, the measured responses of -parameters provided by the filter manufacturers have quite limited use in quantifying the suppression or termination effects. This is because accurate prediction of those effects generally requires a system-level nonlinear simulation. Broadband SPICE models should still be a must for microwave BPFs when used in the nonlinear simulation with active components. Due to the complexity of all kinds of electromagnetic (EM) effects involved, the establishment of broadband models for microwave BPFs is still difficult and challenging. Previous methods include the physical models [1]–[3], EM simulation models [4]–[7], and model-based approaches [8]–[15]. The physical models can take the high-frequency losses, coupling, and parasitic effects into account, but require complete knowledge of every physical component inside a BPF. The EM simulation models can account for the EM phenomena clearly by partitioning the filter geometrical configuration and establishing

Manuscript received March 31, 2006; revised July 1, 2006. This work was supported in part by the Ministry of Education under the Program of Aim for the Top University Plan, Taiwan, R.O.C., and by the National Science Council, Taiwan, R.O.C., under Grant 94-2213-E-110-031. The authors are with the RF and Microwave Laboratory, Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.883603

the partial-element equivalent circuits (PEECs) based on the EM simulation results. However, EM simulation usually takes a long computation time. Besides, it is sometimes difficult to find a proper partition for accurate PEEC extraction without the help of optimization techniques. The model-based approaches can synthesize a real filter response and, thus, are quite helpful in diagnosing and tuning a BPF. However, they usually require the intensive optimization schemes to find the equivalent-circuit parameters [11]–[13]. In addition, the solutions may not be unique. Although in [10] an extraction procedure using the closed-form recursive formulas was demonstrated to find the equivalent-circuit parameters, the modeled filters were limited to some symmetric and known types. To the best of the authors’ knowledge, the equivalent-circuit models for microwave BPFs reported to date in the literature were not yet able to cover a broad frequency range from direct current up to two or more integer times the passband center frequency. In our previous research [16]–[18] for studying and modeling the passive components embedded in a multilayer low-temperature co-fired ceramic (LTCC) substrate, the modified T-equivalent circuit was first found suitable for broadband modeling of spiral inductors of arbitrary kind. Recently we explored the applications of such an equivalent-circuit topology to the LTCC BPFs, and the preliminary modeled results shown in [19] were quite encouraging. In this paper, we aim to provide an evolutionary insight into the broadband characteristics of modified T-equivalent circuit, and compare the accuracy and efficiency between two different approaches, i.e., direct extraction and rational approximation, in establishing the modified T-equivalent circuit. It is emphasized that the proposed modified T-equivalent circuit is only a single-stage model, but can be easily expanded to achieve a bandwidth as large as a distributed circuit model.

0018-9480/$20.00 © 2006 IEEE

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Fig. 2. Design configuration of the LTCC BPF.

II. EVOLUTION OF BPF PROTOTYPE The currently available LTCC technology can implement high-performance miniature BPFs quite successfully because of the capability to realize large-value capacitors in a large number of thin substrate layers. To fully employ this capability, most of the LTCC BPF designs adopt a capacitive coupling of parallel resonators as a lumped-element prototype [20], [21], which is mainly composed of the large-value multilayer capacitors in conjunction with the small-value meander-line inductors, as illustrated in Fig. 2. The BPF configuration shown in Fig. 2 uses the capacitive coupling to link two parallel resonators. It has a small size advantage due to the geometrical simplicity. However, it is based on a second-order BPF prototype that has an inherent lower rolloff in comparison with a higher order design [22], [23]. To improve this drawback, a small ground inductance by means of a proper design of the LTCC ground electrodes and the plated through holes to printed circuit board (PCB) ground can be applied to create a transmission zero in both the lower and higher stopbands for enhancing the rolloff rates. Fig. 3(a) shows a -topology prototype with a series inductive feedback to account for the LTCC BPF configuration shown in Fig. 2. As shown in Fig. 3(b), this prototype can synthesize a transmission response with two angular transmission-zero freand , at both sides of passband. Another quencies, i.e., view of this prototype is in a T-topology with a parallel capacitive feedback, as shown in Fig. 3(c). Generally speaking, the equivalent circuits established based on the prototype shown in Fig. 3(a) or (c) for an LTCC BPF can hardly explain the spurious behavior in the measured -parameter responses. This is because the multilayer capacitors in an LTCC BPF are usually of so large a value as to cause the obvious series and higher order resonance effects [18], [24] in the frequency range of interest. It might be thought that the equivalent circuits, as suggested in [24], for modeling the multilayer capacitors with series and higher order resonances can be included. However, this makes the extraction of the equivalent-circuit elements from the measured -parameters become a formidable task. This paper presents an alternative prototype based on the modified T topology shown in Fig. 3(d) as a foundation to establish the broadband equivalent circuits for LTCC BPFs. The new prototype has a unique feature to put all the capacitance

Fig. 3. (a) LTCC BPF prototype in 5 topology with a series inductive feedback. (b) Magnitude of S in decibel generated from the LTCC BPF prototype. (c) LTCC BPF prototype in T topology with a parallel capacitive feedback. (d) LTCC BPF prototype in modified T topology.

elements ( and ) in the parallel and series feedback circuits. Included with the additional mutual and shunt inductance and ), the modified T-topology prototype elements ( shown in Fig. 3(d) can be equivalent to the prototype shown in Fig. 3(a) or (c) if the following relations hold: (1) (2) (3) It is emphasized that such a modified T-topology prototype for modeling an LTCC BPF is easy to include the series and higher order resonances resulting from the multilayer capacitors by expanding the series and parallel feedback circuits as the multilayer resonators. In addition, direct extraction or rational approximation can be applied to find all the equivalent-circuit elements from the measured -parameters. The detailed procedures are provided in Sections IV and V. III. MODIFIED T-EQUIVALENT CIRCUIT Fig. 4(a) shows a generalized modified T-equivalent network proposed for modeling LTCC BPFs. When compared to the well-known T-equivalent network, the modified T-equivalent network additionally includes the parallel-feedback admittance , series-feedback impedance , and mutual inductive to model the coupling and grounding effects. impedance as a multilayer series/parallel resonator By modeling with a continuous increase of layer numbers, as illustrated in Fig. 4(b), the modified T-equivalent circuit can expand accordingly to an increase in the bandwidth in a way like a distributed circuit, but still remains a single-stage equivalent circuit.

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From (4)–(9), we find that the two-port modified T-equivalent network can be decomposed into two one-port networks with input impedance or admittance defined ass

(10)

(11) Fig. 4. (a) Proposed modified T-equivalent network. (b) Use of expandable multilayer resonators for modeling the high-frequency resonance effects.

Fig. 5. (a) Reduced T-equivalent network at low frequency. (b) Decomposed one-port network with input admittance of Y according to (10). (c) Decomposed one-port network with input impedance of Z according to (11).

At low frequencies, the coupling and grounding effects are negligible, which means mathematically that and as . With this condition, the modified T-equivalent network can reduce to a simple T-equivalent and one network composed of two series impedance shunt impedance only, as shown in Fig. 5(a). When all types of coupling and grounding effects need to be considered at high frequencies, the modified T-equivalent network, as shown in Fig. 4(a), can be generally used. After derivation, its and network parameters are expressed as

From (10), one can know that is equal to the resulting admitin tance for the total of the main series impedance , parallel connection with the parallel-feedback admittance as depicted in Fig. 5(b). From (11), can be looked upon as the , impedance of a series connection of the shunt impedance , and an impedance equal to the series-feedback impedance subparallel connection of two series impedances tracting the mutual inductive impedance , as depicted in and Fig. 5(c). It is noted that, according to (10) and (11), can be practically obtained from and network parameters, respectively, converted from the measured or EM-simulated -parameters. As a matter of fact, the proposed modified T-network topology can be used to establish the mathematically equivalent circuit of any two-port reciprocal component. However, to consider the physical aspects, the actual representation of equivalent circuits using a modified T-network topology in this paper includes the low-frequency extracted parameters and the multilayer resonators to account for the prototype configuration and the high-frequency resonance effects, respectively, for specific use on the LTCC BPFs. IV. DIRECT EXTRACTION For our study case of a 2.45-GHz LTCC BPF, it is quite circuits for straightforward to extract the equivalent series , , and in Fig. 5(a) from the network parameters at low frequencies for low for low for low

(4) (5) (6) (7) (8)

(9)

(12) (13) (14)

Extraction of the other equivalent circuits for , , and can rely on input admittance/impedance of the decomposed netand , with the suggested equivalent circuit shown works, represents the impedance in Fig. 6(a) and (b), respectively. that appears in the BPF protoof the mutual inductance type configuration of Fig. 3(d). and are modeled as the expandable multilayer resonators to account for the higher order resonance effects due to coupling and grounding, respectively. resonant circuit elements can be extracted from the The frequency response of . To determine the reactive elements resonant circuit that is composed of a number of in the series resonators, we need to identify a number of pairs of and angular parallel and series resonant frequencies, i.e., , and , in the imaginary response of within the measurement frequency range, as shown in Fig. 7.

TSAI AND HORNG: BROADBAND SINGLE-STAGE EQUIVALENT CIRCUIT FOR MODELING LTCC BPFs

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can be determined from the first The parallel resistance factor and its corresponding angular frequency peak using the following approximation of under the lowfrequency condition: (19) where (20)

Fig. 6. Suggested equivalent circuits for modeling the decomposed one-port networks. (a) Y network. (b) Z network.

, which is the resistance in series with In (19), and can be extracted from the real part of at low equal to frequencies. Substituting (19) into (18) and setting , one can solve for as (21) , , are deterThe other resistances, i.e., mined from identifying a number of local minima, i.e., at , , as depicted in Fig. 7. The formulation can be described as (22) where

Fig. 7. Specific frequencies used for extracting the Y resonant circuit elements in the direct-extraction procedure.

(23) The formulated equation for reactive elements at these resonant frequencies is written as

After substituting (23) into (22), one can solve for from the following set of equations:

,

(15) (24) where the imaginary part of yields

, which is the inductance extracted from at low frequencies. Solving (15)

where (25)

for

and

(16) (17)

resonant circuit In this approach, the resistances in the response, as shown in are extracted from ’s -factor Fig. 7 rather than ’s real response. The reasons are because the former is more closely related to the frequency dependence of insertion loss in an LTCC BPF and also behaves more smoothly is given as than the latter. The definition of (18)

A side advantage using the response deserves to be menbecomes zero corretioned that the frequencies at which spond to the parallel or series resonant frequencies of . This provides a fast way of getting those resonant frequencies data resonant circuit. for extracting the reactive elements in the In a similar fashion, by identifying the parallel and series anand , gular resonant frequencies, i.e., in the imaginary response of , as shown in Fig. 8, we can and all the reactive elements in the resonant circuit find shown in Fig. 6(b) from the following formulation:

(26)

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where (34)

V. RATIONAL APPROXIMATION Inspired from the equivalent-circuit configurations shown in Fig. 6(a) and (b), we consider the rational approximation of and in the following forms: Fig. 8. Specific frequencies used for extracting the ments in the direct-extraction procedure.

where and nary part of Note that

Z

resonant circuit ele-

(35)

are the inductances extracted from the imagiand , respectively, at low frequencies. as , which implies (27)

Solving (26) yields

for

and

(28) (29)

, As for the resistances, i.e., resonant circuit, they are determined from defined as

’s

(36) where (37) and Note that in (35)–(37), , , and are real constants, denote the real residue and the real pole, respectively, and for are pairs of complex and and conjugate residues and poles, respectively. All these constants, residues, and poles in (35)–(37) are determined based on a well-known vector-fitting procedure [25]–[28]. Under low-loss standing for the transfer function of a complex condition, pole pair can be approximated as

, in the factor (38) (30)

at , By identifying a number of local minima, in the response, as shown in Fig. 8, we can as express

On the other hand, and according to the equivalent circuits shown in Fig. 6(a) and (b) can be derived as

(39) (31) where (40) (32) In (32), and are the resistances extracted from the real and , respectively, at low frequencies. Subpart of , stituting (32) into (31), one can solve for from the following set of equations:

By comparing (39) and (40) with (35) and (36), the relations between the equivalent-circuit elements and the vector-fitting parameters are found as

(41) (42) (33)

(43)

TSAI AND HORNG: BROADBAND SINGLE-STAGE EQUIVALENT CIRCUIT FOR MODELING LTCC BPFs

(44)

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TABLE I PARAMETER VALUES USED IN THE DIRECT-EXTRACTION PROCEDURE FOR EVALUATING THE EQUIVALENT-CIRCUIT ELEMENTS

(45) (46) Thus far, we still need to determine , , and before combining the two one-port equivalent circuits for and into the wanted two-port modified T-equivalent circuit for the LTCC BPF. By referring to Fig. 6(a) and (b), we know that (47) (48) is a known element from (27). Another condition can where to in terms be obtained by estimating the ratio of of the network parameters at low frequencies, which is given as for low From (47)–(49), mined as

,

, and

(49)

can be finally deter-

(50) (51) (52) VI. MODELED RESULTS AND DISCUSSION An LTCC BPF for 2.45-GHz wideband local area network (WLAN) applications was implemented according to the configuration shown in Fig. 2 as our modeling example. The BPF was designed to have an insertion loss less than 2.5 dB in the passband frequency range from 2.4 to 2.5 GHz, and an attenuation more than 25 dB at the second and third harmonic frequencies. To create a transmission zero at both sides of the passband for enhancing the rolloff rate, a small ground inductance was provided, resulting from the plated through holes in the PCB that serves as a mounting substrate. The -parameter measurement for this LTCC BPF was taken up to 8.5 GHz to cover higher than the third harmonic frequency. The measured results met our design goals and also proved our prediction to have the two transmission zeros at approximately 2 and 3 GHz. Converted from the measured -parameters, the two crucial and , for establishing the modified parameters, i.e., T-equivalent circuit were processed through the procedure of direct extraction and rational approximation described in Sections IV and V, respectively, to determine and compare the equivalent-circuit elements. To have a fair comparison, the above two different modeling approaches were conducted on purpose to construct the equivalent circuits of identical configuration with the same number of elements. Tables I and II show the necessary extracted data in both procedures for evaluating

TABLE II PARAMETER VALUES USED IN THE RATIONAL-APPROXIMATION PROCEDURE FOR EVALUATING THE EQUIVALENT-CIRCUIT ELEMENTS

the equivalent-circuit elements. It is noted that the direct-extraction approach utilized the -factor responses of and to find the resonant frequencies, as well as the local maxima and minima points listed in Table I and substituted them into (16),

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Fig. 9. Established modified T-equivalent circuits for the 2.45-GHz LTCC BPF. (a) Direct extraction method. (b) Rational approximation method.

Fig. 11. Comparisons of the modeled results with measurements for the oneport network with input impedance of . (a) Imaginary part of . (b) factor of .

Z

Fig. 10. Comparisons of the modeled results with the measurements for the one-port network with input admittance of . (a) Imaginary part of . (b) factor of .

Y

Y

Y

Q

(17), (21), (24), (28), (29), and (33) for extracting the equivalent and . multilayer resonant circuits for For the rational-approximation approach, it adopts the 3-dB and at the resonant frequencies identibandwidth of fied in the direct-extraction procedure to estimate the complex starting poles to be used in the vector-fitting procedure. This action could avoid the ill-conditioning problems in vector fitting [25], [26], and consequently obtained the accurate poles,

Z

Z

Q

residues, and coefficient constants listed in Table II very efficiently. Note that the real parts of all poles listed in Table II are negative, which can assure the stability of the fitting models for and . Besides, for consideration of passivity in time-doand has main simulation, the positive real property of been also assured by checking all the residues and coefficient constants listed in Table II to satisfy the relation of positive semidefiniteness described in [28]. Since the modeled LTCC BPF has low-loss characteristics, and used in establishing the modified the parameters T-equivalent circuits clearly exhibit multiple resonances in the imaginary responses, as can be seen in Figs. 7 and 8. Identifying the resonant frequencies in the imaginary responses of and is greatly helpful to find good rational models with relatively low order. Therefore, there may be no such need to apply the advanced techniques like Cauchy’s methods with an adaptive selection of sampling points and model order [13]–[15] or the model-order reduction methods [29], [30] for yielding the reduced-order rational models. After substituting the parameters listed in Table II into (43)–(46), we found another set of the equivalent multilayer and . As for the equivalent series resonant circuits for circuits for , , and formulated in (12)–(14) and (50)–(52) during the procedure of direct extraction and rational approximation, respectively, they were primarily extracted at low frequencies.

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Fig. 12. Comparisons of the modeled results of S -parameter magnitudes with measurements for the 2.45-GHz LTCC BPF. (a) Magnitudes of S and S from 0.1 to 8.5 GHz. (b) Magnitudes of S and S from 2 to 3 GHz.

Fig. 13. Comparisons of the modeled results of S -parameter phases with the measurements for the 2.45-GHz LTCC BPF. (a) Phase of S from 0.1 to 8.5 GHz. (b) Phase of S from 0.1 to 8.5 GHz.

As a result, Fig. 9(a) and (b) shows the two-port modified T-equivalent circuit established based on direct extraction and rational approximation, respectively. Figs. 10 and 11 compare the modeling accuracy in the two decomposed one-port ( and ) networks between the two approaches. One can see in Figs. 10(a) and 11(a) that the modeled results of the imagiand from both approaches show excelnary responses of lent agreement with the measured results. However, a moderate discrepancy between the two approaches has been found in the and shown in Figs. 10(b) and 11(b), modeled results of respectively. Due to the specific use of the local maxima and minima points in resistance extraction, the direct-extraction apand having proach can generate the modeled results for better agreement with measurements than the rational-approximation approach. This also implies that the modeled results for and using a rational approximation cannot satisfactorily account for the real responses. Figs. 12–14 show comparisons of the modeled -parameters and group delays with measurements between the two modified T-equivalent circuits shown in Fig. 9(a) and (b). It can be seen that the modeled results from direct extraction can achieve an impressive agreement with the measured results over the entire measurement frequency range up to 8.5 GHz. For the other modeled results using rational approximation with worse matching and parameters, a larger deviation from measureof the ment has been found in the -related responses, such as the

insertion losses in Fig. 12(a) and (b) and the phase and group delays in Figs. 13 and 14. For general application of the proposed modified T-equivalent circuit topology to other types of filters, or even any microwave passive components in two-port configuration, here we attempt to outline a suggested model extraction procedure as follows. Step 1) Find a low-frequency prototype with physical sense for the component to be modeled with the modified T-equivalent circuit. Step 2) Convert the low-frequency prototype into an equivalent circuit in the modified T topology, as described in Section II. Step 3) Expand the parallel- and series-feedback elements of the equivalent circuit in the modified T topology as multilayer resonators to account for the high-frequency resonance effects, as described in Section III. Step 4) Decompose the two-port modified T-equivalent circuit into the two one-port circuits with input adfor one one-port circuit and input mittance of impedance of for the other. Both and data come from the measured or EM-simulated -parameter data, as also described in Section III. and ’s oneStep 5) Determine the circuit elements in port circuits using the direction-extraction method

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REFERENCES

Fig. 14. Comparisons of the modeled results of group delay with the measurements from 2 to 3 GHz for the 2.45-GHz LTCC BPF.

described in Section IV or the rational-approximation method described in Section V. To this step, all the circuit elements in the modified T-equivalent circuit are determined. It is finally noted that the automatic generation of mathematically equivalent circuits for microwave passive components has been reported in the open literature [31]–[34] and even developed as commercial tools [35], [36]. In their typical procedure for modeling a two-port reciprocal component, rational approximation is applied to the three network parameters, i.e., , , and or , , and for establishing the equivalent circuits based on Cauer or Foster network synthesis techniques [37], [38]. When compared to the proposed modified T-equivalent circuits, the equivalent circuits established in their ways generally need more circuit elements to achieve a similarly large bandwidth. This is because the synthesis of modified T-equivalent circuits counts on modeling only and . Besides, their equivalent cirtwo parameters, i.e., cuits consist of , , , and elements often with many additional ideal transformers if generated using a Cauer structure [31], [32] or with negative-valued elements if generated using a Foster structure [33]–[36] and, thus, are not as comprehensible as the modified T-equivalent circuits. VII. CONCLUSION The proposed new equivalent circuit has been found suitable for broadband modeling of LTCC BPFs. This is because the equivalent circuit uses a modified T topology to well characterize the LTCC BPF prototype configurations. In addition, it includes the parallel- and series-feedback resonant circuits to appropriately account for the high-frequency resonance effects. These two resonant circuits can be expanded to meet any need for increased bandwidth. It is emphasized that this new equivalent circuit can be efficiently established because all the circuit elements can be determined from the measured -parameters by means of either direct extraction or rational approximation. Consequently, in the example of modeling a 2.45-GHz WLAN LTCC BPF, the modeled -parameters have good agreement with the measured results over a frequency range more than three times larger than the BPF’s passband center frequency.

[1] K. M. Lakin, “Modeling of thin film resonators and filters,” in IEEE MTT-S Int. Microw. Symp. Dig., 1992, pp. 149–152. [2] S. Wang, W. G. Odendaal, and F. C. Lee, “Extraction of parasitic parameters of EMI filters using scattering parameters,” in Proc. IEEE Ind. Appl. Soc. Conf., 2004, pp. 2672–2678. [3] S.-G. Mao, M.-S. Wu, Y.-Z. Chueh, and C.-H. Chen, “Modeling of symmetric composite right/left-handed coplanar waveguides with applications to compact bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3460–3466, Nov. 2005. [4] K.-L. Wu, R. Zhang, M. Ehlert, and D.-G. Fang, “An explicit knowledge-embedded space mapping technique and its application to optimization of LTCC RF passive circuits,” IEEE Trans. Compon. Packag. Technol., vol. 26, no. 2, pp. 399–406, Jun. 2003. [5] M. A. Ismail, S. A. Panariello, Y. Wang, and M. Yu, “EM-based design of large-scale dielectric-resonator filters and multiplexers by space mapping,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 386–392, Jan. 2004. [6] K.-L. Wu, Y.-J. Zhao, J. Wang, and M. K. K. Cheng, “An effective dynamic coarse model for optimization design of LTCC RF circuits with aggressive space mapping,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 393–402, Jan. 2004. [7] I. A. Eshrah, A. A. Kishk, A. B. Yakovlev, W. G. Glisson, and C. E. Smith, “Analysis of waveguide slot-based structures using wideband equivalent-circuit model,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 12, pp. 2691–2696, Dec. 2004. [8] T. Thal, “Computer-aided filter alignment and diagnosis,” IEEE Trans. Microw. Theory Tech., vol. MTT-26, no. 12, pp. 958–963, Dec. 1978. [9] P. Harscher and R. Vahldieck, “Automated computer-controlled tuning of waveguide filters using adaptive network models,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 11, pp. 2125–2130, Nov. 2001. [10] H.-T. Hsu, Z. Zhang, K. A. Zaki, and A. E. Atia, “Parameter extraction for symmetric coupled resonator filters,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2971–2978, Dec. 2002. [11] P. Harscher and R. Vahldieck, “Automated filter tuning using generalized low-loss prototype networks and gradient-based parameter extraction,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2532–2538, Dec. 2001. [12] M. Kahrizi, S. Safavi-Naeini, S. K. Chaudhuri, and R. Sabry, “Computer diagnosis and tuning of RF and microwave filters using modelbased parameter estimation,” IEEE Trans. Circuits Syst., vol. 49, no. 9, pp. 1263–1270, Sep. 2002. [13] A. Garcia-Lamperez, S. Llorente-Romano, M. Salazar-Palma, and T. K. Sarkar, “Efficient electromagnetic optimization of microwave filters and multiplexers using rational models,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 2, pp. 508–521, Feb. 2004. [14] A. Lamecki, P. Kozakowski, and M. Mrozowski, “Efficient implementation of the Cauchy method for automated CAD-model construction,” IEEE Microw. Guided Wave Lett., vol. 13, no. 7, pp. 268–270, Jul. 2003. [15] S. F. Peik, R. R. Mansour, and Y. L. Chow, “Multidimensional Cauchy method and adaptive sampling for an accurate microwave circuit modeling,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2364–2371, Dec. 1998. [16] T.-S. Horng, J.-M. Wu, L.-Q. Yang, and S.-T. Fang, “A novel modified-T equivalent circuit for modeling LTCC embedded inductors with a large bandwidth,” in IEEE MTT-S Int. Microw. Symp. Dig., 2003, pp. 1015–1018. [17] ——, “A novel modified-T equivalent circuit for modeling LTCC embedded inductors with a large bandwidth,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 2327–2333, Dec. 2003. [18] C.-T. Chiu, T.-S. Horng, H.-L. Ma, S.-M. Wu, and C.-P. Hung, “Super broadband lumped models for embedded passives,” in Proc. 54th Electron. Compon. Technol. Conf., 2004, pp. 1104–1107. [19] Y.-S. Tsai and T.-S. Horng, “Broadband single-stage models for microwave bandpass filters,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 1771–1774. [20] S. Kobayashi and K. Saito, “A miniaturized ceramic bandpass filter for cordless phone systems,” in IEEE MTT-S Int. Microw. Symp. Dig., 1995, pp. 391–394. [21] H.-S. Song and Y.-S. Lee, “A miniaturized 2.4 GHz band multi-layer bandpass filter using capacitively loaded quarter-wavelength slow-wave resonator,” in IEEE MTT-S Int. Microw. Symp. Dig., 2003, pp. 515–518.

TSAI AND HORNG: BROADBAND SINGLE-STAGE EQUIVALENT CIRCUIT FOR MODELING LTCC BPFs

[22] C.-W. Tang, Y.-C. Lin, and C.-Y. Chang, “Realization of transmission zeros in combline filters using an auxiliary inductively coupled ground plane,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 10, pp. 2112–2118, Oct. 2003. [23] C.-W. Tang, “Harmonic-suppression LTCC filter with the stepimpedance quarter-wavelength open stub,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 2, pp. 617–624, Feb. 2004. [24] B. Lakshminarayanan, H. C. Gordon, and T. M. Weller, “A substratedependent CAD model for ceramic multilayer capacitors,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 10, pp. 1687–1963, Oct. 2000. [25] B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Trans. Power Del., vol. 14, no. 3, pp. 1052–1061, Jul. 1999. [26] R. Neumayer, A. Stelzer, F. Haslinger, and R. Weigel, “On the synthesis of equivalent-circuit models for multiports characterized by frequency-dependent parameters,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 5, pp. 2789–2796, May 2002. [27] G. Antonini, “SPICE equivalent circuits of frequency-domain responses,” IEEE Trans. Electromagn. Compat., vol. 45, no. 3, pp. 502–512, Aug. 2003. [28] R. Gao, Y. S. Mekonnen, W. T. Beyene, and S. A. Jose, “Black-box modeling of passive systems by rational function approximation,” IEEE Trans. Adv. Packag., vol. 28, no. 2, pp. 209–215, May 2005. [29] A. Odabasioglu, M. Celik, and L. T. Pileggi, “PRIMA: Passive reduced-order interconnect macromodeling algorithm,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 17, no. 8, pp. 645–654, Aug. 1998. [30] K. Krohne and R. Vahldieck, “On the application of model-order reduction in the fast and reliable optimization of microwave filters and diplexers,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2285–2291, Sep. 2004. [31] T. Mangold and P. Russer, “Full-wave modeling and automatic equivalent-circuit generation of millimeter-wave planar and multilayer structures,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 851–858, Jun. 1999. [32] I. Timmins and K.-L. Wu, “An efficient systematic approach to model extraction for passive microwave circuits,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 9, pp. 1565–1573, Sep. 2000. [33] M. Rencz , V. Székely, and A. Poppe, “A fast algorithm for the layout based electro-thermal simulation,” in Proc. Des., Automat., Test in Eur. Conf. and Exhibition, 2003, pp. 1032–1037. [34] T.-L. Wu, C.-C. Kuo, H.-C. Chang, and J.-S. Hsieh, “A novel systematic approach for equivalent model extraction of embedded high-speed interconnects in time domain,” IEEE Trans. Electromagn. Compat., vol. 45, no. 8, pp. 493–501, Aug. 2003.

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[35] “Signal Integrity Design Assistants (SIDEA) User’s Guide,” Optimal Corporation, San Jose, CA, 2004. [36] “Broadband SPICE product brochure,” Sigrity Inc., Santa Clara, CA, 2004. [37] F. L. Fontaine and S. Basu, “The partial realization problem for complex Hamburger series and complex lossless multiport networks,” IEEE Trans. Circuits Syst., vol. 46, no. 1, pp. 161–177, Jan. 1999. [38] R. Mohan, M. J. Choi, S. E. Mick, F. P. Hart, K. Chandrasekar, A. C. Cangellaris, P. D. Franzon, and M. B. Steer, “Causal reduced-order modeling of distributed structures in a transient circuit simulator,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 1179–1184, Dec. 2003.

Yu-Shun Tsai was born in Kaohsiung, Taiwan, R.O.C. on March 3, 1963. He received the M.S.E.E. degree from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1991, and is currently working toward the Ph.D. degree in electrical engineering at National Sun Yat-Sen University, Kaohsiung, Taiwan, R.O.C. His research interests include design and modeling of microwave components.

Tzyy-Sheng Horng (S’88–M’92–SM’05) was born in Taichung, Taiwan, R.O.C., on December 7, 1963. He received the B.S.E.E. degree from National Taiwan University, Taipei, Taiwan, R.O.C., in 1985, and the M.S.E.E. and Ph.D. degrees from the University of California at Los Angeles (UCLA), in 1990 and 1992, respectively. He is currently a Professor with the Department of Electrical Engineering and also the Director of the Institute of Communications Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, R.O.C. His research interests include RF and microwave integrated circuits, RF systems-on-package, and digitally assisted RF technology.

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Distortion Analysis of Ultra-Wideband OFDM Receiver Front-Ends Mahim Ranjan, Member, IEEE, and Lawrence E. Larson, Fellow, IEEE

Abstract—This paper presents a comprehensive analysis of the effect of nonlinearities in ultra-wideband orthogonal frequency-division multiplexing receivers. The statistical properties of a quadrature phase-shift keying baseband signal are utilized to derive closed-form expressions for the power spectral density of cross-modulation, intermodulation, and harmonic distortion products of modulated signals, arising from second- and third-order nonlinearities in the receiver. Both narrowband and wideband jammers are considered. The derived expressions are then used to predict the effect of these nonidealites on the link budget of the system. Index Terms—Cross-modulation, distortion, nonlinear circuit, orthogonal frequency-division multiplexing (OFDM), spectral analysis, statistics, ultra-wideband (UWB).

Fig. 1. Time-frequency interleaving of a Group 1 MB-OFDM signal [1].

I. INTRODUCTION TRA-WIDEBAND (UWB) orthogonal frequency-division multiplexing (OFDM) systems have been proposed as an emerging solution to wireless communication applications requiring high data rates (up to 400 Mb/s) over short distances. In one proposed version [1], the carrier with a bandwidth of MHz, 528 MHz can hop to one of 14 channels ( ), divided into four groups of three channels and one group of two channels. This representative time-frequency interleaving for a Group 1 only system is depicted in Fig. 1. Since the front-end possesses a wide bandwidth, it is open to reception of undesired narrowband signals such as 802.11 a/b/g and the recently proposed WiMax [2] systems, as shown in Fig. 2. Although OFDM systems are less susceptible to relatively narrowband jammers, nonlinearities in the receiver can result in these narrowband jammers cross-modulating with wideband signals present at the input, resulting in reduced signal-to-noise ratio (SNR) and, ultimately, a degradation in system performance [3]. In addition, wideband signals (from other UWB transmitters) can intermodulate and the resulting products can land in a desired channel. Since the system is inherently wideband, harmonic distortion of a single unwanted UWB transmitter can also produce in-band distortion products

U

Manuscript received March 31, 2006; revised June 6, 2006. This work was supported by the University of California under a Discovery Grant. M. Ranjan is with Qualcomm Inc., San Diego, CA 92121 USA (e-mail: [email protected]; [email protected]). L. E. Larson is with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92037 USA. Color versions of Figs. 4, 7, 9, and 13 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/TMTT.2006.882870

Fig. 2. Representative spectrum at MB-OFDM receiver input.

and reduce SNR. While cross-modulation in code-division multiple-access (CDMA) and wideband code-division multiple-access (W-CDMA) receivers has been extensively studied [6], [7], cross-modulation distortion of a narrowband jammer and a UWB interferer at the receiver input due to third-order nonlinearity was presented in [3]. This paper extends our study in [3] to analyze the effects of multiple UWB jammers at the receiver input due to both second- and third-order nonlinearities such as those observed in [4]. Analysis of the effect of harmonic distortion of a single UWB interferer at the receiver input is also presented. UWB systems, with their wide front-ends, are susceptible to intermodulation (IM), harmonic distortion, and cross-modulation. A comprehensive analysis of the interaction of receiver nonlinearities and jammers present at the input of the receiver is needed to accurately predict the degradation in system parameters. For clarity and ease of design specification, these distortion components should be related to the well-known input-reand input-referred ferred second-order intercept point . third-order intercept point In this paper, we analyze the effect of receiver nonlinearities on a UWB multiband orthogonal frequency-division multiplexing (MB-OFDM) system. We consider the statistics of an

0018-9480/$20.00 © 2006 IEEE

RANJAN AND LARSON: DISTORTION ANALYSIS OF UWB OFDM RECEIVER FRONT-ENDS

MB-OFDM system and derive closed-form expressions for the power spectral density (PSD) of different distortion components at the output resulting from receiver nonlinearities. The PSD obtained with these expressions is then compared with the results of a system simulation of a complete MB-OFDM system and its effect on the link budget of the system is analyzed. The receiver and signal models are developed in Sections II and III. Sections V and VI analyze IM and harmonic distortion of wideband jammers. Analysis of cross-modulation of a narrowband jammer with a UWB interferer is presented in Section VII. II. RECEIVER MODEL

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TABLE I ASSUMED RECEIVER SPECIFICATIONS

where is the rms amplitude of the transmitted signal, is the angular frequency of the transmitted carrier, is the and are the real and imaginary parts subcarrier spacing, of the complex baseband signal and take on the value 1 is a random time (QPSK modulation), is a random phase, is defined as delay for the symbol, and

We model the receiver front-end as a nonlinear system with given by its response to an input

if otherwise.

(5)

(1) The transfer function will also consist of higher order terms, but in most situations, it is operated well below its 1-dB compression point, in which case, a third-order approximation models the receiver front-end quite accurately. AM–PM distortion is also negligible when a receiver is operated well below the 1-dB compression point and, thus, this effect can be neglected. III. MB-OFDM SIGNAL MODEL MB-OFDM signals are quadrature phase-shift keying (QPSK) modulated and the symbols are carried over 128 carriers, occupying a total bandwidth of 528 MHz [1]. The transmitted RF MB-OFDM signal can be written as (2)

IV. MB-OFDM RECEIVED POWER For an MB-OFDM signal given by (4), its average power, for a normalizing impedance of 1 , is give by [3] (6) From [1], the maximum transmit power of an MB-OFDM transmitter is 10.3 dBm. For a receiver located 0.1 m away from the transmitter, the received power at the antenna would be approximately 35 dBm due to free-space path loss. Therefore, 35 dBm will be considered a representative maximum MB-OFDM signal level at the receiver antenna for all calculations. For calculations in the remainder of this paper, the receiver front-end specifications assumed are summarized in Table I. V. IM DISTORTION

is the complex baseband variable representing where is the total number of transthe th OFDM symbol and is the symbol period. is mitted OFDM symbols. represents the frequency hop the center frequency and algorithm that dynamically changes the center frequency of the MB-OFDM signal. is defined as (3) where is the total number of OFDM subcarriers, is the is the subcarrier spacing. complex baseband data, and subcarriers/symbols), the For a single frame (consisting of OFDM signal can be reduced to

(4)

Here, we consider the effects of IM distortion in MB-OFDM systems. IM distortion can arise from both second- and thirdorder nonlinearities, and we will consider the two separately. A. Second-Order IM Distortion Consider the following situation: the receiver is tuned to an MB-OFDM channel at 7128 MHz (Band 8). There are two other nearby transmitters transmitting at 3432 MHz (Band 1) and 3960 MHz (Band 2). Second-order nonlinearity in the receiver will result in these two unwanted received signals intermodulating and creating spurs at their sum and difference frequencies with the bandwidth of the spur spread to twice that of a single MB-OFDM signal. The sum frequency would be 7392 MHz, which will reduce the SNR for a receiver tuned to either Band 8 or Band 9 of an MB-OFDM system. This in-band spur will reduce the SNR and ultimately degrade system performance. Such a situation is depicted in Fig. 3. Unlike narrowband systems, where second-order distortion at the front-end is important mainly due to the occurrence of a dc offset, second-order distortion in wideband systems such as MB-OFDM can directly result in degradation of system performance. An accurate prediction of this distortion product is required to correctly specify second-order distortion performance of the RF front-end.

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are shown at the bottom of this page. Since , , , and random variables, to compute the PSD of this IM product, we need to compute the Fourier transform of the autocorrelation [5], which is given by function of (9) Without loss of generality, we set the variable to zero, corresponding to the assumption of , , , and being stationary random processes. We also state that , , , and are independent processes, we, therefore, have the following properties:

Fig. 3. Second-order IM scenario.

(10) To derive an expression for this second-order IM PSD, we begin with the power series approximation for the low-noise amplifier (LNA) given by (1). The signal at the input of the receiver is a sum of two interfering MB-OFDM signals and can be written as

if otherwise.

(11)

Following analysis similar to [3], the PSD of the IM product can be written as (12), shown at bottom of this page. , To relate this PSD to the more familiar input IP2 in (1) can be replaced with (13)

(7) and are the rms amplitudes of the two where and are their angular freMB-OFDM signals and quencies. Substituting (7) into (1) and collecting terms around , the second-order IM product is given by (8),

To verify the validity of (12), a full system simulation of an MB-OFDM system was performed in MATLAB. The IM spectrum obtained was then compared with (12). The simulation was run for an MB-OFDM receiver, as described in [1], with an of 10 dBm and undesired transmitter power of 20 dBm for each of the unwanted MB-OFDM transmitters. Simulated and calculated spectra are plotted in Fig. 4 and match very closely, verifying the validity of the prediction. Using the IM power calculated above, the effect of receiver on the total link budget can be calculated by adding this second-order IM power to the total in-band output noise power of the LNA. For the situation depicted in Fig. 3, this can be computed by integrating (12) from 6864 to 7392 MHz.

(8)

(12)

RANJAN AND LARSON: DISTORTION ANALYSIS OF UWB OFDM RECEIVER FRONT-ENDS

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Fig. 6. Third-order IM scenario.

Fig. 4. Simulated and calculated second-order IM products. IIP 10 dBm, UWB jammer powers = 20 dBm at 3.5 and 8 GHz.

0

0

=

Fig. 7. Simulated and calculated third-order IM products. IIP = UWB jammer powers = 30 dBm.

0

Fig. 5. Effect of second-order IM distortion on link margin (both jammers of equal magnitude).

Following the link budget analysis in [1] for a 110-Mb/s MB-OFDM system, the effect of second-order IM on total receiver link budget for the situation depicted in Fig. 3 is shown in Fig. 5. Fig. 5 shows the total receiver link margin as a in the presence of unwanted UWB transmitters function of transmitting at 30, 35, and 40 dBm. It can be seen that, in the absence of IM distortion, the total link budget is 6 dB, but this number degrades rapidly in the presence of strong unwanted MB-OFDM transmitters. Specifying the LNA without due consideration to IM can lead to inadequate system performance. B. Third-Order IM Distortion Here, we analyze the effect of third-order IM distortion on system performance. Third-order nonlinearities in the receiver can also result in unwanted signals falling in-band and reducing SNR. For example, transmitters at 3432 MHz (Band 1) and 3960 MHz (Band 2) can, in the presence of third-order nonlinearities, produce an IM product at 4488 MHz, which is in-band

010 dBm,

for a Group 1 MB-OFDM system. This situation is depicted in Fig. 6. Representing the input signal by (7) and substituting into (1), is given by (14), shown at bottom the IM product at of the following page. Following analysis similar to [3], the PSD of this third-order IM product, computed as the autocorrelation function of (14), is given by (15), shown at the bottom of the following page. To represent this cross-modulation component in terms of the , we can represent as [6] more familiar

(16) where is the power gain of the LNA. To evaluate the accuracy of (15), a full system simulation of of 10 dBm was run with an MB-OFDM receiver with an equal unwanted TX powers of 30 dBm. A comparison of simulated and calculated PSD of this third-order IM product is presented in Fig. 7 and the results match closely. Using the IM power calculated in (15), the effect of receiver , due to third-order IM of two nearby unwanted UWB transmitter jammers, on the total link budget can be calculated by adding this third-order IM power to the total output noise

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power of the LNA. For the situation depicted in Fig. 6, this IM noise power can be computed by integrating (15) from 4224 to 4752 MHz. Following the link budget analysis in [1] for a 110-Mb/s MB-OFDM system, the effect of third-order IM on the total receiver link budget for the situation depicted in Fig. 6 is shown in Fig. 8. Fig. 8 shows the receiver link margin for a receiver in the presence tuned to Band 3 of Group 1 as a function of of two unwanted UWB transmitters transmitting at 30, 35, and 40 dBm in Bands 1 and 2 of Group 1 of an MB-OFDM system.

VI. HARMONIC DISTORTION Unlike narrowband systems, harmonic distortion can also be a significant contributor to a degradation in the output SNR of the system. While with narrowband systems, harmonics of in-band signals are far away from the band of interest; in wide band systems such as MB-OFDM, the harmonics of the signal can also land in-band. For example, if the receiver is tuned to an MB-OFDM transmitter at 6.8 GHz, and there is a nearby transmitter present, transmitting at 3.4 GHz, second-order distortion in the receiver front-end will result in the second harmonic of the unwanted MB-OFDM transmitter falling in-band at 6.8 GHz. This will reduce the SNR at the output of the receiver front-end,

Fig. 8. Effect of third-order IM distortion on link margin.

and this effect needs to be quantized to accurately predict system performance in such situations. Representing the input signal by (4) and substituting in (1), the second harmonic is given by (17), shown at the bottom of the following page. Following analysis similar to [3], the PSD of this second harmonic, computed as the autocorrelation function of (17), is given by (18), shown at the bottom of the following page.

(14)

(15)

RANJAN AND LARSON: DISTORTION ANALYSIS OF UWB OFDM RECEIVER FRONT-ENDS

Fig. 9. Simulated and calculated second-order harmonic. IIP = UWB jammer = 10 dBm at 4 GHz.

0

010 dBm,

Fig. 9 compares the simulated and calculated PSD of the of second harmonic product for a UWB receiver with 10 dBm and an unwanted UWB jammer at 10 dBm. Again, to compute the degradation in link margin of a UWB receiver tuned to 6.8 GHz, due to the second harmonic of an unwanted UWB jammer at 3.4 GHz, we add the in-band noise power, computed by integrating (18) from 6.55 to 7.05 GHz to the output noise of the LNA. Fig. 10 shows the degradation in link margin due to second harmonic distortion in an MB-OFDM system.

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Fig. 10. Effect of second harmonic distortion on link margin.

to an MB-OFDM transmitter transmitting in Band 1 of Group 1 (3.432-GHz center frequency)—this is the desired signal. There are two other undesired transmitters in the vicinity, which are: 1) a narrowband jammer (e.g., a relatively narrowband 3.0-GHz WiMAX) and 2) another MB-OFDM transmitter transmitting in one of the other bands in Group 1 (at 3.96 or 4.488 GHz). This situation is depicted in Fig. 11. The receiver then accepts, in addition to the desired signal it is tuned to, another interfering input given by

VII. CROSS-MODULATION DISTORTION A. UWB Interference Scenario Consider the following interference situation, which can limit the performance of an MB-OFDM system: the receiver is tuned

(19)

(17)

(18)

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Fig. 11. Typical UWB cross-modulation scenario.

where is the frequency of the narrowband jammer and is the center frequency of the second unwanted MB-OFDM transis the amplitude of the narrowband jammer, is mitter. the rms amplitude of the second unwanted MB-OFDM transmitter, and is a random phase. The first term in (19) represents the narrowband jammer and the second term represents the unwanted MB-OFDM transmitter.

Fig. 12. Simulated and calculated cross-modulation products (from = 10 dBm, Narrowband jammer power = 10 dBm, [3]). IIP UWB jammer power = 10 dBm.

0

0

0

B. Cross-Modulation Substituting (19) into (1), it can be shown that the cross-modulation product (at frequencies around ) is given by [3]

(20) Since and are random variables, to compute the PSD of the cross-modulation, we need to compute the Fourier transform . of the autocorrelation function of Using the properties in (10) and (11), the autocorrelation function can be simplified to

The PSD of the cross-modulation component can be obtained by taking the Fourier transform of (21). Taking the Fourier transform of (21), the PSD is given by (23), shown at the bottom of this page. It is clear from (23) the spectrum of the jammer is spread to twice the bandwidth of the wideband signal. If the jammer is close enough to the desired band, this cross-modulation spectrum can land on top of the desired signal, reducing the SNR, with the extent of the reduction in SNR depending on the and the narrowband and wideband jammer powers. To verify the validity of (23), a full system simulation of an MB-OFDM system was performed in MATLAB. The cross-modulation spectrum obtained was then compared with the prediction of (23). The simulation was run for an MB-OFDM receiver, of 10 dBm, input narrowband as described in [1], with an jammer power of 10 dBm, and undesired wideband jammer power of 10 dBm. Simulated and calculated spectra are plotted in Fig. 12 and match very closely, verifying the validity of the prediction. C. Effect of Single-Tone Approximation

(21) where

is defined as if otherwise.

(22)

Since in a real-world application the narrowband jammer in (19) would be modulated, it is of interest to compare the crossmodulation spectrum when the jammer is a single tone and when it is modulated. Simulations were performed to compare the calculated cross-modulation spectrum with a single-tone narrowband jammer, an FM modulated jammer with 5-MHz bandwidth, and an FM modulated jammer with 10-MHz bandwidth. The results of these simulations are plotted in Fig. 13. It can be seen that the modulated jammers spread the cross-modulation

(23)

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Fig. 14. Receiver link margin versus IIP in the presence of cross-modulation single-tone jammer power = 20 dBm. Link margin in the absence of cross-modulation = 6 dB.

0

Fig. 13. Simulated and calculated cross-modulation products (from = 10 dBm, Narrowband jammer power = 10 dBm, [3]). IIP UWB jammer power = 10 dBm.

0

0

0

spectrum by approximately their modulation bandwidth. Therefore, for relatively narrowband jammers, the cross-modulation spectrum obtained correlates very well with the spectrum calculated using a single tone approximation of (19). D. Effect of Cross-Modulation on Link Margin To evaluate the effect of this spread jammer on the total SNR at the output of the LNA, we need to integrate (23) within the bandwidth of the desired received signal. For example, consider the case when the receiver is tuned to an MB-OFDM transmitter transmitting in Band 1 of Group 1 (3.15–3.65 GHz). There is also present another MB-OFDM transmitter in the vicinity transmitting in Band 3 of Group 1 (4.15–4.65 GHz) and a narrowband transmitter transmitting at 3.0 GHz. Since the cross-modulation product is twice the bandwidth of the MB-OFDM signal, it will occupy 2.5–3.5 GHz. This means that the cross-modulation product overlaps with the desired channel and we need to integrate (23) from 3.15 to 3.5 GHz to calculate the total noise power contributed by this cross-modulation product. To compare the total noise power, (23) was numerically indBm, dBm, and tegrated with dBm. MATLAB simulations show the complete noise power to be 2.35 dBm and numerical integration of (23) revealed excellent agreement with a total noise power of 2.31 dBm. Using the cross-modulation power calculated above, the efon the total link budget can be calculated fect of receiver by adding this cross-modulation power to the total output noise power of the LNA. Using the link budget analysis in [1] for a 110-Mb/s MB-OFDM system, the effect of cross-modulation on total receiver link budget is shown in Fig. 14–16. These figures show the total receiver link margin for the situation described in the presence of a narrowband above, as a function of jammer of 20, 30, and 40 dBm, when the wideband jammers are at 30, 35, and 40 dBm. It can be seen that, in the absence of cross-modulation distortion, the total link budget

Fig. 15. Receiver link margin versus IIP in the presence of cross-modulation (from [3]) single-tone jammer power = 30 dBm. Link margin in the absence of cross-modulation = 6 dB.

0

is 6 dB, but this number degrades rapidly in the presence of a strong narrowband jammer. Specifying the LNA without due consideration to cross-modulation can lead to inadequate system performance. VIII. EXAMPLE CALCULATION The goal of this paper is to present a framework for system designers to easily specify the linearity requirements of an MB-OFDM-based UWB receiver. This can be achieved either with full system simulations or through analytical methods. The RF simulation of MB-OFDM systems is very computationally intensive due to the large fractional bandwidth of the system, and also due to the statistical nature of the signal, which makes it necessary to simulate multiple random symbols to obtain an average value for the distortion products. The expressions derived thus far ease the analysis to a simple numerical integration.

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cross-modulation power can be immediately calculated for different scenarios. IX. INACCURACIES RESULTING FROM USE OF TWO-TONE IM TEST IN UWB SYSTEMS A very simple and attractive way of estimating harmonic and IM components in narrowband systems is by predicting them through a traditional two-tone analysis. For example, the thirdorder IM product of a narrowband system can be approximated by using the well-known formula (26)

Fig. 16. Receiver link margin versus IIP in the presence of cross-modulation single-tone jammer power = 40 dBm. Link margin in the absence of cross-modulation = 6 dB.

0

To further reduce computation time, estimates of the above distortion products can also be made. We demonstrate a method of arriving at this estimate by computing the noise power for the cross-modulation scenario of Fig. 11. We assume, without significant loss of accuracy, that the total noise power in each function in the summation in (23) lies inside the bandwidth of integration. The integral of each term inside the summation . also reduces to Now, for the frequency of interest (3.4 GHz), we need to consider the cross-modulation products between 3.15–3.5 GHz. In the summation in (23), the term occurs times, and there are two terms in the summation. Therefore, for the given frequencies and assuming MHz (MB-OFDM), (24) the summation in (23) reduces to (25) (MB-OFDM) [see (3)], this results in . For We, therefore, need to substitute for the summation in (23) to compute the total noise power. Using the , , and , this gives a total above-mentioned values for noise power of 0.4 dBm, which is in good agreement with the previous result of 2.31 dBm, based on numerical integration. This method of cross-modulation estimation reduces the complicated problem of wideband RF simulation to a simple summation, reducing the simulation time from hours to almost instantaneous. Even without the above approximation, the cross-modulation formula (23) reduces the problem drastically from a full system simulation and numerical integration of output power. For multiple scenarios (varying TX or jammer or ), one would need to run a simpowers, receiver ulation for each situation to determine its effect on receiver SNR. However, using (23), after the initial numerical integration of the terms inside the summation of the PSD equation,

where is the power of the single tones at the input and is the observed difference between the single tone output and the IM3 product. For example, for a receiver with an of 10 dBm, gain of 15 dB and input single-tone powers of 30 dBm, this would yield an output IM3 power of 55 dBm. However, spread-spectrum analysis and simulation of this receiver show the output IM power in a single MB-OFDM receive band to be 50 dBm. This example demonstrates the high levels of inaccuracy that can be introduced in UWB system analysis if single-tone approximations of these receivers are utilized to predict system performance. The more accurate analysis presented here presents a realistic estimate of the nonlinear distortion that can be expected in these systems. X. CONCLUSION In this paper, we have analyzed the effect of receiver nonlinearities on the performance of MB-OFDM-based UWB systems. Both narrowband and wideband jammers were considered. Analytical expressions relating cross-modulation, IM, and harmonic distortion power spectral densities with jammer powers and receiver nonlinearities were derived. The PSD of these distortion products was compared with that obtained from full system simulations, and simulations were observed to closely match with analytical results. It was shown, with the help of an example, that single-tone approximation of these systems can result in high levels of inaccuracies and true wideband analysis, presented in this paper, is necessary for accurate estimation of system parameters. The equations obtained were used to calculate degradation in the link budget of the system for different scenarios. An approximation method to speed calculation of these expressions was also presented. ACKNOWLEDGMENT The authors wish to acknowledge the assistance and support of Qualcomm Inc., San Diego, CA, the Center for Wireless Communication, University of California at San Diego, La Jolla, Dr. J. Foerster, Intel, Hillsboro, OR, and Prof. L. Milstein, University of California at San Diego, La Jolla, for valuable discussions. REFERENCES [1] A. Batra, J. Balakrishnan, R. Aiello, J. Foerster, and A. Dabak, “Design of a multiband OFDM system for realistic UWB channel environments,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 12, pp. 2123–2138, Sep. 2004.

RANJAN AND LARSON: DISTORTION ANALYSIS OF UWB OFDM RECEIVER FRONT-ENDS

[2] A. Ghosh, D. R. Walter, J. G. Andrews, and R. Chen, “Broadband wireless access with WiMax/802.16: Current performance benchmarks and future potential,” IEEE Commun. Mag., vol. 43, no. 2, pp. 129–136, Feb. 2005. [3] M. Ranjan and L. Larson, “An analysis of cross-modulation distortion in ultra wideband OFDM receivers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, [CD ROM]. [4] D. Leenaerts, “Circuit design for ultra-wideband,” presented at the CICC RF Educ. Session, 2005. [5] J. Proakis, Digital Communications, 4th ed. New York: McGrawHill, 2000. [6] V. Aparin and L. Larson, “Analysis and reduction of cross-modulation distortion in CDMA receivers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 1591–1602, May 2003. [7] ——, “Analysis of cross-modulation in W-CDMA receivers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, vol. 2, pp. 787–790.

Mahim Ranjan (S’99–M’02) received the Bachelor’s degree in electrical engineering from the Indian Institute of Technology, Bombay, India, in 1999, the Master’s degree in electrical and computer engineering from the University of California at San Diego, La Jolla, in 2000, and is currently working toward the Ph.D. degree at the University of California. From 2001 to 2004, he was an Engineer with Magis Networks, San Diego, CA, where he was involved with RF transceivers for wireless multimedia.

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He is currently a Senior Design Engineer with Qualcomm Inc., San Diego, CA, where he designs RF transceivers for cellular applications.

Lawrence E. Larson (S’82–M’86–SM’90–F’00) received the B.S. and M. Eng. degrees in electrical engineering from Cornell University, Ithaca, NY, in 1979 and 1980, respectively, and the Ph.D. degree in electrical engineering and MBA degree from the University of California at Los Angeles (UCLA), in 1986 and 1996, respectively. From 1980 to 1996, he was with Hughes Research Laboratories, Malibu, CA, where he directed the development of high-frequency microelectronics in GaAs, InP, and Si/SiGe and microelectromechanical systems (MEMS) technologies. In 1996, he joined the faculty of the University of California at San Diego (UCSD), La Jolla, where he is the Inaugural Holder of the Communications Industry Chair. He is currently Director of the UCSD Center for Wireless Communications. During the 2000–2001 academic year, he was on leave with IBM Research, San Diego, CA, where he directed the development of RF integrated circuits (RFICs) for third-generation (3G) applications. During the 2004–2005 academic year, he was a Visiting Professor with the Technical University of Delft (TU Delft), Delft, Netherlands. He has authored or coauthored over 250 papers. He holds 31 U.S. patents. Dr. Larson was the recipient of the 1995 Hughes Electronics Sector Patent Award for his work on RF MEMS technology. He was corecipient of the 1996 Lawrence A. Hyland Patent Award of Hughes Electronics for his work on lownoise millimeter-wave high electron-mobility transistors (HEMTs), the 1999 IBM Microelectronics Excellence Award for his work in Si/SiGe HBT technology, and the 2003 Custom Integrated Circuits Conference Best Invited Paper Award.

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A Metric for the Quantification of Memory Effects in Power Amplifiers João Paulo Martins, Student Member, IEEE, Pedro Miguel Cabral, Student Member, IEEE, Nuno Borges Carvalho, Senior Member, IEEE, and José Carlos Pedro, Senior Member, IEEE

Abstract—This paper presents a quantitative metric for memory effects in power amplifiers (PAs) and applies it to various active device technologies and wireless system contexts. The proposed metric is mathematically founded in the dynamic two-tone distortion response, has a clear physical meaning in the important field of PA linearization and can be easily evaluated from either harmonic balance simulations or measurement data gathered in a microwave laboratory. In addition, a memoryless PA linearizer, optimum for reducing the integrated intermodulation distortion (IMD) power in the operation bandwidth for a two-tone excitation, is derived, providing a rigorous figure-of-merit of PA linearizability under static IMD compensation. The application of this figure-of-merit is then illustrated for three different PA prototypes based on Si LDMOS, InGaP/GaAs heterojunction bipolar transistors, and GaN high electron-mobility transistors, designed for 900-MHz (global system for mobile communications), 2.1-GHz (wideband code division multiple access), and 3.5-GHz (WiMax) wireless systems, respectively. Index Terms—Long-term memory, memory effects (MEs), nonlinear systems, power amplifiers (PAs).

I. INTRODUCTION

M

EMORY effects (MEs) have a strong impact on wireless communication systems performance since they increase the error vector magnitude of their modulation schemes. Moreover, they are known to impair most common (memoryless) power amplifier (PA) linearization techniques. As a result, they have been receiving a large amount of attention from PA design engineers. MEs can be subdivided into two different types of phenomena according to the time constants involved. Short-term MEs address time constants of the order of the carrier period and are caused by both the reactive components of the active device and matching networks at the RF band. Since these time constants are much smaller than the ones involved in the information time scale, their effects can be considered as static and the corresponding PAs memoryless.

Manuscript received March 31, 2006; revised June 30, 2006. This work was supported in part by the European Union under the Network of Excellence TARGET Contract IS-1-507893-NoE and under Project ColteMepai POSC/EEA-ESE/55739/2004. The work of J. P. Martins was supported by the Portuguese Science Foundation Fundação para a Ciência e Tecnologia under Ph.D. Grant 22056/2005. The work of P. M. Cabral was supported by the Portuguese Science Foundation Fundação para a Ciência e Tecnologia under Ph.D. Grant 11323/2002. The authors are with the Instituto de Telecomunicações, Universidade de Aveiro, 3810-193 Aveiro, Portugal (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.882871

In contrast, long-term MEs are low-frequency phenomena (from dc to a few kilohertz or megahertz) involving time constants that are comparable to the information time scale, thus pressing dynamic effects onto the signal’s envelope. They are usually attributed to the active device’s dynamic thermal effects (i.e., involving some sort of thermal inertia), the active device’s charge carrier traps, or to the biasing networks [1], [2]. From a behavioral point-of-view, both MEs show up as hysteresis in the AM/AM and AM/PM plots, or as different two-tone intermodulation responses for varying tone spacing [3]. In practice, these MEs play a key role in the PA linearization field since they decrease the performance of most widely used linearization schemes [1], [5]. Considering that traditional PA linearizers are designed as memoryless devices, they are ineffective in the presence of IMD dynamics, having no profitable effect on reducing the PAs’ distortion power. This is so important that the microwave PA industry has been asking for some form of ME metric capable of evaluating the PA linearizability. A first attempt to answer this question was addressed by Moulthrop et al. in [5] and Ku et al. in [6]. In those studies, the authors assumed that the best memoryless linearizer (BML) was the one that exactly compensates the measured PA AM/AM–AM/PM characteristics. The authors then defined a metric for memoryless PA linearization as the normalized ratio between the AM/AM–AM/PM response and the deviations of the actual PA two-tone intermodulation distortion (IMD) from this AM/AM–AM/PM baseline. Although useful, this metric has been difficult to apply in the industrial environment due to two main reasons. First, it was conceived and defined under the development of a PA parallel Wiener behavioral model [6]. This gives the impression that it can only be applied after model extraction. Second, and most important, it relies on the assumption that the BML is the one obtained from the AM/AM–AM/PM characteristics. Effectively, if we recognize that these characteristics are the extrapolated two-tone IMD when the tone separation tends to zero, and considering that the main source of PA MEs is the inductive bias circuitry, we immediately conclude that such a linearizer is not the best among all the possible memoryless implementations. In this paper, an in-depth extension of the concept presented in [7] is given, and the BML theory for a two-tone excitation is revisited. Using the two-tone IMD data obtained after the application of this BML, a new figure-of-merit was proposed for quantifying MEs in PAs, which also provides a measure of the PA maximum memoryless linearizability.

0018-9480/$20.00 © 2006 IEEE

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Fig. 2. Model for the PA’s long-term memory mechanisms. Fig. 1. FET-based PA equivalent-circuit diagram used for the theoretical analysis.

To achieve this goal, the two-tone IMD response is first measured over the operation envelope bandwidth. This equivalent frequency-domain nonlinear transfer function is then converted into a time-domain impulse response, leading to a physical interpretation of the metric’s ability to actually characterize the MEs. Finally, this theory is illustrated through its application to different practical PA prototypes. This paper will thus be organized as follows. First, the BML theory and the memory figure-of-merit (MFOM) definition are presented and discussed in detail with its validity addressed by simulation. We then move to the characterization of an in-house built Si LDMOS PA specially designed to include controllable MEs via an appropriate modification of its bias networks. Next, two different commercial PAs—a WCDMA [8] InGaP/GaAs heterojunction bipoloar transistor (HBT) PA and a WiMax [9] GaN high electron-mobility transistor (HEMT) PA—are measured and evaluated for their MEs. Note that these results are not meant for any form of comparison between the different PAs—since they were based on different device technologies and conceived for distinct wireless environments—but rather to show the characterization capability of the proposed MFOM for real commercial PAs. Finally, the paper ends summarizing the key conclusions of the developed work.

only the third-order IMD transfer function, which corresponds , will be presented in (1), to the spectral regrowth at shown at the bottom of this page, where

(2) and (3) From this simple model, it is easily seen that the output thirdorder IMD will comprise three different components: one is a that does not depend on ; direct term arising from band, which a second-order term arising from the also does not depend on ; and finally a term that can be interpreted as an up-conversion of the baseband components back to the fundamental frequencies. This can be represented by the model shown in Fig. 2 [11] where (4) (5) and

II. LONG-TERM MFOM REVISITED In [7], a new figure-of-merit concept for the evaluation of PA MEs was proposed enabling the comparison between the linearizability of different PAs. In order to provide a clearer understanding of this MFOM, we first start with a discussion of the MEs mechanisms arising in a nonlinear PA. Fig. 1 shows the PA circuit schematic used to model a generic field-effect transistor (FET)-based PA. Using a Volterra-series description, it is possible to relate the IMD behavior with the PA circuit components. Since this type of analysis is well known from previous publications [2], [10],

(6) Assuming that this PA model is excited by a frequency-do, the output IMD at main input signal is given by

(7)

(1)

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If we consider and to be constant with , then the output IMD variation will only depend on and, thus, this term will be the exclusive source for the PA long-term MEs. This assumption is reasonable since, as varies from dc up to a few megahertz, the baseband frequency will vary for some decades, while the second harmonic and the fundamental will only vary a small percentage of the variation can be attributed center frequency. This to baseband impedance, which occurs, for instance, due to bias networks, thermal effects, or trapping. In fact, the most striking factor for the baseband impedance variation is the bias networks, as previously presented in [2]. Important information can be gathered from this model that can be summarized as follows: or terms is significantly • First, if any of the larger than the one involving , we can be misled by may not be evident, the fact that variation in IMD with although the PA still presents MEs that will impair the performance of a memoryless linearizer. • Second, the IMD asymmetry (different upper and lower and , respectively) IMD components at and only appears when both output impedances at are complex. In this simple model, this implies that either the in-band direct path or the second harmonic path contributes with a certain amount of imaginary values [2]. This provides a strong insight into these problems since it states that we can have long-term MEs even without IMD asymmetry. One way or the other, the impact of MEs in the PA will limit the use of memoryless linearizers. That is due to the fact that, in a memoryless linearizer, the upper band IMD is necessarily equal to the lower band one, and cannot track any IMD variation with frequency shown by the PA. In the dynamic IMD case, the upper band is

(8)

Fig. 3. General PA linearization arrangement.

tone spacing . In fact, this is the same assumption behind the widely adopted first-order dynamics truncation of the nonlinear integral model [12] or the nonlinear impulse response two-tone model [13]. Moreover, it should be said that a swept test of a PA around the operating central frequency implicitly assumes this one-dimensional nature. Thus, (7) can be viewed as , which is the measured (or, possibly, calculated) PA two-tone response used for defining the new ME metric. The next step consists of defining the best two-tone memoryless linearizer (i.e., the BML) of the PA. For that, we assume the general block diagram depicted in Fig. 3, in which the linearizer is used to generate an auxiliary IMD that will compensate the one produced by the standalone PA. Note that although Fig. 3 uses a feed-forward topology, it can be easily applied to any cascade (pre- or post-distortion) or feedback arrangement, as the output adder does not necessarily stand for any output signal coupler, but for the conceptual addition (in fact, subtraction) of the IMD produced by the PA and its linearizer. Under this conceptual linearization scheme, we now define the BML for a given PA as the static (or constant with frequency ) auxiliary device of Fig. 3 that produces a constant (with tone-spacing) two-tone IMD response that minimizes the distortion power in the considered operation bandwidth 1 is minimum

(10)

and the lower band becomes

(9) where is a complex quantity that is constant over the tone spacing. , then the difference beIf we now realize that tween the two IMD sidebands come from the addition or subtracand , which will imply tion of the imaginary parts of a different upper and lower IMD value. In order to account for this IMD variation over the operating bandwidth, we should recis of foremost importance since ognize that the term it is the only one that depends on frequency spacing. Indeed, for capturing those desired MEs, we should neglect the constant part of (8) and (9), and retain the only one that changes with the envelope frequency. In (7), the constant part corresponds to and , thus, after the cancellation, only will be obtained. This will lead us to the conclusion that although the two-tone IMD must, in general, be modeled through a three-dimensional nonlinear transfer function, it can also be represented via a one-dimensional frequency-domain transfer function of the

From a mathematical viewpoint, this expression states that our memoryless linearizer is a mean square-error constant estimator, which can thus be determined by

(11) Therefore, the optimum memoryless linearizer of a certain PA (in a two-tone IMD sense) is nothing more than the system whose constant response is the vectorial mean of the response of that PA to a swept envelope frequency two-tone test within the bandwidth of interest. This constant response can 1Note that, although the following discussion is handled in terms of the actual response, not the transfer function as is more usual, one is easily converted into the other because the response to a unity complex exponential (a unity impulse) is numerically equal to the frequency-domain transfer function (the time-domain impulse response).

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be easily estimated in a microwave laboratory by measuring in amplitude and phase over the desired bandwidth. To get a deeper insight into what such an optimum memoryless linearizer would be, we now turn to the time domain. For of that, we perform the inverse Fourier transform of (11) to obtain

(12) where . Two limiting situations of the tested can be studied. First, we will impose no restriction on the bandwidth, letting . In this case, becomes a very narrow function (a Dirac delta function) around zero and (12) gives . This means that the optimum memoryless linearizer is such that it cancels out the PA instantaneous (or memoryless) IMD, exactly what we were expecting it to do. . Now we consider the opposite situation in which This is the case where is made equal to , i.e., the is AM/AM–AM/PM characteristics. The function now a very wide and flat function, and becomes

Fig. 4. Simulated IMD magnitude for the memoryless PA and for the PA presenting memory.

(13) the average of the impulse response tail. Thus, the AM/AM–AM/PM linearizer can only be optimum whenever the amplifier is processing a signal whose envelope bandwidth is much smaller than the PA swept tone spacing IMD characteristics or the temporal IMD dynamics are much slower than the PA memory span.

Fig. 5. Simulated IMD phase for the memoryless PA and for the PA presenting memory.

III. SIMULATED IMPULSE RESPONSE OF THE BML In order to get a deeper understanding of the BML concept, a harmonic-balance simulation was conducted on a simplified PA circuit based on a memoryless transistor model. However, two different bias networks were considered in order to produce different, but controllable MEs. A two-tone signal was then used as the input excitation and the output IMD was obtained in magnitude and phase as a function of the input tone separation (see Figs. 4 and 5, respectively). As expected, in the memoryless case, there are no visible changes in both IMD magnitude and phase plots, while in the dynamic case, a large variation with tone spacing is clearly seen. Moreover, the phase shown in Fig. 5 is always zero for the memoryless PA, and something else (not even necessarily antisymmetrical) when the PA presents memory. Following the formulation presented in Section II, the BML can be determined from the impulse response’s first coefficient , which is equivalent to the average amplitude and phase IMD frequency variation presented in Figs. 4 and 5, respectively.

Fig. 6. Impulse response magnitude for the memoryless PA and for the PA presenting memory.

The impulse response in the memoryless case is a single Dirac delta function at the time origin (see Fig. 6), while in the dynamic case, it expands throughout a certain time span, as expected. One interesting thing to point out is the complex nature of the obtained impulse response, i.e., that it presents a nonnull imaginary part or a phase that can be something other than 0 or 180 , as shown in Fig. 7. Mathematically, this is a consequence of

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Fig. 9. Bias network used in the Si LDMOS-based PA design.

Fig. 7. Impulse response phase for the memoryless PA and for the PA presenting memory.

results from the way the new BML was defined, which is, indeed, optimum for the selected excitation: the standard two-tone stimulus. IV. MFOM FOR LONG-TERM MEs After the explanation of the BML, we are now in a position to define the MFOM of PA linearizability under static conditions [7]. Intuitively this metric should measure the ratio between the unlinearized IMD integrated power in the desired bandwidth and the total IMD integrated power after memoryless linearization in the same bandwidth2

(14)

Fig. 8. Linearizability of the PA presenting memory AM/AM–AM/PM static linearizer and the now defined BML.

using

the

the fact that the frequency response does not present a complex or that the upper conjugate symmetry with respect to and lower IMD sidebands are not symmetrical (even symmetry for the amplitude and odd symmetry for the phase). Realizing is the distortion response of the PA to a two tone, that actually a double-sideband amplitude modulation with a carrier and a carrier envelope of frequency frequency cosine envelope, the amplitude and phase of our impulse response can be interpreted as the evolution in time of the transient response of the AM/AM and AM/PM behavior when the PA is subject to an excitation whose envelope is an ideal impulse. In this sense, it naturally results that the average amplitude is the PA’s AM/AM and the nonnull of the phase is the PA’s AM/PM. average of the Now we compare the performance of our BML with that of the AM/AM–AM/PM static linearizer, respectively, obtained average and the limit of the IMD from the simulated response when tends to zero for the dynamic amplifier. Fig. 8 presents the linearizability of the PA presenting memory when both linearizers are used. As can be seen in Fig. 8, the improved quality of the proposed BML approach lies on the better average linearization obtained along the frequency band when compared with the AM/AM–AM/PM static linearization technique. This directly

Although defined and explained in the frequency domain, such an MFOM can reveal an even more interesting significance when seen in the time domain. For that, we consider again the case where we are interested in the whole PA IMD bandwidth characteristics, i.e., . Since in that case, , Parseval’s theorem states that our MFOM actually is a metric of the power contained only in the PA dynamic IMD, normalized in (14) is indeed a metric of to the total IMD power. Thus, PA long-term MEs. V. IN-HOUSE Si-LDMOS PA EVALUATION In order to validate the proposed theoretical results, a 5-W 900-MHz Si-LDMOS-based PA for global system for mobile communications (GSM) applications [14] was carefully designed using two different bias networks: one memoryless and another one presenting memory in the bandwidth of interest. Fig. 9 presents the generic schematic for both proposed networks. The memoryless bias network was designed to be close to a short circuit in the entire frequency span, while the bias network for dynamic behavior was conceived to present a variable frequency response at baseband. The baseband impedances shown by these two bias networks are depicted in Fig. 10. A two-tone excitation signal was chosen for both the memoryless and dynamic PA, and the center frequency was set to 900 MHz. The tone frequency separation ranged from 4 kHz to 2The figure-of-merit definition herein given is the inverse of the one presented in [8] since, this way, it can be more easily interpreted as a metric of the system’s linearizability.

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Fig. 12. Measured phase values of the third-order transfer function H Fig. 10. Measured S

(1!).

of the bias network.

Fig. 13. Measured magnitude values of the third-order transfer function impulse response h  .

()

Fig. 11. Measured magnitude values of the third-order transfer function H ! .

(1 )

2 MHz [15]. Figs. 11 and 12 present the measured magnitude and phase values of the one-dimensional third-order transfer for both bias network cases. function From Figs. 11 and 12, it can be seen that the memoryless PA presents an almost flat magnitude response and a linear phase variation. The corresponding impulse response, obtained from , is presented in the inverse Fourier transformation of Figs. 13 and 14, and matches a single Dirac delta defining the BML, as was theoretically predicted. After the linearization procedure using the BML, the IMD ratio results where compared with the ones obtained before linearization. Looking at the third-order intermodulation ratio (IMR), the linearized response presented in Fig. 15, a residual value of IMR variation can be observed. This could be attributed to dynamic phenomena other than the one determined by the bias networks (e.g., thermal effects). The good performance of the memoryless PA can be seen from the 22.3-dB MFOM obtained. In the dynamic PA case (Figs. 11 and 12), the magnitude and shows a variation with frequency spacing that phase of even includes some asymmetry. The impulse response now ob, but expands tained is no longer a single Dirac delta at through a certain memory span, but similar to what was done

Fig. 14. Measured phase values of the third-order transfer function impulse response h  .

()

before, the BML was still obtained from only the instantaneous value of this response (refer to Figs 13 and 14). After this linearization procedure, the IMR results were once again compared with the ones obtained before linearization, as shown in Fig. 16. A visible variation in the IMR response can be noticed both in the linearized and nonlinearized tests. As expected, the memoryless linearizability is now much lower than the one measured for the memoryless PA, as quantified by the obtained 7.6-dB MFOM.

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Fig. 15. Measured results of the memoryless Si-LDMOS-based PA before linearization and after linearization with the BML for both upper and lower sidebands.

Fig. 16. Measured results of the Si-LDMOS-based PA presenting memory before linearization and after linearization with the BML for both upper and lower sidebands.

These results show that the MEs appearing in this PA, due to the bias networks, indeed severely degrade the memoryless linearizability of the proposed design. VI. MFOM EVALUATION FOR COMMERCIAL PAs In order to prove the applicability of this new MFOM in real scenarios, the same procedure was followed using two commercial PAs developed for different wireless system applications. The first PA used was a 1.5-W 2.14-GHz InGaP/GaAs HBT-based PA designed for W-CDMA systems [8]. The input excitation used was a two-tone signal with varying tone separation, again, from 4 kHz to 2 MHz. Fig. 17 presents the IMR values obtained before and after the described memoryless linearization procedure.3 In this case, a high value of linearizability could be achieved with this amplifier, expressed by the 24.5-dB MFOM obtained. The second PA used was a 2-W 3.5-GHz GaN HEMT-based PA,intendedforWiMax[9]applications.Fig.18presentstheIMR values obtained before and after the linearization procedure. In this case, a MFOM of 27 dB was achieved, again stating a high value of memoryless linearizability for this PA. 3Since

the purpose of this experimental section is to demonstrate the ability of the proposed figure-of-merit to capture the long-term MEs, the amplifiers were operated in a region beyond their rated specifications in order to show its validity even in limit cases.

Fig. 17. Measured results of the InGaP/GaAs HBT-based PA before linearization and after memoryless linearization with the BML for both upper and lower sidebands.

Fig. 18. Measured results of the GaN HEMT-based PA, before linearization and after linearization with the BML for both upper and lower sidebands.

VII. CONCLUSIONS This paper has presented a metric for the quantification of MEs in PAs. The proposed metric was given as an intuitive and easily measurable MFOM, defined as the unlinearized IMD total power normalized to the IMD power obtained after optimum static linearization. When seen from the time domain, this MFOM can be extremely useful for classify PAs according to their long-term MEs and memoryless linearizability. In order to obtain this MFOM, a novel two-tone memoryless linearizer norm was also established, which proved to be the BML under two-tone excitation when compared to other previously proposed alternatives. Finally, this PA dynamic nonlinearity characterization method was applied to various in-house and commercial PAs, demonstrating its validity. If a PA is now evaluated using this MFOM, then its linearizability can be easily determined, thus possibly reducing the industry’s time to market. ACKNOWLEDGMENT The authors wish to acknowledge the RFHIC Company Ltd., Suwon, Korea, WJ Communications Inc., San Jose, CA, and Freescale Semiconductor Inc., Tempe, AZ, for providing the amplifiers used in this study.

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The authors would also like to express their gratitude to the reviewers for their comments and suggestions. REFERENCES [1] J. H. K. Vuolevi, T. Rahkonen, and J. P. A. Manninen, “Measurement technique for characterizing memory effects in RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 8, pp. 1383–1389, Aug. 2001. [2] N. B. Carvalho and J. C. Pedro, “A comprehensive explanation of distortion sideband asymmetries,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 9, pp. 2090–2101, Sep. 2002. [3] P. M. Cabral, J. C. Pedro, and N. B. Carvalho, “Dynamic AM–AM and AM–PM behavior in microwave PA circuits,” in Asia–Pacific Microw. Conf. Dig., Shangai, China, 2005, pp. 971–974. [4] P. B. Kennington, High-Linearity RF Amplifier Design. Norwood, MA: Artech House, 2000. [5] A. A. Moulthrop, C. J. Clark, C. P. Silva, and M. S. Muha, “A dynamic AM/AM and AM/PM measurement technique,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1997, vol. 3, pp. 1455–1458. [6] H. C. Ku, M. D. McKinley, and J. S. Kenney, “Quantifying memory effects in RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2843–2849, Dec. 2002. [7] J. P. Martins, N. B. Carvalho, and J. C. Pedro, “A figure-of-merit for the evaluation of long term memory effects in RF power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1109–1112. [8] Universal Mobile Telecommunications System (UMTS) physical layer ETSI, Sophia-Antipolis, France, ETSI TS 125 215 V6.4.0, 1999. [9] Local and Metropolitan Area Networks, IEEE Standard 802.16E-2005 & 802.16/COR1, 2005. [10] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits. Norwood, MA: Artech House, 2003. [11] A. Walker, M. Steer, K. Gard, and K. Gharaibeh, “Multi-slice behavioural model of RF systems and devices,” in Radio Wireless Conf. Dig., Atlanta, GA, Sep. 2004, pp. 71–74. [12] F. Filicori, G. Vannini, and V. Monaco, “A nonlinear integral model of electron devices for HB circuit analysis,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 7, pp. 1456–1465, Jul. 1992. [13] E. Ngoya and A. Soury, “Envelope domain methods for behavioral modeling,” in Fundamentals of Nonlinear Behavioral Modeling for RF and Microwave Design, J. Wood and D. Root, Eds. Norwood, MA: Artech House, 2005. [14] Digital Cellular Telecommunications System (phase 2 ); physical layer on the radio path; general description ETSI, Sophia-Antipolis, France, TS 100 573 V7.1.0, 1999. [15] J. Martins and N. Carvalho, “Multitone phase and amplitude measurement for nonlinear device characterization,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 1982–1989, Jun. 2005.

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João Paulo Martins (S’06) was born in Sever do Vouga, Portugal, on May 13, 1973. He received the B.Sc. and M.Sc. degrees from the Universidade de Aveiro, Aveiro, Portugal, in 2001 and 2004, respectively, and is currently working toward the Ph.D. degree in MEs in nonlinear systems at the Universidade de Aveiro. Since 2001, he has been a Researcher with the Instituto de Telecomunicações, Universidade de Aveiro. His main interests are in wireless systems and nonlinear microwave circuit design.

Pedro Miguel Cabral (S’04) was born in Oliveira de Azemeis, Portugal, in October 1979. He received the Bs.C. degree in electrical engineering from the Universidade de Aveiro, Aveiro, Portugal, in 2002, and is currently working toward the Ph.D. degree in nonlinear transistor modeling. He currently lectures several laboratory classes at the Universidade de Aveiro. His main interests are nonlinear modeling and design of microwave circuits and active devices. Mr. Cabral was the recipient of the 2002 prize for the best electrical engineering student at the Universidade de Aveiro. In 2004, he was a finalist of the Student Paper Competition presented at the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS).

Nuno Borges Carvalho (S’92–M’00–SM’05), was born in Luanda in 1972. He received the Diploma and Doctoral degrees in electronics and telecommunications engineering from the Universidade de Aveiro, Aveiro, Portugal, in 1995 and 2000, respectively. From 1997 to 2000, he was an Assistant Lecturer with the Universidade de Aveiro, in 2000 was a Professor, and is currently an Associate Professor. He is also a Senior Research Scientist with the Instituto de Telecomunicações, Universidade de Aveiro. He was a Scientist Researcher with the Instituto de Telecomunicações, during which time he was engaged in different projects on nonlinear computer-aided design (CAD) and circuits and RF system integration. He coauthored Intermodulation in Microwave and Wireless Circuits (Artech House, 2003). He has been a reviewer for several magazines. His main research interests include CAD for nonlinear circuits, design of highly linear RF-microwave PAs, and measurement of nonlinear circuits/systems. Dr. Borges Carvalho is a member of the Portuguese Engineering Association. He is a reviewer for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and an IEEE MTT-11 Technical Committee member. He was the recipient of the 1995 Universidade de Aveiro and the Portuguese Engineering Association Prize for the best 1995 student at the Universidade de Aveiro, the 1998 Student Paper Competition (third place) presented at the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), and the 2000 Institution of Electrical Engineers (IEE), U.K., Measurement Prize.

José Carlos Pedro (S’90–M’95–SM’99) was born in Espinho, Portugal, in 1962. He received the Diploma and Doctoral degrees in electronics and telecommunications engineering from the Universidade de Aveiro, Aveiro, Portugal, in 1985 and 1993, respectively. From 1985 to 1993, he was an Assistant Lecturer with the Universidade de Aveiro, and a Professor since 1993. He is currently a Senior Research Scientist with the Instituto de Telecomunicações, Universidade de Aveiro, as well as a Full Professor. He has authored or coauthored several papers appearing in international journals and symposia. He coauthored Intermodulation Distortion in Microwave and Wireless Circuits (Artech House, 2003). His main scientific interests include active device modeling and the analysis and design of various nonlinear microwave and opto-electronics circuits, in particular, the design of highly linear multicarrier PAs and mixers. Dr. Pedro is an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and is also a reviewer for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He was the recipient of the 1993 Marconi Young Scientist Award and the 2000 Institution of Electrical Engineers (IEE) Measurement Prize.

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Hybrid Space-Discretizing Method—Method of Moments for the Analysis of Transient Interference Rachid Khlifi and Peter Russer, Fellow, IEEE

Abstract—A new efficient hybrid method combining the transmission-line matrix (TLM) and the time-domain method of moments (MoM) is introduced for the accurate modeling of the transient interference between a perfectly conducting thin surface of arbitrary shape and a complex object exhibiting compound with arbitrary electrical properties separated by large free space. For the modeling of the conducting surface, the time-domain electricfield integral equation is used along with the MoM, which relies on a triangular-patch geometrical model of the exterior surface and operates according to the marching-on-in-time technique. The complex inhomogeneous object is modeled by the TLM scheme. The electromagnetic interaction between the objects is provided by the dyadic free-space Green’s function in the time domain. To validate this new approach, we have compared the results with those obtained using the pure TLM method. Index Terms—Electromagnetic compatibility (EMC), integral equations, time-domain analysis, transient scattering, transmission-line matrix (TLM) methods.

I. INTRODUCTION

M

ODELING for electromagnetic compatibility (EMC) requires fine resolution to deal with thin curved structures, the capability to model open boundary problems, and also to model complex objects placed in a nonuniform environment consisting of several materials like dielectrics, lossy material, and conductors. These large differences in physical scale impose severe computational and modeling requirements. Among the algorithms proposed in the literature for time-domain analysis of electromagnetic scattering, we mention the transmission-line matrix (TLM) method [1], which is widely used due to its capability of dealing with complex geometries with arbitrary electrical properties. If we use the pure space-discretizing method such as the TLM, the numerical modeling of problems involving wide free-space regions between the objects requires a high computational effort. One possibility for the reduction of the computational effort is to combine the TLM method and the integral-equation method in a hybrid method that permits the treatment of large free-space regions with very high efficiency because it reduces the complexity of the field problem by one dimension [4], [6]–[8]. In this hybrid method, each of the interacting objects are embedded into a closed spatial subdomain, where the TLM method is applied for the field modeling. The TLM method can analyze medium inhomogeneities Manuscript received April 8, 2006; revised August 8, 2006. The authors are with the Institute for High Frequency Engineering, Technische Universität München, Munich D-80333, Germany (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885580

in a more straightforward manner, but the main drawback of the TLM method is its inability to accurately model the curved thin structure. The Cartesian grid leads to a staircase approximation of the geometry and small details are not resolved at all. The time-domain electric-field integral-equation solution using the marching-on-in-time (MOT) method is well suited for the analysis of arbitrarily shaped conducting surfaces embedded in a homogenous environment using triangular patches and vector basis functions proposed by Rao–Wilton–Glisson (RWG) [9]–[13]. However, the MOT method always suffers from its late-time instability, which is attributed to the accumulation of errors due to the discretization of the integral equation [14]. Many studies have been done for suppressing the late-time instability such as the conjugate degree method [17], weighted Laguerre polynomials [18], [22], smoothing procedures [19], and others, but these methods need more additional computation time. The schemes in [20] pushes the late-time instability further down in time, but could not eliminate it completely unless an implicit scheme, such as the one proposed in [21], which requires solving a large matrix equation, is employed. The solution of the system matrix can become an excessive burden on CPU time. This characteristic is especially burdensome in the time-domain version, where a matrix equation has to be solved at each time step of the MOT algorithm, thus, without matrix inversion, the speed of the MOT method is very fast. In this study, the averaging technique, as proposed in [13], is used because the scheme is simple, accurate, and involves a negligible amount of extra computation. In some applications, only the fast and accurate time response calculation of the system prior to the appearance of the instabilities is of interest. The iterative procedure allows to compute solutions only for as long as necessary and to stop the process after acquiring the needed transient information. Time-domain hybrid methods, which combine the desirable features of two or more different techniques, are being developed to analyze complex electromagnetic problems that cannot be resolved conveniently and/or accurately by using them individually such as the hybrid finite-element (FE)/finite-difference time-domain (FDTD) method [23]. The hybrid algorithm combining the TLM and MoM methods can be used to analyze complex configurations comprising thin curved conducting surfaces in front of arbitrary inhomogeneous complex structures, as shown in Fig. 1. The application of the equivalence principle allows us to divide the three-dimensional space into subregions, and to apply each method in its best domain of application. The electromagnetic interaction between the subregions is provided by the dyadic free-space Green’s functions in the time domain.

0018-9480/$20.00 © 2006 IEEE

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Fig. 1. Time-domain hybrid TLM/MoM scheme. Electromagnetic coupling between a complex object and arbitrarily shaped conducting surface.

Fig. 2. Diagram to show the coupling between a discretized conducting thin surface and a TLM subregion.

In this paper, we extend the hybrid method presented in [5] to deal with more complex EMC problems such as the analysis of the electromagnetic coupling between a complex object and an arbitrarily shaped conducting surface.

where and represent the unknown total tangential field at the TLM interface. The unit vector is normal to the and boundary surface and pointing out of the interface. denote the self-contribution due to the patches belonging and are the contributo the same interface (path 1). tions to the radiated field on the TLM subregion produced via the free-space Green’s functions by the current distribution on the curved thin structure (path 2). In order to calculate the scattered field from the thin conducting structure, we have to determine in advance the current distribution on the scatterer. This is shown in Section II-A.

II. HYBRID TLM/MOM CONCEPT We consider two objects embedded into free space, as shown in Fig. 1. The complex object is embedded into a discretized region, where the TLM method is applied for the field modeling. The arbitrarily curved thin conducting structure is modeled using the time-domain electric-field integral equation (EFIE). To solve the time-domain EFIE for the unknown current, an iterative procedure, usually referred to as a MOT, is employed. With this method, the current on the scatterer at the current time is related to the current at an earlier time. In this hybrid method, we obtain a perfect matching between the two numerical techniques because both of them provide explicit iterative expressions for the electromagnetic quantities. In our specific problem, the source, analyzed by the TLM, and the scattering object, analyzed by the time-domain MoM, are studied separately as two simpler subproblems of the original complex problem. The coupling between the subproblems is provided by the dyadic free-space Green’s function in the time domain. We now analyze the TLM subregion with its boundary interface. According to the Huygens Shelkunoff’s representation of the equivalence theorem, the radiation from the complex object outside its discretized subdomain is expressed replacing the sources inside the object by equivalent surface currents at the TLM interface. The tangential field on the surface represents a distribution of equivalent currents and charges. Inside the discretized TLM subregion, there are sources producing an inciand at the interface, as dent tangential field produced by the TLM algorithm (Fig. 2) (path 0). By applying the continuity of the field at the interface, we derive the following EFIE and magnetic-field integral equation (MFIE), respectively: (1) (2)

A. Current Distribution on the Scatterer The scattering problem is solved through discretization of the EFIE and its direct time-domain solution by means of a MOT procedure. An explicit equation that relates the current at a certain time instant to the currents of previous instants and the incident field is obtained. Let denote a perfectly conducting surface, which may be closed or open, illuminated by a transient electromagnetic field. This field induces on a surface current , which then reradiates. Since the total tangential electric field is zero on the conducting surface for all times, we derive an integro-differential vector equation in the unknown induced surface current [2] (3) where and are the magnetic vector and electric scalar potenis the incident field. The subscript tials, respectively, and denotes the tangential component. The vector and scalar potentials are given by the retarded integrals involving the electric surface current density and the charge density , respectively, as (4) (5)

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Consider (6) at a time instant , and assume that the current does not vary appreciably with time within the pair of triangles so that

(11) (12) Fig. 3. Geometry of triangular patches.

(13) where represents the distance between the observation point and the source point , is the retarded time. The current density and the electric charge are coupled through the conservation of charge equation [9]. Thus, (3) can be written as

(14) and are the positions vectors to the center of the where th and th edges, respectively. Separating the self-term from (12) and applying the inner product

(6) To obtain a numerical solution of (6), we approximate the conducting surface by triangular patches and employ the triangular current expansion on by (7) where is the number of nonboundary edges of the triangles that model the scatterer. Let and be two triangular patches associated with the th edge of length , as shown in Fig. 3. The same procedure as applied in [9] is then for

(15)

where deleted.

represents .

with the self-term denotes the self-term integral

. The scalar potential term becomes

(16) (8)

for

with

and are the length of the edge and the area of where . is the position vectors referenced at the free triangle . Next, the testing functions are the vertex to the centroid of same as the expansion function , presented above, and the inner product is chosen as (9)

where the asterisk represents the conjugate. We begin by applying the testing procedure to (3), which results in (10)

(17)

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where (22) (18) where (19) may then be evaluated at the centroids of the triangles by or (Fig. 3). replacing with By combining all the relationships presented above, we obtain

and

(23)

is the distance between the destination on the boundary surface element of the TLM subregion and source position vectors on the surface of the conducting thin structure is a properly delayed time. After approximating the current distribution by the triangular current expansion on , and inserting (7) and (8) into (21) and (22), we obtain the following approximation of the scattered electromagnetic field at every patch of the TLM interface: (24)

(25)

(20) Equation (20) is a recursion formula relating unknown present in terms of retarded known currents. time currents An important parameter to be noted in (20) is the choice of , which should satisfy the condition the time step , where represents the minimum distance between the edge centers. In order to generate a stable numerical results, the Courant’s stability condition [14] forces the choice of the and, in the present work, we time step to be less than . The analysis presented in [12] revealed chose and , the existence of a lower and upper limit, i.e., of the time step for which system stability is ensured. This interval depends on both size and shape of the triangular elements used for the discretization of the scatterer. In particular, the more uniform and regular the discretization, the wider the interval of the time step, leading to a stable algorithm. Further information can be found in [12].

where the matrices and contain the coupling coefficients of the current values. The indices and are the time indices at the destination patch and at the source points on the center of the th edge, respectively. C. Radiated Field From the TLM Interface The radiation from the complex object towards a destination point outside its discretized TLM subregion is expressed by replacing the sources inside the object by equivalent current sources at the TLM interface. At any destination point on (and outside) the TLM subregion, the field can be derived from the past history of the total tangential field on the interface using the dyadic free-space Green’s function in the time domain, as in [3]

B. Scattered-Field Calculation Once the transient current density on the induced scatterer has been determined, we can easily compute the radiated field and at the boundary of the TLM subregion by summing the effect of each individual current element on the surface of the thin conducting structure. We give numbers to all boundary surface patches on the TLM subregion with the position vector on the center. The radiated electromagnetic field on the center of these patches coming from the surface current distribution along the curved structure is obtained by [3]

(26)

(21) (27)

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where and represent the total tangential fields are the destination and at the interface. The vectors and are the source positions vectors, respectively. The vectors source point vectors, lying on the TLM interface. is the cor; ). The responding distance vector ( unit vector is normal to the boundary of the TLM subregion and pointing out of the interface. The coefficient is defined so that the above equations can be applied to all the space: , for interaction between patches belonging to the same interface , can be used to calculate the radiated field from the TLM interface at every triangular patch on on the scatterer. This field represents the incident field the conducting surface, which is used to calculate the current distribution on the scatterer surface by applying (20). By inserting all the integral representation (21), (26), and the dual equations for the magnetic field into (1) and (2), we observe in the kernel of the operators on the right-hand side of (1) and (2), the time variable is retarded with respect to the same variable on the left-hand side. This allows us to solve the EFIE (1) and MFIE (2) for the total tangential field in an iterative way. is excluded in the evaluation of the Since the point is never zero (we consider prinintegrals (26) and (27), cipal-value integrals). Therefore, the variable is always less than or, in other words, we always have . This implies that the unknown total tangential electromagnetic field at the TLM interface can be directly calculated from the known incident field, coming from the source inside the TLM subregion, and an integral that is also known from the past history of the same field. The EFIE (1) and the dual MFIE (2) are then discretized by expanding the total tangential-field components with appropriate sets of rectangular basis functions, both in time and space; the subdomains of such functions are defined by the TLM grid, and we choose (28) A dual equation holds for the expansion of the magnetic field, as in [7]. In (28), the function denotes a surface pulse function of rectangular type being equal to unity for on the elementary surface patch centered at and zero on all the other is a time pulse function of rectangular type being patches. equal to unity for in the time interval centered at and zero on all the other time steps. represent the unknown expansion coefficients of the tangential field. We consider patches time steps for all the interacting at the TLM interface and objects. By inserting the expanded fields referring to (28) in (1) and following a direct time-domain MoM approach, we derive an equation system whose solution permits us to iteratively recover the expanding coefficients of the field

(29) and represents operators involving integral and where differential operations of the Green’s function formulation of

the radiated field in (26) and (1). The expanding coefficients at time can be directly computed from the incident field at the same time plus the past history of the tangential field on all the surface elements of the interacting objects including the selfcontribution. This process is called the MOT technique. However, the solution obtained suffered from late-time oscillations, which is a commonly observed phenomenon in time-marching solutions of transient scattering problems [14]. To control the late-time oscillations, the averaging technique, as proposed in be the expanding field quantity at the [13], is used. Let using (29) and cell at a time instant . We calculate simply approximate the averaged value as (30) For each time step, the correct value of the tangential field provides the exact radiating boundary for the TLM algorithm at the interface. The electromagnetic field coming from outside the TLM subregion are obtained by superposition of the scattered field from the conducting surface and the radiated field from the neighbored patches belonging to the same interface. These field values at the port on the boundary surfaces of the TLM subregion are mapped on the TLM wave amplitudes , which are defined at the transmission lines, which are cut by the interface, and injected back to the TLM simulation [8]

(31) Moreover, for each time step, the values of the tangential field at the TLM interface are derived following the above equations. After the derivation of the tangential field, the field in every point outside the TLM interface can be calculated applying (26) and (27). The hybrid TLM/MoM algorithm consists of a TLM program in which, for every time step, the total tangential field at the TLM interface is evaluated by means of a proper set of integral equations. III. NUMERICAL VALIDATION We consider the electromagnetic interaction between a microstrip line forming a loop and a circular cylinder, as indicated mm, in Fig. 4. The dimensions, as specified in Fig. 4, are mm, mm, mm, mm, and mm. The total length and radius of the circular cylinder are mm and mm, respectively. The cylinder is placed mm from the upper plane of the TLM at a distance of subregion. The electromagnetic field inside the TLM subregion is computed by the TLM algorithm, the field in the external region is described by means of the free-space Green’s functions, the circular cylinder is modeled using the MoM, which relies on a triangular-patch geometrical model of its exterior surface. We excite the field by an electric pulse of Gaussian-type propagating . The excitation is placed in the -direction with amplitude at the boundary between the ground plane and the feeding microstrip, as depicted in Fig. 4. The dielectric substrate has a per. In the current case, the TLM subregion mittivity of

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Fig. 5. Time evolution of the E -field calculated by the TLM and the hybrid TLM/MoM methods at point P .

Fig. 4. Microstrip loop interfering with a perfectly conducting circular cylinder.

interface surrounds the structure in the geometrical form of rectangular box, as shown in Fig. 4. For comparing the results, we apply the hybrid TLM/MoM method, as well as the pure TLM method to this problem. The circular cylinder is modeled by 96 triangular surface patches. For the pure TLM simulation, we have to discretize a region, which encloses the microstrip loop, the circular cylinder with a staircase approximation, the entire near-field region, and to apply the absorbing boundary conditions, as shown in Fig. 4. The dimensions of the discretized 120 mm space for the pure TLM method are 120 mm 110 mm. For both the pure TLM and the hybrid method, the mm. TLM grid is uniform with The time step is also the same with ps. We (normalized with respect to ) at evaluate the electric field mm between the interacting objects at a distance of mm, mm, mm). The field the point ( evaluated using the hybrid method is closer to the field calculated by TLM, as shown in Fig. 5. In Fig. 6, the same comparison is performed in the frequency domain after a fast Fourier transform (FFT), a good agreement is remarkable. The deviations in amplitude are caused by the different boundary conditions, which are used in the different methods. Fig. 7 reports the at the point , the radiated different parts of the electric field field coming from the equivalent sources at the TLM interface calculated with (26), and the scattered field coming from the circular cylinder calculated with (21). The superposition of these performed in Fig. 5 both parts gives the total electric field using the hybrid method. The surface current density induced at the center patch of the circular cylinder, as indicated in Fig. 4, is performed in Fig. 8 using the hybrid method. We should mention that the hybrid TLM/MOM technique may suffer from late-time instabilities, although these usually have a slow growth rates. To study this phenomenon, we have compared the responses of several regular objects by using the hybrid TLM/MOM. For the example studied in this paper, we have found that the instabilities appear after 7000 time steps.

Fig. 6. Spectrum of the E -field at point P evaluated by the hybrid TLM/MOM method versus the pure TLM method after FFT.

Fig. 7. Comparison of the time evolution of the radiated and scattered part of the total E -field component at point P evaluated by the hybrid TLM/MoM method.

It means the early-time transient response is usually calculated accurately, prior to the appearance of the instabilities. Furthermore, after using the averaging scheme proposed by [13], the late-time instabilities are pushed further down in time or eliminated completely by reducing the mesh points. In particular, the

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Fig. 8. Transient current induced at the center patch of the circular cylinder.

more uniform and regular the discretization, the more stable the algorithm with the averaging procedure. In some applications, only the early time response of the system is of interest, thus, a time-domain method is preferred, as it can effectively be truncated, allowing us to compute solutions only for as long as necessary. In our opinion, this instability does not appreciably affect the problem solution because the iterative procedure allows the process to stop after acquiring the needed information. IV. CONCLUSION We have presented the theoretical basis of the new efficient hybrid TLM/MoM method, which allows the treatment of the transient interference between a complex inhomogeneous object and a perfectly conducting surface of arbitrary shape, separated by large free space, with a high efficiency. The benefits of this approach are that the curved thin structure can be modeled efficiently using the time-domain MoM, which relies on a triangular-patch geometrical model of the exterior surface of the scattering body without imposing the burden of modeling fine features on the space-discretizing TLM method, the capability to model the electromagnetic radiation, and coupling phenomena in large free-space regions, where the space-discretizing methods are no longer applicable. All interactions and backscattering processes have been considered. The numerical results of the hybrid TLM/MoM method have been compared with results of the pure TLM method showing very good agreement. REFERENCES [1] M. Krumpholz and P. Russer, “A field theoretical derivation of TLM,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 9, pp. 1660–1668, Sep. 1994. [2] R. F. Harrington, Field Computation by Moment Methods. New York: Krieger, 1982. [3] J. J. H. Wang, Generalized Moment Methods in Electromagnetics. New York: Wiley, 1991. [4] R. Attari, K. Barkeshli, F. Ndagijmana, and J. Dansou, “A hybrid implementation of the TLM method for the analysis of high frequency interference,” in Asia-Pacific Appl. Electromagn. Conf., Aug. 2003, pp. 124–127.

[5] R. Khlifi and P. Russer, “A hybrid method combining TLM and MoM method for efficient analysis of scattering problems,” presented at the IEEE MTT-S Int. Microwave Symp., San Francisco, CA, Jun. 2006. [6] L. Pierantoni, A. D. Donato, and T. Rozzi, “Full-wave analysis of photonic bandgap integrated optical components by the TLM-IE method,” J. Lightw. Technol., vol. 22, no. 10, pp. 2348–2358, Oct. 2004. [7] L. Pierantoni, S. Lindenmeier, and P. Russer, “Efficient analysis and modeling of the radiation of microstrip lines and patch antennas by the TLM-integral equation TLM-IE method,” Int. J. Numer. Modeling, vol. 12, pp. 329–340, Jul. 1999. [8] S. Lindenmeier, C. Christopoulos, and P. Russer, “Methods for the modeling of thin wire structures with the TLM method,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2000, pp. 387–390. [9] S. M. Rao and D. R. Wilton, “Transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 39, no. 1, pp. 56–61, Jan. 1991. [10] S. M. Rao and T. K. Sarkar, “Numerical solution of time domain integral equations for arbitrarily shaped conductor/dielectric composite bodies,” IEEE Trans. Antennas Propag., vol. 50, no. 12, pp. 1831–1837, Dec. 2002. [11] T. K. Sarkar, W. Lee, and M. Rao, “Analysis of transient scattering from composite arbitrarily shaped complex structures,” IEEE Trans. Antennas Propag., vol. 48, no. 10, pp. 1625–1634, Oct. 2000. [12] G. Manara, A. Monorchio, and R. Reggiannini, “A space-time discretization criterion for a stable time-marching solution of the electric field integral equation,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 527–532, Mar. 1997. [13] D. A. Vechinski and S. M. Rao, “A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 40, no. 6, pp. 661–665, Jun. 1992. [14] B. P. Rynne and P. D. Smith, “Stability of time marching algorithms for the electric field equation,” J. Electromagn. Waves Applicat., vol. 4, no. 12, pp. 1181–1205, 1990. [15] B. P. Rynne, “Time domain scattering from arbitrary surfaces using the electric field equation,” J. Electromagn. Waves Applicat., vol. 5, no. 1, pp. 93–112, 1991. [16] J. P. J. Davies, “On the stability of time-marching schemes for the general surface electric-field integral equation,” IEEE Trans. Antennas Propag., vol. 44, no. 11, pp. 1467–1473, Nov. 1996. [17] X. M. Dai and W. Cao, “The MOT method and the conjugate degree method of transient electromagnetic field research,” J. Nanjing Posts Telecommun. College, vol. 10, pp. 43–51, 1990. [18] J. Zhong and H. J. Baek, “A stable solution of time domain electric field integral equation for thin-wire antennas using the Laguerre polynomials,” IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2641–2649, Oct. 2004. [19] W. B. Wang, Transient Electromagnetic Field. Xi’an, Japan: Xi’an Jiaotong Univ. Press, 1991. [20] J.-L. Hu and C. H. Chan, “An improved temporal basis function for the time domain electric field integral equation method,” Electron. Lett., vol. 35, pp. 883–885, May 1999. [21] D. S. Weile, A. A. Ergin, B. Shanker, and E. Michielssen, “An accurate discretization scheme for the numerical solution of time domain integral equations,” in IEEE AP-S Int. Symp. Dig., Salt Lake City, UT, Jul. 2000, pp. 741–744. [22] Y. S. Chung, T. K. Sarkar, B. H. Jung, M. Salazar-Palma, Z. Ji, S. Jang, and K. Kim, “Solution of time domain electric field integral equation using the Laguerre polynomials,” IEEE Trans. Antennas Propag., vol. 52, no. 9, pp. 2319–2328, Sep. 2004. [23] A. Monorchio and R. Mittra, “A hybrid finite-element/finite-difference time-domain (FE/FDTD) technique for solving complex electromagnetic problems,” IEEE Microw. Guided Waves Lett., vol. 8, no. 2, pp. 93–95, Feb. 1998.

Rachid Khlifi received the Dipl.-Ing. degree in microwave engineering from the Technical University of Bochum, Bochum, Germany, in 1997. From 1998 to 2005, he was with Communication Networks, Siemens AG, Munich, Germany, where he was responsible for the modeling and simulation of high-speed digital systems with respect to their high-frequency and EMC behavior. In 2005, he joined the Institute of High-Frequency Engineering, Technische Universität München, Munich, Germany, as Research Scientist. His current research interests include the development and application of numerical methods for investigating EMC problems, microwaves, and antennas.

KHLIFI AND RUSSER: HYBRID SPACE-DISCRETIZING METHOD—MoM FOR ANALYSIS OF TRANSIENT INTERFERENCE

Peter Russer (SM’81–F’94) received the Dipl.-Ing. and Dr. techn. degrees in electrical engineering from the Technische Universität Wien, Vienna, Austria, in 1967 and 1971, respectively. From 1968 to 1971, he was an Assistant Professor with the Technische Universität Wien. In 1971, he joined the Research Institute of AEG-Telefunken, Ulm, Germany, where he was involved with fiber-optic communication, broad-band solid-state electronic circuits, statistical noise analysis of microwave circuits, laser modulation, and fiber-optic gyroscopes. Since 1981, he has been a Full Professor and Head of the Institute for High-Frequency Engineering, Technische Universität München (TUM), Munich, Germany. From October 1997 to September 1999, he was the Dean of the Department of Electrical Engineering and Information Technology, TUM. In 1990, he was a Visiting Professor with the University of Ottawa. In 1993, he was a Visiting Professor with the University of Victoria. From October 1992 to March 1995, he was Director of the Ferdinand-Braun-Institut für Höchstfrequenztechnik, Berlin, Germany. He has authored or coauthored over 600 scientific papers in refereed journals and conference proceedings. He has developed a variety of courses in RF techniques, microwaves, quantum electronics and optical communications. He is the Program Director of the

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international graduate program “Master of Science in Microwave Engineering” at the TUM. Over the years, he has graduated over 500 students of which over 50 have received the Ph.D. degree. Thus far, eight of his former students have become professors. He has served a member of the Editorial Board of several international journals including Electromagnetics and the International Journal of Numerical Modeling. His current research interests are electromagnetic fields, numerical electromagnetics, metamaterials, integrated microwave and millimeter-wave circuits, statistical noise analysis of microwave circuits, time-domain measurement methods in EMC, and methods for computer-aided design of microwave circuits. Dr. Russer has served as a member of the Technical Programme Committee and Steering Committee of various international conferences [IEEE Microwave Theory and Techniques Society (IEEE MTT-S)], European Microwave Conference. From 1999 to 2002 he was co-chair and from 2002 to 2005 he was chair of URSI Commission D. From 1997 to 2004, he was a member of the Board of Directors of the European Microwave Association. In 1999, he was the general chairman of European Microwave Week, Munich, Germany. He is a member of the German Informationstechnische Gesellschaft (ITG) and the German as well as Austrian Physical Societies. He was the corecipient of the 1979 Nachrichtentechnische Gesellschaft (NTG) Award. He was also the recipient of the 2006 Distinguished Educator Award of the IEEE MTT-S.

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InAs/AlSb HEMT and Its Application to Ultra-Low-Power Wideband High-Gain Low-Noise Amplifiers Bob Yintat Ma, Member, IEEE, Joshua Bergman, Member, IEEE, Peter Chen, Jonathan B. Hacker, Senior Member, IEEE, Gerard Sullivan, Gabor Nagy, and Bobby Brar, Member, IEEE

Abstract—Two antimonide-based compound semiconductor (ABCS) microstrip monolithic microwave integrated circuits (MMICs), i.e., single- and three-stage ultra-low-power wideband 0.3–11-GHz low-noise amplifiers (LNAs) using 0.1- m gate-length InAs/AlSb metamorphic high electron-mobility transistors (HEMTs), have been fabricated and characterized on a GaAs substrate. The single-stage wideband LNA demonstrated a typical associated gain of 16 dB (0.3–11 GHz) with less than a 1.7-dB noise figure (2–11 GHz) at 5-mW dc power dissipation, and the three-stage wideband LNA demonstrated a typical associated gain of 30 dB (0.3–11 GHz) with less than a 2.6-dB noise figure (2–11 GHz) at 7.5-mW dc power dissipation. We believe these wideband LNA MMICs demonstrate the lowest dc power consumption with the highest gain-bandwidth product of any MMIC to date. These results demonstrate the outstanding potential of ABCS HEMT technology for ultra-low-power wideband applications. Index Terms—Antimonide-based compound semiconductor (ABCS) high electron-mobility transistor (HEMT), InAs/AlSb heterostructure field-effect transistor (HFET), low-noise amplifier (LNA), low power, monolithic microwave integrated circuit (MMIC), ultra-wideband.

I. INTRODUCTION LTRA-LOW dc-power wideband high-gain low-noise amplifiers (LNAs) represent a critical component for low power applications such as space-borne or mobile wideband receivers. For such applications, antimonide-based compound semiconductor (ABCS) InAs/AlSb high electron-mobility transistors (HEMTs) are particularly promising because of their combination of high electron mobility and peak velocity, along with high electron concentration in the two-dimensional electron gas (2DEG) that results in unparalleled speed-power performance [1]–[5]. The ABCS InAs/AlSb HEMT device’s below 0.5 V, can reinherent low-voltage operation, with duce dc power dissipation by an order of magnitude compared with an equivalent GaAs pseudomorphic high electron-mobility transistor (pHEMT) device, and by a factor of 2–4 compared to an equivalent InP HEMT device. In the case of space applications, ABCS ultra-low dc-power LNAs permit a substantial reduction in the dc power consumption and corresponding

U

Fig. 1. Microphotographs of the: (a) single- and (b) three-stage ABCS HEMT MMIC wideband LNAs.

payload weight and cost. Additionally, the high gain provided by the ABCS transistors potentially allows the LNA to be used for low-noise wideband op-amp-like applications at microwave frequency. Only recently have InAs channel devices reached sufficient maturity to permit the realization of multistage monolithic-microwave integrated-circuit (MMIC) amplifiers. To date, all ABCS amplifier MMICs reported have been narrowband op-band [6] and -band [7], [8], and recently erating at the at the -band [9], all with exceptional RF and low-power performance. In this paper, we report on the first InAs/AlSb HEMT ultra-low-power wideband LNAs with the lowest dc power and the highest gain-bandwidth products ever reported (Fig. 1). The LNAs with their 0.1- m gate-length ABCS HEMT devices operate from 0.3 to 11 GHz. The success of these designs is due primarily to a stable ABCS HEMT MMIC technology, high-quality ABCS epitaxial material, accurate active and passive models, and a proven design approach. II. HEMT DESIGN AND PERFORMANCE

Manuscript received March 31, 2006; revised June 30, 2006. The authors are with the Rockwell Scientific Company, Thousand Oaks, CA 91360 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; gnagy@rwsc. com; [email protected]). Color versions of Figs. 1–5 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.883604

A. Device Epitaxial Growth and Fabrication The HEMT is grown by solid-source molecular beam epitaxy (MBE) with valved arsenic and antimony crackers on a semi-insulating GaAs substrate. A 1–2- m-thick AlSb

0018-9480/$20.00 © 2006 IEEE

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Fig. 2. DC output characteristics for the 2 40 m HEMT. Points A–C represent bias points for operation at peak f and peak f , and 0.1-V drain bias, respectively.

metamorphic buffer is used to transition from the 5.65-Å lattice constant of the GaAs substrate to the 6.1-Å lattice constant of the ABCS HEMT. The HEMT layers consist of a 100-Å-thick InAs channel, an 80-Å-thick AlSb upper barrier, and a 50-Å In Al As Schottky cap layer. The upper AlSb barrier includes remote tellurium -doping to achieve the desired electron density. Hall measurements of the as-grown material determine the sheet electron concentration and mobility at a temperature of 295 K to be 2.0 10 cm and 20 000 cm V s, corresponding to a channel sheet resistance of 155 square. The HEMT processing starts with the patterning and evaporation of Pd-based diffused ohmic contacts to serve as the source and drain of the HEMT. The active area is subsequently defined by wet chemical mesa isolation etch. The ohmic contacts exmm hibit very low end resistances below 0.1 cm . The excellent contact resistances are essential for low-voltage and low-noise operation, and are needed to realize the benefit of the inherently low sheet resistance of the ABCS HEMT. The 0.1- m Ti/Pt/Au Schottky T-gates are formed via electron beam lithography and liftoff using a multilayer resist process. The HEMT is subsequently passivated with PECVD SiN . The ABCS HEMT structure have been further detailed in [2]–[4]. Since the InAs HEMT is metamorphically integrated with conventional GaAs substrates, the ABCS MMIC process leverages the RSC’s ISO 9000 certified GaAs pHEMT MMIC process. After evaporating a Ti/Au first metal interconnect, metal–insulator–metal (MIM) capacitors (270 pF/mm ) are formed by depositing PECVD SiN followed by patterning via conventional photolithography and dry etching. The front-side process is completed with the evaporation of 2 m of air-bridged Ti/Au to serve as the second interconnect metal. The backside process is similar to the typical backside process used for the GaAs MMIC. B. HEMT DC Characteristics The HEMT exhibits good low-leakage dc output characteristics, as indicated in Fig. 2. The overall drain-to-source access

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Fig. 3. Measured extrinsic transconductance for a 0.1-m ABCS HEMT.

mm, which is half that of state-of-the-art resistance is 0.276 InP-based HEMTs [10], and should be as small as possible to achieve high speed low-noise performance at low drain voltages. Due to the narrow bandgap of InAs (0.36 eV), holes generated by impact-ionization enhance the dc output conductance by forward biasing the gate-to-source barrier, often referred to as the “kink-effect” [4], [11]. Nevertheless, the on-state soft breakdown voltage is 0.50–0.55 V, which is sufficient for the low-voltage applications for which the ABCS HEMT is targeted. The 0.1- m gate-length HEMT shows a peak dc transconof 0.3 and 0.4 V, reductance of 1.64 and 1.91 S/mm at values are enhanced by imspectively. While these dc peak pact-generated holes, due to the relatively large time delay involved, this enhancement is entirely a low-frequency phenomwith the steady-state ac enon [4]. Fig. 3 plots the extrinsic dc extracted from the measured -parameters from 5 to 10 GHz. tracks its dc counterpart at low drain bias voltages, The ac but it is less sharply peaked as the drain bias is raised above values are thus slightly lower, yielding 0.3 V. The peak ac of 0.3 and 0.4 V. Finally, it values of 1.42 and 1.54 S/mm at should be noted that the relatively high dc output conductance, as seen in Fig. 2, is also attributable to impact-generation of holes, and is likewise much reduced under ac operation. Impact ionization has a much larger relative effect on the output conductance because the steady-state ac is an order of magnitude smaller than . Thus, quickly settles to its steady-state value as the frequency of operation is increased, allowing the HEMT to offer good power gain at microwave frequencies. C. HEMT RF Performance The RF performance of the ABCS HEMT has been characterized with on-wafer -parameter measurements up to 50 GHz. Pad parasitics have been determined from on-wafer pad open, short, and thru test structures. For the sake of calculating the figures-of-merit, only the pad parasitic capacitance has been deembedded from the measured data. The maximum frequency of osof a 2 40 m device peaks at 225 GHz, at a drain cillation bias of 0.40 V [see Fig. 4(a)]. The corresponding at this bias

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Fig. 5. RF performance figures-of-merit as a function of dc power consumption for a 2 40 m ABCS HEMT.

2

Fig. 6. Measured minimum noise figure of a 2 for low noise.

Fig. 4. Extrapolation of f and f from h and U when biased for: (a) peak f , (b) peak f , and (c) ultra-low power consumption.

point is 255 GHz. This same device exhibits a peak cutoff frequency of 270 GHz at a drain voltage of 0.45 V, as shown in Fig. 4(b). The capability of the ABCS HEMT to operate in amplifiers with ultra-low voltage is highlighted by the realization

2 20 m ABCS HEMT biased

of a simultaneous of 112/107 GHz at a drain–source voltage of only 0.1 V, as illustrated in Fig. 4(c). The improvement in power consumption is dramatic, with the HEMT consuming only 4.3 mW/mm. By contrast, when biased for peak or peak cutoff frequency , the unilateral power gain dc power dissipation is 73 and 143 mW/mm, respectively. Fig. 5 illustrates the suitability of the ABCS HEMT technology to low-power LNAs by plotting the simultaneous and with the measured maximum available gain (MAG)/maximum stable gain (MSG) at 40 GHz as a function of the specific power consumption. Note that the degradation in performance is graceful as the dc power consumption is radically reduced, even to below 10 mW/mm. The ability of the ABCS HEMT to offer gain at these levels at such low specific dc power is unparalleled in other modern HEMT integrated circuit (IC) technologies. The minimum noise figure of a 2 20 m ABCS transistor is shown in Fig. 6. The best bias condition for minimum noise figure depends on the frequency of operation due to the combined contributions of the shot noise from gate leakage and the output thermal noise [12]. A 4 40 m ABCS HEMT as used in the amplifier designs can be biased at a nominal drain bias

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Fig. 7. Schematic of the three-stage ABCS HEMT MMIC LNA. The one-stage ABCS HEMT LNA is similar in design.

Fig. 9. Measured noise figure of: (a) one-stage LNA (5 mW) and (b) three-stage LNA (7.5 mW). Dash line: simulated noise figure.

Fig. 8. Measured gain (s21), input (s11), and output (s22) return loss of: (a) one-stage LNA (5 mW) and (b) three-stage LNA (7.5 mW). Dash line: simulated s21.

voltage from 0.2 to 0.5 V and nominal drain current from 2.5 to 10 mA. The optimal bias condition for a given LNA design is dictated by the tradeoff between gain, linearity, noise figure, and dc power consumption. III. AMPLIFIER DESIGN The goal of this study was to design a wideband LNA meeting the requirements of high gain ( 20 dB) with low noise figure ( 2.5 dB) while achieving the lowest dc power consumption

possible. Achieving the noise-figure specification was particularly challenging because the device optimum input impedance for minimum noise figure is frequency dependent and, over the enthus, it is practically impossible to achieve tire bandwidth. As a result, achieving a good noise figure for a wideband LNA is more challenging than that of narrowband LNAs. Several amplifier architectures were considered including the distributed amplifier and the lumped feedback amplifier. Although distributed amplifiers have the widest bandwidth, they typically require more transistors than the lumped feedback approach, and that results in higher dc power consumption. The distributed amplifier also suffers from lower efficiency when designed for high gain, and typically has higher noise due to its 50- termination on the input. To achieve the aggressive performance targets for this study, a multistage feedback amplifier with a low RC constant for each stage, achieved by using shunt feedback, was found to be a better choice. However, the shunt feedback for the input stage must be minimized to avoid introducing additional noise. A delicate optimization of feedback is

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Fig. 11. Measured output power at 1-dB compression and TOI at 2 and 6 GHz versus dc power for: (a) one-stage LNA and (b) three-stage LNA. Fig. 10. Measured gain (s21) and noise figure versus dc power consumption for: (a) one-stage LNA and (b) three-stage LNA.

required to achieve the desired bandwidth, acceptable input return loss, and the lowest noise figure simultaneously. A particularly challenging aspect of the design of the lumped feedback LNA is found in the dc RF choke optimization. Since the amplifier is required to operate down to 300 MHz, the RF choke needs to provide large inductance at low frequencies, while still providing good inductance performance up to 11 GHz. These two conflicting requirements result in the need for an RF choke with a large inductance with a moderate resonance frequency for low-frequency operation, and a moderate inductance, but with a high resonant frequency, for high-frequency operation. A large inductance RF choke requires many turns for a planar spiral inductor. Due to substrate coupling between the spirals and ground, and coupling between turns, an on-chip choke using a single printed spiral inductor is difficult to achieve with the required properties. Instead, an RF choke network was used consisting of two or more inductors in series with the addition of a resistor and a capacitor in shunt between the inductors. As shown in Fig. 7, the inductor nearest to the power supply has the largest inductance, and progressively smaller inductors are used closer to the transistor. Between the inductors, capacitors shunted to ground are employed with the capacitor closest to the power supply having the largest capacitance, and smaller capacitances used for those closer to the transistor. In series with each capacitor is a resistor that serves as a matched termination for the unwanted signal

energy. With this series inductance network, the desired RF choke performance can be achieved. Additionally, to minimize the coupling to ground, a thick 200- m GaAs substrate is used to reduce the capacitance and increase the resonance frequency of each spiral inductor. Segmented air-bridges are used for the spiral inductor metallization to lift the spirals off the substrate and further reduce capacitance. One- and the three-stage LNAs were designed with the primary difference being the overall amplifier circuit gain. The schematic of the three-stage LNA is shown in Fig. 7, while the one-stage LNA is similar. To enhance the return loss, distributed transmission-line stubs are added at the input and output for better impedance match at high frequency. The LNAs were designed using 0.1- m gate-length ABCS HEMTs. The device noise parameters were measured and characterized from 2 to 26 GHz with the pad parasitic deembedded from the raw meafor surements. To improve the circuit match to the device low noise, a larger transistor size of 4 40 m is used for the first stage. The three-stage LNA uses 2 40 m devices for the second and third stages for lower dc power. The chip area is 1.0 2.3 mm for the one-stage and 2.5 2.3 mm for the three-stage LNA. IV. AMPLIFIER MEASUREMENT Performance of the LNAs was measured on-wafer. For the best noise figure and gain, the one-stage LNA is biased at 0.5 V and 10 mA (5 mW), and the three-stage LNA is biased at 0.5 V and 15 mA (7.5 mW). The -parameters are shown in Fig. 8(a)

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TABLE I COMPARISON OF WIDEBAND LNA PERFORMANCES

for the one-stage LNA and Fig. 8(b) for the three-stage LNA. From 0.3 to 11 GHz, the gain is 16 dB for the one-stage LNA and 30 dB for the three-stage LNA. The measured noise figure is shown in Fig. 9(a) for the one-stage LNA and in Fig. 9(b) for the three-stage LNA. From 2 to 11 GHz, the noise figure is 1.2 1.7 dB for the one-stage LNA and 0.9 2.6 dB for the three-stage LNA. Fig. 9 seems to indicate that the three-stage LNA has the best noise figure matching for a limited frequency range (4–6 GHz), while the one-stage LNA has a good noise match for a wider frequency range, but at an expense of slight higher noise figure. The LNAs are unconditionally stable for all frequencies. The one- and three-stage LNAs were also biased at lower drain currents to determine the dependence of gain and noise figure with dc power consumption. The one-stage LNA is biased with 0.5 V at 7.5 mA (3.75 mW), 5 mA (2.5 mW), and 2.5 mA (1.25 mW). The three-stage LNA is biased with 0.5 V at 10 mA (5 mW). Degradation in gain and noise figure is observed as the dc power consumption is reduced as shown in Fig. 10(a) for the one-stage LNA and Fig. 10(b) for the three-stage LNA. The output power and third-order intercept (TOI) also have dependence on dc power consumption. The measured output power at 1-dB compression and TOI versus dc power at 2 and 6 GHz for the one-stage LNA [see Fig. 11(a)] and the three-stage LNA [see Fig. 11(b)] are shown. Due to the lower dc power consumption, the output power and TOI are low, as expected. Both output power and TOI increase as the dc power increases. Due to smaller transistor size used for the second and third stage of the three-stage LNA, the three-stage LNA has lower and TOI than the one-stage LNA. Table I summarizes the measurement results, along with a figure-of-merit, of the ABCS LNA at different dc power consumption and compares them with previous reported wideband LNA amplifiers using different device technologies and circuit topologies. The figure-of-merit is Bandwidth [GHz] mW

as defined in [15]. Although the silicon CMOS LNA may have low power consumption, wideband silicon CMOS LNA has less bandwidth, less gain, and worse noise figure [13]. For comparable bandwidth and gain, the dc power consumption of the ABCS LNA is lower than the SiGe LNAs [14], [15] and GaAs HBT [16]. Furthermore, the ABCS HEMT’s high gain allows a single-stage ABCS LNA to achieve the same gain as an metamorphic high electron-mobility transistor (MHEMT) two-stage LNA [17]. The FOM confirmed that the ABCS LNAs have the best compromise in gain, bandwidth, noise figure, and dc power consumption. Based on this comparison, it is the authors’ belief that the ABCS wideband LNAs reported here have the lowest dc power consumption and the highest gain-bandwidth product ever reported. V. CONCLUSION This paper has reported on the first ABCS 0.1- m gate-length HEMT wideband LNAs with record low dc power consumption and high gain-bandwidth product. One- and three-stage ABCS HEMT ultra-low-power wideband LNAs are demonstrated with bandwidth from 0.3 to 11 GHz. The dc power consumption of the LNAs are 5 mW for the one-stage and 7.5 mW for threestage MMICs. For the one-stage LNA, the amplifier achieved 16-dB gain and less than 1.7-dB noise figure (2–11 GHz). For the three-stage LNA, the amplifier achieved 30-dB gain and less than 2.6-dB noise figure (2–11 GHz). These results demonstrate the outstanding potential of ABCS HEMT technology for low dc power applications. ACKNOWLEDGMENT The authors thank D. Deakin, A. Paniagua, P. Hundal, C. Regan, J. Greer, L. Tran, J. Lewis, and A. Ikhlassi, for device fabrication and E. Regan, for mask layout, all with the Rockwell Scientific Company, Thousand Oaks, CA.

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REFERENCES [1] J. B. Boos, W. Kruppa, B. R. Bennett, D. Park, S. W. Kirchoefer, R. Bass, and H. B. Dietrich, “AlSb/InAs HEMT’s for low-voltage, highspeed applications,” IEEE Trans. Electron Devices, vol. 45, no. 9, pp. 1869–1875, Sep. 1998. [2] J. Bergman, G. Nagy, G. Sullivan, B. Brar, C. Kadow, H.-K. Lin, A. Gossard, and M. Rodwell, “InAs/AlSb HFETs with ft and f max above 150 GHz for low-power MMICs,” in Proc. Int. InP and Relat. Mater. Conf., May 2003, pp. 219–222. [3] J. Bergman, G. Nagy, G. Sullivan, B. Brar, C. Kadow, H.-K. Lin, A. Gossard, and M. Rodwell, “Low-voltage, high-performance InAs/AlSb HEMTs with power gain above 100 GHz at 100 mV drain bias,” in Proc. Device Res. Conf., Jun. 2004, pp. 243–244. [4] B. Brar, G. Nagy, J. Bergman, G. Sullivan, P. Rowell, H. K. Lin, M. Dahlstrom, C. Kadow, and M. Rodwell, “RF and DC characteristics of low-leakage InAs/AlSb HFETs,” in Proc. Lester Eastman Conf., Jul. 2002, pp. 409–412. [5] R. Tsai, M. Barsky, J. B. Boos, B. R. Bennett, J. Lee, N. A. Papanicolaou, R. Magno, C. Namba, P. H. Liu, D. Park, R. Grundbacher, and A. Gutierrez, “Metamorphic AlSb/InAs HEMT for low-power, highspeed electronics,” in IEEE GaAs IC Tech. Symp. Dig., Nov. 2003, pp. 294–297. [6] J. B. Hacker, J. Bergman, G. Nagy, G. Sullivan, C. Kadow, H.-K. Lin, A. C. Gossard, M. Rodwell, and B. Brar, “An ultra-low power InAs/ AlSb HEMT Ka-band low-noise amplifier,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 4, pp. 156–158, Apr. 2004. [7] W. R. Deal, R. Tsai, M. D. Lange, J. B. Boos, B. R. Bennett, and A. Gutierrez, “A W -band InAs/AlSb low-noise/low-power amplifier,” IEEE Microw. Compon. Lett., vol. 15, no. 4, pp. 208–210, Apr. 2005. [8] J. B. Hacker, J. Bergman, G. Nagy, G. Sullivan, C. Kadow, H.-K. Lin, A. C. Gossard, M. Rodwell, and B. Brar, “An ultra-low power InAs/ AlSb HEMT W -band low-noise amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1029–1032. [9] ——, “An ultra-low power InAs/AlSb HEMT X -band low-noise amplifier and RF switch,” in Int. Compon. Semiconduct. Manuf. Technol. Conf. Tech. Dig., Apr. 2006. [10] K. Shinohara, P. S. Chen, J. Bergman, H. Kazemi, B. Brar, I. Watanabe, T. Matsui, Y. Yamashita, A. Endoh, K. Hikosaka, T. Mimura, and S. Hiyamizu, “Ultra-high-speed low-noise InP-HEMT technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 337–340. [11] B. Brar and H. Kroemer, “Influence of impact ionization on the drain conductance in InAs/AlSb quantum well heterostructure field-effect transistors,” IEEE Electron Device Lett., vol. 16, no. 12, pp. 548–580, Dec. 1995. [12] J. Bergman, G. Nagy, G. Sullivan, B. Brar, C. Kadow, H.-K. Lin, A. Gossard, and M. Rodwell, “RF noise performance of low power InAs/ AlSb HFETs,” in Proc. Device Res. Conf., Jun. 2003, pp. 147–148. [13] A. Bevilacqua and A. M. Niknejad, “An ultra-wideband CMOS LNA for 3.1 to 10.6 GHz wireless receiver,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., 2004, pp. 383–383. [14] Y. Park, C. Lee, J. Cressler, J. Laskar, and A. Joseph, “A very low power SiGe LNA for UWB application,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1041–1044. [15] N. Shiramizu, T. Masuda, M. Tanabe, and K. Washio, “A 3–10 GHz bandwidth low-noise and low-power amplifier for fullband UWB communications in 0.25-m SiGe BiCMOS technology,” in IEEE Radio Freq. Integr. Circuits Symp. Tech. Dig., Jun. 2005, pp. 39–42. [16] K. Kobayashi and A. Oki, “A DC–10 GHz high gain low noise GaAs HBT direct coupled amplifier,” IEEE Microw. Guided Wave Lett., vol. 5, no. 9, pp. 308–310, Sep. 1995. [17] O. Tang, K. Hwang, P. Chao, K. Nichols, L. Mt. Pleasant, B. Schmanski, M. Lang, K. Duh, P. Smith, S. Valenti, R. Melcher, and W. Taft, “An ultra-low DC power ultra-flat multi-octave MHEMT LNA MMIC,” in IEEE GaAs IC Symp. Tech. Dig., Nov. 2000, pp. 147–150.

Bob Yintat Ma (S’94–M’95) received the B.S. degree in electrical engineering from the University of California at Los Angeles (UCLA), in 1985, and the M.S. and Ph.D. degrees in electrical engineering from the University of California at Irvine, in 1996 and 2004, respectively. His doctoral dissertation concerns the area of electrostatic discharge (ESD) protection for MMIC and ESD characterization for devices. Since 2003, he has been a Senior Scientist with the Rockwell Scientific Company, Thousand Oaks, CA, where he is involved in designing microwave and millimeter-wave MMICs using GaAs, InP, GaN, and InAs/AlSb devices. He has authored or coauthored over ten papers in technical journals.

Joshua Bergman (S’96–A’98–M’01) received the B.A. degree from Rice University, Houston, TX, in 1995, and the M.S.ECE and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 1997 and 2004, respectively. In 1996, he joined the Microwave Applications Group (MAG), Georgia Institute of Technology, as a Research Assistant. During the course of his doctoral research, he was involved with Raytheon Systems, Dallas, TX, where he developed device fabrication methods for InAs–quantum well (QW) resonant tunneling devices (RTDs) on InP substrates, and was involved with their research laboratories from July 1998 to September 1999. Since February 2002, he has been with the Rockwell Scientific Company, Thousand Oaks, CA, where he develops antimonide-based superlattice photodiodes for very-long wave infrared (VLWIR) applications and InAs/AlSb MHEMTs for ultra-low power receivers. The antimonide-based HEMT MMIC technology has produced the world’s first antimonide-based MMICs, including low-power low-noise amplifiers (LP LNAs) ranging in frequency to 100 GHz, as well as very low-loss RF switches.

Peter Chen is a Research Scientist with the Rockwell Scientific Company, Thousand Oaks, CA, where he is involved in designing microwave and RF circuits. He has designed RF high-power amplifier using widebandgap technologies such as SiC MESFETs. He has authored or coauthored over five papers in technical journals.

Jonathan B. Hacker (S’86–M’86–SM’05) received the B.A. Sc. degree in electrical engineering from the University of British Columbia, Vancouver, BC, Canada, in 1986, and the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 1990 and 1994, respectively. He is currently the Department Manager of the High Frequency Sources and Sensors Department, Rockwell Scientific Company, Thousand Oaks, CA, where he is involved in research and development efforts in low-cost batch-fabricated phased-array antenna systems and MMICs including GaAs, InP, and ABCS HEMT and HBT devices, MMIC packaging, and millimeter-wave quasi-optic power amplifiers and multipliers. He has performed pioneering research on quasi-optical power-combining and frequency-multiplication techniques, as well as advanced MMIC devices integrating microelectromechanical systems (MEMS) RF switches and HEMT structures. From 1993 to 1997, prior to joining the Rockwell Scientific Company, he was a Member of the Technical Staff with Bell Communications Research, where he was involved in the development of advanced digital ICs and multichip modules (MCMs) for SONET and ATM applications. He has authored or coauthored over 60 papers in the area of microwave and millimeter-wave technologies. He holds three patents. Dr. Hacker has been the electronic paper manager for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) for the last two years.

Gerard Sullivan is currently with the Rockwell Scientific Company, Thousand Oaks, CA, where he is involved in the design, growth, and characterization of a wide range of III–V materials and devices including AlGaInAs HBTs, HFETs, detectors, and lasers on GaAs and InP substrates, n- and p-channel AlGaSb/InAs HFETs, AlGaN HFETs, and detectors, and GaInSb/InAs superlattice detectors. He has authored or coauthored over 70 papers in technical journals.

MA et al.: InAs/AlSb HEMT AND ITS APPLICATION TO ULTRA-LOW-POWER WIDEBAND HIGH-GAIN LNAs

Gabor Nagy received the Ph.D. degree in physics from Clarkson University, Potsdam, NY, in 1996. He is currently a Research Scientist with the Rockwell Scientific Company, Thousand Oaks, CA, where he is involved with process development for InP-, GaN-, GaSb-, and GaAs-based device technologies. Prior to working with the Rockwell Scientific Company, he led efforts in nanoscale process development for compound semiconductors, initially as a Post-Doctoral Fellow with Columbia University and then as a Research Engineer with the Nanofabrication Facility, Cornell University, Ithaca, NY. He has authored or coauthored approximately 20 publications, mostly in the area of semiconductor device processing.

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Bobby Brar (M’96) received the Ph.D. degree in electrical engineering from the University of California at Santa Barbara (UCSB), in 1995. While with UCSB, he studied the InAs/AlSb/GaSb material system for high-speed electronic and opto-electronic applications. In 1995, he joined the Nanoelectronics Branch, Central Research Laboratories, Texas Instruments Incorporated, to work on InP-based resonant tunneling devices and FETs for high-speed mixed-signal applications. Under the Ultra Program sponsored by the Defense Advanced Research Projects Agency (DARPA), he also conducted research in ultrathin crystalline layers grown on silicon substrates to build resonant tunneling structures for silicon-based quantum devices. In 1999, he joined the Rockwell Scientific Company, Thousand Oaks, CA, where he managed the Advanced III–V Devices and Materials Department for five years in the development of GaAs-, InP-, and ABCSs for low-power mixed-signal and low-noise MMIC applications. He is currently the Executive Director of the Electronics Division, Rockwell Scientific Company. He has authored or coauthored over 50 papers in technical journals.

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AlGaN/GaN

Ka-Band 5-W MMIC Amplifier

Ali Mohamed Darwish, Member, IEEE, K. Boutros, Senior Member, IEEE, B. Luo, Benjamin D. Huebschman, Member, IEEE, E. Viveiros, Member, IEEE, and H. Alfred Hung, Senior Member, IEEE

Abstract—A broadband -band AlGaN/GaN on SiC high electron-mobility transistor monolithic-microwave integrated-circuit (MMIC) power amplifier was developed for millimeter-wave antenna applications. The 0.18- m gate two-stage 50- matched MMIC produces 13 1 dB of gain from 26 to 36 GHz. At 35 GHz, the measured continuous wave (CW) saturated output power out was 4 W (5 W pulsed), indicating a CW power density of 3.3 W/mm (4.2 W/mm pulsed). The CW power-added efficiency was 23%. Across the band, the measured CW out was 2 W (2.5 W pulsed). While individual (or partially matched single stage) devices have been demonstrated with good output power, to the best of our knowledge, this is the first report of a 10-GHz-band-band GaN MMIC with high output power and gain. A width unique aspect of the design, contributing to the wide bandwidth, is the use of positive feedback in the first stage to increase the gain. RF power stress test and detailed investigation of the channel temperature effect are presented. A preliminary RF power stress test indicates a lifetime of 1000 h at 191 C channel temperature, and elevated temperature operation indicates that out decreases by 0.013 dB/ C.



(P )

P

P

Index Terms—GaN high electron-mobility transistor (HEMT), high power, -band power amplifier (PA), millimeter-wave monolithic microwave integrated circuit (MMIC).

at 28 GHz from a 3.2-mm gate periphery device at the output stage (1.25-W/mm power density) with 23.8% power-added efficiency (PAE). This paper is an expansion of a previously published paper [14]. We report the development of a two-stage broadband -band MMIC PA achieving 13 1 dB of gain from 26 to 36 GHz. At 35 GHz, the measured continuous wave (CW) output power was 4 W, indicating a power density of 3.3 W/mm. The PAE was 23%. The minimum output power across the band was 2 W, at the low-frequency portion of the band. The pulsed saturated was 5 W at 35 GHz. Across the band, was 2.5 W. This first-pass design the measured pulsed was successful due to high performance of the device, and the extensive full-wave modeling and broadband design of the MMIC. To our knowledge, this is the best combination of output power, gain, and bandwidth reported in a two-stage GaN MMIC technology. This combination of high power and bandwidth represents one of the clear advantages of GaN technology over GaAs, where a relatively small device (here, 0.6 mm) can produce a significant amount (approximately 2 W) of output power, while having an optimum output load close to 50 .

I. INTRODUCTION ALLIUM–NITRIDE devices have shown significant performance advantage over GaAs and InP. The AlGaN/GaN on SiC is particularly desirable due to the high thermal conductivity of SiC. At the device level (or partially matched single-stage circuits), record performance has been reported at millimeter-wave frequencies [1]–[7], [5]. Specifically, at 30 GHz, 3.4 W/mm [1] and 5.1 W/mm [2] were reported. At 35 GHz, 3.3 W/mm [1] and 4.9 W/mm [2] were also reported. At 40 GHz, 2.8 W/mm [6] and, recently, 10 W/mm [4], [5] have been reported. In addition, record of 230 GHz was reported [4], [5]. In spite of these excellent results at the device level, very few fully integrated monolithic microwave integrated circuits (MMICs) were demonstrated [8]–[10]. In [8], a single-stage MMIC with 9 dB of linear gain at 27 GHz and 2.2 W of output power was reported. In [9], a low-noise amplifier (LNA) MMIC was reported along with a power amplifier (PA) MMIC providing a saturated output power of 4 W

G

Manuscript received March 31, 2006; revised July 5, 2006. This work was supported in part by the Army Research Laboratory under the Collaborative Technology Alliance Program Contract DAAD19-01-2-0008. A. M. Darwish, B. D. Huebschman, E. Viveiros, and H. A. Hung are with the Army Research Laboratory, Adelphi, MD 20783 USA (e-mail: ali@darwish. org; [email protected]). K. Boutros and B. Luo are with the Rockwell Scientific Company LLC, Thousand Oaks, CA 91360 USA. Color versions of Figs. 1–4, 6, 7, 9, 10, and 15–26 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.883599

II. HIGH ELECTRON-MOBILITY TRANSISTOR (HEMT) PERFORMANCE A. Device Fabrication The GaN HEMT devices used in the current MMIC design were fabricated on 2-in semi-insulating 4H-SiC substrates. The epitaxial layer consisted of an AlGaN/GaN HEMT structure grown by metal–organic chemical vapor deposition (MOCVD). The devices were defined using implant isolation, Ta-based mm, and 0.18- m-long ohmic contacts with T-gates. A Si N layer was used as a device passivation layer, and as dielectric for metal–insulator–metal (MIM) capacitors. Thin-film resistors were fabricated using Ni–Cr metal lines, and two-level interconnects with air-bridge technology were used to complete the front-end device fabrication process. Through-substrate vias with 50- m diameter were fabricated in the 3-mil thinned substrate to complete the MMIC back-end fabrication. A thin substrate provides lower thermal resistance and lower via-hole inductance (particularly critical at millimeter wave). Typical dc and RF device characteristics of a microstrip-loaded 400- m gatewidth device showed a saturation current of 1 A/mm, a maximum transconductance, of 290 mS/mm, a cutoff frequency of 84 GHz, of 114 GHz. The device’s and a unity-gain frequency equivalent circuit is shown in Fig. 1. Frequency response from the equivalent-circuit model versus measured -parameters of the device, shown in Fig. 2, indicate good agreement between

U.S. Government work not protected by U.S. copyright.

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-BAND 5-W MMIC AMPLIFIER

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Fig. 1. RF equivalent small-signal model of the field-effect transistor (FET).

2

Fig. 3. I–V curves for 2 75 m device, normalized to 1 mm, at room temperature. V gs is swept between 6–0 V. The slope of the V gs = 0 V curve is related to the resistance (sum of the drain and source resistances).

Fig. 2. Device model versus measured S -parameters for a unit cell device showing a good match between the simulated and measured characteristics.

0

Fig. 4. Saturated current dependence on channel temperature. I sured at 10-V drain voltage.

was mea-

the modeled and measured characteristics. The HEMT was characterized with a source and load optimized for best input match and maximum output power. With the data extracted from this measurement, the MMIC can be designed to meet the optimum source/load impedances. This eliminates the need for a large-signal model. B. Device I–V Characteristic Over Temperature The performance of the measured device was characterized as a function of temperature to predict the effect of channel temperature on gain, output power, and cutoff frequency of the PA. Scaling the device to a larger gate periphery device was successfully achieved through impedance scaling and the careful deembedding of input/output electromagnetic feeding structures. The dc parameters, current–voltage (I–V) curves, , and scattering parameters were measured at base plate temperature of 25 C, 0 C, 25 C, 50 C, 75 C, 100 C, and 125 C. The dc I–V curves of the 2 75 m are shown in Fig. 3, where the current has been scaled to a 1-mm device. The saturation current was measured as function of channel temperature. The channel temperature was estimated based on a detailed finite-element simulation of the thermal resistance of the device (using ANSYS). The simulation yielded a 9- C/W mm thermal resistance for the 2 75 m device. In addition, the source resistance was calversus curve at . culated from the slope of the The source resistance is assumed to be half of the total resistance, i.e., the inverse slope of the line (see Fig. 3). The dependence of the source resistance and the drain saturation current

Fig. 5. Source resistance dependence on chuck temperature.

on the channel temperature are shown on Figs. 4 and 5. The dc (defined as ) was calculated transconductance versus curve and plotted for different basefrom the plate temperatures in Fig. 6. The peak of the transconductance is plotted as a function of temperature in Fig. 7. The peak displays a linear dependence on temperature. At the operating ), the RF was obtained by fitbias point (10 V, 40% ting the measured -parameters against the small-signal model (Figs. 1 and 2). Both the dc and RF versus channel temperaand RF are ture are plotted in Fig. 8. As expected, the dc 100 C almost equal. However, at high channel temperature they diverge. This divergence could be due to buffer layer current leakage contributing to the dc, but not RF, current.

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2

Fig. 9. Measured f as a function of channel temperature for two 2 75 m devices. A best linear fit line is shown for both cases. The best fit line has a slope of approximately 0.9 GHz=10 C.

0

Fig. 6. Measured dc transconductance g for a 2 75 m devices.

2

as a function of channel temperature

2

Fig. 10. Measured f as a function of channel temperature for two 2 75 m devices. A best linear fit line is shown for both cases. The best fit line has a slope of approximately 1.45 GHz=10 C.

0

Fig. 7. Maximum of transconductance g (peak value of curve above) as a function of channel temperature for a 2 75 m devices. The best fit line has a slope of approximately 0.1 mS= C.

0

2

Fig. 8. Measured change of transconductance with channel temperature for dc g (solid diamonds) and RF g (void squares).

Figs. 9 and 10 show the measured and as a function of channel temperature for a 2 75 m device. A best linear has a fit line is shown for both cases. The best fit line for has a slope of approximately 0.9 GHz 10 C, and for slope of approximately 1.45 GHz 10 C. The temperature coefficient (TC), defined as , for equals equals to to 1.7 10 parts per million ppm C for 1.4 10 ppm C. To understand the origins of the decrease in cutoff and maximum frequency performance of the device, we examine the dependence of the transconductance on channel tembest fit line has a slope of approximately perature. The RF 0.42 mS 10 C. The TC for is 1.76 10 ppm C. This is nearly equal to the TC of . Given that and are

C C , a similar TC for related by [11] and indicates that the input capacitance C C does not change with temperature. In fact, if we consider the data points where the channel temperature is below 100 C, we will find that , , and , all have a TC of approximately for , 1.7 10 ppm C. Our earlier analysis of a large number of devices from five manufacturers (with varying epi-structures) is 1.87 0.8 10 ppm C. In [12] indicates that the current case, the measured TC is close to the average. This suggests that the TC is closely associated with fundamental material properties of GaN. Thus, the conclusions derived from this small set of data may be indicative of this broad class of devices, namely, GaN HEMT devices. III. DEVICE THERMAL RESISTANCE The thermal resistance of the device can be estimated through numerical simulations or through the use of analytical thermal models that were shown to be highly accurate [15], [16]. Based on analytical models presented in [15], the thermal resistance is (see Fig. 11)

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-BAND 5-W MMIC AMPLIFIER

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Fig. 12. Ideal feedback loop.

Fig. 11. HEMT dimensions. Gate dimensions are L , x, W , substrate thickness is t , and gate-to-gate spacing is s.

where Fig. 13. Generalized feedback loop.

use of negative (let alone positive) feedback at microwave and millimeter-wave frequencies for fear of oscillation. The ideal feedback loop analysis (see Figs. 12 and 13) assumes that both the amplifier and feedback are unidirectional. In the ideal case, the gain with feedback equals the gate length is , gatewidth , gate–gate spacing , the GaN layer thickness , and the SiC thickness . The thermal conductivity of the GaN and SiC layers are and , respectively. In the current case, m, m, m, m, m, W/cm K, and W/cm K. For the two 75 m output devices, the analysis results in a thermal 8 resistance equal to 8.2 C/W, and channel temperature of 90.6 C, under typical operating conditions (drain bias of 24 V and 500 mA at room temperature with 33% drain efficiency). Based on the thermal resistance equation above, one can realize that the channel temperature is 30 C cooler than a comparable size device with more compact layout ( m, m). The advantage of using angate-to-gate spacing alytical models is the ease of calculation, and the ability to concurrently optimize the thermal and electrical performance of different device geometries (gatewidth, substrate thickness, number of fingers, etc.). IV. MMIC DESIGN The MMIC consisted of a two-stage design with inter-stage matching. The first and second stages consisted of device unit cells with total gate periphery of 0.6 and 1.2 mm, respectively. The 1 : 2 driver/power-stage device ratio is a conservative design choice. The advantage of this choice is the ability of the driver stage to saturate the output stage over most of the band, even with less than optimal impedance match. The disadvantage is that it results in lower PAE as the driver stage consumes more dc power. One novel aspect of the MMIC design used here is the utilization of positive feedback. In most cases, designers avoid the

where is the forward gain and is feedback gain. Negative feedback is typically used to flatten the gain across the frequency band and decrease amplifier sensitivity at the expense of lower gain. However, in the current case at millimeter-wave frequencies, gain is at a premium and the use of negative feedback is unfavorable. Positive feedback, on the other hand, provides gain enhancements. as well as flatness, if used properly. The important aspect is to carefully consider stability of the closed loop to avoid oscillation. To that end, the theory of developed by Bode [13] is employed. Bode’s theory treats the general case (Fig. 13) of bi-directional amplifier and feedback paths and includes the ideal feedback model as a special case. It also accommodates arbitrary input and output coupling blocks. To apply Bode’s theory, the controlled source (in this case, the transconductance) is configured as a two-port network connected to a general four-port network (see Fig. 14). The return difference is then defined. This function, i.e., , can be considof the ered as a generalization of the feedback factor ideal feedback model above. The zeros of in the complex of a frequency plane determine the stability of the circuit. feedback network with respect to element (in our case, ) is defined as the ratio of the network determinant under: 1) the condition that the element assumes its nominal value and 2) the conditions that the element assumes the value zero

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Fig. 14. Voltage loop gain is obtained by placing a 1-V source at the input of the current controlled source and measuring V . The voltage loop gain can be calculated using return ratio function T .

Fig. 15. Schematic of MMIC PA design. The feedback in the first stage is implemented using a bond wire. The bond wire ties the two gates together and providing a single bias point for both gates.

where

is the determinant of the -matrix when . For the current case (Fig. 14),

Fig. 16. Simulated voltage gain for first-stage amplifier employing a feedback loop.

and

where is the 43 co-factor of the -matrix. The return ratio representing the loop voltage gain is defined as Fig. 17. Fully fabricated MMIC consisting of a two-stage layout with interstage matching. The input and output stages had a total gate periphery of 0.6 and 1.2 mm, respectively.

The circuit is stable if a plot of in the complex frequency plane does not enclose the point . The positive feedback is applied to the first stage to increase the gain. A feedback loop is implemented around the first HEMT device. Positive feedback was not applied to the power (second) stage in order to simplify the optimum load matching and secure maximum power performance. To ensure unconditional stability, the feedback path, of the first stage, is designed with sufficient losses to guarantee sub-unity loop gain. It is composed of a resistor (50 ) in series with an inductance (approximately 0.25 nH implemented with a bond wire for initial proof of concept) (see Fig. 15 for circuit schematics). The bond wire can be readily replaced with an on-chip inductor in the future. Carrying out the return ratio analysis, a plot in the complex plane is shown in Fig. 16. As this figure indicates, the frequency sweep of produces values within the unit circle for all frequencies. This ensures unconditional loop stability for all frequencies. V. MMIC PERFORMANCE -band MMIC is shown in Fig. 17. Each A fully fabricated of the three HEMT cells was grounded with two via-holes.

The small-signal -parameter measurements of the MMIC are shown in Fig. 18. The results indicate a gain of 13 1 dB from 26 to 36 GHz with feedback. Without feedback (bond wire removed), the gain is several decibels lower and the frequency response is no longer flat across the frequency band. All of the improvement in gain comes from the feedback at the first stage. The higher gain of the first stage enables it to compress the second stage at lower input powers (proportional to the gain improvement). The bias conditions were V and for the first and second stages during small-signal and power measurements. The MMIC did not need any tuning. In fact, load–pull optimization of the source/load impedances for gain (or output power) showed no improvement at other impedance matches, except 50 . Power testing of packaged MMIC was performed at a drain bias of 24 V. The chip was mounted on a THERMKON metal block with an Au–Sn eutectic die attach for heat sinking. Constant temperature was maintained using a controlled temperature recirculating chiller. The temperature of the metal block was maintained at approximately 25 C during power measurements.

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Fig. 21. Pulsed output power at 35 GHz Fig. 18. Small-signal S -parameter measurements of the MMIC with (thick line) and without (thin dashed line) feedback. The feedback is added through the inter-stage bond wire.

Fig. 22. Pulsed P3dB output power, as a function of frequency.

Fig. 19. Measured MMIC CW output power at 35 GHz showing a linear gain of 13 dB, a saturated power of 36 dBm, and a peak efficiency of 23%.

Fig. 23. Small-signal gain as a function of channel temperature.

Fig. 20. Measured P3dB of MMIC under CW conditions across the frequency band.

The measured on-wafer output power, gain, and PAE at -dB output power 35 GHz are shown in Fig. 19, and the is shown as a function of frequency in Fig. 20. At 35 GHz, the MMIC showed a linear gain of 12 dB. At the peak PAE

(3 dB into compression), a of 3.8 W was measured, corresponding to a power-density of 3.2 W/mm (with 9 dB of gain). A saturated output power of 4 W was measured. The output power (at peak PAE) was measured across the band. The minimum output power measured was 2 W at the low-frequency portion of the band. The pulsed (200-ns was 5 W at 35 GHz (see Fig. 21). pulses) saturated was 2.5 W (see Across the band, the measured pulsed is Fig. 22). The channel temperature effect on gain and presented in Figs. 23 and 24. The output power decreases by 0.013 dB C. This indicates that if the channel temperature can be kept close to room temperature that there should be approximately 1 dB of improvement in output power. This is the same level of output power enhancement between the

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VI. CONCLUSIONS A broadband -band MMIC PA has been demonstrated. This may pave the way for the replacement of the travelingwave-tube amplifiers with GaN solid-state amplifiers if the reliability and efficiency of the technology can be improved. The -band, MMIC has a bandwidth of 32%, covering most of the while producing output powers of 2–4-W CW and 2.5–5 W pulsed across the band. Positive feedback and careful reduction of the channel temperature were keys to obtaining state-ofthe-art performance. The development of broadband PA MMICs is critical for cost reduction in multiband multifunction phasedarray systems. Fig. 24. CW P3dB output power as a function of channel temperature.

ACKNOWLEDGMENT The authors would like to thank K. Kingkeo, Army Research Laboratory, Adelphi, MD, for his support in the device and MMIC RF characterizations. REFERENCES

Fig. 25. Assembled and packaged MMIC.

Fig. 26. Reliability data for fixtured Ka MMIC under RF stress at 35 GHz, 24 V, 40% I , and 2-dB into compression at a channel temperature of 191 C.

CW and pulsed measurements. The MMIC was packaged in a metal housing and tested (see Fig. 25). The fully packaged MMIC had similar performance with the on-wafer measured MMIC after accounting for the loss of the K-connectors and 50- input/output fused silica substrates. Reliability data for the fixtured MMIC under RF stress at 35 GHz, 24 V, 40% , and 2 dB into compression at a channel temperature of 191 C is shown on Fig. 26. Linear extrapolation of the time dB at 1000 h. Although the access indicates a lifetime is expected to improve appreciably with lower channel temperature and bias, this results points to the need to improve the reliability of AlGaN/GaN HEMT devices.

[1] Y.-F. Wu, M. Moore, A. Saxler, P. Smith, P. M. Chavarkar, and P. Parikh, “3.5-watt AlGaN/GaN HEMTs and amplifiers at 35 GHz,” in Proc. IEEE Int. Electron Devices Meeting, 2003, pp. 23.5.1–23.5.2. [2] Y.-F. Wu, M. Moore, A. Saxler, T. Wisleder, U. K. Mishra, and P. Parikh, “8-watt GaN HEMTs at millimeter-wave frequencies,” in Proc. IEEE Int. Electron Devices Meeting, 2005, pp. 583–585. [3] R. Quay, A. Tessmann, R. Kiefer, R. Weber, F. van Raay, M. Kuri, M. Riessle, H. Massler, S. Muller, M. Schlechtweg, and G. Weimann, “AlGaN/GaN HEMTs on SiC: Towards power operation at V -band,” in Proc. IEEE Int. Electron Devices Meeting, 2003, pp. 23.2.1–23.2.2. [4] T. Palacios, A. Chakraborty, S. Rajan, C. Poblenz, S. Keller, S. P. DenBaars, J. S. Speck, and U. K. Mishra, “High-power AlGaN/GaN HEMTs for Ka-band applications,” IEEE Electron Device Lett., vol. 26, no. 11, pp. 781–783, Nov. 2005. [5] T. Palacios, A. Chakraborty, S. Keller, S. P. DenBaars, and U. K. Mishra, “High power AlGaN/GaN HEMTs for millimeter-wave applications,” in Government Microcircuit Applicat. Critical Technol. Conf., San Diego, CA, 2006, Paper 11.3. [6] K. Boutros, M. Regan, P. Rowell, D. Gotthold, R. Birkhahn, and B. Brar, “High performance GaN HEMTs at 40 GHz with power density of 2.8 W/mm,” in Proc. IEEE Int. Electron Devices Meeting, 2003, pp. 12.5.1–12.5.2. [7] J. Moon, S. Wu, D. Wong, I. Milosavljevic, P. Hashimoto, M. Hu, M. Antcliffe, and M. Micovic, “Deep submicron gate-recessed and fieldplated AlGaN/GaN HFETs for millimeter-wave applications,” in Proc. Mater. Res. Soc. Fall Meeting, Dec. 2004, vol. E6-1, pp. 119–125. [8] M. Micovic, A. Kurdoghlian, H. P. Moyer, P. Hashimoto, A. Schmitz, I. Milosavljevic, P. J. Willadesn, W.-S. Wong, J. Duvall, M. Hu, M. J. Delaney, and D. H. Chow, “Ka-band MMIC power amplifier in GaN HFET technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, pp. 1653–1656. [9] M. Micovic, A. Kurdoghlian, H. P. Moyer, P. Hashimoto, A. Schmitz, I. Milosavljevic, P. J. Willadesn, W.-S. Wong, J. Duvall, M. Hu, M. Wetzel, and D. H. Chow, “GaN MMIC technology for microwave and millimeter-wave applications,” in IEEE Compound Semiconduct. Integr. Circuits Symp., Oct. 2005, Session J. [10] B. M. Green, S. Lee, K. Chu, K. J. Webb, and L. F. Eastman, “High efficiency monolithic gallium nitride distributed amplifier,” IEEE Microw. Guided Wave Lett., vol. 10, no. 7, pp. 270–272, Jul. 2000. [11] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981, p. 333. [12] A. M. Darwish, B. Huebschman, R. Del Rosario, E. Viveiros, and H. A. Hung, “Temperature behavior of AlGaN/GaN on SiC HEMTs,” in IEEE Compound Semiconduct. Conf., Palm Springs, CA, 2005, Paper H.3. [13] H. W. Bode, Network Analysis and Feedback Amplifier Design. New York: Van Nostrand, 1945. [14] A. M. Darwish, K. Boutros, B. Luo, B. Huebschman, E. Viveiros, and H. A. Hung, “4-watt Ka-band AlGaN/GaN power amplifier MMIC,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, 2006, Paper WE3B-07.

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[15] A. M. Darwish, A. Bayba, and H. A. Hung, “Thermal resistance calculation of AlGaN/GaN devices,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2611–2620, Nov. 2004. [16] ——, “Accurate determination of thermal resistance of FETs,” IEEE Trans. Microw. Theory Tech, vol. 53, no. 1, pp. 306–313, Jan. 2005.

Ali Mohamed Darwish (M’95) was born in Manhattan, KS, in 1969. He received the B.Sc. and M.S. degrees (with honors) in electrical engineering from University of Maryland at College Park, in 1990 and 1992, respectively, and the Ph.D. degree from the Massachusetts Institute of Technology (MIT), Cambridge, in 1996. In 1990, he joined COMSAT Laboratories, where he conducted the experimental work for his M.S. thesis. In 1992, he was a Research Assistant with the Optics and Quantum Electronics Group, MIT. In 1997, he co-founded Amcom Communications Inc. a leading supplier of high-power microwave devices. In May 2003, he joined the RF Electronics Division, Army Research Laboratory, Adelphi, MD, where he currently conducts research on wide-bandgap materials (GaN), thermal analysis, and novel MMIC concepts. Dr. Darwish was the recipient of the National Science Foundation (NSF) Fellowship.

K. Boutros (S’87–M’90–SM’05) received the M.S. and Ph.D. degree in electrical engineering from North Carolina State University, Raleigh, in 1991 and 1996, respectively. In 1999, he joined Rockwell Scientific as a Senior Scientist, where he has been involved in the development of wide bandgap semiconductor microelectronic devices and circuits. Prior to joining Rockwell Scientific, he was a Senior Member of Technical Staff with Spectrolab, a wholly owned subsidiary of Boeing, where he was in charge of developing a product line based on the GaAs/GaInP heterojunction bipolar transistor (HBT) devices. He authored or coauthored over 50 technical publications and holds several patents in the field of semiconductor materials and devices.

B. Luo, photograph and biography not available at time of publication.

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Benjamin D. Huebschman (M’94) received the B.S. degree from Purdue University, West Lafayette, IN, in 1995, and the M.S. degree from the University of Maryland at College Park, in 2002. He is currently with the Army Research Laboratory, Adelphi, MD. His area of interests includes high-frequency high-power amplifiers and semiconductor physics.

E. Viveiros (M’95) received the B.S.E.E. degree from Rutgers University, New Brunswick, NJ, in 1984, and the M.S.E.E. degree from The John Hopkins University, Baltimore, MD, in 1991. He is currently a Team Leader with the RF Electronics Branch, U.S. Army Research Laboratory, where he leads research and development efforts in advanced device, circuit and integration technologies including GaAs, InP, GaN, SiGe, microelectromechanical systems (MEMS) for SATCOM, radar, and multifunction RF applications.

H. Alfred Hung (S’74–M’75–SM’81) received the S.B. degree in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, and the M.S., and Ph.D. degrees from Cornell University, Ithaca, NY. In 2001, he joined the Army Research Laboratory, Adelphi, MD, where he is currently involved with the research of new device and integration technologies for sensors, communication, and multifunction RF systems. He is the Army lead for a number of Defense Advanced Research Projects Agency (DARPA) programs (WBGS-RF, TFAST, and SWIFT). He has previously held research, functional, and program management positions with General Technical Services [with the Army Research Laboratory (ARL)], TRW, Raytheon, and COMSAT Laboratories. He has worked in the areas of GaAs and InP HEMT and HBT MMICs and their associated reliability, control circuits, and subsystems integration, as well as optical/microwave techniques, for wireless and radar systems, terrestrial and satellite communications. He was also an Adjunct Professor with George Washington University. He has authored or coauthored over 110 publications in journals, book chapters, and conference proceedings. He has been on the Editorial Boards of various technical journals. His research interests include wide bandgap (GaN), compound semiconductor (InP, SiGe), and RF MEMS technologies for millimeter-wave/sub-millimeter-wave and mixed-signal integrated circuits and system applications. He has been involved in the areas of GaAs and InP HEMTs and HBTs, related MMICs, and subsystems integration, as well as optical/microwave techniques for wireless and radar systems and terrestrial and satellite communications. Dr. Hung has been active on IEEE technical conference committees and on the Editorial Boards for IEEE TRANSACTIONS and LETTERS.

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Experiment and Spectral Analysis of a Low-Power -Band Heartbeat Detector Measuring From Four Sides of a Human Body

Ka

Changzhi Li, Student Member, IEEE, Yanming Xiao, Student Member, IEEE, and Jenshan Lin, Senior Member, IEEE

Abstract—The accuracy of a -band physiological movement detector was tested and compared for measurements from four different body orientations and at five different distances. A rigorous spectral analysis approach is developed when previously adopted small-angle approximation model is not applicable. This theory analyzes in detail the harmonics observed in phase-mod-band Doppler radar, explaining the reason for better ulated heart-rate accuracy when detected from the back of the body. It also explains the advantage of double-sideband transmission in avoiding the null point problem. Simulations have been performed to illustrate this theory and provide design guidelines for the system. This theory has also been verified by experiments. Index Terms—Biomedicine, cardiopulmonary, detector, double -band, life sign, low sideband, electromagnetic wave, heartbeat, power, microwave, millimeter wave, noncontact, remote sensing, respiration, RF, sensor, spectral analysis, telemedicine, vital sign, wireless.

I. INTRODUCTION

I

T HAS been decades since microwave Doppler radar was used for wireless sensor applications. Most common applications include volume change sensing [1], life detection for finding human subjects trapped in earthquake rubble [2], and cardiopulmonary monitoring for sleep apnea syndrome detection [3]. Previously reported microwave sensing systems [1]–[5] transmit an RF single-tone continuous-wave (CW) signal, which is reflected off a target and then demodulated in the receiver. CW radar with the human body as the target will receive a signal with its phase modulated by the time-varying chest-wall position. Demodulating the phase will then give a signal proportional to the chest-wall position that contains information about movement due to heartbeat and respiration. Recently, a -band system using double-sideband transmission was reported [6]. It has been shown that the short -band sensor is more sensitive to small wavelength of the chest-wall motion. Meantime, double-sideband transmission can avoid a severe null point problem at short wavelength without using quadrature demodulation. The system configuration is also simplified without using image-reject filters [7]. Manuscript received April 1, 2006; revised July 10, 2006. This work was supported in part by the National Science Foundation under Grant 0421218. The authors are with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.884652

-band detector, we have done measurements using Using the different transmitting power levels at different distances from four sides of a body [8], showing that this detector achieved high detection accuracy. We also found that measuring from the back of the body gives better accuracy than measuring from all other sides. While showing advantages over previously reported lower -band physfrequency single-tone sensing systems, the iological movement sensor brings a few new questions to -band be answered. Firstly, as the frequency moves into with wavelength in centimeter or even millimeter range, chest-wall movement due to respiration may go out of the range of small-angle approximation [5], rendering the previously well-adopted model to no avail. Thus, how to model the radar system more properly to guide future design? Secondly, as observed in experiments, while it is very easy to accurately detect heartbeat when holding the breath, sometimes the detection accuracy seems to be reversely affected when breathing is added. How to explain this and how to avoid this phenomenon? Thirdly, what is the reason for better heart-rate accuracy when detected from the back of the body? In this paper, in addition to presenting the results measured on human body under different experimental conditions, we perform a rigorous spectral analysis of Doppler radar sensing of physiological movement. While in accordance with the results obtained from the simple small-angle approximation model [5]–[7] for low-frequency operation, the theory is readily to be used for more general cases such as high-frequency operation with large-angle phase modulation. Based on the theory to be presented, the aforementioned questions have been answered. The theory also explains from a spectral viewpoint the reason double-sideband transmission can be used to increase the detection accuracy. Furthermore, harmonic effects caused by the physical nature of phase-modulated Doppler radar are analyzed in detail. Numerical simulations by MATLAB and system-level simulations by Agilent Technologies’ Advanced Design System (ADS) were performed to illustrate the theory -band sensors. The harmonics and provide design tips for and the null/optimum point were observed and verified by experiment. The results of measurement on the human body, following -band system, are presented in a brief description of the Section II. The theory based on spectral analysis is developed in Section III. Simulations are presented in Section IV. Supporting experimental results are given in Section V, and a conclusion is drawn in Section VI.

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Fig. 1. Block diagram of the Ka-band Doppler-radar system using doublesideband transmission, and the target with four different orientations.

II. MEASUREMENT FROM FOUR SIDES OF A HUMAN BODY -band physiological movement The block diagram of the detector and the orientation of the body in measurement are illustrated in Fig. 1. The transmitter chain contains a transmitting antenna (labeled as TXA) and an up-converter. The receiver chain includes a receiving antenna (RXA), a low-noise amplifier (LNA), two down-converters, and an IF amplifier (IF_AMP). The baseband circuit contains a preamplifier (PreAMP), a bandpass filter (BPF), and a low-frequency amplifier (LF_AMP). Two 3-dB power splitters are used to divide the power generated by the RF local oscillator (RF_LO) and the IF local oscillator (IF_LO), with half of the power sent to the transmitter chain and the other half sent to the receiver chain. The output of the transmitting antenna has two main freand quency components: lower sideband (LSB) . The LSB and USB freupper sideband (USB) quencies are 26.54 and 27.66 GHz ( GHz and MHz) with combined power being either 350 or 14.2 W. The power is switched from 350 to 14.2 W when an attenuator (AT) is inserted in the transmitter chain between the IF local oscillator and the up-converter. The components of the transceiver are all operating in the linear region so that the received signal would not cause any compression in any stage to produce strong harmonics that will be observed in experiment. Therefore, the strong harmonics sometimes observed in experiment must be due to some other reason. The remote detection of physiological movement was measured from four sides of the body, as indicated in Fig. 1. The four measurement angles are defined as the front, back, left, and right cases. The subject, breathing normally, was seated at a distance away from the antenna. A wired fingertip pulse sensor (UFI_1010 pulse transducer) was attached to the index finger during the measurement to provide the reference heartbeat. The experimental conditions were designed as combinations of the following parameters: two power levels of 350 and 14.2 W; five different distances from the antenna: 0.5, 1, 1.5, 2, and 2.5 m; and measuring from four sides of the body. The signal processing part is similar to that in [6] and [7]. The heartbeat signal was first separated from the respiration signal by a Butterworth BPF with passband from 0.7 to 3 Hz. The filtered signal was then windowed and auto-correlated. After that,

Fig. 2. Heart-rate comparison at 2-m distance measured in the: (a) front case and (b) back case. The output power of the detector is 350 W. (a) is from [8].

TABLE I (DATA FROM [8]) SUMMARY OF HEART-RATE DETECTION ACCURACY

a fast Fourier transform (FFT) was applied to the auto-correlated signal to obtain the heartbeat rate. Finally, the measured heartbeat rate was evaluated by “heart-rate accuracy.” Heart-rate accuracy is calculated as the percentage of time the detected rate is within 2% of the reference rate [9], [10]. As an example, Fig. 2 shows 27 s of heart rate measured in the front case and in the back case at 2-m distance using 350- W power. The black solid curve shows the detected heartbeat rate in beats per minute (BPM), the gray solid curve shows the referenced heartbeat rate in BPM. Two gray dotted lines show the upper and lower limits of the acceptable heartbeat rate, which is 2% variation from the referenced heartbeat rate. The region defined by the two limits is called the confidence interval. When the detected heart rate falls into this confidence interval, it is considered accurate. The measured results of the heart-rate accuracy for all the combinational experimental conditions are listed in Table I. In the experiment, the 27-s detection accuracy from any side of the body and at any of the five tested distances is better than 80%. In addition, the measurement in the back case shows the best performance. The results also indicate that better accuracy can be achieved with higher power, as expected.

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traveled between the transmitter and receiver is . Therefore, the received signal can be approximated as (2) where is the signal’s propagation velocity (the speed of light) . and is the signal’s wavelength in air, which equals to after two-step down-conversion is The baseband signal approximated as (3) where is the constant phase shift due to the distance to the and reflections at the surface, and is the total target residual phase noise [5]. A. Spectral Analysis of Doppler Radar Sensor From the theory of Fourier series, any time-varying periodic can be viewed as the combination of a series displacement of single-tone signals. Therefore, for the ease of analysis and is assumed to be single tone, without loss of generality, i.e., . In this case, the detected phase-modulated signal can be represented as

(4) Fig. 3. Normalized spectrum comparison at 2-m distance for the: (a) front case and (b) back case under power level of 350 W. (Insets: corresponding real time signals, with time span of 27 s). Similar spectra are presented in [8] at 1.5-m distance under the power level of 350 W.

The exponential term can be expanded using Fourier series [11] (5)

The unexpected result that the heart-rate accuracy is better in the back case than in other cases is related to the spectra of different cases. For example, Fig. 3 shows the normalized spectra and the baseband signals detected in the front case and in the back case at 2-m distance and under the power level of 350 W. It is observed that besides the respiration and heartbeat tones, other tones exist in the spectra. Those frequency components, known as “harmonics,” are relatively stronger in the front case than in the back case. In Section III, we will apply spectral analysis to explain the cause of those harmonics and their effects on detection accuracy. III. SPECTRAL ANALYSIS Consider one tone of the double-sideband signal first. Neglecting amplitude variations, each tone transmitted by the CW radar is (1) where the transmitting frequency is either or , is the is the phase noise of the oscillator. If elapsed time, and this signal is reflected by a target at a nominal distance with a time-varying displacement given by , the total distance

is the th-order Bessel function of the first kind. where Therefore, the Fourier-series representation of the phase-modulated signal in (4) is

(6) where is the total residual phase. Based on the above Fourier expansion, the phase-modulated baseband signal is decomposed into frequency components with times the basic frequency of the periodic movement. The baseband signal can thus be analyzed in the frequency domain. B. Sensitivity The body movement may consist of due to respiration and due to heartbeat. Since usually is much larger than , the sensitivity is mainly the issue for heartbeat detection. Equation (6) shows that the sensitivity for heartbeat detection, , is decided dependent on the frequency component with

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Fig. 4. Bessel coefficients.

by the value of , where is the amplitude of . is For body movement due to heartbeat, the amplitude normally in the range of 0.01 mm [12], which corresponds to for transmitting frequency up a very small value of GHz and mm, to 50 GHz (e.g., for mm, then ), thus a linear approximation of the Bessel function is applicable as follows: (7) When is small, decreases rapidly as increases. If we take into consideration, the expression of the received baseband signal is essentially equivalent to the widely used small-angle approximation [5] for low RF radars. Based on the small-signal linear approximation in (7), the , heart-rate detection sensitivity is proportional to which is, in turn, proportional to the working frequency. Therefore, more sensitivity is gained as we increase the frequency. This is the reason for our interest to increase the transmitting -band. frequency to C. Harmonic Interference For respiration, it can be observed directly from chest wall movement that can be as large as several millimeters. mm and transmitting frequency GHz, Taking for example, the corresponding wavelength is mm and , which is out of the safety range for linear approximation or, equivalently, the small-angle approximation. In this case, a good estimation of the received baseband spectrum is to directly investigate the Bessel coefficients, which are plotted in Fig. 4. Investigating (6) with the help of Fig. 4, we can see that to be detected has a single although the periodic signal tone , the actually received baseband signal may contain frequency components at any harmonic position of , i.e., . For the convenience of discussion, we will refer the in (6) as “fundamental” since they contains term with the signal at the desired frequency. We refer other terms with as the th-order harmonic. For , it corresponds to

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Fig. 5. Surface formed by the values of J (4m =)=J (4m =) as a function of m and m ; a contour plot is drawn beneath the surface on the z = 0 plane. Inset: frequency allocation of the breathing fundamental, the second- to fourth-order harmonics (spikes with circular end), and the heartbeat fundamental (spike with arrow end).

the dc in the baseband and will be neglected in the following discussion since it can be removed by the baseband filter. The amplitude of the th-order harmonic is determined by the th-order as the variable. Therefore, when Bessel function with two-tone signals exist simultaneously, the phase-modulation nature of the Doppler radar sensor inevitably brings another effect that is not desired, i.e., harmonic interference generated by the signal with a lower frequency and larger amplitude. This effect plays a destructive role when any of the harmonic coincides with the desired signal with a higher frequency, especially when the latter is weaker compared with the former. As an illustration of this scenario, the inset of Fig. 5 plots an example of the frequency allocation of the breathing fundamental, its second to forth order harmonics, as well as the heartbeat fundamental. Since normally the frequency of the fourthorder breathing harmonic is most likely to be close to that of the to heartbeat fundamental, the relative strength of is used as an estimation of the harmonics effect. is calculated In Fig. 5, the value of varies from 1 to 2 mm and for the 27-GHz system, as varies from 0.05 to 0.15 mm. A contour plot of this value is also drawn beneath the three-dimensional (3-D) plot on the plane. In Fig. 5, as increases and decreases, the ratio of the fourth-order breathing harmonic to the heartbeat fundamental becomes larger, which means harmonic interference is more likely to occur. To reduce the impact of harmonic interference, it is desirable or not to use very high transmitting to reduce the amplitude frequency. By comparing the measured spectra in the front and back cases, it is seen that the movement due to respiration is reduced relative to that due to heartbeat. Therefore, harmonic interference is reduced and better accuracy is obtained in the back case. D. Residual Phase—Optimum/Null Points Manipulation Equation (6) shows that Doppler radar inevitably brings the effect of harmonic interference, whose strength is decided by

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. Meanwhile, the detection accuracy is also controlled and by the residual phase . To address this issue, the terms in (6) should be combined. The negative- and positive-order Bessel functions are related by for even for odd

(8)

Therefore, (6) can be reduced to

carrier frequency. The same result can be obtained by simultaneously considering two tones, each with a null point distance decided by (11) based on spectral analysis. Therefore, the distance between null points is made much larger by double-sideband transmission. Furthermore, double-sideband transmission can always make an accurate detection by slightly tuning the IF local oscillator to change an arbitrary position into an optimum point. IV. SIMULATION

(9) Note that the term is neglected in (9) since this is the dc term and has nothing to do with successful detection. The last two terms of (9) correspond to the odd- and evenorder harmonics in the baseband spectra, respectively. Based on this equation, successful detection of the periodic movement, in the which is related to the fundamental frequency [ last term of (9)], is also dependent on the residual phase . Taking two extreme cases as an example, when is equal to odd order of 90 , the even-order frequencies in (9) vanish, thus desired fundamental frequency is emphasized while even-order harmonics are minimized. When is equal to even order of 90 , the odd-order frequencies in (9) vanish, thus desired fundamental frequency is minimized. The residual phase is contributed by two factors, which are: 1) the constant phase shift due to the distance to the target and reflections at the target surface and 2) the total phase noise. Due to the range correlation effect [13], the phase noise plays a minor role and is, to a large extent, determined by the distance to the target (10) where can be treated as unchanged during experiment. Therefore, a series of optimum points and null points for accurate detection exist along the path away from the radar. For single-tone transmission, the distance between null points is decided by (11) Intuitively, if two tones are used for transmission with a slightly difference in due to wavelength difference, the occurrence of a global null point, where both tones are at their respective null points, is largely reduced. Our previous study [7] based on the small-angle approximation model has demonstrated that the global null points for double-sideband transmission are encoun, where is the wavelength corresponding to tered every the IF local oscillator with a frequency much lower than RF

The above analysis was implemented in simulation in two ways, which are: 1) numerically analyzing the spectra of the modeled time-domain signals constructed in MATLAB and 2) investigating the system performance using “envelope simulation” via Agilent Technologies’ ADS. Both of them achieved the same result, demonstrating the theory in Section II and providing some guidelines for the frequency planning of the physiological movement sensor. It should be noted that the spectrum of respiration and the spectrum of heartbeat are simulated separately here to focus on the effects of interest, i.e., harmonics and optimum/null points. In the real case, the body movements caused by respiration and heartbeat are overlapped and will lead to intermodulation between respiration and heartbeat signal due to the nonlinear property of the cosine transfer function of the baseband signal. Therefore, there are other baseband spectrum components for vital sign detection. However, they only have a minor effect and are not considered in this paper. A. Spectrum In the front case, the amplitude of is on the order of is on the millimeter range. 0.01 mm [12], but that of However, a precise decision of is difficult because of the complex pattern of chest wall movement, different body status, is estimated and different subjects. Therefore, the value of for matching the simulated spectra with an experimental result on the subject under test. For our subject (a 1.75-m-tall man), is estiseated still and completely relaxed in a chair, the mated to be 1 mm in the front case and 0.2 mm in the back case. under Fig. 6(a) shows the simulated baseband spectrum of mm and mm when the RF frequency is 27 GHz. The residual phase is assumed to be 45 for both sidebands, which means the target is seated halfway between the optimum point and the null point. The second- and third-order harmonics of respiration are clearly discernible in the spectrum. It can be inferred that two effects may lead to destructive interference to heartbeat signal. Firstly, as the subjects’ respiration increases in frequency, the third-order harmonic may move closer to the location of the heartbeat in the spectrum. Secondly, as the subject breathes more heavily, the fourth-order harmonic may grow larger, and become a source of interference. On the other hand, experimental results in Section II imply on the back is reduced relative to that the amplitude of . In this case, the problem of harmonics is signifthat of icantly reduced. Fig. 6(b) shows the simulated spectrum when mm and mm), measured from the back ( when the RF frequency is 27 GHz.

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Fig. 6. Simulated normalized spectrum comparison for the: (a) front case and (b) back case. Residual phase is assumed to be 45 . From [8].

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Fig. 7. Spectral intensity of breathing fundamental, breathing harmonics, and heartbeat fundamental when: (a) measuring from the front and (b) measuring from the back.

B. Choice of Carrier Frequency As discussed in Section II, a significant factor influencing the system performance is the RF carrier frequency. As the RF frequency increases from 2 to 30 GHz, the breathing fundamental, the second- to fourth-order breathing harmonics, and the heartbeat fundamental are simulated. The results are plotted in Fig. 7(a) and (b) for detection in the front and back cases, respectively. The amplitudes of chest wall movement due to respiration and heartbeat are the same as in Section IV-A: mm, mm for the front case, and mm, mm for the back case. The residual phase is assumed for detection to be 45 . For comparison, the amplitudes of from the front and back are all normalized to unity, as expressed in (3). It is clearly shown from the simulation result that, as the frequency increases, the amplitudes of detected heartbeat spectra increase accordingly, thus better sensitivity is gained for small heartbeat signal detection. However, the harmonics of the respiration signal increase at the same time. It is also shown by comparing Fig. 7(a) and (b) that the respiration harmonics are reduced in the back case, identifying the advantage of detection from the back. In the front case, the second-order respiration harmonic is larger than the heartbeat fundamental at GHz, and the third-order harmonic has an almost similar amplitude as the heartbeat fundamental at GHz. Therefore, if the body is breathing fast so that one of those harmonics

moves close to the desired heartbeat signal in the spectrum, it would desensitize the heart-rate detection accuracy. On the other hand, in the back case, all the breathing harmonics, except for the fundamental, have amplitudes smaller than that of heartbeat fundamental, thus eliminating the potential hazard of harmonics interference. V. EXPERIMENT Because the artifacts around the human body bring noise and uncertainty for quantitative analysis, we used a mechanical device for harmonics and null/optimum point observation. The measured result is compared with the prediction by the theory based on the spectral analysis in Section II. A mechanical device with a flat metal reflector swinging at a frequency around 1.8 Hz and amplitude of a few millimeters was used as the target to test the theory of harmonics and null/ -band optimum points. The transmitting frequency of the detector was chosen to be 27.1 GHz. The harmonic interference effect was observed. By adjusting the distance from the subject to the radar, different spectra were then observed at positions close to the null point and the optimum point. Since the swinging frequency of the subject does not affect the relative strength of harmonics in the spectrum, the frequency is normalized to the fundamental frequency (the actual swinging frequency) in the

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Fig. 8. Measured and calculated baseband spectrum when residual phase is found to be 51.77 , both odd- and even-order harmonics exist. The swinging amplitude is calculated to be m = 2:4 mm. The frequency is normalized to the fundamental frequency.

Fig. 9. Measured baseband spectrum when even-order harmonics dominate, corresponding to a null detection point.

following spectrum graphs and the amplitude of the spectrum is normalized to unity. A. Harmonics Observation When the residual phase is around 45 , or the two tones have a nearly 90 difference in residual phase, both even- and odd-order harmonics exist in the baseband signal. This is observed in experiment by adjusting the position of the subject. The measured baseband spectrum is shown as the solid line in Fig. 8. A powerful aspect of the Fourier expansion spectral analysis is that the amplitude and residual phase of the periodic movement can be derived from the measured spectrum as long as the RF frequency is known. By comparing the strength of the thirdorder harmonics with the fundamental, the swinging amplitude mm to satisfy the is calculated as relation from measurement. Using the value of and evaluating the relative strength between odd- and evenorder harmonics, the residual phase is found to be 51.77 according to (9). Plugging these values back into (9), the theoretical baseband spectrum is then obtained and shown as the dashed stems in Fig. 8. Comparing the two spectra, the theoretical value matches well with the measurement. B. Even-Order Harmonics Dominant—Null Point As predicted by (9), when the distance from the radar to the target produces a residual phase equal to even orders of 90 , odd-order harmonics will vanish, corresponding to a null detection point. A similar effect is observed in the experiment, and the resulting baseband spectrum is recorded in Fig. 9. However, since double-sideband transmission is used in our experiment, it is difficult to completely eliminate all the odd-order harmonics. Therefore, there is still small fundamental frequency discernible in Fig. 9. The difficulty in observing a complete null point also reflects the effectiveness of the double-sideband transmission scheme.

Fig. 10. Measured baseband spectrum when odd-order harmonics dominate, corresponding to an optimum detection point.

C. Odd-Order Harmonics Dominant—Optimum Point Similarly, when the distance from the radar to the target produces a residual phase equal to odd orders of 90 , even-order harmonics will vanish, corresponding to an optimum detection point since fundamental tone is maximized while even-order harmonics are minimized in the spectrum. This was verified experimentally and the resulting baseband spectrum is shown in Fig. 10. Once again, however, since double-sideband transmission is used in our experiment and there could be small nonlinear intermodulation in the RF receiver circuit, the even-order harmonics are not completely eliminated and they are still discernible in the spectrum. VI. CONCLUSION -band noncontact heartbeat detection A low-power system has been demonstrated. Experiments on the human -band detector achieves high accuracy body show that the and has better performance when measuring from the back of the body than from all other sides. A rigorous spectral analysis -band technique is used to analyze the harmonic effect in the sensor, showing that minimizing the harmonics interference leads to the advantage of detecting from the back. The theory also illustrates from the spectral analysis that double-sideband transmission can avoid a severe null point problem for short wavelength detection. Simulations have been performed to

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demonstrate this theory, providing guidelines for system design. Experiments have successfully verified this theory by the observation of harmonics that match with the theoretical value, and the observation of the null/optimum point.

ACKNOWLEDGMENT The authors would like to thank J. Jun, Motorola, Plantation, FL, for help on experiment, Agilent Technologies, Orlando, FL, for support on test equipment, National Instruments, Austin, TX, for providing LabVIEW, and the Rogers Corporation, Rogers, CT, for providing microwave substrates.

REFERENCES [1] J. C. Lin, “Microwave sensing of physiological movement and volume change: A review,” Bioelectromagnetics, vol. 13, pp. 557–565, 1992. [2] K. M. Chen, Y. Huang, J. Zhang, and A. Norman, “Microwave life-detection systems for searching human subjects under earthquake rubble and behind barrier,” IEEE Trans. Biomed. Eng., vol. 47, no. 1, pp. 105–114, Jan. 2000. [3] A. D. Droitcour, V. M. Lubecke, J. Lin, and O. Boric-Lubecke, “A microwave radio for Doppler radar sensing of vital signs,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2001, pp. 175–178. [4] A. D. Droitcour, O. Boric-Lubecke, V. M. Lubecke, and J. Lin, “0.25 m CMOS and BiCMOS single chip direct conversion Doppler radars for remote sensing of vital signs,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2002, pp. 348–349. [5] A. D. Droitcour, O. Boric-Lubecke, V. M. Lubecke, J. Lin, and G. T. A. Kovac, “Range correlation and I/Q performance benefits in single-chip silicon Doppler radars for noncontact cardiopulmonary monitoring,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 838–848, Mar. 2004. [6] Y. Xiao, J. Lin, O. Boric-Lubecke, and V. M. Lubecke, “A Ka-band low power Doppler radar system for remote detection of cardiopulmonary motion,” presented at the 27th IEEE Annu. Eng. Med. Biol. Soc. Conf., Sep. 1–4, 2005. [7] Y. Xiao, J. Lin, Boric-Lubecke, and V. M. Lubecke, “Frequency tuning technique for remote detection of heartbeat and respiration using lowpower double-sideband transmission in Ka-band,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2023–2032, May 2006. [8] Y. Xiao, C. Li, and J. Lin, “Accuracy of a low-power Ka-band noncontact heartbeat detector measured from four sides of a human body,” presented at the IEEE MTT-S Int. Microw. Symp., Jun. 2006. [9] B. Lohman, O. Boric-Lubecke, V. M. Lubecke, P. W. Ong, and M. M. Sondhi, “A digital signal processor for Doppler radar sensing of vital signs,” in Proc. 23rd IEEE Annu. Eng. Med. Biol. Soc. Conf., 2001, vol. 4, pp. 3359–3362. [10] B. H. Yang and S Rhee, “Development of the ring sensor for healthcare automation,” Robot. Autonom. Syst., vol. 30, pp. 273–281, 2000. [11] D. C. Champeney, Fourier Transforms and their Physical Applications. New York: Academic, 1973. [12] M. Singh and G. Ramachandran, “Reconstruction of sequential cardiac in-plane displacement patterns on the chest wall by laser speckle interferometry,” IEEE Trans. Biomed. Eng., vol. 38, no. 5, pp. 483–489, May 1991. [13] M. C. Budge, Jr. and M. P. Burt, “Range correlation effects on phase and amplitude noise,” in Proc. IEEE Southeastcon, Charlotte, NC, 1993, 5 pp.

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Changzhi Li (S’06) received the B.S. degree in electrical engineering from Zhejiang University, Hangzhou, China, in 2004, and is currently working toward the Ph.D. degree in electrical engineering at the University of Florida, Gainesville. From 2004 to 2005, he was with the Department of Electronic Engineering, Tsinghua University, Beijing, China. His research interests include biomedical applications of microwave/RF, wireless sensor, and microwave/millimeter-wave circuits. Mr. Li is a student member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and the IEEE Engineering in Medicine and Biology Society.

Yanming Xiao (S’01) received the B.S. degree in electronic engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1994, the M.S. degree in electrical and computer engineering from the University of Florida, Gainesville, in 2002, and is currently working toward the Ph.D. degree in electrical and computer engineering at the University of Florida. From 1994 to 2000, she was with the Nanjing Electronic Devices Institute, Nanjing, China, where her research involved RF/microwave circuit design. Her current research interests include wireless sensor, biomedical applications, sensor networks, and microwave system-on-chip.

Jenshan Lin (S’91–M’94–SM’00) received the B.S. degree from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1987, and the M.S. and Ph.D. degrees in electrical engineering from the University of California at Los Angeles (UCLA), in 1991 and 1994, respectively. In 1994, he joined AT&T Bell Laboratories (later Lucent Bell Laboratories), Murray Hill, NJ, as a Member of Technical Staff, and became the Technical Manager of RF and High Speed Circuit Design Research in 2000, where he was involved with RF integrated circuits using various technologies for wireless communications. In September 2001, he joined Agere Systems, a spin-off from Lucent Technologies, where he was involved with high-speed CMOS circuit design for optical and backplane communications. In July 2003, he joined the University of Florida, Gainesville, as an Associate Professor. His current research interests include RF system-on-chip integration, high-speed broadband circuits, high efficiency transmitters, wireless sensors, biomedical applications of microwave and millimeter-wave technologies, and software-configurable radios. He has authored or coauthored over 120 technical publications in refereed journals and conferences proceedings. He holds six patents. Dr. Lin has been active in the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He is an elected Administrative Committee (AdCom) member serving the term of 2006–2008 and a member of the Wireless Technology Technical Committee. He is an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He has been serving on several conference Steering Committees and Technical Program Committees including the IEEE MTT-S International Microwave Symposium (IMS), the Radio Frequency Integrated Circuits Symposium (RFIC), the Radio and Wireless Symposium (RWS), and the Wireless and Microwave Technology Conference (WAMICON). He is currently the Technical Program co-chair of the 2006 and 2007 RFIC Symposium, and the finance chair of the 2007 RWS. He was the recipient of the 1994 UCLA Outstanding Ph.D. Award and the 1997 Eta Kappa Nu Outstanding Young Electrical Engineer Honorable Mention Award. He has also coauthored/advised several IEEE MTT-S IMS Best Student Paper Awards. He is an advisor for the IEEE MTT-S Undergraduate/Pre-Graduate Scholarship Award.

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Evaluations of Specific Absorption Rate and Temperature Increase Within Pregnant Female Models in Magnetic Resonance Imaging Birdcage Coils Dagang Wu, Student Member, IEEE, Saad Shamsi, Ji Chen, Member, IEEE, and Wolfgang Kainz, Member, IEEE

Abstract—This paper presents a detailed numerical study of specific absorption rate (SAR) and temperature increase calculations within pregnant female models exposed to magnetic resonance imaging (MRI). Nine pregnant female models, representing different pregnant stages, were used for this study. SAR and temperature increase within and around fetuses at different pregnancy stages were calculated for two MRI operating modes (normal mode and first-level controlled mode) at 64 and 128 MHz. Local fetus energy deposition exceeds the International Electrotechnical Commission limit of 10 W/kg in the first-level controlled mode at 64 MHz. Fetus temperature exceeds or approaches 38 C for both frequencies in the first-level controlled mode at later stages of pregnancy. The core temperature limits for both modes and both frequencies are not exceeded. The results show higher maximum SAR and higher temperature at 64 MHz and during later pregnancy stages with a significant increase starting with the fifth month of pregnancy. Based on the results of this study, radiologists can minimize local fetus heating, especially late in pregnancy, by using normal mode sequences, which minimize the whole body SAR in the mother. Index Terms—Electromagnetic heating, finite-difference method, magnetic resonance imaging (MRI), pregnant woman, safety standards.

I. INTRODUCTION

M

AGNETIC resonance imaging (MRI) exams are widely used in the medical field to obtain topographic images of patients’ internal structures. This procedure can produce images with millimeter resolution. Physicians use these images to diagnose defects in ligaments, muscles, brain tissue, and other soft tissues. During the imaging, patients are subjected to several kinds of electromagnetic fields produced by MRI coils [1]. While these electromagnetic fields are required for the purpose of imaging, they also deposit electromagnetic energy within patients. Due to such energy deposition, temperature increase within patients is inevitable [2], [3]. Manuscript received April 20, 2006; revised July 21, 2006. This work was supported in part by the National Science Foundation under Grant BES-0332957. D. Wu, S. Shamsi, and J. Chen are with the Electrical and Computer Engineering Department, University of Houston, Houston, TX 77204 USA (e-mail: [email protected]). W. Kainz is with the Center for Devices and Radiological Health, U.S. Food and Drug Administration, Rockville, MD 20852 USA (e-mail: [email protected]). Color versions of Figs. 1–11 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.884655

To ensure patient safety, the International Electrotechnical Commission (IEC) has developed a standard to limit the maximum energy deposition within human subjects undergoing an MRI [4]. This standard sets the limits for the specific absorption rate (SAR) for whole-body SAR, partial-body SAR, and local SAR and limits for the increase of the body core temperature and the localized temperature. Since MRI procedures can be operated at two different modes (normal mode and first-level controlled mode), limits for both modes are specified in [4]. The normal mode is suitable for all individuals, while the first-level controlled mode is more suitable for patients who can tolerate a higher dosage of energy deposition. For example, the maximum 10-g SAR and the core temperature increase are limited to 10 W/kg and 0.5 C during normal mode operation, whereas the limits are 10 W/kg and 1 C for first-level controlled mode operation. These limits were developed and tested using many adult male and female models and have been used to guide practical MRI exams [5]–[9]. While these limits are proven to be accurate for males and females, their application to pregnant women or fetuses needs to be further investigated since the fetus is surrounded by high-conductive liquid [10]. Due to the high-conductive fluid, high doses of electromagnetic energy deposition may be expected, which could then lead to a high temperature increase around the fetus. To address these concerns, some research on fetus MRI safety have been conducted, but only on animals. However, these investigations are not very conclusive. The results can vary significantly depending on factors such as animal species, strength of the magnetic field, and duration of the scan. Some studies indicated a considerable rate of infant mortality or abnormalities in animal fetuses [11], [12], while others established that there were no harmful effects of MRI on animal fetuses [13]–[15]. To evaluate the energy deposition within pregnant women undergoing an MRI, pregnant female models were recently developed and numerical evaluations were performed [16], [17]. However, only preliminary investigations on energy deposition around fetuses were performed, and no temperature increase near fetuses was calculated. The purpose of this study is to perform a comprehensive numerical evaluation of the energy deposition and the temperature increase within pregnant female models exposed to MRI electromagnetic radiation generated by RF birdcage coils at 64 and 128 MHz. The simulations were carried out using the finite-difference time-domain (FDTD) method. Nine models, one

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for each month of pregnancy, were used in the study to determine if a certain stage of pregnancy was more susceptible to absorbing more electromagnetic radiation. A computer model of a physical birdcage coil, rather than pre-extracted current distributions, was used in this study [6], [7], [16]–[20]. This enables us to obtain a more realistic study on the interactions between the coils and the pregnant female models. The remainder of this paper is organized as follows. In Section II, we describe the methodologies and the models (including both the birdcage coil model and the nine pregnant female models) used in the study. Section III presents the results from both electromagnetic and thermal simulations. Detailed discussions are also given in Section III. Based on the results and discussions, a conclusion is given in Section IV. II. METHODOLOGY AND MODELS A. Simulation Methods The simulation methods used in this study are described in [17]. The FDTD scheme was applied to both Maxwell’s equations and bio-heat equation to obtain the SAR distributions and the temperature increase within our models [22]–[25]. SAR, used as a fundamental metric for RF heating, is defined as [5]–[7]

(1) In this expression, is the conductivity (in siemens per meter), is the mass density (kg m ), and is the rms value of electric fields (volts per meter) within the biological subjects. The strength of the electric field at any location within the biological tissue can be directly obtained from the results of electromagnetic FDTD simulations [22], [23]. To evaluate the temperature increase within biological tissues, the finite-difference technique is applied to the bio-heat equation [22]. With electric fields obtained from the previous electromagnetic simulations, temperature distribution ( ) inside biological tissues can then be evaluated via (2) where is the specific heat capacity (J kg C), is the thermal conductivity (W m C), is the blood perfusion coefficient is the metabolic heat production rate (W m ), (W m C), is the blood temperature. Including the blood perfusion and in the modeling generally will reduce the temperature variation due to energy deposition. This is a more accurate model for our applications. At the external surfaces between the biological tissue and the surrounding air, the following convective boundary condition is applied: (3) where is the convection coefficient (W m C), is the ambient temperature, and is the normal direction to the surface. Using the convection coefficient as a boundary condition has limited accuracy. Detailed discussion on using convection, radiation, and evaporation are given in [25].

Fig. 1. Nine pregnant female models used in this investigation from [17]. The upper row shows the models month-1 to month-4 using the same body model. The lower row shows the models month-5 to month-9 using the scaled pregnant female model. For all nine models, the uterus, placenta, and fetus were scaled according to the different sizes for the different gestational age.

The simulation procedure starts with using the electromagnetic FDTD method to evaluate the electric and magnetic fields within the pregnant female models due to the RF field of the birdcage coil. Once the electric field distributions are obtained, we can predict the temperature increase using (2) and (3). It should be noted that a basal temperature distribution within the biological tissue should be evaluated first. This is evaluated by setting the value of the electric field equal to zero in (2). In the is set at 37 following studies, the temperature of the blood C, and the ambient temperature is assumed to be 24 C. A of 10.5 W m C is used in all simconvection coefficient ulations [25]. B. Pregnant Female Models The nine pregnant female models used in this study were co-developed by the University of Houston, Houston, TX, and the Food Drug Administration (FDA), Rockville, MD [30]. Data that describe the shape of the body surface of a pregnant woman in the 34th gestational week (body 1) were obtained from FarField Technology Limited, Christchurch, New Zealand. A second computer-aided design (CAD) model of a nonpregnant female body surface (body 2), was obtained from 21st Century Solutions Ltd., Gibraltar, U.K. Fetus, bladder, uterus, placenta, and bones are based on MRI data of a woman in the 35th gestational week. The MRI data has a resolution of 5 mm and was provided by Stanford University, Stanford, CA. We converted the data sets to stereolithography (STL) format and combined them into one CAD model. For the models month-1 to month-4 we used body 2, and for the models month-5 to month-9 we used body 1. Assuming the belly of a pregnant woman begins noticeable growing between the third and fourth month, we scaled the belly from body 1 for the pregnant female models month-5 to month-7. Body 2, used for the models month-1 to month-4, and body 1, used for the models month-8 and month-9, remained unchanged. Uterus, placenta, and fetus were scaled according to the different sizes for the different gestational age. These nine models are shown in Fig. 1. The dielectric properties of each tissue, obtained from the materials database at 64 and 128 MHz are tabulated

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TABLE I DIELECTRIC PROPERTIES OF TISSUES

TABLE II THERMAL PROPERTIES OF TISSUES

Fig. 2. Constructed birdcage coil used in this study from [17]. (a) Side view. (b) Top view. (c) Three-dimensional view. (d) Coil with shielding.

in Table I [31]. Blood perfusion rates are 277 mL/kg/min for the uterus and 1760 mL/kg/min for the placenta [26]–[28]. Based on an approximate proportional relation between blood and [25], we calculated the values and perfusion and for the uterus and the placenta accordingly (see Table II). The thermal properties for the fetus are a weighted average of muscle and fat (55% muscle, 45% fat). The thermal properties for the body are also a weighted average of muscle and fat (70% muscle, 30% fat). We found that varying the placenta perfusion rate from 1760 mL/kg/min to 200 mL/kg/min does not give a significant difference (less than 0.2 C) in the temperature variation for the fetus region. C. Birdcage Coil Model The MRI coil used in this study is the commonly used birdcage coil. The coil was designed using the birdcage builder software package developed by Pennsylvania State University, Hershey, PA [33]. Like most birdcage coils, this coil is composed of two end-rings connected by 16 equally spaced rungs, as shown in Fig. 2. The rungs and rings of the birdcage coil are constructed using a perfect electric conductor (PEC). Each rung is split, and a capacitor is placed inside the gap. The parasitic capacitance between gaps must also be considered in the design since it also affects the coil resonant frequency. To reduce RF interference, the coil is surrounded by an RF shield, which is also modeled as a PEC. This shield affects the coil tuning because eddy currents induced in the shield affect the resonant frequency [34]. When the female models are added to the structure, the coil needs to be re-tuned in order to achieve the exact MRI resonant frequency. The detailed dimensions for the coil are shown in Fig. 2. For our coil design, we used the quadrature excitation. In the quadrature excitation, two voltage sources are used to ex-

Fig. 3. Positioning of the pregnant female models within the MRI RF coil from [17].

cite the 16-leg birdcage coil. These two sources need to be on one end-ring, 90 spatially separated, with 90 out-of-phase in the excitation waveform. Theoretically, having such an arrangement would quadruple the effective power of the coil. The resulting magnetic field is highly homogenous, leading to a larger operating region [1]. The next step is to tune the capacitors to achieve either 64or 128-MHz coil resonance. To determine the correct capacitor values, we used Gaussian pulse excitation and recorded time-domain signals at various locations within the coil. The capacitor value was altered until the highest response is detected at 64 or 128 MHz. After this tuning, we can obtain the capacitor value for an empty coil without any model placed within it (unloaded coil). D. Simulation Setup and Final Tuning Fig. 3 shows the positioning of the model in the coil. Each model had to be placed within the coil consistently, while considering the changes in the size of the models. To simulate the effect of a woman supine on a bed while being scanned, the back of the model is always placed 22.7 cm away from the inner edge

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Fig. 4. Normalized maximum 10-g averaged SAR (64-MHz normal mode) as a function of pregnant stage. From [17]. Fig. 5. Maximum temperature within different tissues as a function of pregnant stage (64-MHz normal mode).

of the coil [17]. The navel of the model is always placed on the – -plane, as shown in Fig. 3. This positioning ensured that the models would be in the same location for each simulation. Once the coil is loaded, the resonant frequency can shift due to the coupling between the coil and models. The tuning procedure needs to be repeated in order to bring the resonant frequency back to 64 or 128 MHz. This procedure was repeated for each of the nine pregnant female models because each model had a different effect on the coil loading. The detuning of the coil due to the pregnant woman for both frequencies was 1%–3%. Several iterations were necessary before the correct capacitor value was found. After setting up the simulation for each month of the pregnant model and final capacitor tuning, the simulations were executed in series. Computation time for each month typically takes around one day, depending on the exact mesh used in simulations. After the simulations were complete, a post processing procedure was used to extract the distributions of temperature increase and energy deposition.

Fig. 6. Normalized maximum 10-g averaged SAR (64-MHz first-level controlled mode) as a function of pregnant stage. From [17].

III. RESULTS AND DISCUSSIONS Here, the calculated maximum 10-g cubical averaged SAR and the maximum temperature increase within various tissues are given. These values are calculated for 64 and 128 MHz. All values (SARs and temperature) are normalized to the IEC 60601-2-33 whole-body averaged SAR limit [4], which are 2 and 4 W/kg for normal mode and first-level controlled mode, respectively. The local 10-g averaged SAR is 10 W/kg for both modes. The core body temperature increase limits are 0.5 C for the normal mode and 1 C for the first-level controlled mode. The maximum local temperature limits are defined as 38 C for the head and 39 C for the torso. A. SAR and Local Temperature Increase for the 64-MHz Birdcage Coil For the 64-MHz normal mode, the 10-g averaged SARs for each tissue at different stages of pregnancy shown in Fig. 4 are below the limit of 10 W/kg for all tissues, except the body.

The maximum temperatures within the body and the amniotic fluid (amn. fluid)) reaches 38 C starting at the fifth month of pregnancy, as shown in Fig. 5. The maximum fetus heating, including the fetus brain, does not exceed 38 C. The figures only show the maximum SAR and the local temperature increase. Therefore, slight fluctuations on both were observed for the different months. Especially for the critical tissues, fetus, placenta, uterus, and amniotic fluid, the maximum SAR and the temperature increase are, in general, higher in later pregnancy stages. For the first level controlled mode, the maximum 10-g averaged SAR and the maximum temperature for each tissue at different pregnant stages are shown in Figs. 6 and 7. Due to increased RF power, the maximum energy depositions within the fetus exceed the 10-W/kg limit beyond the fourth month of pregnancy. The maximum temperature for the body is above the limit of 39 C starting with the sixth month. The maximum fetus and amniotic fluid temperature exceeds 38 C after the fifth month.

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Fig. 7. Maximum temperature within different tissues as a function of pregnant stage (64-MHz first-level controlled mode).

Fig. 8. Normalized maximum 10-g averaged SAR as a function of pregnant stage (128-MHz normal mode).

Fig. 9. Maximum temperature within different tissues as a function of pregnant stage (128-MHz normal mode).

Fig. 10. Normalized maximum 10-g averaged SAR as a function of pregnant stage (128-MHz first-level controlled mode).

B. SAR and Local Temperature Increase for the 128-MHz Birdcage Coil For normal mode operation at 128 MHz, the maximum 10-g averaged SAR and the maximum temperature increase in each tissue are plotted in Figs. 8 and 9. We found that SAR for the body tissue exceeds the limit for all months by approximately 60%, whereas for all other tissues, the 10-g averaged SAR is well below the limit. The maximum temperatures for all tissues are below 38 C. However, the same trend as for 64 MHz can be observed: later stages of pregnancy are more susceptible to fetus heating. The maximum 10-g averaged SAR for each tissue under the first-level controlled mode is shown in Fig. 10. Again, due to the increased RF power, the energy deposition within body, bone, uterus, and amniotic fluid exceed the limit at some stages of pregnancy. However, the energy depositions within the fetus are below the limit for all stages of pregnancy, but reach the limit in the ninth month. The maximum temperature increase of each tissue is shown in Fig. 11. Although a higher temperature increase within the fetus is observed for later stages of pregnancy,

Fig. 11. Maximum temperature within different tissues as a function of pregnant stage (128-MHz first-level controlled mode).

the maximum temperature within the fetus are all below the limit of 38 C. Similar to the results for normal mode, the maximum

WU et al.: EVALUATIONS OF SAR AND TEMPERATURE INCREASE WITHIN PREGNANT FEMALE MODELS IN MRI BIRDCAGE COILS

TABLE III CORE TEMPERATURE INCREASE WITHIN FETUS (UNIT IN DEGREES CELSIUS)

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for the first level controlled mode is almost twice as that of the normal mode, but in both modes and for both frequencies, the IEC limits for core temperature are not exceeded. We see that the distributions of energy deposition and temperature increase are quite different at the two frequencies. Our simulation results seem to suggest higher maximum SAR and higher temperature at 64 MHz. This can be explained by the reduced penetration depth at 128 MHz. IV. CONCLUSIONS

TABLE IV CORE TEMPERATURE INCREASE WITHIN THE ENTIRE PREGNANT FEMALE MODEL (UNIT IN DEGREES CELSIUS)

temperatures within body and liquid exceed the maximum temperature within the fetus. From these results, we find that, for 64 MHz, the maximum 10-g averaged SARs within the fetus are below the IEC limit under normal mode operation, whereas these values exceed the limit during the first-level controlled-mode scans. As expected, the maximum temperatures at the first-level controlled mode within all tissues are also larger than those at normal mode operation. For 128 MHz, the maximum 10-g averaged SAR and temperature increase inside the fetus models are below the limits for both operating modes. A different SAR increase pattern was observed for 64 and 128 MHz. This is mainly caused by the fact the maximum value of SAR is related to both the MRI operating frequency, as well as the conductivity of the pregnant models. The core temperature increase for fetus is defined as the average temperature within the entire fetus region, while the core temperature increase for the entire pregnant model is defined as the average temperature increase within the entire female model. Tables III and IV gives the fetus and pregnant woman core temperature increase for both operating modes and for both frequencies. As indicated in the tables, the core temperature increase within the fetus actually decreases as the pregnant stages increase. This appears to be contradictory to the previous results. However, further analysis shows that due to the increase of the fetus, the average temperature increase can indeed decrease. Overall, the average temperature within the entire pregnant female model is directly related to the total energy deposition with the body. As expected, the core temperature increase

We have found for both frequencies an increase in SAR and temperature at later stages of pregnancy. The SAR within the body exceeds the IEC limit for both frequencies and both operating modes with a maximum of 3.8 times higher than the recommended limit of 10 W/kg. The 10-g averaged SAR for the fetus is only exceeded for the first-level controlled mode at 64 MHz. The results suggest that the relation of the local SAR to the whole body averaged SAR needs to be further evaluated using anatomically correct models for all types of human beings undergoing an MRI. The results also indicate that, for pregnant women, instead of the whole body averaged SAR, the local 10-g averaged SAR might be the limiting factor. Whole body heterogeneous models of pregnant women for different stages of pregnancy would be needed to answer this question. Only for the first-level controlled mode at 64 MHz does the local fetus temperature exceeds 38 C, while it approaches the limit of 38 C also for the first-level controlled mode at 128 MHz for later stages of pregnancy. Based on the results of this study, radiologists can minimize local fetus heating, especially late in pregnancy, by using normal mode sequences, which minimize the whole-body SAR in the mother. REFERENCES [1] J. Jin, Electromagnetic Analysis and Design in Magnetic Resonance Imaging. New York: CRC, 1999. [2] D. J. Schaefer, “Safety aspects of radio-frequency power deposition in magnetic resonance,” Magn. Reson. Imaging Clin. N. Amer., vol. 6, pp. 775–789, 1998. [3] F. G. Shellock, “Radiofrequency-induced heating during MR procedures: A review,” J. Magn. Reson. Imaging, vol. 12, pp. 30–36, 2000. [4] Medical Equipment–Part 2: Particular Requirements for the Safety of Magnetic Resonance Equipment for Medical Diagnosis, IEC Standard 60601-2-33, 2004. [5] O. P. Gandhi and X. B. Chen, “Specific absorption rates and induced current densities for an anatomy-based model of the human for exposure to time varying magnetic fields of MRI,” Magn. Res. Med., vol. 41, no. 5, pp. 816–823, 1999. [6] C. M. Collins, W. Liu, J. Wang, R. Gruetter, J. T. Vaughan, K. Ugurbill, and M. B. Smith, “Temperature and specific absorption rate calculations for a human head within volume and surface coils at 64 and 300 MHz,” J. Magn. Res., vol. 19, pp. 650–656, 2004. [7] U. D. Nguyen, S. Brown, I. A. Chang, J. Krycia, and M. S. Mirotznik, “Numerical evaluation of heating of the human head due to magnetic resonance imaging,” IEEE Trans. Biomed. Eng., vol. 51, no. 8, pp. 1301–1309, Aug. 2004. [8] L. A. Zaremba, “FDA guidelines for magnetic resonance equipment safety,” Center for Devices and Radiol. Health, Food, Drug Admin., Rockville, MD, YEAR [Online]. Available: http://www.aapm.org/meetings/02AM/pdf/8356-8054.pdf [9] J. Behrens, “Module #5: MRI safety,” Siemens Med. Syst., Greensboro, NC, 2002. [10] J. P. De Wilde, A. W. Rivers, and D. L. Price, “A review of the current use of magnetic resonance imaging in pregnancy and safety implications for the fetus,” Prog. Biophys. Molecular Biol., vol. 87, pp. 335–353, 2005.

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[11] K. I. Carnes and R. L. Magin, “Effects of in utero exposure to 4.7 T MR imaging conditions on fetal growth and testicular development in the mouse,” Magn. Res. Imag., vol. 14, pp. 263–274, 2003. [12] Y. P. Yip, C. Capriotti, S. G. Norbash, S. L. Talagala, and J. W. Yip, “Effects of MR exposure on axonal outgrowth in the sympathetic nervous system of the chick,” Magn. Res. Imag., vol. 4, pp. 742–748, 1994. [13] K. P. Behr, H. W. Tiffe, K. H. Hinz, H. Luders, M. Friederichs, M. Ryll, and H. Hundeshagen, “Nuclear magnetic resonance (NMR) and the development of chicken embryos,” Tsche. Tierarztl. Wochenschr., vol. 98, pp. 149–152, 1991. [14] Y. P. Yip, C. Capriotti, S. L. Talagala, and J. W. Yip, “Effects of MR exposure at 1.5 T on early embryonic development of the chick,” Magn. Res. Imag., vol. 5, pp. 457–462, 1994. [15] Y. P. Yip, C. Capriotti, and J. W. Yip, “Effects of MR exposure on cellproliferation and migration of chick motonuerons,” Magn. Res. Imag., vol. 5, no. 4, pp. 457–462, 1995. [16] M. Strydom, K. Caputa, M. A. Stuchly, and P. Gowland, “Numerical modeling interaction of RF field in MRI with a pregnant female model,” in IEEE/ACES Wireless Commun. Appl. Comput. Electromagn. Conf., Honolulu, HI, 2005, pp. 389–392. [17] S. Shamsi, D. Wu, J. Chen, R. Liu, and W. Kainz, “Specific absorption rate evaluation in pregnant woman models radiated from MRI birdcage coil,” presented at the IEEE MTT-S Int. Microw. Symp., San Francisco, CA, Jun. 2006. [18] C. M. Collins, S. Li, and M. B. Smith, “Specific absorption rate and B 1 field distributions in a heterogeneous human head model within a birdcage coil,” Magn. Res. Med., vol. 40, pp. 847–856, 1998. [19] J. Jin and J. Chen, “On the specific absorption rate and field inhomogeneity of birdcage coils loaded with the human head,” Magn. Res. Med., vol. 38, pp. 953–963, 1997. [20] T. S. Ibramhim, A. M. Abduljalil, B. A. Baertlein, R. Lee, and P. M. Robitaille, “Analysis of B 1 field profiles and specific absorption rate values for multi-strut transverse electromagnetic RF coils in high field MRI applications,” Phys. Med. Biol., vol. 46, pp. 2545–2555, 2001. [21] T. S. Ibrahim, “A numerical analysis of radiofrequency power requirements in magnetic resonance imaging experiments,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1999–2003, Aug. 2004. [22] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, 1995. [23] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetic.s. Boca Raton, FL: CRC, 1993. [24] H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Physiol., vol. 1, pp. 93–122, 1948. [25] P. Bernardi, M. Cavagnaro, S. Pisa, and E. Piuzzi, “Specific absorption rate and temperature increases in the head of a cellular-phone user,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 7, pp. 1118–1125, Jul. 2000. [26] W. E. Huckabee, J. Metcalfe, H. Prystowsky, and D. H. Barron, “Blood flow and oxygen consumption of the pregnant uterus,” Amer. J. Physiol., vol. 200, pp. 274–278, 1961. [27] P. A. Gowland, S. T. Francis, K. R. Duncan, A. J. Freeman, B. Issa, R. J. Moore, Bowtell, P. N. Baker, I. R. Johnson, and B. S. Worthington, “In vivo perfusion measurements in the human placenta using echo planar imaging at 0.5 T,” Magn. Reson. Med., vol. 40, no. 3, pp. 467–473, 1998. [28] S. T. Francis, K. R. Duncan, R. J. Moore, P. N. Baker, I. R. Johnson, and P. A. Gowland, “Non-invasive mapping of placental perfusion,” Lancet, vol. 351, pp. 1397–1399, 1998. [29] A. Ibrahiem, “Analysis of the temperature increase linked to the power included by RF source,” Prog. Electromagn. Res., vol. PIER 52, pp. 23–46, 2005. [30] W. Kainz, T. Kellom, R. Qiang, and J. Chen, “Development of pregnant woman models for nine gestational ages and calculation of fetus heating during magnetic resonance imaging (MRI),” in BEMS Conf., Dublin, Ireland, Jun. 2005, pp. 137–139. [31] C. Gabriel, “Compilation of the dielectric properties of body tissues at RF and microwave frequencies,” Brooks AFB, Brooks AFB, TX, Tech. Rep. AL/OE-TR-1996-0037, 1996.

[32] F. A. Duck, Physical Properties of Tissues: A Comprehensive Reference Book. New York: Academic, 1990. [33] Birdcage Builder. Pennsylvania State Univ., Philadelphia, PA, 2006 [Online]. Available: http://psunmr.hmc.psu.edu/birdcage/index.htm [34] W. Renhart, O. Biro, P. Wach, and R. Strollberger, “Investigation of the resonance behavior of an MR-birdcage applying a 3-D FEM code,” IEEE Trans. Magn., vol. 37, no. 9, pp. 3688–3692, Sep. 2001.

Dagang Wu (S’99) was born in Nanjing, China, on November 10, 1978. He received the B.S. and M.S. degrees in electrical engineering from Southeast University, Nanjing, China, in 1999 and 2002, respectively. Since September 2002, he has been a Research Assistant with the Department of Electrical and Computer Engineering, University of Houston, Houston, TX. His current research interests include computational electromagnetics, bioelectromagnetics and numerical logging-while-drilling (LWD)/measurement-while-drilling (MWD) modeling. Saad Shamsi, photograph and biography not available at time of publication. Ji Chen (S’87–M’90) received the Bachelor’s degree from the Huazhong University of Science and Technology, Wuhan, Hubei, China, in 1989, the Master’s degree from McMaster University, Hamilton, ON, Canada, in 1994, and the Ph.D. degree from the University of Illinois at Urbana-Champaign in 1998, all in electrical engineering. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, University of Houston, Houston, TX. Prior to joining the University of Houston, he was a Staff Engineer with Motorola Personal Communication Research Laboratories, Chicago, IL, from 1998 to 2001. Dr. Chen was the recipient of the 2000 Motorola Engineering Award. Wolfgang Kainz (M’02) received the M.S. and Ph.D. degrees in electrical engineering from the Vienna University of Technology, Vienna, Austria, in 1997 and 2000, respectively. Following his affiliation with the Austrian Research Centers Seibersdorf (ARCS), where he was involved with electromagnetic compatibility of electronic implants and exposure setups for bio-experiments, he joined The Foundation for Research on Information Technologies in Society (IT’IS), Zürich, Switzerland, as Associate Director. He co-managed the IT’IS together with Prof. N. Kuster and was involved with the development of in vivo and in vitro exposure setups for bioexperiments. In 2002, he moved to the U.S., where he is currently with the U.S. Food and Drug Administration, Center for Devices and Radiological Health, Rockville, MD. His research interest is focused on the safety and effectiveness of medical devices and safety in electromagnetic fields. This includes computational electrodynamics (FDTD and finite-element method (FEM) simulations) for safety and effectiveness evaluations, MRI safety, performance and safety of wireless technology used in medical devices, electromagnetic compatibility of medical devices, especially electronic implants, and dosimetric exposure assessments. Dr. Kainz is chairman of the IEEE Standard Coordination Committee 34, Sub-Committee 2, which develops compliance techniques for wireless devices.

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Linearity Improvement of HBT-Based Doherty Power Amplifiers Based on a Simple Analytical Model Yu Zhao, Student Member, IEEE, Andre G. Metzger, Student Member, IEEE, Peter J. Zampardi, Senior Member, IEEE, Masaya Iwamoto, Member, IEEE, and Peter M. Asbeck, Fellow, IEEE

Abstract—A simple analytical model is proposed and shown to be effective in predicting the nonlinear behavior of single-ended amplifiers, as well as Doherty amplifiers implemented with GaAs heterojunction bipolar transistors (HBTs) for handset applications. The analytical model is based on linear and nonlinear components extracted from a vertical bipolar inter-company model for Skyworks Solutions Inc.’s InGaP/GaAs HBT devices. Equations derived from the model provide insights into effects of individual components on the gain and phase of both the single-ended and Doherty amplifiers. The model indicates that tuning the phase delay inserted in front of the auxiliary power amplifier (PA) within the Doherty can improve linearity at a high input power. The efficacy of the model is demonstrated by experimental results in which, for a Doherty PA with a tuned phase delay at the auxiliary PA side, the measured gain and phase agree with the simulation results. Furthermore, the third-order intermodulation distortion performance is improved as much as 8 dB when compared with a Doherty PA without phase delay tuning.

Fig. 1. Doherty amplifier architecture.

Index Terms—Code division multiple access (CDMA), Doherty amplifier, heterojunction bipolar transistor (HBT).

I. INTRODUCTION

D

OHERTY amplifiers have demonstrated high efficiency over a wide output power range [1]–[4]. Recently, many publications have shown that the Doherty structure is promising for improving efficiency of power amplifiers (PAs) in base stations and handsets for spectrally efficient modulation schemes such as code division multiple access (CDMA) [5]–[15]. The Doherty amplifier can achieve an extended high efficiency range and can meet demanding linearity specifications at the same time. However, it is still difficult to obtain optimum efficiency and high linearity performance in the same Doherty amplifier. In order to do a better design tradeoff between efficiency and the linearity, it is critical to achieve a better understanding of the nonlinear behavior of the Doherty amplifier. The Doherty amplifier (Fig. 1) operates with a class AB biased main amplifier providing output power in the low-power region and a class C biased auxiliary amplifier additionally providing power in the high-power region. Nonideal transitions between these two power regions caused by the device,

Manuscript received March 31, 2006; revised June 30, 2006. This work was supported in part by Conexant, by Nokia, and by the University of California under a Discovery Grant. Y. Zhao and P. M. Asbeck are with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093 USA (e-mail: [email protected]). A. G. Metzger and P. J. Zampardi are with Skyworks Solutions Inc., Newbury Park, CA 91320 USA. M. Iwamoto is with Agilent Technologies, Santa Rosa, CA 94543 USA. Digital Object Identifier 10.1109/TMTT.2006.883245

Fig. 2. Schematic of proposed HBT amplifier model.

parasitics, and other factors can lead to AM–AM and AM–PM distortions in the Doherty amplifier. To develop insights into the nonlinear behavior of Doherty amplifiers, a simple physically based nonlinear analytical model for GaAs heterojunction bipolar transistors (HBTs) is developed here and applied to single-ended PAs and to Doherty PAs designed for handset applications. A representative schematic of the model is shown in Fig. 2. Unlike nonlinear analyses using Volterra series [16], the nonlinear components in this model are functions of the operating power level, and contain nonlinearities of all orders. Yamada et al. has analyzed phase distortion of an HBT PA using a similar method [17]. With the simplicity of the model, closed-form

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expressions for gain and phase transfer functions of the PA circuits can be derived, and insights of how the gain and phase are shaped by individual nonlinear and linear components can be achieved. The modeling shows that tuning the phase delay of the signal fed to the auxiliary amplifier of the Doherty can be used to improve the linearity performance. Experimentally, a Doherty with 150 phase delay is shown to improve third-order intermodulation distortion (IMD3) by as much as 8 dB over a Doherty amplifier with 90 phase delay. This paper is organized as follows. In Section II, the analytical model for single-ended class AB and C amplifiers is discussed. In Section III, the extracted nonlinear components from both of these amplifiers are then used to build an analytical mode for a Doherty amplifier. The analytical model results are discussed for Doherty amplifiers with different configurations. Section IV describes the load dependence of the extracted components and its impact on the modeling. Next, experimental results are given in Section V. Finally, conclusions are then provided in Section VI.

Solving Kirchoff’s current and voltage law for the circuit shown in Fig. 2 gives the complex voltage transfer function in the model as follows:

(2) is small and can be neglected, then the analytical model If can be simplified and (2) becomes (3)

II. MODEL FOR A SINGLE-ENDED AMPLIFIER The nonlinear components in the proposed model of Fig. 2 are: 1) base–emitter junction capacitance , and conductance ; 2) output capacitance and conductance ; and 3) trans-conductance . For simplicity, effects are incorporated within the input and output admittances. The remaining components (base resistance and emitter resistance ) are considered to be linear. The nonlinear components are dependent on the bias conditions of the transistor, on the input power and, in general, on the circuit embedding. The transistor used for this evaluation was an InGaP/GaAs HBT from the high-volume manufacturing process of Skyworks Solutions Inc., Newbury Park, CA. The technology of 115, GHz (at , features a dc gain mA m ), and a breakdown voltage ( ) of approximately 15 V. In this study, the linear and nonlinear components values were extracted from a foundry-provided vertical bipolar inter-company (VBIC) device model using Agilent Technologies’ Advanced Design System (ADS) in harmonicbalance simulation. For the extraction of the nonlinear elements, appropriate ratios of current and voltage components at the fundamental frequency were calculated under large-signal conditions. The nonlinear elements are defined through the following:

(1) Here, superscript (1) indicates that the fundamental frequency component of the time waveform should be used. Following the definitions, the nonlinear elements can be determined, e.g., , , and real . While the element values are valid only for a fixed circuit embedding, in this study, we use them approximately over a range of power levels and circuit contexts that are different (although not very different) from those used in their definition.

In the following, the analytical model is applied to class AB and C amplifiers, which are the two basic active components in the Doherty amplifier. A. Class AB Amplifier The class AB amplifier uses a Skyworks Solutions Inc.’s HBT device with active emitter area of 1600 m . From the VBIC is found to be 0.336 and is 0.0372 . A simmodel, ulation was set up in Agilent Technologies’ ADS for the model parameter extractions. The base quiescent bias current of 53 mA is provided by a current mirror bias circuit. A source impedance is used to achieve proper input matching. , which is the value the class The load impedance is AB main amplifier sees within the Doherty amplifier before the auxiliary amplifier turns on. First, a large-signal -parameter simulation is carried out from which can be calculated as , and further elements can be and real . determined through Second, a harmonic-balance simulation is done. From its results, the remaining nonlinear components for the analytical model can be calculated following , , real , and . The extracted magnitude of , , and are shown in Fig. 3(a). The extracted , , , and values are shown in Fig. 3(b). With an increasing power level, is found to decrease slowly with RF power as a result of clipping of the current waveform in cutoff, and to drop rapidly above 25 dBm as a result of the onset of saturation at the minimum of the voltage waveform. Similarly, decreases with an increasing power level (as does ) as a result of clipping, but increases as saturation is reached. has a complex value of 10 / 55 at low power, and changes slightly with power level. The emitter resistance of 0.0372 is negligible in this case and (3) can be used for the analysis. The calculated output gain and phase according to (3) are shown in Fig. 4(a), and for comparison, the simulated gain and phase from ADS using the

ZHAO et al.: LINEARITY IMPROVEMENT OF HBT-BASED DOHERTY PAs BASED ON SIMPLE ANALYTICAL MODEL

Fig. 3. Extracted components for a class AB and C PA. (a) and (c) Magnitude of g , Y !C , and g for class AB PA (b) and class C PA (d).

and Y

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for class AB PA (a) and class C PA (c). (b) and (d) !C , g ,

Fig. 4. Results from the analytical model for a class AB and class C PA. (a) and (c) Gain and phase from simulation (solid) and the analytical model (triangle) for class AB PA (a) and class C PA (c). (b) and (d) Voltage gain (solid), gm (triangle), d (circle), and d (line) for class AB PA (b) and class C PA (d).

complete Skyworks Solutions Inc.’s device model. Good agreement between the two is found. The analytical model can be used to achieve insights into the amplifier’s nonlinear behavior. Fig. 4(b) shows the magnitudes , , , and of the

the calculated voltage gain on a linear scale. As indicated by is the contribution to gain by components the subscripts, from the circuit input side and by components from the affects and, consequently, the output side. complex voltage gain, which implies that source impedance can

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be optimized for linearity, as reported by Yamada et al. in [17]. Moreover, as can be seen in Fig. 4(b), the nonlinearity of is largely cancelled by that of (within the factor) in the clipping region, leading to nearly flat gain before the saturation region. This phenomenon has been originally reported in papers by Maas et al. [18], Samelis et al. [19], and others. B. Class C Amplifier The class C biased amplifier uses the same device as the class AB amplifier described above. The same current mirror circuit (with a different reference voltage) is used to provide a quiescent current of 1 mA. The same simulation set up as for the class AB amplifier is also used for the class C case. A load impedance of was used, which is the value a class C auxiliary amplifier sees in the Doherty context. The magnitude of extracted , , and are shown in Fig. 3(c), while the extracted , , , and values are shown in Fig. 3(d). The values differ considerably from those found for class AB operation. increases sharply with power as a result of the In Fig. 3(c), class C self-bias effect, and reaches saturation at approximately 30 dBm. The input capacitance also increases significantly with ). The output capacitance increases dramatipower (as does ), when the base–collector cally at peak power levels (as does junction reaches saturation at the extremes of the voltage waveform. It should be pointed out that this analytical model incorinto and . The effect of change conporates and changes at high power levels, tributes to large as shown in Fig. 3(d). Compared with the admittance, the conand are both small in the class C amplifier. ductance of The calculated output gain and phase according to (3) is shown in Fig. 4(c) and, for comparison, the simulated gain and phase from ADS using the complete Skyworks Solutions Inc.’s device model. Good agreement between the two is found. , , Based on (3), the magnitudes of and the calculated voltage gain and in linear scale for the case of the class C biased amplifier are , the voltage gain shown in Fig. 4(d). For comparison with has been divided by a factor of 4.2 , which is the small-signal . The sharply increasing value of the product of dominates the gain in most power levels and the increase of (within the factor ) leads to a minor gain compression at high power. is extracted as It should be pointed out that since for both class AB and C amplifiers, it is not has a small constrained to be real. For the current amplifiers, imaginary part, which is necessary to include in the modeling to give accurate phase predictions for the amplifiers. III. MODEL FOR A DOHERTY AMPLIFIER The analytical model was applied to analyze a Doherty amplifier using identical transistors. The Doherty simplified factor applied schematic is shown in Fig. 5. There is an to the source of the auxiliary PA, which denotes the delay line inserted in front of the auxiliary PA in a typical Doherty structure. The nominal value for is 90 . The derivation of the output voltage expression for the Doherty is more complicated

Fig. 5. Schematic of the proposed model applied to Doherty architecture.

than for the single-ended PA, however, it is still analytically tractable. From the voltage and current relations in the Doherty schematic, we have

(4) The model elements extracted for the class AB and C cases are used in the Doherty amplifier for the main and auxiliary amplifiers, respectively. Subscripts 1 and 2 in (4) indicate elements extracted from the class AB and C amplifiers, respectively. Since the circuits used for extracting nonlinear and linear components in class AB and C amplifiers are configured the same as they appear in the Doherty amplifier, the extracted parameters from the two separate amplifiers can be used approximately to analyze the full Doherty amplifier. In both the separate and Doherty cases, the class AB and C amplifiers have the same input matching, bias condition, output impedance, and also the same input power level, respectively. is small and can be Equation (4) can be simplified since neglected in this case, and the expression for the transfer function becomes (5), shown at bottom of the following page. Using (5), the gain and phase of a Doherty amplifier, with set equal to 90 as a nominal case, were calculated and are compared with full ADS simulation results in Fig. 6(a). Good agreement between the two cases is found. The gain differences between the two approaches are less than 1 dB over all the power levels and, most importantly, the analytical results show the same trends as the simulation with changing power level. The phase difference at peak power is approximately 5 , however, the analytical results also show similar trends with changing power. The analytical and simulated results show that the Doherty behavior is nonideal in that the gain drops at high power and phase distortion is large (more than 20 ). Further analyses

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Fig. 6. Results from the analytical model for the Doherty amplifier. (a) Gain and phase from simulation (solid) and the analytical model (triangle). (b) Magnitudes of N ; N ; N N , and D . (c) Phases of N ; N ; N N , and D . (d)–(f) Same results as (a)–(c) for the Doherty PA with  set to equal 150 .

+

+

based on the model provide insights into the causes of the distortion. In (5), for the numerator, we define and . For the is denominator, defined. With these definitions, the gain of the Doherty amplifier beand the output phase of the comes phase . Doherty amplifier becomes phase is the contribution to gain by the main PA, and is the contribution by the auxiliary PA weighted by a coefficient of . includes contributions from and .

, , , and are The magnitude and phase of shown in Fig. 6(b) and (c). Their behaviors are different at different power levels. In Fig. 6, region I indicates low-power levels before the auxiliary amplifier turns on. Region II indicates a transition region where the auxiliary PA turns on while the main amplifier remains in saturation. Region III indicates the highpower region where the overall Doherty amplifier saturates. As can be seen, the main amplifier dominates the gain in region I, while the auxiliary amplifier compensates for the drop of gain in region II [although it does not do so completely, as seen in and (in ) to the Fig. 6(b)]. The contribution from variation of gain is insignificant.

(5)

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Fig. 7. Effect of tuning the phase delay  on output of Doherty amplifier.

The output phase distortion of the Doherty amplifier comes in region I at low mainly from the main PA phase power because the contribution from the auxiliary amplitude is small in magnitude. At high power (regions II and III), the output phase is a result of contributions from both the main amplifier and auxiliary amplifier, combined vectorially. In and additionally provide a negative phase region III, contribution. The large output phase distortion of the Doherty may be seen and . to result from the phase difference of 70 between The contributions from the main and auxiliary amplifiers to the gain of the Doherty amplifier have a phase offset, which is not compensated effectively by the insertion of a quarter-wave line in front of the auxiliary amplifier. A major part of that phase factor in , which has a 55 inseroffset comes from the tion phase (changing slightly with power) by itself. This phase offset reduces the effectiveness of the vector combination of and , and leads to inadequate gain compensation from the auxiliary amplifier to the main amplifier in region II. The analysis implies that correcting the phase offset brought between and would improve both the gain and by phase of the Doherty amplifier. Tuning the phase delay at the input of the auxiliary PA is one way to correct that phase offset. We demonstrate here that this is an effective way to improve the behavior of the Doherty PA. Shown in Fig. 6(d) are the gain and phase results calculated with equal to 150 both by the analytical model and by full Agilent Technologies’ ADS simulation. The analytical results match well with the simulation results. Both the gain and phase are improved, leading to a corresponding linearity improvement for the Doherty PA. To further illustrate the effect of tuning to the performance, simulated gain and output phase with varying from 90 to 150 are given in Fig. 7. Arrows show the direction of change as increases. , the magnitude and phase of , For the case of , and , and are shown in Fig. 6(e) and (f). Due to the reduced phase offset between and (15 ), the gain contributions from the auxiliary amplifier now compensate for the decrease of gain from the main PA more effectively, causing in Fig. 6(e) accordingly. Allowing the a flatter phase of to remain 15 –20 larger than that of generates in region III, which coma positive slope for phase pensates for the negative phase change from and achieves the

lowest overall output phase variation for the Doherty amplifier. The value of that optimizes performance will, in general, vary with device, bias condition, and circuit configurations. The above analysis shows that by adding an additional phase shift in front of the auxiliary amplifier, the phase offset by in is compensated and the resultant linearity performance of the Doherty PA is improved. A similar offset line had been used at output of the Doherty PA, as reported in [6] and [12]. That offset line was used to compensate for nonopen off-state output impedance of the auxiliary PA for leakage current and efficiency improvement. In this paper, the delay line is used for linearity improvement. The analytical model provides a convenient way to analyze changes of Doherty behavior in the case of other changes to the amplifier structure such as bias or device size changes in transistors and uneven input power split. For the latter case, with a power split ratio 1 : 2 between the main and auxiliary amplifiers, is added to the input voltage of the auxiliary ama factor of . plifier, which then becomes Based on (5), the output gain and phase for this case (1 : 2 ) is calculated and shown in Fig. 8. input power split, An improved gain in region II results from the increased input power of the auxiliary amplifier. This is reflected in the inmagnitude shown in Fig. 8(b). However, the phase crease of is worsened and changes by as much as 40 . This is because and , the without correction of the phase offset between aggravates its effect on the phase of increased magnitude of , leading to a larger phase variation of in region II. This analysis suggests that tuning the delay line is a better choice than changing the input power split ratio in improving the linearity of the Doherty amplifier. Furthermore, tuning the delay line will result in optimum power-added efficiency (PAE) performance since the use of a 1 : 2 power split reduces the overall gain and, therefore, sacrifices PAE. More thorough and complete examination of the Doherty configuration with an uneven power split can be found in [13]. The analytical model is useful in identifying nonlinearity contributions from each of the individual nonlinear components. The nonlinearity of each individual component can be turned off in the analytical model by using its linear value at the smallsignal level. Output gain and phase can be calculated and IMD3 can be subsequently calculated by using the output gain and phase as inputs to a MATLAB behavioral model (similar to the one used in [20]). Shown in Fig. 9 are the IMD3 contributions calculated using this method for different cases. ” case, in which and are set In the “no as constants, the major nonlinearities from the main amplifier are eliminated, leading to lower IMD3 in the low-power region. ” case, IMD3 is high in the high-power region In the “no is kept at its small-signal value and the auxiliary when the ” case has a higher IMD3 amplifier is not turned on. The “no at low power indicating that nonlinearity is necessary to nonlinearity in that power region. cancel the The analysis suggests that the IMD3 of the full Doherty (about 30 dBc) is mainly amplifier around 20-dBm from the nonlinearity of the main amplifier. It should be noted that there were no harmonic traps implemented in the simulation. The linearity of the main amplifier and also of the overall

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Fig. 10. Load impedances seen by main and auxiliary amplifiers in the improved Doherty (with  set to 150 ). Circles: for main PA. Solid: for auxiliary PA.

IV. IMPEDANCE DEPENDENCE OF MODEL COMPONENTS

Fig. 8. Results from the analytical model for the Doherty with 1 : 2 input power split ratio. (a) Gain and phase from the model. (b) Magnitudes of the contributing elements. (c) Phases of the contributing elements.

Fig. 9. Calculated IMD3 showing effect of individual nonlinear components.

Doherty at low power could be further improved with proper harmonic traps at the output of the main amplifier.

One distinctive phenomenon in the Doherty amplifier is that the load impedances seen by the main and auxiliary amplifiers change with input power level. The impedances seen by the and (see main and auxiliary PA are defined as Fig. 1), and calculated in large-signal analysis by taking the ratios of the fundamental components of the overall voltage and overall current. The active load–pulling by the auxiliary amplifier on the main amplifier is a key reason why the Doherty amplifier can achieve high efficiency at low power levels. As calculated by Iwamoto et al. [4], in the ideal case, the main amplifier should have a high resistance load (16 in this design with and ) at low power, and with the auxiliary PA turning on at high power levels, that (8 ). The resistance value should change gradually to at auxiliary amplifier experiences a peak power. In the real circuit, with reactive output impedances and are no longer constrained from the transistor, to be pure real. An example can be seen in Fig. 10, which shows the impedances seen by the main and auxiliary amplifiers with the improved Doherty amplifier (in which has been chosen to be 150 ). It should be noted that while the analytical model presented above describes the key phenomena leading to Doherty amplifier distortion, it does not accurately represent the full Doherty , , and with behavior. For this, the changes of load impedance should be taken into account since the load seen by the amplifiers changes with power level. The initial load impedances are chosen to be 16 and 4 , but with the load–pulling effect between the main and auxiliary PA, the load impedance seen by the main PA changes to around 8 and the load impedance seen by the auxiliary PA is highly reactive. In the current model, the effect of changing load impedance can , only be accounted for approximately by considering the , and values at representative load values. To illustrate the effect of the load impedance changes to the extracted model and of the main PA extracted parameters, representative with three load impedances are shown in Fig. 11. With an understanding of the load dependence of the model parameters, modifications can be made to the model. Load imfor the main PA, and for the pedances (

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Fig. 11. Extracted g impedances.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

and Y

for the main amplifier with three different load

Fig. 12. Output gain and phase for Doherty amplifier. Triangles: analytical results with optimized load impedances. Solid: simulated.

Fig. 13. Schematic of the experimental Doherty amplifier.

Fig. 14. Measured gain and phase for the Doherty amplifier with 90 and 150 phase delays feeding auxiliary amplifier. Triangles: 90 . Solid: 150 .

auxiliary PA) closer to the values the two amplifiers experience at high power can be selected for use in the parameter-extraction procedure. This generates extracted components that better characterize Doherty’s behavior at high power. Consequently, the prediction of the model matches more accurately with the full simulation results in high power, shown in Fig. 12. Noticeable is that the gain calculated from the model is increased for low-power levels in this case. V. EXPERIMENTAL RESULTS To demonstrate the efficacy of the analytical model, a Doherty amplifier was fabricated on Roger 4350 printed circuit board (PCB) using Skyworks Solutions Inc.’s InGaP/GaAs HBTs as represented by the models. Two PA chips (inside the boxes in Fig. 13) with input matching and bias circuit integrated on chip were mounted on the board. A circuit diagram is shown in Fig. 13. The base bias of the main and auxiliary PA is provided by current mirror circuits, which operate close to a constant voltage source. The quiescent base bias current is set as 55 mA for the main amplifier (class AB) and 2 mA for the auxiliary amplifier (class C). The bias current was optimized to achieve an acceptable tradeoff of efficiency and linearity behavior. The output circuits were realized by transmission lines implemented on the PCB board, while the input match was implemented with discrete components on chip. A Wilkinson power divider was used at the input to split the power equally between the main and auxiliary amplifiers. On board are transmission lines with different length used in phase delay tuning.

Fig. 15. Measured IMD3 for the Doherty amplifier with 90 and 150 phase delays.

The Doherty amplifier was design to work at 1.88 GHz, and the maximum output power reached 29 dBm (with single tone tests). Predictions by the analytical model are verified in the following experimental results. Fig. 14 compares the measured gain and phase for the Doherty amplifier when the phase delay in front of the auxiliary PA is 90 and when the phase delay is switched to 150 . With the 150 delay, the Doherty PA shows flatter gain and smaller phase variation (similar to the simulation results) and consequently achieves better IMD3 performance (with improvement as much as 8 dB at 23 dBm), shown in Fig. 15.

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by tuning the phase delay at the input of the auxiliary amplifier, better output gain, phase, and consequently better linearity can be obtained for the Doherty amplifier. An explanation has been provided based on the analytical model. The efficacy of the model has been demonstrated by experimental results in which a Doherty amplifier with 150 phase delay at the auxiliary amplifier input shows significant linearity improvement. Overall, the simple analytical model has been shown to be an effective tool for analyzing nonlinear behavior in Doherty amplifiers. The model can also be applied to other structures with nonlinearly interacting amplifiers. Fig. 16. Measured PAE (with two-tone input) for the Doherty amplifier with 90 and 150 phase delays.

ACKNOWLEDGMENT The authors would like to thank Dr. S. Hongxiao, Skyworks Solutions Inc., Newbury Park, CA, for help with the simulation kit, and Dr. D. Root, Agilent Technologies, Santa Rosa, CA, for helpful discussions. REFERENCES

Fig. 17. Measured and calculated IMD3 for the Doherty amplifier with 150 phase delays feeding the auxiliary amplifier. Also shown are calculated results using only the gain distortion and only the phase distortion.

As pointed out earlier, is the point at which we can achieve lowest phase predistortion. In the experiment, it proves to be the best tradeoff point for overall linearity as well. The experimental results clearly show linearity improvement as the analytical model has predicted, although with there is some discrepancy between the measured phase and the case. simulated one for the Fig. 16 shows the measured PAE with a two-tone input signal. The Doherty amplifier with 150 delay shows better efficiency, particularly at the power level where the auxiliary amplifier turns on. Using the measured gain and phase data for the case of 150 delay as input for a behavioral model, we can calculate the IMD3, as well as the IMD3 contributions from the gain and phase distortions individually. Shown in Fig. 17 are the measured and calculated IMD3, as well as the IMD3 values resulting from gain and phase distortion alone. It can be seen that the phase is the major cause of IMD3 for output power between levels, the 8–23 dBm in this Doherty amplifier. At higher gain distortion is dominant. VI. CONCLUSION A simple analytical model has been shown to be effective in predicting the nonlinear behavior of single-ended HBT amplifiers, as well as Doherty amplifiers. It has been found that

[1] W. H. Doherty, “A new high efficiency power amplifier for modulated waves,” Proc. IRE, vol. 24, no. 9, pp. 1163–1182, Sep. 1936. [2] F. H. Raab, “Efficiency of Doherty RF power-amplifier systems,” IEEE Trans. Broadcast., vol. BC-33, no. 3, pp. 77–83, Sep. 1987. [3] K. W. Kobayashi, A. K. Oki, A. Guitierrez-Aitken, P. Chin, L. Yang, E. Kaneshiro, P. C. Grossman, K. Sato, T. R. Block, H. C. Yen, and D. C. Streit, “An 18–21 GHz InP DHBT linear microwave Doherty amplifier,” in IEEE RFIC Symp. Dig., 2000, pp. 179–182. [4] M. Iwamoto, A. Williams, P.-F. Chen, A. Metzger, L. Larson, and P. Asbeck, “An extended Doherty amplifier with high efficiency over a wide power range,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2472–2479, Dec. 2001. [5] N. Srirattana, A. Raghavan, D. Heo, P. E. Allen, and J. Laskar, “Analysis and design of a high-efficiency multistage Doherty power amplifier for wireless communications,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 852–860, Mar. 2005. [6] Y. Yang, J. Cha, B. Shin, B. Kim, and , “A fully matched -way Doherty amplifier with optimized linearity,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 986–993, Mar. 2003. [7] S. Wood, , R. S. Pengelly, and M. Suto, “A high efficiency, high power UMTS amplifier using a novel Doherty configuration,” in IEEE RAWCON Dig., Aug. 2003, pp. 329–332. [8] I. Takenaka, H. Takahashi, K. Ishikura, K. Hasegawa, K. Asano, and M. Kanamori, “A 240 W Doherty GaAs power FET amplifier with high efficiency and low distortion for WCDMA base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 525–528. [9] J. Cha, J. Kim, B. Kim, J. S. Lee, and S. H. Him, “Highly efficient power amplifier for CDMA base station using Doherty configuration,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 533–536. [10] T. Ogawa, T. Iwasaki, H. Maruyama, H. Horiguchi, M. Nakayama, Y. Ikeda, and H. Kurebayashi, “High efficiency feed-forward amplifier using RF predistortion linearizer and modified Doherty amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 537–540. [11] J. Gajadharsing, O. Bosma, and P. van Western, “Analysis and design of a 200 W LDMOS based Doherty amplifier for 3-G base station,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 529–532. [12] K.-J. Cho, J.-H. Kim, and S. T. Stapleton, “A highly efficient Doherty feedforward linear power amplifier for W-CDMA base-station applications,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 292–300, Jan. 2005. [13] J. Kim, J. Cha, I. Kim, and B. Kim, “Optimum operation of asymmetrical-cell-based linear Doherty power amplifiers—Uneven power drive and power matching,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1802–1809, May 2005. [14] N. Wongkomet, L. Tee, and P. R. Gray, “A 1.7 GHz 1.5 W CMOS RF Doherty power amplifier for wireless communications,” in IEEE Int. Solid-State Circuits Conf. Dig., 2006, pp. 486–487. [15] Y. Zhao, M. Iwamoto, L. E. Larson, and P. M. Asbeck, “Doherty amplifier with DSP control to improve performance in CDMA operation,” in IEEE MTT-S Int. Microw. Symp. Dig., 2003, pp. 687–690.

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[16] J. Deng, P. S. Gudem, L. E. Larson, and P. M. Asbeck, “A high averageefficiency SiGe HBT power amplifier for WCDMA handset applications,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 529–537, Feb. 2005. [17] H. Yamada, S. Ohara, T. Iwai, Y. Yamaguchi, K. Imanishi, and K. Joshin, “Self-linearizing technique for L-band HBT power amplifier: Effect of source impedance on phase distortion,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 2398–2402, Dec. 1996. [18] S. Maas, B. Nelson, and D. L. Tait, “Intermodulation in heterojunction bipolar transistors,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 3, pp. 442–448, Mar. 1992. [19] A. Samelis and D. Pavlidis, “Mechanisms determining third order intermodulation distortion in AlGaAs/GaAs heterojunction bipolar transistors,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 12, pp. 2374–2380, Dec. 1992. [20] J. Staudinger, “A consideration of phase distortion in linear power amplification of QPSK and two tone sinusoidal stimuli,” in Wireless Commun. Conf. Dig., 1997, pp. 105–109. [21] Y. Zhao, A. G. Metzger, P. J. Zampardi, M. Iwamoto, and P. M. Asbeck, “Linearity improvement of HBT-based Doherty amplifiers based on a simple analytical model,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, [CD ROM].

Yu Zhao (S’99) was born in Nanjing, China, in 1976. He received the B.S. and M.S. degrees in electrical engineering from Southeast University, Nanjing, China, in 1998, and 2001, respectively, and is currently working toward the Ph.D. degree at the University of California at San Diego, La Jolla. During the summer of 2004, he was an Intern with Skyworks Solutions Inc., Newbury Park, CA, where he was involved with InGaP/GaAs HBT based advanced PA designs for CDMA mobile handset applications. His research interests include RF PA and integrated circuits design for wireless communications.

Andre G. Metzger (S’93) received the B.S. and M.S. degrees in electrical engineering from the University of California at San Diego (UCSD), La Jolla, in 1995 and 1996, respectively, and is currently working toward the Ph.D. degree at . His doctoral thesis involves data recovery in dispersed fiber transmission systems. He is a currently a Senior Design Engineer with Skyworks Solutions Inc., Newbury Park, CA, where he is involved with the research and development of advanced PAs for CDMA mobile handsets and related applications. Since 1995, he has been involved in research with the High Speed Device Group, Skyworks Solutions Inc. From 1995 to 1997, he was a key member in the design of a 12 12 10-Gb/s crosspoint switch that made up the core of a Defense Advanced Research Projects Agency (DARPA) sponsored 40-Gb/s 3 3 opto-electronic switch project called WEST. He has interned with Rockwell Science Center, Newbury Park, CA, and consulted for Conexant Systems, Newport Beach, CA. He has also collaborated internationally with the University of Bologna, Bologna, Italy. His primary research focus with UCSD is circuit design for high-speed fiber-optic communications and PA applications in III–V technologies.

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Peter J. Zampardi (S’93–M’96–SM’02) received the B.E. degree in engineering physics from the Stevens Institute of Technology, Hoboken, NY, in 1986, the M.S. degree in applied physics from the California Institute of Technology, Pasadena, in 1988, and the Ph.D. degree from the University of California at Los Angeles (UCLA), in 1997. While with the California Institute of Technology, he studied molecular beam epitaxy (MBE)-grown GaAs/AlGaAs structures and investigated tellurium clustering in ZnSe : Te for use in visible light emitters. In 1988, he joined the Ring Laser Gyroscope Test Laboratory, Rockwell Science Center, were he was responsible for development and testing of ring laser gyros for use in inertial measurement units. In 1990, he joined the Optics Technology Department, Rockwell Science Center, were he developed processes and procedures for the characterization and fabrication of infrared (IR) etalon filters. In 1991, he joined the High Speed Circuits Department, Rockwell Science Center, were he performed device and circuit development, characterization, and modeling of GaAs, InP, and SiGe HBTs, MESFETs, high electron-mobility transistors (HEMTs), BiFET, and resonant tunneling diode (RTD) technologies. In 1999, he led the technical development of SiGe RF models for the Analog and Mixed Signal Foundry business at IBM, Burlington, VT. Since 2001, he has been with Conexant/Skyworks Solutions Inc., Newbury Park, CA, were he is Technical Director for device design, characterization, and modeling. The group’s interests are technologies, characterization, modeling, and circuit design for wireless applications. He has authored or coauthored over 120 papers related to circuits and devices. Dr. Zampardi actively participates in several IEEE technical conference committees.

Masaya Iwamoto (S’99–M’04) received the B.S. degree in electrical engineering from Cornell University, Ithaca, NY, in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the University of California at San Diego, La Jolla, in 2003. During the summers of 1997–2002, he was an Intern with Agilent Technologies, Santa Rosa, CA (formerly the Hewlett-Packard Company), where he was responsible for HBT characterization, modeling, and amplifier designs. He is currently with Agilent Technologies on a full-time basis where he is involved in the area of GaAs- and InP-based HBT technology development.

Peter M. Asbeck (M’75–SM’97–F’00) received the B.S. and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, in 1969 and 1975, respectively. His professional experience includes affiliations with the Sarnoff Research Center, Princeton, NJ, and Philips Laboratory, Briarcliff Manor, NY. In 1978, he joined the Rockwell International Science Center, Thousand Oaks, CA, where he was involved in the development of high-speed devices and circuits using III–V compounds and heterojunctions. He pioneered the effort to develop HBTs based on GaAlAs/GaAs and InAlAs/InGaAs materials. In 1991, he joined the University of California at San Diego, La Jolla, as a Professor with the Department of Electrical and Computer Engineering. His research has led to over 300 publications. Dr. Asbeck was the recipient of the 2003 Sarnoff Award for his work on HBTs.

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RF Chipset for Impulse UWB Radar Using 0.13-m InP-HEMT Technology Yoichi Kawano, Yasuhiro Nakasha, Member, IEEE, Kaoru Yokoo, Satoshi Masuda, Member, IEEE, Tsuyoshi Takahashi, Tatsuya Hirose, Member, IEEE, Yasuyuki Oishi, and Kiyoshi Hamaguchi, Member, IEEE

Abstract—A novel ultra-wideband impulse radar architecture for 24-GHz-band short-range radar was developed using 0.13- m InP high electron-mobility technology. The transmitter part generates an extremely wideband impulse from a pulse generator and then filters it through a bandpass filter. The obtained impulse had a full width at half maximum of 9 ps. Its frequency spectrum spread from dc to over 40 GHz and achieved sufficient flatness in the target band. The power amplifier (PA) for the transmitter had a gain of 15 0.1 dB, and the low-noise amplifier (LNA) for the receiver had a gain of 40 1 dB and a minimum noise figure of 1.9 dB. The achieved flatness of integration gain including the PA, LNA, and RF switch was less than 1.2 dB. These RF circuits with gain flatness make a simple matched filter configuration possible without the use of a conventional correlator composed of a local oscillator. An ultra high-speed sample and hold circuit having an ultra-long hold time of more than 3 ns was also developed to detect the output pulses from the matched filter.

I. INTRODUCTION

I

N 2002, the Federal Communications Commission (FCC), Washington, DC, authorized the development of ultra-wideband (UWB) technologies for commercial applications [1]. UWB has attracted a great deal of attention as an indoor short-range radar and in high-speed wireless communication systems. As communication systems have been allocated 3.1–10.6 GHz (microwave UWB) and radar systems have been allocated 22–29 GHz (quasi-millimeter-wave UWB) as available frequency bands to be operated by unlicensed users, they are expected to be widely used in the consumer market. Various UWB applications based on various transmission methods are being developed worldwide [2]–[9]. One of the most noted for UWB is impulse radio (UWB-IR), which generates ultra-short pulses covering an extremely wide frequency spectrum and then filters these to match the spectrum mask. The system configuration is very simple because the need for an up/down converter and frequency recovery loops in the system can be eliminated. The simple RF structure makes the fabrication of a low-cost and low-power transceiver set possible. Moreover, the fine timing resolution provided by ultra-short pulses provides the advantage of extremely high path resolution. This advantage is

Manuscript received March 31, 2006; revised June 28, 2006. Y. Kawano, Y. Nakasha, K. Yokoo, S. Masuda, T. Takahashi, T. Hirose, and Y. Oishi are with Fujitsu Laboratories Ltd., Atsugi, Kanagawa 246-0197, Japan (e-mail: [email protected]). K. Hamaguchi is with the National Institute of Information Communication Technology, Kanagawa 239-0847, Japan.. Color versions of Figs. 1(a), 11(b), and 13(a) are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.885908

extremely attractive for achieving fine resolution impulse radar systems. However, UWB-IR requires superior device performances to implement a system compared with other methods, such as multiband-orthogonal frequency-division multiplexing (MB-OFDM) because it involves an UWB impulse generator and broadband amplifiers. The use of quasi-millimeter wave UWB has also become increasingly popular. Compound semiconductor technologies with high-speed performance provide powerful means of solving problems with this band. In this paper, we focus our attention on quasi-millimeter-wave UWB-IR and report on the performance of an RF chipset implemented in a system using 0.13- m InP high electron-mobility transistor (HEMT) technology. As is well known, the greatest advantage of an InP-HEMT is its high-speed performance [10], [11]. We exploited this advantage to further simplify the conventional configuration for UWB-IR. We also developed prototype radar equipment based on our UWB-IR and tested its operation in measuring distance. II. CONFIGURATION FOR UWB TRANCEIVER Fig. 1(a) is an RF block diagram of the proposed UWB-IR system. The transmitter generates an extremely wideband impulse from the pulse generator (PG) and then filters it through the bandpass filter (BPF) to match the spectrum mask. After the received signal in the receiver passes through the low-noise amplifier (LNA), BPF, and 90 hybrid circuit, the peak value of the signal is directly detected by the high-speed sample and hold (S/H) circuit. The detected data is processed by the next stage analog–digital (A/D) converter. We will first describe the received matched filter for our system. In general, a matched filter is defined as a filter that maximizes the signal-to-noise ratio (SNR) at filter output. Fig. 1(b) illustrates a general receiver model. The SNR of this is given by model at (1) where and are the Fourier transform of the input is the transfer function of the filter and output signals. is the spectrum density of the external white [12]. noise, which exhibits flatness in all frequency bands. This is satisfies maximized when (2) is the input signal for the receiver BPF. In our system, Here, if: 1) the bandwidth of the impulse is much larger than that

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Fig. 1. (a) RF block diagram of UWB-IR system. (b) Schematic of general receiver model.

of the BPF and has flatness in the target band and 2) the transfer characteristics ( ) of the power amplifier (PA), RF switch can be expressed (SW), and LNA are flat in the band , where is the transfer function of as is the sum of the integration gain the transmitter BPF, and and free-space propagation loss. We assumed propagation loss would be independent of the frequency in the band. The received matched filter under the above conditions can become a BPF that has the same transfer characteristics as the transmitter’s. Another feature of this RF configuration is being able to utilize a high-speed S/H circuit instead of a conventional diode detector. Since the S/H circuit detects both the magnitude and phase of UWB signals, bi-phase pulses, which are encoded with pulse polarity, can be decoded. This implies the possibility of producing a data communication system based on a bi-phase modulation scheme. The proposed system is simpler than a conventional UWB-IR using a local oscillator and a mixer [5], [8]. However, device technology and RF circuit design techniques were required to satisfy the above conditions because considerable high-integration gain also has to be achieved to detect ultra-weak signals. Developing such RF circuits is definitely extremely challenging work.

Fig. 2. (a) Block diagram of PG. (b) Operating principle in pulse generation. (c) Schematic of PG core. (d) Conventional type.

based on an AND circuit to obtain ultra-short pulses. Instead of a level-shift diode in a conventional AND, as shown in Fig. 2(d), and , located between there is a differential pair, i.e., and switching transistor . The differential load resistance pair called a “balance circuit” has been fixed in the low state for and the high state for . Maximizing the switching of is a key factor to achieve short duration pulses. By biasing the on state, and behave as a cascode circuit. As is well , which expresses the equivalent known, the Miller effect of gate–drain capacitance of as , is less in the cascode stage than in simple common-source stages. In our PG, from node to in Fig. 2(c) the effective voltage gain is given by

III. RF DEVICE PERFORMANCE FOR PROPOSED IMPULSE RADIO We employed 0.13- m InP-HEMT technology with an of 183 GHz and a of 1520 mS/mm. The integrated circuits (ICs) described in this paper had four metal interconnect layers and three layers of benzocycrobutene (BCB) film. NiCr resistors with a sheet resistance of 50 square and an SiN metal–insulater–metal (MIM) capacitor were also employed in the ICs. A. PG Fig. 2(a) is a block diagram of the PG. The circuit mainly consists of delay control buffers and a PG core. We can control the duration of pulses by changing the overlap time between and , as shown in Fig. 2(b). Fig. 2(c) shows the PG core

(3) from node and is given by

to

in the conventional type in Fig. 2(d) (4)

is the transconductance of and is that of where . Estimated from the typical transistor size for and , the Miller effect in our circuit is less than half that in the conventional type (5)

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Fig. 3. (a) Chip microphotograph. (b) Measured outputs larged view.

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Q and NQ. (c) En-

Therefore, this results in a shorter switching time for than that for the conventional type. Fig. 3(a) shows a chip microphotograph of the PG IC. The power consumption was 620 mW. Fig. 3(b) and (c) plots the and that have a measured outputs. Ultra-sharp pulses 9-ps FWHM were obtained even after including degradation for cable loss and the 70-GHz bandwidth of the sampling head. As far as we know, this result is a record for PGs fabricated entirely with semiconductor transistors. B. BPF When an extremely wideband impulse, shown in Figs. 3(b) and (c), is input to the BPF, the shape of the output pulse becomes a wavelet with a long tail. Since the distance resolution for impulse radar strongly depends on the transmission pulsewidth, pulse-shaping techniques are very important to suppress the tail in the spectrum mask as far as possible. The pulse-shaping block corresponds to the BPF in our UWB-IR configuration. We first investigated the of the BPF to obtain an transfer function optimum transmission pulse for the impulse radar. We chose a of the BPF, cosine-rolloff type for the transfer function which define the attenuation rates from the center frequency to is given by the band edges as a cosine curve. Here,

(6) , is the where is the cosine-rolloff factor bandwidth, and is the center frequency in the band. Fig. 4(a) in a typical and the plots the calculated profile of was chosen spectrum mask. Here, the bandwidth for each to be within 24.0–29.0 GHz, taking the restricted frequency (23.6–24.0 GHz) allocated for radio astronomy and passive

Fig. 4. (a) Profile of the transfer function sponses. (c) Magnitude of the envelope.

F (f ). (b) Calculated impulse re-

, satellite-based remote sensors into consideration. When at both band edges changes to step function. Meanwhile, , changes to the cosine function. when Fig. 4(b) plots the impulse responses derived from the in. As we can see from these verted Fourier transform of figures, when , the width of the main wavelet is relatively , on the other hand, the width of the main short. When wavelet is relatively wide, but the amplitude of the th wavelets is very suppressed compared with those of . In the cosine-rolloff BPF, there is generally a tradeoff between the main wavelet width and the suppression of th wavelets. If we only use the main wavelet for the impulse radar, the th wavelets should be considered as noise. Fig. 4(c) illustrates the absolute value of the envelope for output wavelets. We defined the SNR for the transmission signal as (7) is the amplitude of the main wavelet, and is where the amplitude of the second wavelet. Accordingly, the effective pulsewidth of the output signal can be considered to be , as indicated by the arrowed line. To obtain an optimum , we caland the reciprocal pulsewidth culated the product of the in each . Fig. 5 plots the dependence of on . In the region of , increases monotonically with increasing , and when is over 0.8, it increases rapidly. Therefore, we decided a value for in the reas optimum. gion of We next considered the circuit configuration for the BPF. If ideal lumped elements are employed, an th-order BPF (e.g., can easily be fabricated using Chebyshev filter) with optimum values for , . However, it is difficult to achieve a lumped-element BPF in the millimeter-wave band because of parasitic capacitance and series resistance. We designed a BPF combining a distributed high-pass filter (HPF) and lowpass filter (LPF). Fig. 6 outlines the configuration for the BPF, which has one stage for the HPF and five stages for the LPF, and

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Fig. 5. Product of SNR

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

and 1= as function of cosine-rolloff factor .

Fig. 6. Configuration for BPF.

unit cells. In each stage, the shunt inductor and the capacitor are obtained by using a radial-line stub. The filter design technique using the radial-line stub has previously been discussed [15]. Since the frequency characteristics of a radial-line stub change slowly around the resonant frequency compared with that of a straight-line stub, it is suitable for a BPF with a cosine-rolloff curve. Here, the former three stages ( – ) in the LPF are used to obtain a cosine-rolloff curve of around 29 GHz, and the latter and ) are to suppress the residual signal at two stages ( higher frequencies ( 40 GHz) because of the extremely UWB impulse of 9 ps. We calculated the parameters for radial-line , capacitance , and line to obtain the required stub BPF characteristics. Fig. 7(b) plots the -parameter characteristics of the BPF. The insertion loss is 2.6 dB at a center frequency of 26.5 GHz. The attenuation at 24.0 GHz is 16.4 dB and 29.0 GHz at 26.4 dB. is also illusThe insertion loss curve simulated with trated. As we can see from this figure, there is good agreement between the simulated and measured results. Fig. 7(c) shows the insertion loss of the BPF in the full band. Those in higher and lower frequency bands were well suppressed. In particular, that in the lower frequency band ( 10 GHz), including the global positioning system (GPS) band where spectral regulation is extremely stringent, was less than 40 dB. Therefore, if we design the radiated power in the 24-GHz band to be less than 41.3 dBm defined by the FCC, the radiated power around the GPS band can be suppressed to be less than the defined spectrum mask ( 75.3 dBm). Fig. 8 shows the measured output pulse for the BPF when the impulse in Fig. 3 was input. The voltage ratio between the main wavelet and the second wavelet was more than 20 dB and the effective pulsewidth was less than 500 ps ( 0.15 m in air).

Fig. 7. (a) Chip microphotograph of the BPF. (b) Its S -parameter characteristics in the 24–29 GHz band and (c) in the full band.

Fig. 8. Output pulse of the BPF.

C. PA, RF SW, and LNA We will next describe the performance of the fabricated PA, RF SW, and LNA. As described in Section II, analog circuits such as amplifiers and RF SWs not only require high gain and isolation characteristics, but also flatness in the UWBs. Fig. 9(a) has a chip microphotograph of the PA and Fig. 9(b) plots its measured and simulated -parameter characteristics. The topology we chose is that of a four-stage distributed amplifier to obtain gain flatness in the UWB[12], [13]. The

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Fig. 9. (a) Chip microphotograph. (b) S -parameter characteristics of the PA.

unit cell illustrated in this figure has a cascade configuration. As we can see from this figure, we achieved a gain of 15 dB, a saturation power of 8 dBm at 26.5 GHz, and an extreme flatness less than the uncertainty of measurement ( 0.1 dB). ) were in good agreement with the The measured results ( simulated results. The chip area was 1.7 0.8 mm. The power dissipation was 0.04 W. We will next describe the performance of the SW, which is required to have both excellent isolation characteristics and lower insertion loss. Insertion loss is an especially important factor in UWB because it deteriorates the noise-figure characteristics of the receiver. Fig. 10(a) outlines the circuit configuration for the SW. The SW is a single-pole double-throw (SPDT) switch that has the circuit topology of a three-stage distributed switch. Insertion loss using shunt transistors is reduced more in the broadband than that with an SW composed of series transistors. There was at the gate input terminal to prevent also damping resistance RF signals from leaking. Fig. 10(b)–(d) shows a chip microphotograph of the SW, its isolation characteristics, and insertion loss. Simulated results were also included in the measured results. We can see from the graph that there is isolation of more than 35 dB (Tx antenna, Rx antenna), insertion loss of 1.9 dB, and a flatness of less than 0.1 dB (uncertainty of measurement). There is good agreement between the simulated and measured results. A switch driver with a 2V-LVCMOS interface was also built into the chip, and this obtained a very short switching time of less than 50 ps. The power dissipation was 0.09 W. The transmission power density in a UWB system is ultraweak due to limitations defined by equivalent isotropic radiated power (EIRP). The LNA is required to have both flatness in the band and considerably high gain. There is a chip microphotograph of the LNA and the measured -parameter characteristics in Fig. 11(a) and (b). The circuit topology is five-stage single ended with input and output matched to 50 . As shown in this figure, a gain of 40 dB and a flatness of less than 1 dB were obtained. The power dissipation was 0.04 W. We also report that LNA had a noise figure (NF) of approximately 2 dB at 24–26 GHz and had a minimum NF of 1.9 dB at 23 GHz [16]. These analog ICs support the RF configuration of our UWB-IR.

Fig. 10. (a) Circuit configuration. (b) Chip microphotograph. (c) Isolation. (d) Insertion characteristics of the SPDT switch.

D. S/H We will now describe the S/H circuit, where the most important policy on circuit design is to reduce voltage drop, so-called droop, due to the leak current from hold capacitance. An S/H circuit with large hold capacitance can generally hold data for a long time because the charge in capacitance is large enough to neglect leaking current. However, such a circuit cannot respond in the ultra-high-frequency region. Usually, an appropriate hold capacitance is chosen to take the bandwidth of RF signals and required hold time into consideration. There is a simis the input plified model of the S/H core in Fig. 12(a), where is the transconductance of , is the RF frequency, net leak current, and is the hold time [see Fig. 12(b)], which is defined as the time to decrease the hold voltage to 10%; the should be designed to satisfy

(8) In (8), the allowable region for decreases with inand the required hold time creasing input RF frequency . The input RF signal in our system is the wavelet oscillating at a center frequency of 26.5 GHz. The required hold time for using commercial A/D converters products, on the other hand, extends to several nanoseconds, and the ratio between the

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Fig. 13. (a) Block diagram of S/H circuit. (b) Operating principle.

Fig. 11. (a) Chip microphotograph. (b) LNA.

S -parameter

characteristics of the

Fig. 14. Circuit configuration for S/H core.

Fig. 12. (a) Simplified model of S/H core. (b) Definition of hold time.

input RF period and the required hold time comes to over one hundred. Although the allowable region for also depends on , , and , it is generally difficult to achieve in the above situation. Fig. 13(a) is a block diagram of the S/H circuit. To solve problems, we designed the S/H circuit with a two-stage configuration. The first-stage S/H circuit has small hold capacitance and is superior for high-speed operation. However, the droop time is relatively short. The second stage circuit has large capacitance and has a long droop time. Fig. 13(b) illustrates the operating principle. After the first stage circuit holds input data for a short time at the fall edge of CLK1, the second stage circuit holds output data (D1) from the first stage for a long time. Here, the timing difference ( , typically approximately 300 ps) between CLK1 and CLK2 should be enough small to neglect the droop in D1 (typically approximately 50 ps). Fig. 14 shows the circuit configuration for the S/H core circuit, which is comprised of the input buffer and S/H core. The through the input buffer, and RF signal is input to transistor a charge corresponding to the input RF level is held in hold ca. To suppress leaking current through , we pacitance employed a Gilbert-cell circuit as the input buffer instead of a conventional buffer using a simple source-coupled FET logic

(SCFL) circuit. When the S/H circuit is in sample mode (CLK is high level), the input buffer operates as an amplifier. When the circuit is in hold mode (CLK is low level), however, it operates indepenas a constant voltage source to fix the off state for dently of RF input. Therefore, this type of buffer is good for S/H operation compared with a conventional SCFL buffer. Fig. 15(a) shows a microphotograph and the size of the chip is 1.8 1.6 mm. The chip comprises both I-ch and Q-ch S/H circuits. Fig. 15(b) shows the measurement results for the I-ch outputs. A sinusoidal wave with a frequency of 27.0125 GHz was input as input data. A clock frequency of 100 MHz was chosen taking the next-stage A/D converter into consideration. As we can see from this figure, the S/H circuit could hold sample data for a few nanoseconds. The common level of the outputs was . Therefore, 2.4 V, and the full scale was approximately 1.0 we can utilize an A/D converter as the next stage circuit, which has performance of 100 MHz and 14-bit resolution. The power dissipation was 1.1 W. IV. RF MODULE We also tried to mount the RF chipset in a module. Fig. 16(a) shows photographs of the RF modules, which consist of three modules (PG, SW, SH) that were mounted on the printed circuit board (PCB) bias supply board through the surface mounting connector. The PG module includes the PG IC, and and has a -band connector for extremely UWB outputs . The SW module includes the BPF, PA, SW, LNA ICs, and the SH module includes the BPF, pre-amplifier, S/H ICs, and also a Wilkinson 90 divider to divide the signal into I-ch and Q-ch. Each module is connected directly via a coaxial

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TABLE I CHIP SPECIFICATIONS

Fig. 15. (a) Chip microphotograph. (b) Input clock and I-ch outputs of the S/H circuit.

connection to a computer, and a monitor terminal for PG output. We tested its operation in measuring distance. We chose a reflector plate as the object to test, which has a radar cross section the same as that of an ordinary vehicle. Fig. 15(c) shows a distance measurement test, when the reflector plate being tested was at a distance of 8 m. As we can see from this figure, the plate was successfully detected. We could also detect the plate from 0.05 to 10 m with an accuracy of 0.05 m. We can also see some spikes in the 3–7-m range were observed. These spikes were detected even if the reflector plate was eliminated. Reflections from the wall, ceiling, and floor can be speculated to be one cause. The effects of the reflections from these stationary objects could be eliminated with a software process after the reflections from these objects in the radar scan area were obtained as calibration data. V. SUMMARY

Fig. 16. (a) Photograph of RF module. (b) UWB short range radar equipment. (c) Example distance measurement test.

connector. The module sizes are 26.7 16.5 12.6 mm for PG, 34.0 21.0 12.6 for SW, and 26.0 37.5 12.6 for SH. Finally, we will introduce the prototype of the UWB short-range radar equipment mounted in the RF modules described above and the baseband signal processing board. Fig. 15(b) shows a photograph of the radar equipment. It has a horn antenna with 15-dBi gain, a USB terminal to enable

A novel architecture for UWB-IR was developed using 0.13- m InP-HEMT technology. The chip specifications are summarized in Table I. These ICs are targeted at quasi-millimeter-wave UWB short range radar systems. The transmission pulse was generated by filtering an extremely sharp pulse of 9 ps. The transfer function of a cosine-rolloff BPF was optimized to obtain a shorter output wavelet, and a wavelet width of 500 ps was obtained. The gain flatness of the PA was 0.1 dB (measurement uncertainty) and that of the LNA was 1 dB, despite the high gain of 40 dB for the LNA. An isolation of more than 35 dB and an insertion loss of 1.9 0.1 dB (measurement uncertainty) for the SW IC were also obtained. These RF ICs make a simple matched filter configuration possible without the use of a conventional correlator composed of a local oscillator. RF modules employing these ICs and a prototype of the radar equipment were also developed and we demonstrated their operation in distance measurement. ACKNOWLEDGMENT The authors would like to thank Dr. H. Ogawa, Director of Yokosuka Radio Communications Research Center, National Institute of Information Communication Technology (NICT),

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Kanagawa, Japan, and Prof. R. Kohno, Yokohama National University, Yokohama, Japan, for fruitful discussions and support for this research. REFERENCES [1] “First report and order,” FCC, Washington, DC, FCCO2.V48, Apr. 2002. [2] H. Y. Liu, C. C. Lin, Y. W. Lin, C. C. Chung, K. L. Lin, W. C. Chang, L. H. Chen, H. C. Chang, and C. Y. Lee, “A 480 Mb/s LDPC-COFDMbased UWB baseband transceiver,” in Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2005, pp. 444–445. [3] S. Iida, K. Tanaka, H. Suzuki, N. Yoshikawa, N. Shoji, B. Griffiths, D. Mellor, F. Hayden, I. Butler, and J. Chatwin, “A 3.1 to 5 GHz CMOS DSSS UWB transceiver for WPANs,” in Int. Solid-State Circuits Conf. Tech. Dig., 2005, pp. 214–215. [4] A. Ismail and A. Abidi, “A 3.1 to 8.2 GHz direct conversion receiver for MB-OFDM UWB communications,” in Int. Solid-State Ciircuits Conf. Tech. Dig. , 2005, pp. 208–209. [5] C. H. Yang, K. H. Chen, and T. D. Chiueh, “A 1.2 V 6.7 mW impulseradio UWB baseband transceiver,” in Int. Solid-State Ciircuits Conf. Tech. Dig., 2005, pp. 442–443. [6] Y. Kawano, Y. Nakasha, K. Yokoo, S. Masuda, T. Takahashi, T. Hirose, Y. Oishi, and K. Hamaguchi, “RF chipset for impulse radio UWB using 0.13 m InP-HEMT technology,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 316–319. [7] H. Ogawa, K. Hamaguchi, Y. Yamamoto, T. Hirose, T. Kobayashi, and R. Kohno, “Technology development of short range ultrawide-band radar system,” in Proc. IEEE Joint UWBST/IWUWBS, May 2004, pp. 351–355. [8] I. Gresham, A. Jenkins, R. Egri, C. Eswarappa, F. Kolak, R. Wohlert, J. Bennett, and J. P. Lanteri, “Ultra wide band 24 GHz automotive radar front-end,” in IEEE MTT-S Int. Microw. Symp., 2003, pp. 369–372. [9] R. J. Fontana, “Recent system applications of short-pulse ultra-wideband (UWB) technology,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2087–2104, Sep. 2004. [10] K. Makiyama, T. Takahashi, T. Suzuki, K. Sawada, T. Ohki, M. Nishi, N. Hara, and M. Takikawa, “Improvement of circuit-speed of HEMTs IC by reducing the parasitic capacitance,” in Int. IEEE Electron Device Meeting Tech. Dig., 2003, pp. 30.6.1–30.6.4. [11] T. Suzuki, Y. Nakasha, T. Takahashi, K. Makiyama, T. Hirose, and M. Takikawa, “144-Gbit/s selector and 100-Gbit/s 4 : 1 multiplexer using InP HEMTs,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 117–120. [12] M. A. Richard, Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005, p. 161. [13] M. Sato, H. Shigematsu, Y. Inoue, T. Arai, K. Sawada, T. Takahashi, K. Makiyama, and T. Hirose, “1.4-THz gain-bandwidth product InPHEMTs preamplifier using an improved Cherry–Hooper topology,” in IEEE GaAs IC Symp. Tech. Dig., 2002, pp. 167–170. [14] S. Masuda, T. Takahashi, and K. Joshin, “An over-110-GHz InP HEMT flip-chip distributed baseband amplifier with inverted microstrip line structure for optical transmission system,” IEEE J. Solid-State Circuits, vol. 38, no. 9, pp. 1479–1484, Sep. 2003. [15] D. W. Gardner and M. A. Wickert, “Microwave filter design using radial line stubs,” in IEEE Region 5 Conf., 1988, pp. 68–72. [16] S. Masuda, T. Ohki, and T. Hirose, “Very compact high-gain broadband low-noise amplifier in InP HEMT technology,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 77–80.

Yoichi Kawano was born in Oita, Japan, in 1974. He received the M.E. and D.E. degrees in quantum engineering from Nagoya University, Aichi, Japan, in 2000 and 2003, respectively. In 2003, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan.

Yasuhiro Nakasha (M’04) was born in Aichi, Japan, in 1964. He received the B.E. and M.E. degrees in electrical engineering from Nagoya University, Nagoya, Japan, in 1987 and 1989, respectively. In 1989, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan, where he is engaged in research and development on high-speed ICs using compound semiconductor heterostructure devices for communication systems.

Kaoru Yokoo was born in Chiba, Japan, in 1977. He received the M.E. degree in electronic engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 2002. In 2002, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan.

Satoshi Masuda (M’99) was born in Tokyo, Japan, in 1971. He received the B.E. and M.E. degrees in electrical engineering from Waseda University, Tokyo, Japan, in 1995 and 1997, respectively. In 1997, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan, where he has been engaged in research and development of millimeter-wave monolithic ICs. His current research interests include modeling of active and passive components, millimeterwave monolithic IC design, and flip-chip packaging. Mr. Masuda was the recipient of the 2002 Best Paper Award presented at the IEEE GaAs IC Symposium, the 2004 Young Award presented at the International Conference on Electronics Packaging (ICEP) from the IEEE Components, Packaging, and Manufacturing Technology (CPMT) Japan Chapter, the 2004 Microwave Prize presented at the 34th European Microwave Conference (EuMC), and the 2006 Young Scientists’ Prize presented by the Minister of Education, Culture, Sports, Science, and Technology.

Tsuyoshi Takahashi was born in Tochigi, Japan, in 1963. He received the B. E. and M. E. degrees in science and engineering from the University of Tsukuba, Tsukuba, Japan, in 1985 and 1987, respectively. In 1987, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan, where he has been engaged in research on fabrication technology for InP-based HEMTs and InGaP-emitter heterojunction bipolar transistors (HBTs).

Tatsuya Hirose (M’00) received the B.E. degree from Tokyo Denki University, Tokyo, Japan, in 1987, the M.E. degree from Hokkaido University, Sapporo, Japan, in 1989, and the Ph.D. degree from Tohoku University, Sendai, Japan, in 2004. In 1989, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan, where he has engaged in research on design and modeling of HEMTs and development of monolithic microwave integrated circuits (MMICs) base on their technologies. His current research interest includes high-speed and highfrequency ICs for automotive radar sensors and wireless communication systems. Dr. Hirose was the recipient of the 2003 Outstanding Young Engineer Award of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

KAWANO et al.: RF CHIPSET FOR IMPULSE UWB RADAR USING 0.13- m InP-HEMT TECHNOLOGY

Yasuyuki Oishi received the B.S. degree in applied physics from the University of Tsukuba, Tsukuba, Japan, in 1984. In 1984, he joined Fujitsu Laboratories Ltd., Atsugi, Kanagawa, Japan, where he has been engaged the research and development for mobile communication systems. Mr. Oishi is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

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Kiyoshi Hamaguchi (M’00) received the B.Eng. and M.Eng. degrees in electrical engineering from the Science University of Tokyo, Tokyo, Japan, in 1989 and 1991, respectively, and the D.Eng. degree from Osaka University, Osaka, Japan, in 2000. Since 1993 he has been with the National Institute of Information and Communications Technology (formerly the Communications Research Laboratory), Kanagawa, Japan, where he has been engaged in research and development on digital radio mobile communications and multimedia wireless systems. From 2002 to 2003, he was a Visiting Researcher with the University of Southampton, Southampton, U.K. Dr. Hamaguchi is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 1997 Young Engineer Award presented by the IEICE, the 2004 YRP Award presented by the YRP Research and Development Promotion Committee, and the 2006 Young Scientist Award from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

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Study of 2-bit Antenna–Filter–Antenna Elements for Reconfigurable Millimeter-Wave Lens Arrays Chih-Chieh Cheng, Student Member, IEEE, and Abbas Abbaspour-Tamijani, Member, IEEE

Abstract—This paper presents a new reconfigurable antenna–filter–antenna (AFA) element based on slot antennas and switchable resonators. This reconfigurable AFA can operate in four modes of operation as a three- or four-pole filter, and yields a 2-bit variable phase delay. As a result, the multimode AFA can be used as the building block of 2-bit adaptive lens arrays. This paper details design, modeling, and miniaturization of the reconfigurable AFA, and demonstrates its performance through preconfigured prototypes. The proposed AFA has a loss of 1.4–1.6 dB measured at 32 GHz in both three- and four-pole filter modes, and exhibits a frequency response that is almost insensitive to the angle of incidence. Several proof-of-concept fixed lens arrays have been also fabricated for output beams scanned to 0 , 15 , 30 , 45 , and 60 in the - and -plane. The measurement results show that the output beam can be scanned to 60 in both principle planes, with a worst case sidelobe level of less than 11 dB and a scan loss that hardly exceeds the theoretical limit. Index Terms—Antenna–filter–antennas, beam steering, frequency-selective surface (FSS), microelectromechanical systems (MEMS) antennas, phase shifters, reconfigurable antennas.

I. INTRODUCTION

I

N millimeter-wave frequencies (30–300 GHz), beam forming is usually achieved by using antenna arrays with free-space feeding schemes, commonly known as quasi-optical systems. Space-feeding eliminates the loss and parasitic effects of the conventional (constrained) feed networks and can dramatically improve the radiation performance. Free-space beam-forming arrays can be realized as transmission type (lens arrays) [1] or reflection type (reflect arrays) [2]. In both cases, the array elements are designed to compensate the spherical phase error of an input wave generated by the low-gain feed antenna and produce a directive output beam. Inexpensive beam-steering systems can be implemented using fixed arrays either by mechanical rotation of the array (in the case of reflect arrays) or through using multiple feed antennas (matrix) and an RF switch. These methods are extensively used in commercial radars and multibeam satellite communication antennas [3]–[5]. A fully electronic high-resolution scanning, however, requires integration of phase-shifting devices within the array elements to form reconfigurable arrays. A reconfigurable array

Manuscript received April 14, 2006; revised August 30, 2006. This work was supported by the National Science Foundation under Award ECS-0524805. The authors are with the Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885993

eliminates the feed matrix and can overcome the scanning degradations due to the phase aberration of the fixed arrays for off-axis feed positions. However, due to the large number of elements and small cell area in millimeter-wave arrays, the only viable scenario for implementing the phase-shifting capability is resorting to fully integrated architectures. Implementation of quasi-optical array with built-in phase shifters using solid-state and microelectromechanical systems (MEMS) technology has been a subject of research at least since the late 1980s, and has been addressed by a number of researchers. Probably the first reported implementation of an integrated free-space beam-steering system can be found in a paper by Lam et al. published in 1988 [6], demonstrating a reflective phase-shifting grid of 1600 Schottky barrier diodes with a maximum phase shift of 70 and 7-dB loss at 93 GHz. The authors theorize the use multilayer grids for realizing larger phase shifts and one- or two-directional beam steerers. Later, Sjogren et al. [7] demonstrated a reflective 8640 Schottky diode grid with 60 flat amplitude phase shift and 3.5-dB loss at 132 GHz, and for the first time reported the measured performance of the grid for beam steering ( 16 scan width), focusing ( 7-dB focusing gain), and polarization control ( 12-dB change in axial ratio). Reference [8] reports a grid with improved diode design that could achieve 130 reflective phase shift and 2.7-dB loss at 62 GHz. The major limitations associated with the use of Schottky diodes are the large series resistance, inadequate capacitive ratio, and dc power consumption. In this respect, MEMS switches present ideal substitutes for the Schottky diodes for alleviating these limitations. The earliest conception of a reconfigurable array based on MEMS switches can be tracked to 1994 in a paper by Chiao and Rutledge [9]. In this paper, the authors propose a quasi-optical transmittive beam steerer as a two-dimensional (2-D) array of switch-loaded rectangular (or rhombic) waveguides. The waveguide array is constructed using a stack of lapped silicon wafers (slices), each containing an array of metallized micromachined holes (waveguide sections). DC contact MEMS switches are fabricated on SiO N membranes and are used to implement a switchable capacitive/inductive septum inside each waveguide section. By selectively biasing the switches, a quantized phase shift of 0 –360 can be obtained from a multiwafer structure. Although interesting in concept, the system is next to impossible to fabricate, at least due to the difficulties associated with three-dimensional (3-D) biasing and control, and stress control and stiction in the membrane [10]. The early onset of grating lobes and surface wave modes due to that the large distance between elements also limits the scanning width [11]. In 1999, Mazotta et al. [10] used a modified method, based on TEM

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CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS

waves and a series of metallic screens, also loaded with switchable reactive loads. The concept was verified for single layer arrays at 3 GHz using discrete p-i-n diode switches, and at 5 GHz using conductive tapes (to simulate MEMS switches in up and down states). Steering angles of up to 20 and 12.5 and insertion losses of 6 and 2 dB were measured for 3- and 5-GHz arrays, respectively. A later study [12] demonstrated functions such as focusing, scanning, and beam splitting using preconfigured prototypes at 5 GHz. With a reported insertion loss of 2 dB for a 45 phase shift per grid, the insertion loss of a eightfold 3-bit 360 system is estimated to be 16 dB at only 5 GHz, suggesting that multigrid techniques are not suitable for millimeter-wave application. In this paper, we investigate a new reconfigurable MEMS lens array comprised of reconfigurable antenna–filter–antenna (AFA) elements. AFAs are three-layer metallic structures composed of receive and transmit antennas and interconnecting resonant circuits, and acts as filters with radiation ports. Reference [11] describes a class of AFA elements based on microstrip antennas and coplanar waveguide (CPW) resonators and demonstrates their application for constructing frequency-selective surfaces (FSSs). These AFA elements have also been demonstrated in nonuniform array configurations for implementing fixed lens arrays [13], [14]. To form a fixed lens array, the AFA elements are stagger tuned to implement a location-dependent phase-delay function. A lens array with beam-forming capability can be formed as an array of reconfigurable AFA elements. A multimode bandpass AFA element composed of slot antennas and stripline resonators has been demonstrated in [15]. This element is designed to toggle between four different modes of operation using five series switches built into the resonator layer. A reconfigurable AFA of this type functions as a 2-bit filter/phase-shifter module with radiative ports, and can be used as the building block of a digital reconfigurable lens array. The simple switching scheme and the confinement of the switches to the middle layer renders this structure very suitable for fabrication as a self-packaged monolithic array. In this paper, we detail the underlying concepts and design methodology for the 2-bit AFA element reported in [15], and present an improved design based on stepped-impedance resonators and slot antennas [16]–[18]. The new design is considerably more compact and dramatically improves the scanning capability. A complete circuit model is presented and used for simulation and optimization of the AFA elements. The performance of the proposed AFA is demonstrated experimentally through fixed uniform arrays in the form of FSSs and lens-array prototypes configured for beams at 0 , 15 , 30 , 45 , and 60 in both - and -planes. II. RECONFIGURABLE AFA ELEMENTS A. Basic Concept A reconfigurable AFA can be formed using fixed receive and transmit antennas and a reconfigurable resonator middle layer. Fig. 1 shows the AFA structure based on two layers of 381- m -thick Roger’s 5880 microwave laminate ( , ) and three 18- m-thick layers of electroplated copper.

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Fig. 1. (a) AFA array structure based on two Rogers 5880 laminates and 3001 bonding film. (b) Three layers of the AFA element.

Fig. 2. Reconfigurable stripline middle-layer composed of line segments, capacitive gaps, and series switches.

The top and bottom metal layers contain the slot antennas that function as the first and last resonators of the AFA. The middle layer accommodates the stripline resonators. An incident wave with proper polarization is received by the top slot antenna in the input side, passes through an active (switched on) stripline resonator sub-circuit, and reradiates from the bottom slot antenna on the output side with orthogonal polarization. The topology of the middle layer of the AFA is presented in Fig. 2, where transmission-line segments, switches, and coupling capacitors are denoted by , , and , respectively. Fig. 3 shows the resonator configurations in different modes of operation. In each mode, subsets of the t-line segments are configured through the active switches to form a resonant circuit between the top and bottom slot antennas. In modes 1 and 2 [see Fig. 3(a) and (b)], the AFA element functions as a threepole filter, as it consists of two resonant antennas and a single stripline resonator. Modes 3 and 4 [see Fig. 3(c) and (d)], on the other hand, can be recognized as four-pole filters, as they

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for modes 1 and 2 and where we have used modes 3 and 4. The phase differences can be written as

for

(3) which indicates that, in its four modes of operation, the reconfigurable AFA can provide all of the phase values required for 2-bit phase shifting. Although the phase relationships in (3) are exact only at the center frequency, simulation of the phase response shows that they are valid within 10% for the entire passband of the three- and four-pole filters (see Section II-B). B. Design Method and Circuit Model Fig. 3. Four modes of the operation of the AFA. (a) Mode1: S on, other switches off, R and R are active and the rest of the resonators are inactive. (b) Mode2: S on, other switches off, resonators R and R are active and the rest of the resonators are inactive. (c) Mode3: S , S on, others switches off, resonators R , R , R and R are active and the rest of the resonators are inactive. (d) Mode4: S , S on, other switches off, resonators R , R , R and R are active and the rest of the resonators are inactive. Phase delays are indicated for each mode.

each contain a pair of capacitively coupled (through or ) stripline resonators and the antennas. From the above description, it is evident that a 1-bit phase control (0 or 180 ) can be readily achieved by inverting the direction of the polarization rotation through switching between modes 1 and 2 or 3 and 4. We now show that a second bit of phase control (an additional 90 ) is attainable by switching from mode 1 to mode 3 or from mode 2 to mode 4. First, let us remember from basic filter theory that a lossless bandpass filter presents a purely reactive behavior at dc, resulting in . Since the transmission coefficients in modes 1 and 2 and modes 3 and 4 are 180 out-of-phase, we take the liberty of indexing the modes so that

(1) denotes the AFA transmission coefficient in mode where . Also, we notice that for an -pole filter (with no transmission zeros), the total variation of the phase of the transmisbetween dc and the upper rejection band is equal to sion . The phase variation between dc and center frequency is half of this value, i.e., . Combining this with (1), we can write

(2)

The advantage of utilizing slot antennas is their potential to result in very low-loss arrays [19]. The slot lengths are designed for resonance at the center of the operation band and the slot widths are adjusted for the required value of radiation bandwidth of the filter). The polarization rotation be(equivalent to tween input and output is necessary for three reasons, which are: (1) to prevent the formation of transmission zeros as a result of direct coupling between the top and bottom antennas; (2) to provide a mechanism for achieving 1-bit phase shift through selecting the direction of the rotation; and (3) to block the disturbance caused by the spillovers of the feed antenna. The t-line segments in the middle layer (Fig. 2) are positioned so as to achieve the required value of coupling with the slots. The coupling coefficient can be controlled by the length of the portion of the stripline that is exposed to the slot antenna and the distance of the coupling region from the center of the slots. The topology of the stripline structure is derived based on circuit concepts, but fine tuning of the layout heavily relies on full-wave finite-element method (FEM) simulations. This is primarily due to the presence of mutual coupling and the critical tradeoffs involving the inter-modal isolations and geometrical compactness. However, understanding the parasitic coupling mechanisms and an insightful handling of the layout parameters can streamline the layout optimization process. Circuit models prove invaluable in understanding the design tradeoffs, and evaluating the effects of parasitics. Switches that cannot be easily included in the electromagnetic model may also be readily incorporated into the circuit model. Notional circuit models for three- and four-pole AFA topologies are given in [15]. A complete circuit model of the multimode AFA can be formed as shown in Fig. 4, where the slot antennas are modeled by parallel RLC circuits and the stripline middle layer is modeled by t-line segments. Transformers represent the coupling between antennas and resonators, and capacitors model the coupling gaps between the stripline resonators used in four-pole in the configurations. Switches are modeled by capacitors in the on state (Fig. 5). Parasitic off state and by resistors capacitors and model the gap in the stripline where the switches are embedded. The model parameters can be determined by FEM simulations of the complete geometry and/or

CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS

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Fig. 4. Complete circuit model of the 2-bit reconfigurable AFA.

Fig. 6. Simulated frequency response of AFA for in different modes of operation. (a) Amplitude. (b) Phase. Fig. 5. Model of switches in: (a) off state and (b) on state.

TABLE I MODEL PARAMETERS FOR THE RECONFIGURABLE AFA

2, and by 0.2–0.7 dB in modes 3 and 4. It was found that the can cause a noticeable distortion in the off-state capacitor frequency response, which is more pronounced in the three-pole modes of operation. However, this effect maybe compensated by minor adjustments in the lengths of the t-line segments for up to 10 fF. These values of and are atvalues of tainable using typical high-isolation MEMS cantilever switches [20], [21]. C. Measurement Results

partial structures. Table I shows the values of the model paramand are typical eters for the AFA element of Fig. 2. values chosen to represent a small cantilever dc contact MEMS switch similar to the one reported [20]. Fig. 6 presents the simulated frequency response of the 32-GHz AFA in its different modes of operation. FEM simulations are performed for normal incidence. Periodic boundary conditions are used to emulate the array environment and to account for the effects of mutual coupling. Switches are replaced by perfect conductor strips in the on state and by 75- m gaps in the off state. Circuit model simulations are also given for and are set to zero to comply with the comparison. FEM simulation. The effect of switch imperfections can be easily evaluated using the circuit model. Simulations show that for , the insertion loss increases by 0.1–0.4 dB in modes 1 and

To verify the design and simulation method, uniform arrays of the proposed AFA were fabricated in three- and four-pole configurations using a standard printed circuit board (PCB) process. The periodic arrays of this type may be considered as FSS structures and can be easily characterized using the method described in [11]. The measurement setup consists of an Agilent 8510C vector network analyzer and two hard horns [22], which act as transitions between the coaxial input/output and planar wavefronts. A free-space thru-reflect-line (TRL) calibration and time gating are applied to eliminate the effects of cables, connectors, and hard horns and the residual errors of the higher order modes. The measured transmission and reflection coefficients for normal incidence have been given in [15] for three- and four-pole FSS structures. The normal incidence responses are quite similar to the simulated results of Fig. 6, except for the insertion loss of that is nearly 1 dB higher in both cases. The performance of these FSS structures, however, is very sensitive to angle of incidence and quickly deteriorates for oblique incidence. Fig. 7 shows the transmission response of the four-pole

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Fig. 7. Measured transmission coefficient of the four-pole FSS for different angles of incidences. Fig. 8. Layout of the compact AFA element with stepped-impedance resonators.

FSS for different angles of incidence. It is observed that scanning by only 30 drastically distorts the frequency response and introduces a transmission zero at 34 GHz. This situation can become very problematic in large-aperture lens arrays with , and even for large values of can small values of limit the scan width. In Section III, we propose an improved AFA design that can mitigate this difficulty. III. COMPACT STEPPED-IMPEDANCE AFA ELEMENT A. Floquet-Mode Analysis Deterioration of the frequency response for oblique incidence can be explained using Floquet’s theory [23]. When one of the Floquet modes (i.e., the modes of the periodic array) coincides with a guided mode of the structure, a resonance phenomenon occurs that manifests in the form of a transmission zero. In multilayer structures the guided modes are the surface waves. In the current case, where the dielectric structure is confined between two metallic sheets, the guided modes are those of the resulting parallel plate waveguide. The frequency of the lowest order resonance can be calculated from

(4) where is the speed of light, is the periodicity, is the relative is the incidence angle. The permittivity of the substrate, and lowest order mode can be excited by an incident wave scanned in either - or -planes. Equation (4) can be viewed as a relationship between the lowest transmission zero of the AFA frequency response and mm the scan angle. For the AFA element of Fig. 2 with , the transmission zero for 30 incidence is calcuand lated at 33.1 GHz, which is within 3% of the measured value (see Fig. 7). The error is believed to be due to the tolerance of the dielectric constant. In single-polarized structures, the Floquet mode resonances may not be encountered for structures excited by incidence in the -plane, as the coupling between the Floquet mode and the

guided mode is minimized. With the current AFA array, however, there is not a distinction between - and -plane scans due to the polarization rotation between input and output. An incident wave in the -plane generates a transmitted wave in the -plane and vice versa so that the resonance always occurs at least on one side of the array. In the lens array configuration, however, only one side of the array sees a plane wave and obeys Floquet’s theorem. As a result, the transmission zero is present when the lens is configured for an -plane scan, but not when it is configured for an -plane scan. This conclusion complies with the results reported in [15] for 2-bit lens-array prototypes. B. Improved AFA Element Using Stepped-Impedance Resonators Besides using a low substrate, the onset of the Floquet mode resonance can only be deterred by reducing the grid length through using smaller unit cells [24]. The AFA element of Fig. 2 can be considerably miniaturized by using stepped-impedance concepts to reduce the length of stripline resonators and slot antennas. For the slot antennas, miniaturization is achieved by reducing the slot width in the middle region and increasing the width in the ends [18]. For the stripline resonators, the resonant length can be reduced by widening the lines at the open ends and reducing their width in the middle [17]. In both cases, these modification increase the effective values of capacitance and inductance in the predominantly capacitive and predominantly inductive regions, respectively. The layout of the modified AFA element is shown in Fig. 8. This compact element can reduce the cell area by 50% and by 30%. Using mm and in (4), the transmission zero is calculated at 38 GHz, which is with a large margin above the frequency band of operation. As a result, the AFA array is expected to show a much better performance for oblique incidence. Fig. 9 shows the measured frequency response of the compact AFA for incident waves at 0 , 15 , 30 , and 45 . The improved design shows an extremely stable amplitude response in both three- and four-pole configurations. The phase

CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS

Fig. 9. Measured frequency response of the compact AFA in three- and fourpole configurations for different angles of incidence. (a) Amplitude. (b) Phase.

response is also quite consistent in the three-pole mode, but it shows nearly 40 variation in the four-pole configuration. IV.

-BAND ADAPTIVE LENS ARRAY

The phase offsets existing between the different modes of operation of the reconfigurable AFA can be utilized to generate a 2-bit adaptive lens array. Elements in the lens array are configured to compensate for the spherical phase delay of the input wavefront and generate a phase distribution corresponding to the desired output wavefront. For a single beam output, the output phase will be a 2-bit approximation of a planar phase distribution. The state of each AFA element in the array can be calculated based on the location of the element in the array, focal distance, output phase, and operation frequency. In a real adapat tive lens array, the decision on the states of the element coordinates is made dynamically using the following equation for the mode index : (5) where is the focal distance, is the free-space wavenumber, is the desired output phase. indicates and equality in modules of 360 and within an error of 45. To verify the capability of the AFA elements for producing adaptive lens arrays, five 32-GHz lens arrays were fabricated with the AFA elements configured to produce output beams at 0 , 15 , 30 , 45 , and 60 from a spherical input wave emanating at a focal distance of 12 cm. By exchanging the role of

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Fig. 10. Map of the state of the AFA elements in the adaptive lens array for different positions of the output beam.

input and output sides, a single set of array prototypes can be used to characterize beam steering in both - and -planes. 1021 AFA elements are arranged on a rectangular grid to form a circular array with diameter of 12 cm and a total effective area of 104 cm . Fig. 10 shows the modal arrangement of the AFA elements for different beam angles. Fig. 11 shows the measured radiation patterns for arrays with beams scanned in the -plane. Simulated results are also included for comparison. These simulations are based on the simplistic approach described in [14]. The measured patterns show an overall good agreement with the simulations. The discrepancy in the location of the main beam is within 10 and is believed to be mainly due to the human errors in the placement and orientation of the arrays (as the lens prototypes must be replaced for each measurement). The measured patterns for the -plane scan are given in Fig. 12. The simulation results are identical to the previous case, as the simulation method cannot differentiate the - and -plane scans. Some important data related to the radiation performances for different beam positions are summarized in Table II. The scan loss at 60 is nearly 4 dB in the -plane, which is only 1 dB more than the theoretical cosine scan loss of an ideal aperture. Besides the additional phase errors that might be introduced due to the nonideal operation of the AFA elements at 60 , the element pattern is believed to contribute to the scan loss. Scan loss in the -plane is 6 dB for a 60 scan, which is in perfect agreement with the theoretical value, taking into account the cosine scan loss of the aperture and the cosine pattern of the short slot antennas. The lower value of gain in the 0 scan compared to 15

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Fig. 11. Measured radiation pattern of the lens array with the beam scanned in the E -plane. (a) 0 . (b) 15 . (c) 30 . (d) 45 . (e) 60 scan.

is counterintuitive. Part of this discrepancy may be attributed to the misalignment of the main beam of antenna under test and the measurement plane. It is also possible that the lower gain of the 0 scan case is caused by the edge diffraction from the array boundary, which can have a subtractive effect in the boresight. The measured polarization ratio is better than 20 dB in all of the studied cases. The discrepancy between gain and polarization ratio in - and -planes at zero scan is believed to be due to the measurement errors. It is also interesting to investigate the efficiency of the proposed lens array. The theoretical aperture directivity for the aperture area of 104 cm is equal to 31.75 dBi at 32 GHz. The maximum gain of the lens array is 26.5 dBi, measured for the -plane scan of 15 . There is a good reason to believe that this is close to the actual gain for the 0 scan should the effect of edge diffraction and misalignment be eliminated from the measurements. A systematic power analysis using the simulation method of [14] has been used to determine different components of the loss. The result of this analysis is summarized in Table III. The spherical taper loss refers to the effect of the aperture taper caused by the longer distance and off-boresight angle of edge elements relative to the feed. This effect is shared by all planar lens arrays. Aperture phase-error loss reflects the effect of the quantization error of the 2-bit phase shifters, and the insertion loss

Fig. 12. Measured radiation pattern of the lens array with the beam scanned in the H -plane. (a) 0 . (b) 15 . (c) 30 . (d) 45 . (e) 60 scan. TABLE II SCANNING PERFORMANCE

is the loss of the AFA elements. These two components can be recognized as the design-specific loss of the adaptive lens-array structure, collectively amounting to 2.25 dB. By assuming an increase of nearly 0.55 dB corresponding to switch resistance of 1 (averaged for three- and four-pole modes, see Section II-B), this loss component is expected to remain less than 3 dB. The remaining 2.45-dB loss is related to effect of the 16-dB feed horn used for the measurements. This loss can be reduced to approximately 0.6–0.8 dB through using an optimally designed 4 4 focal plane array. As the AFA elements are primarily bandpass filters, the adaptive lens array exhibits a bandpass frequency response. Fig. 13 presents the simulated gain of the array for 0 scan. The actual measured frequency response of the AFA elements has been used in this simulation. The result is a frequency response that

CHENG AND ABBASPOUR-TAMIJANI: STUDY OF 2-bit AFA ELEMENTS FOR RECONFIGURABLE MILLIMETER-WAVE LENS ARRAYS

TABLE III LENS-ARRAY LOSS ANALYSIS

Fig. 13. Simulated gain as a function of frequency of the lens array.

can be considered as the average of the three- and four-pole responses of Fig. 9. The added slope of the gain response can be attributed to the increase in the electrical area of the lens at higher frequencies (20 dB/dec 0.27 dB/GHz at 32 GHz). V. CONCLUSION A novel reconfigurable AFA element has been proposed that can be used to construct adaptive lens-array antennas. Preconfigured lens-array prototypes using this AFA elements suggest the possibility of a high-performance scanning in both the and -planes, comparable with the best fixed beam lens-array designs. The total loss due to the 2-bit phase quantization error and switches is estimated be less than 3 dB. Considering the structural simplicity of the switchable resonator topology and the minimal number of switches, the proposed AFA array presents a suitable design for implementation of wafer-scale integrated beam-forming systems based on MEMS or p-i-n diode switch technologies. A full-scale adaptive array with integrated MEMS switches is currently under investigation. ACKNOWLEDGMENT The authors wish to thank Prof. A. Mortazawi, The University of Michigan at Ann Arbor, for providing the hard horns, and S.-H. Hsu, Texas A&M University, College Station, for performing the pattern measurements. The authors also wish to thank Prof. J. Aberle, Arizona State University, Tempe, for reviewing this paper’s manuscript and Prof. L. Lunardi, National Science Foundation, Arlington, VA, for providing the support for this project.

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REFERENCES [1] D. T. McGrath, “Planar three-dimensional constrained lens,” Electron. Lett., vol. 32, pp. 2109–2111, Nov. 1986. [2] D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag., vol. 45, no. 2, pp. 287–296, Feb. 1997. [3] D. Popovic and Z. Popovic, “Multi-beam antennas with polarization and angle diversity,” IEEE Trans. Antennas Propag., vol. 50, no. 5, pp. 651–657, May 2002. [4] S. Hollug, A. E. Cox, and Z. B. Popovic, “A bi-directional quasi-optical lens amplifier,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 12, pp. 2352–2357, Dec. 1997. [5] W. Menzel, D. Pliz, and M. Al-Tikriti, “Millimeter-wave folded reflector antennas with high gain, low loss, and low profile,” IEEE Antennas Propag. Mag., vol. 44, pp. 24–29, Jun. 2002. [6] W. Lam, C. Jou, H. Chen, K. Stolt, N. Luhmann, and D. Rutledge, “Millimeter-wave grid phase-shifters,” IEEE Trans. Microw. Theory Tech., vol. 36, no. 5, pp. 902–907, May 1988. [7] L. Sjogren, H. X. Liu, X. Qin, C. Domier, and N. Luhmann, Jr., “Phased-array operation of a diode-grid impedance surface,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 4, pp. 565–572, Apr. 1994. [8] X. Qin, W. Zhang, C. Domier, N. Luhmann, Jr., W. Berk, S. Duncan, and D. Tu, “Monolithic millimeter-wave beam control array,” in IEEE MTT-S Int. Microw. Symp. Dig., 1995, pp. 1669–1672. [9] J. C. Chiao and D. B. Rutledge, “Microswitch beam-steering grid,” in Proc. Int. Millim. and Submillim. Waves and Applicat. Conf., Jan. 1994, pp. 537–538. [10] J. Mazotta, M. DeLisio, and J. C. Chiao, “Quasi-optical discrete beamsteering grids,” in IEEE MTT-S Int. Microw. Symp. Dig., 1999, pp. 1825–1828. [11] A. Abbaspour-Tamijani, K. Sarabandi, and G. M. Rebeiz, “Antenna–filter–antenna arrays as a class of bandpass frequency selective surfaces,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1781–1789, Aug. 2004. [12] J. Mozatta, L. Y. Chen, and J. C. Chiao, “Reconfigurable transmissiontype beamformer,” in IEEE MTT-S Int. Microw. Symp. Dig., 2000, pp. 585–588. [13] A. Abbaspour-Tamijani, K. Sarabandi, and G. M. Rebeiz, “A planar filter-lens array for millimeter-wave applications,” in IEEE AP-S Int. Symp., Jun. 2004, vol. 1, no. 20–25, pp. 657–658. [14] ——, “A millimeter-wave bandpass filter-lens array,” Proc. Inst. Elect. Eng.—Microw., Antennas, Propag., to be published. [15] C. C. Cheng, A. Abbaspour-Tamijani, and C. Bircher, “Millimeterwave beam-steering using an array of reconfigurable antenna–filter–antenna elements,” in IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 449–452. [16] M. Makimoto and S. Yamashita, “Bandpass filters using parallel coupled stripline stepped impedance resonators,” IEEE Trans. Microw. Theory Tech., vol. MTT-28, no. 12, pp. 1413–1417, Dec. 1980. [17] M. Sagawa, M. Makimoto, and S. Yamashita, “Geometrical structures and fundamental characteristics of microwave stepped-impedance resonators,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 7, pp. 1078–1085, Jul. 1997. [18] W. H. Tu and K. Chang, “Miniaturized CPW-fed slot antenna using stepped impedance resonator,” in IEEE AP-S Int. Symp., Jul. 2005, vol. 4A, no. 3–8, pp. 351–354. [19] A. Abbaspour-Tamijani and G. M. Rebeiz, “Low-loss bandpass antenna–filter–antenna-arrays for applications in quasi-optical systems,” in Proc. 35th Eur. Microw. Conf., 2005, pp. 1027–1029. [20] A. Pothier, J.-C. Orlianges, G. Zheng, C. Champeax, A. Catherinot, D. Cros, P. Blondy, and J. Papapolymerou, “Low-loss 2-bit tunable bandpass filters using MEMS DC contact switches,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 354–360, Jan. 2005. [21] G. M. Rebeiz, RF MEMS, Theory, Design, and Technology. New York: Wiley, 2002. [22] M. A. Ali, S. C. Ortiz, T. Ivanov, and A. Mortazawi, “Analysis and measurement of hard-horn feeds for the excitation of quasi-optical amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 479–487, Apr. 1999. [23] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering. Englewood Cliffs, NJ: Prentice-Hall, 1991. [24] B. A. Munk, Frequency Selective Surface. Hoboken, NJ: Wiley, 2000.

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Chih-Chieh Cheng (S’06) received the B.S. degree in aerospace engineering (with a minor in electrical engineering) from National Cheng Kung University, Taiwan, R.O.C., in 2001, the M.S. degree in electrical engineering from the University of Wisconsin–Madison, in 2004, and is currently working toward the Ph.D. degree in electrical engineering at Arizona State University, Tempe. During the summers of 2003 and 2004, he was an Intern for 3eTI, Washington, DC, and Media Tek, Hsinchu, Taiwan, R.O.C. His research interest is millimeter-wave beam steering using MEMS fabrication techniques.

Abbas Abbaspour-Tamijani (S’00–M’04) received the B.S. and M.S. degrees from The University of Tehran, Tehran, Iran, in 1994 and 1997, respectively, and the Ph.D. degree from The University of Michigan at Ann Arbor, in 2003, all in electrical engineering. From 1996 to 1999, he was an Antenna and RF Engineer in industry. In 2004, he was a Research Fellow with the Radiation Laboratory, The University of Michigan at Ann Arbor. He is currently an Assistant Professor of electrical engineering with Arizona State University, Tempe. His research interests include RF MEMS technology and applications, reconfigurable and intelligent front-end electronics, integrated antennas, and biomedical application of microwaves. Dr. Abbaspour-Tamijani is a member of the IEEE Microwave Theory and Techniques, Antennas and Propagation, and Engineering in Medicine and Biology societies.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

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Two-Port Vector Network Analyzer Measurements in the 218–344- and 356–500-GHz Frequency Bands Andy Fung, Member, IEEE, Douglas Dawson, Member, IEEE, Lorene Samoska, Senior Member, IEEE, Karen Lee, Todd Gaier, Pekka Kangaslahti, Member, IEEE, Charles Oleson, Anthony Denning, Yuenie Lau, and Greg Boll

Abstract—We discuss methods for full two-port vector network analyzer measurements in the 218–344- (using WR3) and 356–500-GHz (using WR2.2) frequency bands. Waveguide test sets (WR3 and WR2.2) utilize Oleson Microwave Laboratories Inc. frequency extenders with the Agilent 8510C network analyzer. On-wafer measurements in the 220–325-GHz band are demonstrated with GGB Industries Inc. coplanar-waveguide probes. This paper primarily reviews the performance capabilities of the WR3 test set and introduces initial calibration results of the WR2.2 test set. For WR3, calibration methods are compared, and dynamic range and frequency extender output power data are presented. Index Terms—Coplanar transmission lines, coplanar waveguides (CPWs), measurement, monolithic-microwave integrated-circuit (MMIC) amplifiers.

I. INTRODUCTION HE NEED to develop active and passive components for higher frequencies has led to the development of test equipment and procedures for characterizing -parameters at ever-increasing frequency bands. The first full two-port on-wafer vector network analyzer (VNA) measurement capability up to 220 GHz was reported in 1999 [1]. Since then, further developments have enabled the first full two-port on-wafer VNA measurements up to 325 GHz [2], [3]. In this paper, we discuss the performance of the hardware and calibration methods used in [2] and [3]. In addition, we present the first calibration results of a new VNA test set in the 356–500-GHz band. Currently, WR3 (0.034 in 0.017 in inside waveguide dimensions, 220–325-GHz waveguide band) waveguide components are commercially available, and WR2.2 (0.022 in 0.011 in inside waveguide dimensions, 325–500-GHz waveguide band) components are still in development. Recent research in InP high electron-mobility transistor (HEMT) and heterojunction bipolar transistor (HBT) technologies have resulted in transistors with extrapolated current gain and power gain cutoff frequencies well in cutoff

T

Manuscript received April 9, 2006; revised June 26, 2006. This work was supported by the National Aeronautics and Space Administration. This work was supported in part by the Defense Advanced Research Projects Agency under the SWIFT Program. A. Fung, D. Dawson, L. Samoska, K. Lee, T. Gaier, and P. Kangaslahti are with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]). C. Oleson, A. Denning, and Y. Lau are with Oleson Microwave Laboratories Inc., Morgan Hill, CA 95037 USA. G. Boll is with GGB Industries Inc., Naples, FL 34101 USA. Digital Object Identifier 10.1109/TMTT.2006.885919

Fig. 1. Schematic diagram of the WR3 on-wafer S -parameter VNA test set. Port 2 is implemented in a similar fashion as port 1 and is not shown in the diagram. From [3].

excess of 220 GHz [4]–[10]. Advances in these devices benefit electronics for communications, millimeter-wave imaging systems, and radiometers for earth remote sensing and astrophysics. Components such as InP HEMT amplifiers with more than 10-dB gain at 225 GHz [11] and 10-dB gain at 235 GHz [2] have been demonstrated. To progress monolithic-microwave integrated-circuit (MMIC) circuits into the submillimeter-wave range ( 300 GHz), characterization of -parameters above 220 GHz is essential for new device modeling and verification of designs. II. WR3 AND WR2.2 TEST SET DESCRIPTION The WR3 and WR2.2 test sets consist of the 50-GHz VNA -parameter test set, which is composed of the Agilent 85101C display/processor, Agilent 85102B IF/detector, Agilent 8517B -parameter test set, Agilent 83651A synthesized sweeper, and Agilent 83620B swept signal generator. To extend the 50-GHz test set to the WR3 or WR2.2 frequency band, Oleson Microwave Laboratories Inc. (OML Inc.), Morgan Hill, CA, V03VNA2-T/R [12] or V02.2VNA2-T/R [13] frequency extenders are interfaced with the 50-GHz VNA -parameter test set, respectively (see Fig. 1). For the WR3 test set, harmonic and supmultipliers of 18 are used with both the plied to the OML Inc. module to reach 220–325 GHz. Similarly for the WR2.2 test set, harmonic multipliers of 30 and 28 are and , respectively, to reach 325–500 GHz. used for Per VNA -parameter port, one frequency extension module is required with external amplifiers and attenuators to adjust signal levels between the 50-GHz test set and OML Inc. modules. To do on-wafer probing, GGB Industries Inc., Naples, FL, has developed custom-manufactured WR3 waveguide wafer probes. The Model 325 Picoprobes are 60- m-pitch coplanar waveguide (CPW) probes. They are used to transition from the output ports of the OML Inc. WR3 frequency

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extenders to the ground–signal–ground CPW probe pads of the device-under-test on a wafer. In this paper, we present data on the performance of different calibration methods on dynamic range, the maximum frequency range the WR3 test set can operate over, and the output power of the WR3 test set. For the Model 325 Picoprobes, we provide data on the calibrated dynamic range established at the probe tip reference planes in the 220–325-GHz range. For the WR2.2 test set, we show initial waveguide calibration results in the 356–500-GHz band. III. WR3 VNA MEASUREMENTS Previously with the WR3 test set, we have measured the -parameters of a three-stage 0.07- m gate-length InP HEMT amplifier with a peak gain of 10 dB at 235 GHz [2]. Additionally, with the same test set, we determined that the GGB Industries Inc. Model 325 Picoprobes can have an upper limit of loss per probe of 3.0–4.8 dB across the conventional WR3 frequency band [3]. In order to characterize components, the characteristics of the device-under-test must be in the detectable range of the test set. To determine the dynamic range (0 dB to lower limit) of our WR3 test set, we compare the -parameter response of calibration standards after a calibration is performed. For the WR3 test set, we have examined the calibrated dynamic range in the conventional WR3 band after a line-reflect-line (LRL) and short-offset–short-load-thru (SOSLT) calibration. The waveguide calibrations in this paper are made with standards from an OML Inc. WR3 calibration kit. A. WR3 Waveguide Test Set Dynamic Range, Frequency Range, and Output Power The LRL calibration utilizes two WR3 shims of length 2.537 and 2.911 mm. The equivalent phase difference between these two line standards is 45 and 170 at 220 and 325 GHz, respectively. The length difference of the two lines is near a quarter wavelength (0.368 mm) at the geometric mean frequency of 267.4 GHz of the conventional WR3 band. The reflect standard is implemented with a waveguide flange short and is used to define the port 1 and port 2 reference planes at the flange openings of the OML Inc. frequency extenders. After calibration, -parameters of standards are compared to determine the calibrated dynamic range. Fig. 2 shows the typical return and insertion-loss range that can be measured by the system. Variation in both return loss and insertion loss of the short and thru standards, respectively, is generally within 0.15 dB from 0 dB across the frequency band. For the SOSLT calibration, the short is implemented with the 2.537-mm shim with a waveguide flange short, the offset short uses the 2.911-mm shim and a flange short, the load standard is a well-terminated WR3 waveguide section with return loss specified better than 35 dB, and the thru is made by placing the WR3 output flanges together. Measured -parameters of standards are displayed in Fig. 3 to show the typical calibrated dynamic range. Variation in return loss and insertion loss of the short and thru standard is within approximately 0.8 and 0.15 dB from 0 dB, respectively, across the frequency band. Comparing the LRL calibration and SOSLT calibrations, they both have similar insertion-loss dynamic range. However, the

Fig. 2. Dynamic range of return-loss S 11; 22 and insertion-loss S 21; 12 capabilities established with the LRL calibration. The load standard is a well-terminated waveguide that isolates signals from propagating between port 1 and port 2.

SOSLT calibration shows a slightly greater return-loss dynamic range and a greater uncertainty in return-loss measurement. To determine the maximum frequency range that the WR3 waveguide test set can function over with adequate dynamic range, signal fidelity, and accurate calibration, we utilize a wide frequency sweep range and the SOSLT calibration procedure previously described. The results of the calibration indicate the test set can be useful beyond the specified conventional WR3 frequency band, to approximately 218–344 GHz (see Fig. 4). For insertion-loss dynamic range, in determining the minimum measurable level, a load and short are used for isolation. This should, however, not result in any significant difference compared to if only loads are used at both ports simultaneously. The dynamic range indicated by this calibration (Fig. 4) may also differ from that of the other SOSLT calibration in Fig. 3 at common frequencies due to modifications made to the WR3 frequency extenders by OML Inc. between the two calibrations, and/or differences in how the two calibrations are implemented. In characterizing the WR3 test set, we also measure the output power that it sources. This measurement is made with an Erickson Instruments, Amherst, MA, PM2 calorimeter. A WR3–WR10 transition is used to couple the ports of the test set to the power meter. The output power level is taken from the instantaneous meter reading of the difference of the ON

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Fig. 3. Dynamic range of return loss S 11; 22 and insertion loss S 21; 12 established with the SOSLT calibration. The short used here to determine the return-loss dynamic range is made without a shim.

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Fig. 4. Typical frequency range capability of the WR3 test set. Dynamic range results are established with the SOSLT calibration method. The return loss of the open WR3 waveguide to air is provided for an additional reference check.

and OFF state of a port after approximately 5-s settling time. The measured power as a function of VNA frequency setting for the two ports of the test set are shown in Fig. 5. It should be noted that the measured power at each frequency setting may contain power from spurious harmonics so that the data represents an upper limit of power that can be supplied at the indicated frequency. Additionally, during measurements, we experienced variations in the meter reading and estimate an error of 0.4 W in the measured output power due to the test method. B. WR3 On-Wafer CPW Probe Dynamic Range The on-wafer WR3 test set calibration is also performed with an LRL method. Standards for this CPW probe calibration are taken from a modified GGB Industries Inc. CS-15-14-6704 alumina calibration substrate. The first and second line standards are CPW with lengths 175 and 280 m with impedances of 50 . The phase difference between the two line standards is 60 and 90 at 220 and 325 GHz, respectively. The reflect (open) standard is implemented with both GGB Industries Inc. probes lifted off from the substrate and suspended in air. Once calibrated, the reference planes are set at the tip of the CPW probes. Typical dynamic range of the WR3 test set with CPW probes

Fig. 5. Output power of port 1 (using frequency extender SN20329-1) and port 2 (using extender SN20329-2) as a function of the VNA frequency setting. An interpolated curve between indicated data points is provided to aid visualization for each frequency extender.

is shown in Fig. 6. The dynamic range does not appear to degrade much with the addition of the CPW probes, as indicated by Figs. 2, 3, and 6. These three calibrations are made less than three months apart and are prior to WR3 frequency extender modifications, unlike the calibration in Fig. 4. For measurement

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Fig. 6. Dynamic range of the WR3 test set with CPW probes for on-wafer measurements. Single port calibration structures on the GGB Industries Inc. CS-15 substrate such as shorts and opens are less well isolated at the higher frequency portion of the band. The open with the probes up in air has better port-to-port isolation.

error, variation in return loss and insertion loss of the short and thru standard is within approximately 1 and 0.2 dB from 0 dB, respectively, across the frequency band. IV. WR2.2 VNA TEST SET MEASUREMENTS Initial calibrations have been made on the OML Inc. WR2.2 frequency extenders with the OML Inc. WR2.2 calibration kit in the 356–500-GHz band. LRL, thru-line-reflect (TRL), and SOSLT calibration methods show similar dynamic range. Fig. 7 displays results from the LRL calibration method. For this method, two WR2.2 shims of length 2.538 and 2.786 mm are used. These two lines have an equivalent phase difference of 70 and 126 at 356 and 500 GHz, respectively. The difference in length of the two lines corresponds approximately to an electrical phase difference of a quarter wavelength (0.249 mm) at the geometric mean frequency 403.1 GHz of the OML Inc. specified WR2.2 band (325–500 GHz). For the reflect standard, waveguide flange shorts are used. These shorts are also used to set the location of the port 1 and port 2 reference planes at the WR2.2 frequency extender waveguide flange openings. To improve WR2.2 calibration in the future, we need to align standards and flanges more precisely by using more alignment pins. With smaller waveguides, misalignment tolerances are

Fig. 7. First dynamic range data of the WR2.2 test set. An LRL calibration method uses two shims and waveguide flange shorts as the standards. The thru standard is implemented by connecting the frequency extender waveguide port 1 and port 2 flanges together. The load standard is a WR2.2 waveguide section that is well terminated to minimize reflections.

also reduced [14]. In Fig. 7, although not plotted to reduce clutter, the return loss of a load standard at some frequencies is greater than the thru. Since lines are used to establish the match condition in the calibration, the thru, which is a direct connection of the frequency extender port 1 and port 2 flanges without one of the original lines, may have more physical misalignment present or more waveguide size difference present. To reduce systematic glitches at around 434 and 493 GHz, where a few data points in Fig. 7 have been omitted, we also believe optimization of the harmonics used for frequency conversion in the OML Inc. frequency extenders may alleviate this problem. V. CONCLUSION Two-port VNA measurements have been demonstrated in the 218–344-GHz band with a WR3 waveguide test set. Two-port VNA on-wafer CPW probe measurements have also been shown in the conventional WR3 frequency band of 220–325 GHz. Addition of the CPW probes result in a slight reduction in the dynamic range of the overall WR3 test set. Comparison of the LRL and SOSLT calibration methods in the conventional WR3 band show that LRL produces a more variable return loss for the thru standard as a function of frequency, where as for the SOSLT method, a slight variation of the return loss for the short standard results over frequency. For both calibration procedures,

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the insertion-loss dynamic ranges are about the same. However, the SOSLT return-loss dynamic range is slightly better. For the WR2.2 VNA test set, two-port calibration in the 356–500-GHz (WR2.2) band is presented. To improve calibrations with the current WR2.2 test set, misalignments of calibration standards need to be minimized, and optimization of harmonics used for frequency conversion is required. In addition, for future study above 325 GHz, the development of WR2.2 wafer probes will prove extremely useful for the progress of MMIC and device measurements and modeling up to 500 GHz.

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[11] A. Tessmann, A. Leuther, H. Massler, M. Kurl, C. Schwoerer, M. Schlechtweg, and G. Weimann, “A 220 GHz metamorphic HEMT amplifier MMIC,” in IEEE Compound Semiconduct. Integrated Circuit Dig., Oct. 2004, pp. 297–300. [12] “OML Inc. Manual,” OML Inc., Morgan Hill, CA, 2004, (see, e.g., “325 GHz with a 8510 using OML millimeter wave frequency extension modules with the Agilent 8510 vector network analyzer”). [13] C. Oleson, A. Denning, and Y. Lau, “325 to 500 GHz vector network analysis system,” in 66th ARFTG Microw. Meas. Conf. Dig., Washington DC, Dec. 2005, pp. 16–22. [14] C. Oleson and A. Denning, “Millimeter wave vector network analysis calibration and measurement problems caused by common waveguide component irregularities,” in 56th ARFTG Microw. Meas. Conf. Dig., Boulder, CO, Dec. 2005, pp. 54–62.

ACKNOWLEDGMENT The authors would like to thank S. Weinreb, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, for use of laboratory space and equipment. The authors would like to thank Dr. M. Rosker, Defense Advanced Research Projects Agency (DARPA), for his support. This study was conducted in part at the JPL.

Andy Fung (S’97–M’99) received the B.E.E., M.S.E.E., and Ph.D. degrees in electrical engineering from the University of Minnesota, Minneapolis–St. Paul, in 1993, 1995 and 1999, respectively. In 1999, he joined the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. His research has involved the development of InP HBTs and GaAs Schottky diodes for millimeter- and submillimeter-wave applications. His current interest is in the development of high-frequency test methods.

REFERENCES [1] T. Gaier, L. Samoska, C. Oleson, and G. Boll, “On-wafer testing of circuits through 220 GHz,” in Ultrafast Opt. Electron. Conf., Snowmass, CO, Apr. 1999, vol. 28, pp. 20–26, OSA Trends in Opt. Photon. series. [2] D. Dawson, L. Samoska, A. K. Fung, K. Lee, R. Lai, R. Grundbacher, P.-H. Liu, and R. Raja, “Beyond G-band: A 235 GHz InP MMIC amplifier,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 874–876, Dec. 2005. [3] A. K. Fung, D. Dawson, L. Samoska, K. Lee, C. Oleson, and G. Boll, “On-wafer vector network analyzer measurements in the 220–325 GHz frequency band,” presented at the IEEE MTT-S Int. Microw. Symp., 2006. [4] K. Shinohara, Y. Yamashita, A. Endoh, I. Watanabe, K. Hikosaka, T. Matsui, T. Mimura, and S. Hiyamizu, “547-GHz f In Ga As–In Al As HEMTs with reduced source and drain resistance,” IEEE Electron Device Lett., vol. 25, no. 5, pp. 241–243, May 2004. [5] Z. Griffith, M. Dahlström, M. J. W. Rodwell, X.-M. Fang, D. Lubyshev, Y. Wu, J. M. Fastenau, and W. K. Liu, “InGaAs–InP DHBTs for increased digital IC bandwidth having a 391-GHz f and 505-GHz f ,” IEEE Electron Device Lett., vol. 26, no. 1, pp. 11–13, Jan. 2005. [6] D. Sawdai, P. C. Chang, V. Gambin, X. Zeng, J. Wang, M. Barsky, B. Chan, B. Oyama, A. Gutierrez-Aitken, and A. Oki, “Vertical scaling of planarized InP/InGaAs heterojunction bipolar transistors with f > > 500 GHz,” in Int. InP Relat. Mater. Conf., 350 GHz and f Glasgow, U.K., May 2005, pp. 335–338. [7] T. Hussain, Y. Royter, D. Hitko, M. Montes, M. Madhav, I. Milosavljevic, R. Rajavel, S. Thomas, M. Antcliffe, A. Arthur, Y. Boegeman, M. Sokolich, J. Li, and P. Asbeck, “First demonstration of sub-0.25 m-width emitter InP-DHBTs with > 400 GHz f and > 400 GHz f ,” in Int. Electron Devices Meeting, San Francisco, CA, Dec. 2004, pp. 553–556. [8] G. He, J. Howard, M. Le, P. Partyka, B. Li, G. Kim, R. Hess, R. Bryie, R. Lee, S. Rustomji, J. Pepper, M. Kail, M. Helix, R. B. Elder, D. S. Jansen, N. E. Harff, J. F. Prairie, E. S. Daniel, and B. K. Gilbert, “Self-aligned InP DHBT with f and f over 300 GHz in a new manufacturable technology,” IEEE Electron Device Lett., vol. 25, no. 8, pp. 520–522, Aug. 2004. [9] W. Hafez and M. Feng, “Experimental demonstration of pseudomorphic heterojunction bipolar transistors with cutoff frequencies above 600 GHz,” Appl. Phys. Lett., vol. 86, no. 15, pp. 152101-1–152101-3, Apr. 2005. [10] A. K. Fung, L. Samoska, J. Velebir, P. Siegel, M. Rodwell, V. Paidi, Z. Griffith, and R. Malik, “Indium phosphide double heterojunction bipolar transistors with T-shaped emitter metal features having cutoff frequencies in excess of 200 GHz,” ECS Trans., vol. 1, no. 2, pp. 44–49, 2005.

Douglas Dawson (S’94–M’00) received the B.S. degree in physics and the M.S. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 1994 and 1996, respectively. From 1995 to 1999, he was with EMS Technologies. In May 1999 he joined the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where he has been involved with the designing and building of microwave and millimeter-wave hardware. He is currently focused on radiometric instruments for airplane earth science and space planetary missions.

Lorene Samoska (M’95–SM’04) received the B.S. degree in engineering physics from the University of Illinois at Urbana-Champaign, in 1989, and the Ph.D. degree in materials engineering from the University of California at Santa Barbara, in 1995. She was subsequently a Post-Doctoral Researcher with the Electrical and Computer Engineering Department, University of California at Santa Barbara, where she was engaged in the design and fabrication of state-of-the-art microwave digital circuits based on InP HBTs. In 1998, she joined the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where she is currently a Senior Engineer involved in the designing and testing of 100–400-GHz HEMT and HBT MMIC power amplifiers for local oscillator sources and transmitters in future space missions.

Karen Lee received the B.S.E.E. degree from the California Polytechnic State University, San Luis Obispo, in 1986, and the M.S.E.E. degree from the California Institute of Technology, Pasadena, in 1990. In 1986, she joined the Jet Propulsion Laboratory (JPL), California Institute of Technology, where she developed high-frequency heterodyne receivers. Her interests include the development of microwave to submillimeter-wave technology for instruments used in the investigation of earth and planetary atmospheres, and the transfer of technology to space-flight applications.

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Todd Gaier received the Ph.D. degree in physics from the University of California at Santa Barbara, in 1993. He is currently a Group Supervisor and Principle Member of the Technical Staff with the Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena, where he has been involved in a variety of millimeter-wave instruments using HEMT amplifiers including receivers for radio astronomy at 15, 23, 30, 44, and 94 GHz. He is the Technical Lead on the technology for a program to develop MMICbased receivers for earth remote-sensing applications up to 210 GHz.

Charles Oleson, photograph and biography not available at time of publication.

Anthony Denning, photograph and biography not available at time of publication.

Yuenie Lau, photograph and biography not available at time of publication.

Greg Boll, photograph and biography not available at time of publication. Pekka Kangaslahti (S’94–M’98) received the M.Sc. and Ph.D. degrees from the Helsinki University of Technology, Espoo, Finland, in 1992 and 1999, respectively. He is currently a Senior Engineer with the Microwave Systems Section, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. His current interest is in the development of millimeter-wave and submillimeter-wave MMICs and modules for large arrays.

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A Distortion-Cancelled Doherty High-Power Amplifier Using 28-V GaAs Heterojunction FETs for W-CDMA Base Stations Isao Takenaka, Member, IEEE, Kohji Ishikura, Hidemasa Takahashi, Kouichi Hasegawa, Takashi Ueda, Toshimichi Kurihara, Kazunori Asano, and Naotaka Iwata, Senior Member, IEEE

Abstract—An -band 330-W distortion-cancelled Doherty GaAs field-effect transistor (FET) amplifier has been successfully developed optimizing the main and peak amplifiers load impedance shift. The amplifier employed a pair of 28-V operation 150-W GaAs heterojunction FETs. It demonstrated low third-order intermodulation of 37 dBc with a drain efficiency of 42% at an output power of 49 dBm around 6-dB backoff level under the two-carrier wideband code-division multiple-access (W-CDMA) signals of 2.135 and 2.145 GHz. To our knowledge, these represent the best results ever reported among the simple high-power FET amplifiers for W-CDMA base stations. In addition, we proposed the evaluation techniques to obtain each AM–AM and AM–PM characteristics of the main and peak amplifiers in an operating Doherty amplifier, and have experimentally proven the distortion cancellation effect in the GaAs FET Doherty amplifier. Index Terms—Distortion cancellation, Doherty amplifier, efficiency, heterojunction field-effect transistors (HFETs), high power, wideband code division multiple access (W-CDMA).

I. INTRODUCTION OTH HIGH efficiency and low distortion are strongly required for multicarrier amplifiers used in modern mobile communication base stations. In current base-station systems with a high peak factor such as W-CDMA signals, a feed-forward and a digital predistortion have been main linearization methods. In addition, various efficiency enhancement techniques such as class-F, Doherty, envelope elimination and restoration, Chireix outphasing, and envelope tracking have been investigated for practical use [1]–[4]. Among these circuit investigations, Doherty configuration is one of the most promising candidates for this purpose due to the advantages of circuitry simplicity, wide bandwidth, and high stability. In recent years, the Doherty amplifiers applying a feed-forward and a digital predistortion have been actively studied [5], [6]. However, the Doherty configuration using a class-C peak amplifier has a common problem to deteriorate distortion

B

Manuscript received March 31, 2006; revised July 6, 2006. I. Takenaka, K. Ishikura, H. Takahashi, T. Ueda, and N. Iwata are with the NEC Electronics Corporation, Shiga 520-0833, Japan (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). K. Hasegawa, T. Kurihara, and K. Asano are with the NEC Electronics Corporation, Kanagawa 211-8668, Japan (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.883606

characteristics compared to the class-AB operation because of nonconstant gain and phase behavior. Thus far, many publications have been reported for Doherty amplifier performance, but the design methodology has not yet been clearly reported for high-efficiency and low-distortion performance [7]–[9]. In this study, we suggested a distortion-cancelled Doherty amplifier due to the distortion cancellation at the vector combination of the main and peak amplifiers in a Doherty configuration. Optimizing the main and peak load impedance shift, a 330-W Doherty 28-V GaAs heterojunction FET (HJFET) amplifier with high efficiency and low distortion has been successfully developed [10]. Furthermore, in order to clarify the distortion improvement mechanism, we proposed the evaluation technique to obtain each AM–AM and AM–PM characteristics of the main and peak amplifiers in actual Doherty amplifier operation. For the first time, it was experimentally proven that the distortion cancellation of the main and peak amplifiers contributes to improve the distortion characteristics in a Doherty configuration. Section II presents the outline of the 28-V operation GaAs HJFETs developed for wideband code-division multiple-access (W-CDMA) base-station amplifiers. Section III describes the circuit design methodology for high-efficiency and low-distortion Doherty amplifiers. Section IV presents the measured RF performance of the newly developed Doherty amplifier. Section V will discuss the verification of the distortion improvement mechanism on the Doherty amplifier. II. 28-V OPERATION GaAs HJFETs A schematic cross section of the developed 28-V operation AlGaAs/InGaAs/AlGaAs HJFET is shown in Fig. 1. For high-voltage operation, we employed dual field-modulating-plate (FP) technology in which one of the FP electrodes (first FP) is connected to the gate and the other (second FP) to the ground [11]. These FP electrodes contribute to obtain high breakdown voltage relaxing the electric field between gate and drain electrodes. The electric field relaxation due to the FP electrodes also results in decreasing the pulse drain current dispersion. In addition, the second FP improves the gain characteristics decreasing the gate-to-drain capacitance. The second FP length is 1.0 m. The recess length between the gate and the recess edge in the drain side is 3.0 m. Fig. 2 shows the top view of newly developed 28-V operation ) of a chip with 150-W single-end HJFETs. The gatewidth ( 20 unit cells was 82 mm. The unit finger width was 1000 m.

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Fig. 1. Schematic cross section of a newly developed dual-FP HJFET.

Fig. 5. Circuit design strategy.

Fig. 2. Top view of a newly developed 28-V operation 150-W GaAs HJFET.

Fig. 6. Measured PAE contours and P out contours at the 2-dB gain compression point in class-AB under a CW of 2 GHz for a unit-cell FET.

Fig. 3. Equivalent circuit of a 150-W GaAs HJFET.

Fig. 4. Doherty configuration.

Three dual-FP FET chips (i.e., total mm) were mounted on a single plastic package with pre-matching circuits. The package size is 21.7 34 mm . Fig. 3 shows the equivalent circuit of a 150-W GaAs HJFET. The internal input matching circuit consists of two-stage LC low-pass filter networks, and the internal output matching circuit consists of transmission lines and one-stage LC low-pass filter networks. III. HIGH-EFFICIENCY AND LOW-DISTORTION CIRCUIT DESIGN OF A DOHERTY AMPLIFIER A. Circuit Design Strategy As shown in Fig. 4, both the class-AB main amplifier and class-C peak amplifier on a Doherty configuration are not iso-

Fig. 7. Measured ACPR contours at the constant P out of around 10-dB output B.O. in class AB under a W-CDMA signal of 2 GHz.

lated from each other. Therefore, it is a serious problem to robustly design the optimum load impedance shift presented to both the field-effect transistors (FETs) for high efficiency and low distortion [8]. Fig. 5 shows our circuit design strategy. First, for a more accurate design, using the load–pull measurement, we confirmed the optimum load impedance of the FETs as a function of the input power level in class AB and class C, respectively. Next, utilizing large-signal simulation, we simultaneously optimized the load impedance shift presented to the

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Fig. 8. Measured gain contours at the small signal and the P sat level in class-C for a unit-cell FET under a CW of 2 GHz.

Fig. 9. Measured: (a) AM–AM and (b) AM–PM characteristics at the smallsignal gain matching point versus the maximum P out point in class C at 2 GHz.

Fig. 10. Location of measured PAE max point and measured P out max point to select the Doherty circuit configuration. (a) Inverted Doherty configuration. (b) Original Doherty configuration.

main and the peak amplifier FETs as a function of the input power level. B. Load–Pull Measurement Results For a main amplifier design, we measured the load–pull characteristics as a function of the input power level in class-AB. Fig. 6 shows measured power-added efficiency (PAE) contours ) contours at the 2-dB gain and measured output power ( compression point under a continuous wave (CW) of 2 GHz for a unit-cell FET. In order to achieve high-efficiency operation, the main amplifier load impedance should be designed ) point to maximum to change from maximum PAE ( ( ) point as an arrow in Fig. 6 according to the increase of input power level. Furthermore, Fig. 7 shows measured adjacent leakage power ratio (ACPR) contours at the of around 10-dB output backoff (B.O.) under constant a W-CDMA signal of 2 GHz. As shown in Fig. 7, the PAE matching point is close to the low-distortion matching point. Therefore, low-distortion operation can be expected in addition to high-efficiency operation for the main amplifier.

Next, for a peak amplifier design, we measured the gain contours as a function of input power level in class C. Fig. 8 shows measured gain contours at the small-signal and the satu) level in class C for a unit-cell FET rated output power ( under a CW of 2 GHz. The maximum gain point (Gain ) level in class C moves to the same point as the at the point in class AB. Fig. 9(a) and (b) shows measured AM–AM and AM–PM characteristics at the small-signal point versus the point in class C at Gain point shows very small 2 GHz. The small-signal Gain AM–AM and AM–PM variation compared to the point. Therefore, in order to minimize the gain expansion of the peak amplifier, the peak amplifier load impedance should point in class C according to keep the small-signal Gain the increase of input power level. Finally, the peak amplifier point to gain the load impedance should shift to the as an arrow in Fig. 8 according to the increase of the input power level. Thus, low-distortion operation can be expected by minimizing the gain expansion of the peak amplifier.

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Fig. 11. Basic configuration of the developed Doherty amplifier.

C. Optimum Load Impedance Shift Design From the load–pull measurement for a unit cell, we presented that, in order to obtain high efficiency and low distortion, the main amplifier load impedance should change from the point to the point at class AB, and the peak amplifier load impedance should shift from the point in class C to the point, small-signal Gain according to the increase of input power level. Fig. 10 shows point and measured the location of the measured point for a unit-cell 28-V HJFET in order to select the Doherty circuit configuration. It is found that the impedance is lower than the impedance. In this case, as shown in Fig. 10(a), the inverted Doherty configuratransformer is tion of which the quarter-wave length connected to the output of the peak amplifier is suitable to realize the load impedance shift from low impedance to high impedance according to the increase of the input power level. As mentioned in the operation principle of the original Doherty configuration shown in Fig. 10(b), the load line of the main amplifier changes from high impedance to low impedance according to the increase of the input power level. As shown in Fig. 10, although the real part of the impedance in the region point, the load line (A) is lower than that of the introduced by the RC parallel model is higher than that of the point. That is to say, on the load impedance shift point to the point for the 28-V from the HJFET according to the increase of input power level, the load line changes from high impedance to low impedance in the same way as the Doherty operation principle. Fig. 11 shows the basic configuration of the developed Doherty amplifier. This Doherty amplifier is composed of a main and a peak amplifier employing a pair of developed 150-W 28-V GaAs HJFETs. We combined the output power of the main and the peak amplifiers employing the inverted Doherty network transformers of 50 and 35 . A 90 -hybrid coupler with the is used in the input circuits to achieve the distortion bandwidth characteristics improvement isolating each other’s input signals of the main and the peak amplifiers. The load impedance shift of the main and the peak amplifiers affects each other. Therefore, utilizing a large-signal model (EEHEMT1), we designed the output matching circuits with the internal matching networks (IMNs) and the external matching networks (EMNs) in order to simultaneously optimize the load impedance shift presented to both the main and the peak amplifier FETs as a function of the input power level.

Fig. 12. Initial output circuit parameter optimization at: (a) low input power level and (b) high input power level.

Fig. 13. Simulated optimum load impedance shift of the main and the peak amplifier FETs as a function of input power level.

Fig. 14. Simulation results of AM–AM and AM–PM characteristics about the main and the peak amplifier FETs.

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Fig. 17. Pulsed CW performance of the developed Doherty amplifier within the UMTS band (2.11–2.17 GHz).

Fig. 15. Simulated load line about the main and the peak amplifier FETs as a function of input power level from the 8-dB B.O. level to the P sat level. (a) Load line of the main amplifier FETs. (b) Load line of the peak amplifier FETs.

Fig. 16. Developed Doherty amplifier.

As shown in Fig. 12, the initial output circuit parameters were determined to simultaneously satisfy the optimum impedance of both the small- and large-signal condition minimizing the output return loss. The phase-adjusting lines of 50 were inserted between the EMNs and the Doherty network in order to be easy to match. Fig. 13 shows the results of simulated optimum load impedance shift for a unit cell. The load impedance of the class-AB main amplifier FETs is changed from the point to the point according to the increase of the input power level. The class-C peak amplifier FETs load point to the impedance shift is changed from the Gain point according to the increase of the input power level. Fig. 14 shows AM–AM and AM–PM characteristics calculated about the main and the peak amplifier FETs. Above all, suppressed AM–AM and AM–PM variation of the peak amplifier FETs is effective to low distortion characteristics of overall amplifier. Behaviors around the 8-dB B.O. level are

Fig. 18. Performance of the developed Doherty amplifier with the two-carrier W-CDMA signals of 10-MHz carrier spacing at three center frequencies (2.12, 2.14, and 2.16 GHz). (a) IM3 and IM5 versus P out. (b) Drain efficiency versus P out.

crucial under the W-CDMA signal conditions. Fig. 15 shows the load line simulated about the main and the peak amplifier FETs as a function of the input power level from the 8-dB B.O. level. It is found that the load line of the main level to the amplifier FETs changes from high to low impedance in the inverted Doherty amplifier. IV. MEASURED RF PERFORMANCE A photograph of the developed Doherty amplifier is shown in Fig. 16. External circuits including Doherty networks and bias

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Fig. 21. Distortion improvement mechanism on a Doherty amplifier. Fig. 19. Peak amplifier V gs dependence of the two-carrier W-CDMA signals performance with 10-MHz carrier spacing (2.135 and 2.145 GHz).

Fig. 20. Correlation between IM3 and drain efficiency with two-carrier W-CDMA signals of the Doherty amplifier and the push-pull amplifier.

circuits were formed on a printed Teflon board with a thickness of 0.8 mm. A ceramic chip 90 hybrid coupler was used at the input circuits. The main amplifier was biased at a drain–source ) of 28 V with a quiescent drain-source current voltage ( ( ) of 1.2 A. The bias condition of the peak amplifier was a of 28 V and a gate–source voltage ( ) of 1.2 V, which is a class-C bias condition. The W-CDMA signal condition is a 3GPP test model 64ch with a peak-to-average power ratio (PAR) of 8 dB at 0.01% on the complementary cumulative distribution function (CCDF). versus the input power ( ) charFig. 17 shows the acteristics under the pulsed CW condition with the pulsewidth and the pulse period of 1 ms within the UMTS band of 8 (2.11–2.17 GHz). The developed Doherty amplifier attained superior output-power bandwidth characteristics. It demonstrated of 55.2 dBm dBm and a 14-dB linear gain a dBm at 2.14 GHz. Fig. 18 also presents the performance of the developed Doherty amplifier with the two-carrier W-CDMA signals of 10-MHz carrier spacing at three center frequencies of 2.12, 2.14, and 2.16 GHz. Under the W-CDMA signal conditions, excellent bandwidth characteristics of distortion and efficiency were obtained in the UMTS band. The amplifier exhibited low third-order intermodulation (IM3) characteristics of less than

Fig. 22. Measurement system of AM–AM and AM–PM characteristics of the main and the peak amplifier in an operating Doherty amplifier. (a) Main amplifier measurement configuration. (b) Peak amplifier measurement configuration.

37.5 dBc with a 37% drain efficiency at an average of 47 dBm around the 8-dB B.O. output power level using two carriers of 2.135 and 2.145 GHz. It also revealed low fifth-order of intermodulation (IM5). Moreover, at an average 49 dBm around the 6-dB B.O. level, it delivered a 42% drain efficiency maintaining 37-dBc IM3. To our knowledge, these are the best values ever reported among the simple high-power FET amplifiers for W-CDMA base stations [12]–[14]. dependence of the Fig. 19 shows the peak amplifier two-carrier W-CDMA signals performance with 10-MHz carrier spacing (2.135 and 2.145 GHz). Biasing the peak amplifier in 1.3 V, the amplifier reached a 43.5% drain efficiency at of 49 dBm with no degradation in distortion. an average Fig. 20 shows the correlation between IM3 and drain efficiency with two-carrier W-CDMA signals of the Doherty amplifier versus the class-AB push-pull configuration. The developed Doherty amplifier greatly improved tradeoff between distortion

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Fig. 24. Measured AM–AM and AM–PM characteristics of the class-AB and the class-C single-ended device (power matched).

The voltage amplitude and the phase nation vector can be expressed as follows:

of the combi-

(1)

Fig. 23. Measured AM–AM and AM–PM characteristics of: (a) the main and the peak amplifiers, the vector combination, and (b) the total Doherty amplifier.

and efficiency. It has the capability to provide both high-efficiency and low-distortion characteristics. V. VERIFICATION OF THE DISTORTION IMPROVEMENT MECHANISM ON A DOHERTY AMPLIFIER The developed GaAs FET Doherty amplifier could improve efficiency with no degradation of distortion characteristics. Fig. 21 shows the distortion improvement mechanism due to the distortion cancellation at the vector combination of the main and the peak amplifiers in a Doherty configuration. If the distortion cancellation of the main and the peak amplifiers contributes to the distortion improvement, the extremely flat AM–PM characteristics are expected to be obtained without the phase deviation at the vector combination of the main and the peak amplifiers output voltage.

and are the amplitude and the phase of the main where are the ampliamplifier output voltage, respectively, and tude and the phase of the peak amplifier output voltage, respectively. Here, it is necessary to pay attention that each AM–AM and AM–PM characteristics of the main and the peak amplifiers cannot be evaluated isolating each other of the main and the peak amplifiers so that the load impedance shifts of the main and the peak amplifiers are in need of the injection signals from each other. In order to verify the distortion improvement mechanism, we proposed the evaluation technique to obtain each AM–AM and AM–PM characteristics of the main and the peak amplifiers in actual Doherty amplifier operation. Fig. 22 shows the measurement system employing three 90 -hybrid couplers in the input circuits without isolating each other of the main and the peak amplifiers. Operating the Doherty amplifier by inputting GHz dBm the large signal of to one 90 hybrid coupler, the forward transducer gain characteristics of the main and the peak amplifiers, respectively, GHz were obtained by inputting the small signal of dBm from a vector network analyzer (VNA) to the other 90 hybrid couplers. Fig. 23 shows the measured AM–AM and AM–PM characteristics of the main and the peak amplifiers, and the vector combination calculated from (1). In particular, it was observed that the AM–PM characteristics of the main and the peak amplifiers on an actual Doherty amplifier

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are significantly different from the results of the class-AB and the class-C single-ended device shown in Fig. 24. Furthermore, as shown in Fig. 23, the output voltage combination of the main and the peak amplifiers exhibited flat AM–PM characteristics in accordance with the results of the total Doherty amplifier. From these results, it was confirmed that the distortion cancellation of the main and the peak amplifiers contributes to the distortion improvement. It can also be said that the optimum load impedance shift condition estimated about the main and the peak amplifiers is equivalent to the distortion cancellation condition of the main and the peak amplifiers on a GaAs FET Doherty amplifier. VI. CONCLUSION -band 330-W distortion-cancelled Doherty GaAs An FET amplifier has been successfully developed. The amplifier demonstrated, under a two-carrier W-CDMA condition, low IM3 of less than 37 dBc with a 42% drain efficiency at a of 49 dBm. It achieved significant improvements in efficiency without degradation in linearity. In addition, we proposed the evaluation techniques of each AM–AM and AM–PM characteristics of the main and the peak amplifiers in an operating Doherty amplifier, and have also experimentally proven the distortion cancellation of the main and the peak amplifiers in Doherty amplifier linearity.

[9] J. Kim, J. Cha, I. Kim, and B. Kim, “Optimum operation of asymmetrical-cells-based linear Doherty power amplifiers—Uneven power drive and power matching,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1802–1809, May 2005. [10] I. Takenaka, K. Ishikura, H. Takahashi, K. Hasegawa, T. Ueda, T. Kurihara, K. Asano, and N. Iwata, “A 330 W distortion-cancelled Doherty 28 V GaAs HJFET amplifier with 42% efficiency for W-CDMA base stations,” presented at the IEEE MTT-S Int. Microw. Symp., 2006. [11] K. Ishikura, I. Takenaka, H. Takahashi, K. Hasegawa, K. Asano, and M. Kanamori, “A 28 V over 300 W GaAs heterojunction FET with dual field-modulating-plates for W-CDMA base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., 2005, pp. 823–826. [12] I. Takenaka, H. Takahashi, K. Ishikura, K. Hasegawa, K. Asano, and M. Kanamori, “A 240 W Doherty GaAs power FET amplifier with high efficiency and low distortion for W-CDMA base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 525–528. [13] J. R. Gajadharsing, O. Bosma, and P. V. Westen, “Analysis and design of a 200 W LDMOS based Doherty amplifier for 3G base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 529–532. [14] T. Kikkawa, T. Maniwa, H. Hayashi, M. Kanamura, S. Yokokawa, M. Nishi, N. Adachi, M. Yokoyama, Y. Tateno, and K. Joshin, “An over 200-W output power GaN HEMT push–pull amplifier with high reliability,” in IEEE MTT-S Int. Microw. Symp. Dig., 2004, pp. 1347–1350. Isao Takenaka (M’04) received the B.S. and M.S. degrees in physical engineering from Osaka University, Osaka, Japan, in 1991 and 1993, respectively. In 1993, he joined the NEC Corporation. He is currently a Manager with the NEC Electronics Corporation, Shiga, Japan, where he is engaged in the research and development of internally matched highpower transistors.

ACKNOWLEDGMENT The authors would like to thank Dr. T. Noguchi, Dr. K. Ueda, Dr. N. Higashiyama, and Dr. H. Hirayama, all with the NEC Electronics Corporation, Kanagawa, Japan, for encouragement throughout this study. REFERENCES [1] D. Kimball, P. Draxler, J. Jeong, C. Hsia, S. Lanfranco, W. Nagy, K. Linthicum, L. Larson, and P. Asbeck, “50% PAE WCDMA basestation amplifier implemented with GaN HFETs,” in IEEE CSIC Symp. Dig., 2005, pp. 89–92. [2] F. Lepine, A. Adahl, and H. Zirath, “A high efficient LDMOS power amplifier based on an inverse class F architecture,” in 34th Eur. Microw. Conf., Amsterdam, The Netherlands, 2004, pp. 1181–1184. [3] I. Hakala, L. Gharavi, and R. Kaunisto, “Chireix power combining with saturated class-B power amplifiers,” in 12th GaAs Symp., Amsterdam, The Netherlands, 2004, pp. 379–382. [4] R. H. Raab, B. E. Sigmon, R. G. Myers, and R. M. Jackson, “L-band transmitter using Kahn EER technique,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2220–2225, Dec. 1998. [5] T. Ogawa, T. Iwasaki, H. Maruyama, K. Horiguchi, M. Nakayama, Y. Ikeda, and H. Kurebayashi, “High efficiency feed-forward amplifier using RF predistortion linearizer and the modified Doherty amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, Jun. 2004, pp. 537–540. [6] W. J. Kim, S. P. Stapleton, K. J. Cho, and J. H. Kim, “Digital predistortion of a Doherty amplifier with a weak memory within a connected solution,” in 60th IEEE Veh. Technol. Conf., Sep. 26–29, 2004, vol. 3, pp. 2020–2023. [7] K. J. Cho, I. H. Hwang, J. H. Kim, and S. P. Stapleton, “Linearity optimization of a high power Doherty amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1387–1390. [8] J. Sirois, S. Boumaiza, M. Helaoui, G. Brassard, and F. M. Ghannouchi, “A robust modeling and design approach for dynamically loaded and digitally linearized Doherty amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2875–2883, Sep. 2005.

Kohji Ishikura received the B.S. and M.S. degrees in chemical science from the University of Tsukuba, Tsukuba, Japan, in 1992 and 1994, respectively. In 1994, he joined the NEC Corporation. He is currently an Assistant Manager with the NEC Electronics Corporation, Shiga, Japan, where he is engaged in the research and development of high-power GaAs FETs.

Hidemasa Takahashi received the B.S. and M.S. degrees in physics from Keio University, Tokyo, Japan, in 1985 and 1987, respectively. In 1987, he joined the NEC Corporation. He is currently a Manager with the NEC Electronics Corporation, Shiga, Japan. He is engaged in the research and development of power GaAs FETs.

Kouichi Hasegawa joined the NEC Corporation in 1996. He is currently an Assistant Manager with the NEC Electronics Corporation, Kanagawa, Japan, where he is engaged in the development of power GaAs FETs.

TAKENAKA et al.: DISTORTION-CANCELLED DOHERTY HIGH-POWER AMPLIFIER USING 28-V GaAs HJFETs

Takashi Ueda joined NEC Kansai Ltd. in 1986. He is currently an Assistant Manager with the NEC Electronics Corporation, Shiga, Japan, where he is engaged in the development of high-power FETs.

Toshimichi Kurihara received the B.S. degree in physics from Kyushu University, Fukuoka, Japan, in 1986. In 1986, he joined the NEC Corporation in 1986. He is currently a Manager with the NEC Electronics Corporation, Kanagawa, Japan, where he is engaged in the research and development of high-power FETs.

Kazunori Asano received the B.S. and M.S. degrees in electronic engineering from Waseda University, Tokyo, Japan, in 1984 and 1986, respectively. In 1986, he joined the NEC Corporation. He is currently a Manager with the NEC Electronics Corporation, Kanagawa, Japan, where he is engaged in the research and development of high-power GaAs FETs.

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Naotaka Iwata (A’93–SM’00) received the B.E. degree in materials science from the University of Electro-Communications, Tokyo, Japan, in 1981, and the M.E. and D.E. degrees in materials science from the University of Tsukuba, Tsukuba, Japan, in 1983 and 1999, respectively. In 1983, he joined Fundamental Research Laboratories, NEC Corporation, where he was engaged in the characterization and growth of III–V compound semiconductors. Since 1989, he has been engaged in the research and development of high-power FETs utilizing III–V compound semiconductor heterojunctions for mobile communication systems with Microelectronics Research Laboratories and Kansai Electronics Research Laboratories, NEC Corporation. From 1993 to 1994, he was a Visiting Scholar with Stanford University, where he studied III–V compound semiconductor HJFETs. Upon his return to Kansai Electronics Research Laboratories, he was also engaged in the research and development of power HJFETs for mobile phones. He is currently a Team Manager with the NEC Electronics Corporation, Shiga, Japan, where he is responsible for the development of HJFETs and HBTs for mobile communication systems. He is also a Visiting Professor with the University of Electro-Communications. Dr. Iwata is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 2002 Ichimura Prizes in Industry–Meritorious Achievement Prize, a 2003 Commendation by the Minister of Education, Culture, Sports, Science and Technology as a Person of Scientific and Technological Research Merits, and the 2004 University of Electro-Communications Alumni Prize.

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A 60-GHz-Band 12-Multiplier MMIC With Reduced Power Consumption Masaharu Ito, Member, IEEE, Shuya Kishimoto, Member, IEEE, Yasuhiro Hamada, Member, IEEE, and Kenichi Maruhashi, Member, IEEE

Abstract—This paper presents a 60-GHz-band 12 multiplier and its application to a transceiver module. The multiplier consists of a quadrupler and a following tripler. For low dc power consumption, gatewidths of field-effect transistors are optimized. A cascode amplifier is adopted to obtain required output power levels. The fabricated multiplier exhibits output power higher than 0 dBm from 57 to 62 GHz with input power higher than 10 dBm. Spurious harmonic suppressions up to the 20th order are larger than 20 dBc with a desired 12th signal at a frequency of 60 GHz. DC power consumption is 185 mW. A transmitter module with the multiplier is assembled using a flip-chip bonding technique. Bit error rate is measured using amplitude shift-keying modulation with a data rate over 1 Gb/s.

Fig. 1. Block diagram of

212 multiplier.

TABLE I DESIGN SPECIFICATION OF 12 MULTIPLIER

2

Index Terms—Amplitude shift keying (ASK), flip-chip devices, frequency conversion, millimeter-wave devices, monolithic microwave integrated circuits (MMICs), MODFETs, transceivers.

I. INTRODUCTION HE increasing demand for high-speed multimedia links, such as wireless local area networks (LANs) [1] and wireless personal area networks [2], [3], has stimulated the development of millimeter-wave transceivers. These systems not only require highly stable, but also low-cost signal sources. One approach to signal generation is a millimeter-wave oscillator, and another is combining a lower frequency oscillator and a frequency multiplier. In the millimeter-wave band, direct oscillation satisfying the above requirements is more difficult due to the insufficient gain of active devices than the lower frequency case. We believe that using a multiplier with a high multiplication factor is the best solution to satisfy the requirements. Although many millimeter-wave field-effect transistor (FET) multipliers have been reported thus far, they have a multiplication factor up to 4. Recently, an 8 multiplier was fabricated in a single chip [4]; however, its 5 mm 1.6 mm size may not be compact enough. In [5], we reported the first 12 FET-multiplier MMIC with a compact chip size of 2.5 mm 1.15 mm in millimeter-wave frequencies. The multiplier operating in the 60-GHz band enables us to employ a cost-effective 5-GHz-band signal source, which is adopted for existing commercial applications, e.g., wireless LANs (IEEE 802.11a) and electronic toll collection (ETC) systems. One crucial issue is reducing dc power consumption, especially for a mobile system that operates with a battery.

T

Manuscript received April 12, 2006; revised July 25, 2006. The authors are with System Devices Research Laboratories, NEC Corporation, Otsu, Shiga 520-0833, Japan (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.885911

In this paper, we reduced dc power consumption in an 12-multiplier MMIC and present a transceiver module that utilizes the multiplier. To reduce dc power consumption without decreasing output power, we employed a cascode amplifier for higher gain operation in the output stage of the multiplier and reduced the FET gatewidths. Without deterioration in conversion characteristics, we attained a 1/3 reduction of dc power consumption compared to the previously reported multiplier [5]. We also evaluated a transmitter module assembled using a flip-chip bonding technique. II. CIRCUIT DESIGN A. Block Diagram Fig. 1 shows a block diagram of the 12 multiplier [5]. We adopted a cascade configuration of a quadrupler and a tripler. For both low input and high output power operation, we placed driver amplifiers (DAs) in the input and interstages and placed a buffer amplifier (BA) in the output stage. In Table I, design specifications are shown. In this study, we aimed to reduce dc power consumption to the same level as a frequency doubler in our previously reported transceiver module [3]. B. Reduction of DC Power Consumption Table II shows the calculated dc power consumption of each block in our previously reported 12 multiplier [5]. DC power consumption was reduced as follows. From the viewpoint of the input power level, the gatewidths of DAs in input and interstages can be reduced. However, in this study, the set bias point was

0018-9480/$20.00 © 2006 IEEE

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TABLE II CALCULATED DC POWER CONSUMPTION OF PREVIOUSLY REPORTED

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212 MULTIPLIER [5]

Fig. 2. Circuit diagram of cascode amplifier with self-bias configuration. Fig. 3. Calculated conversion characteristics of types 1 and 2.

deepened instead of the gatewidth reduction to provide a wider bandwidth in matching networks compared to the reduction of gatewidths. For further reduction of dc power consumption, we reduced the gatewidths of the multiplier stages, which consume relatively high dc power. Based on this consideration, we designed an 12 multiplier (type 1) with gatewidths of 50 2 m and 25 2 m in each multiplier stage. However, gatewidth reduction caused a severe decrease in output power because it was mainly determined by the saturated powers of multiplier stages. For further improvement, we also designed a 12 multiplier (type 2) incorporating a cascode configuration [6], [7] in the output BA stage, which has a doubled gain of a generally used common-source FET configuration. In a cascode configuration, common-source and common-gate FETs are cascaded, and the current is reused in these two FETs. Using this technique, we can obtain sufficient output power without an increase in dc power consumption. Fig. 2 shows the circuit diagram of the cascode amplifier with a gatewidth of 25 m 2. To reduce the number of biases, gate bias for the common-gate FET was generated by dividing the drain bias . On the other hand, a self-bias configuration was used for the common-source FET.

Fig. 4. Calculated spurious harmonic suppressions of types 1 and 2.

C. Design Performance We adopted the following approaches to integrate the five blocks, i.e., two multiplier and three amplifier stages, in a single chip [5]. 1) Direct (non-50 interstage matching between the multiplier and amplifier stages avoids duplication of matching networks. 2) Gate biasing for multipliers by a high-impedance resistor and self-biasing for amplifiers eliminate gate-bias networks. 3) Introduction of spiral inductors to matching networks.

Fig. 5. Calculated gain profiles of cascode amplifier and common-source FET amplifier.

4) Introduction of metal–insulator–metal (MIM) capacitors for spurious harmonic suppression stubs.

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TABLE III CALCULATED DC POWER CONSUMPTION OF

Fig. 6. Chip photograph of

212 MULTIPLIERS

212-multiplier MMIC (2.5 mm 2 1.15 mm 2 0.2 mm).

Further, to achieve sufficient harmonic suppression over wide frequency band, we adopted a capacitively coupled stub configuration, which works as a high-pass filter, in the output matching network of the quadrupler. On the other hand, in the output matching network of the tripler, we adopted directly coupled stub configuration with two stubs for the eighth harmonic (i.e., 40-GHz band), which have different rejection bands to each other because the capacitively coupled configuration needed very small capacitance for a MIM capacitor [5]. In Fig. 3, the calculated conversion characteristics of types 1 and 2 are shown. In type 1, output power did not reach the specification of 0 dBm due to decreases in the saturated output powers of multiplier stages. On the other hand, in type 2, required bandwidth with output power higher than 0 dBm was obtained due to an increase in gain caused by the cascode configuration of the output BA stage. Fig. 4 shows the calculated harmonic suppressions to the 20th order. In type 1, they were suppressed by approximately 20 dBc. Type 2 suppression level improved approximately 10 dB compared to type 1, which was caused by the frequency response of the cascode amplifier with a narrower bandwidth, as shown in Fig. 5. The calculated dc power consumption of each block in the multiplier is shown in Table III. Type 2 output power was approximately 3 dB higher than type 1. Despite that, since total type 2 dc power consumption was still at the same level as type 1, consumption satisfied requirements. III. MEASURED RESULTS Fig. 6 shows a chip photograph of a fabricated 12-multiplier MMIC (type 2). The active devices are AlGaAs/InGaAs FETs

with a gate length of 0.15 m. The maximum oscillation freand the cutoff frequency are 155 and 95 GHz, quency respectively. The transmission lines are coplanar waveguides (CPWs) suitable for a flip-chip bonding technique. Fig. 7 shows the measured conversion characteristics of ( 0.6 V) of the the multiplier. In this study, gate bias quadrupler was chosen to obtain the highest spurious suppres( 0.8 V) of the tripler was chosen sion, while gate bias was 3.3 V. to obtain the highest output power. Drain bias DC power consumption was 185 mW, which satisfies design specifications and is 2/3 of that previously reported (295 mW) [5]. At an input power of 5 dBm, output power higher than 0 dBm was obtained from 57 to 62 GHz. Although a center frequency of 60 GHz was lower than the designed one by 2 GHz, a 5-GHz bandwidth was wide enough to include the required band. The shift of center frequency may have been caused by inaccuracies in the electromagnetic simulation of the spiral inductor in the matching network. The adjacent 11th and 13th harmonic suppressions were measured to be larger than 25 dBc at around the center frequency. The 13th harmonic increased rapidly with a decrease in input frequency. As a result, the adjacent harmonic suppressions were limited to 13 dBc in the band where output power was higher than 0 dBm. In Fig. 7(b), conversion gain had a maximum value of 14 dB at an input power of 12 dBm. Compared to the previous example [5], maximum conversion gain and associated input power were improved by 3 dB. The improvements, i.e., higher conversion gain and lower input power operation, were caused by the cascode amplifier with higher gain and reduction of the gatewidth, respectively. Saturated output power of 2 dBm was obtained at an input power higher than 12 dBm, which is

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Fig. 8. Measured spurious harmonic suppressions at input frequency of 5.0 GHz.

Fig. 7. Measured conversion characteristics of multiplier. (a) Output power versus input frequency at input power of 5 dBm. (b) Output power, conversion gain, and dc power consumption versus input power at input frequency of 5.0 GHz. Solid lines show characteristics at gate bias points V = 0:6 V and V = 0:8 V. Dashed lines show characteristics at V = 0:7 V and V = 0:9 V.

0

0

0

0

Fig. 9. Measured spectrum of input and

212-multiplied signals.

0

much lower than the design specification of 5 dBm (Table I). At an input power of 10 dBm, output power higher than 0 dBm was obtained across almost the same frequency band. DC power consumption increased with an increase in input power, as shown in Fig. 7(b), indicating that a reduction of input power resulted in a decrease in dc power consumption of the multiplier, as well as a reduction of output power requirement for a 5-GHz-band signal source. Actually, dc power consumption was reduced by approximately 15 mW at an input power of 10 dBm. Besides, we observed a reduction of spurious harmonics as an overall trend. In Fig. 7(b), conversion characteristics at slightly different gate bias conditions are V and also shown, where the biases were set as V. In the linear region with lower input power, output power significantly changed, while it hardly changed in the saturation region with higher input power. This can be explained by self-compensation for the dc gate–source voltage due to an operating point shift [8] in the saturation region. Since multipliers are usually used in the saturation region to avoid output power change due to input power change, the sensitivity to biases is small enough on practical use. Fig. 8 shows the measured spurious harmonic suppressions up to the 20th order. The measured results agree well with the calculated ones. All spurious harmonics were sufficiently suppressed at a suppression level higher than 20 dBc. Harmonic

numbers , generated by nonlinearity in the tripler stage, were dominant in the harmonics where is an integer. The th harmonics, where is an integer from 1 to 3, increased th harmonics with an increase in input power, while the were almost constant because larger th harmonics were generated by the quadrupler stage due to higher input power and mixed with the saturated fourth harmonic at the tripler stage. Signal purity is one crucial requirement for a signal source. Fig. 9 shows the measured output spectrum of the 12-multiplied signal. We confirmed that additional increase in phase dB for noise from ideal value, which is 12-multiplication, was negligible to a phase noise level of 75 dBc/Hz at a 10-kHz offset frequency and 95 dBc/Hz at a 100-kHz offset frequency at least, where the noise level was limited by the input signal source used in the measurements. For example, the obtained noise level satisfies the requirement for quadrature phase-shift keying [9]. IV. TRANSCEIVER MODULE We evaluated a transmitter module incorporating the fabricated 12-multiplier MMIC. Fig. 10 shows a photograph of the transmitter module. The transmitter resembled our previously reported amplitude shift-keying (ASK) module [3], which consisted of four chips, i.e., a modulator (MOD), a dielectric waveguide filter (FIL), a medium power amplifier (MPA), and a 30/60-GHz-band frequency doubler. The 12 multiplier was adopted in the module instead of the doubler. All four chips were mounted in a low temperature co-fired ceramic (LTCC)

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We measured bit error rate (BER) using our previously reported receiver module [10], which consists of a low-noise amplifier, a dielectric waveguide filter, and a demodulator. Fig. 12 shows measured BER for a change in data rate. Transmission was successfully performed at a data rate over 1 Gb/s. At a data rate lower than 1.15 Gb/s, the minimum receiving power, defined at a BER of 10 , was obtained as 49 dBm. V. CONCLUSION Fig. 10. 60-GHz-band transmitter module (35 mm

2 12 mm).

An 12-multiplier MMIC was developed for a 60-GHz-band transceiver module. The multiplier consisted of a quadrupler and a tripler. To reduce dc power consumption, gatewidths of the FETs were reduced. In addition, a cascode amplifier with higher gain was adopted for an output BA to compensate for a decrease in output power due to the reduction of gatewidths. The fabricated multiplier showed conversion characteristics comparable to a previously reported model with a 1/3 reduction of dc power consumption. A transmitter module incorporating the multiplier was also assembled using a flip-chip bonding technique. Transmission was successfully confirmed and performed. A module utilizing the multiplier is promising for wireless communication systems with a data rate over 1 Gb/s. ACKNOWLEDGMENT

Fig. 11. Measured output power modulated at data rate of 1.5 Gb/s.

The authors wish to thank T. Otsuka, NEC Corporation, Sagamihara, Japan, for flip-chip bonding. The authors also wish to acknowledge the support of T. Mori, K. Baba, Y. Shimada, and N. Sumihiro, NEC Corporation, Sagamihara, Japan, and T. Morimoto, K. Ohata, and H. Shimawaki, all with the NEC Corporation, Otsu, Japan. REFERENCES

Fig. 12. Measured BER.

[1] T. Ninomiya, T. Saito, Y. Ohashi, and H. Yatsuka, “60-GHz transceiver for high-speed wireless LAN system,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 1996, pp. 1171–1174. [2] K. Ohata, K. Maruhashi, J. Matsuda, M. Ito, W. Domon, and S. Yamazaki, “A 500 Mbps 60 GHz-band transceiver for IEEE 1394 wireless home networks,” in Proc. Eur. Microw. Conf., Paris, France, Oct. 2000, vol. 1, pp. 289–292. [3] K. Ohata, K. Maruhashi, M. Ito, S. Kishimoto, K. Ikuina, T. Hashiguchi, K. Ikeda, and N. Takahashi, “1.25 Gb/s wireless gigabit Ethernet link at 60 GHz-band,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 373–376. [4] C. Karnfelt, R. Kozhuharov, and H. Zirath, “A high purity 60 GHzband single chip 8 multiplier with low phase noise,” in Proc. GAAS Symp., Paris, France, Oct. 2005, pp. 253–256. [5] M. Ito, S. Kishimoto, T. Morimoto, Y. Hamada, and K. Maruhashi, “Highly integrated 60 GHz-band 12 multiplier MMIC,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1697–1700. [6] R. M. Ahy, C. Nishimoto, M. Riaziat, M. Glenn, S. Silverman, S. L. Weng, Y. C. Pao, G. Zdasiuk, S. Bandy, and Z. Tan, “100-GHz highgain InP MMIC cascode amplifier,” IEEE J. Solid-State Circuits, vol. 26, no. 10, pp. 1370–1378, Oct. 1991. [7] A. Tessmann, W. H. Haydl, A. Hulsmann, and M. Schlechtweg, “Highgain cascode MMIC’s in coplanar technology at -band frequencies,” IEEE Microw. Guided Wave Lett., vol. 8, no. 12, pp. 430–431, Dec. 1998. [8] J. E. Johnson and G. R. Branner, “DC operating point shifts in active RF/microwave frequency multipliers,” in IEEE Int. MWSCAS Midwest Circuits Syst. Symp. Dig., Hiroshima, Japan, Jul. 2004, pp. III-355–III358. [9] E. Camargo, Design of FET Frequency Multipliers and Harmonic Oscillators. Norwood, MA: Artech House, 1998.

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package using a flip-chip bonding technique. The signal is output to a waveguide (WR-15) by the CPW-to-waveguide transition (CPW-WG TRANS). Fig. 11 shows the peak powers of the modulated signal measured by a spectrum analyzer for the required 12th signal and adjacent 11th and 13th harmonic signals. Carrier frequency and data rate were set at 60.5 GHz and 1.5 Gb/s with 50% duty, respectively. The required 12th signal power was saturated for input power higher than 13 dBm. Saturated average power measured by a power meter was set at 7 dBm by the gate bias of the MPA to satisfy technical regulations for a 60-GHz unlicensed band in Japan. Spurious harmonic signals were completely suppressed to a noise level ( 50 dB) of the spectrum analyzer by the filter integrated in the module.

2

W

ITO et al.: 60-GHz-BAND

12-MULTIPLIER MMIC WITH REDUCED POWER CONSUMPTION

[10] K. Maruhashi, S. Kishimoto, M. Ito, K. Ohata, Y. Hamada, T. Morimoto, and H. Shimawaki, “Wireless uncompressed-HDTV-signal transmission system utilizing compact 60-GHz-band transmitter and receiver,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1867–1870. Masaharu Ito (M’00) received the B.E. and M.E. degrees in electronic engineering from Kobe University, Kobe, Japan, in 1995 and 1997, respectively. In 1997, he joined the NEC Corporation, Otsu, Japan, where he develops millimeter-wave integrated circuits (ICs), passive components, and their packaging techniques. His current research interests include multipliers and oscillators. Mr. Ito is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

Shuya Kishimoto (M’04) received the B.E., M.E., and Ph.D. degrees in electronic engineering from Tohoku University, Sendai, Japan, in 1995, 1997, and 2000, respectively. Since joining NEC Corporation, Otsu, Japan, in 2001, he has been engaged in the research and development of millimeter-wave integrated circuits. Dr. Kishimoto is a member of the Japan Society of Applied Physics and the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

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Yasuhiro Hamada (M’06) received the B.S. and M.S. degrees in chemistry from the University of Tokyo, Tokyo, Japan, in 2001 and 2003, respectively. In 2003, he joined the NEC Corporation, Otsu, Japan, where he has been engaged in the research and development of millimeter-wave integrated circuits. Mr. Hamada is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

Kenichi Maruhashi (M’95) received the B.S. and M.S. degrees in physics from Kobe University, Kobe, Japan, in 1989 and 1991, respectively. In 1991, he joined the NEC Corporation, Otsu, Japan, where he has been involved with the modeling, design, and the characterization of heterojunction field-effect transistors (HFETs) and the development of millimeter-wave monolithic microwave integrated circuits (MMICs) based on their technologies. His current research interests include the development of millimeter-wave integrated circuits and RF front-end modules for high-speed wireless communication systems. He is currently a Principal Researcher with the System Devices Research Laboratories, NEC Corporation. Mr. Maruhashi is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

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EM-Based Monte Carlo Analysis and Yield Prediction of Microwave Circuits Using Linear-Input Neural-Output Space Mapping José Ernesto Rayas-Sánchez, Senior Member, IEEE, and Vladimir Gutiérrez-Ayala, Student Member, IEEE

Abstract—A computationally efficient method for highly accurate electromagnetics-based statistical analysis and yield estimation of RF and microwave circuits is described in this paper. The statistical analysis is realized around a space-mapped nominal solution. Our method consists of applying a constrained Broyden-based linear input space-mapping approach to design, followed by an output neural space-mapping modeling process in which not only the responses, but the design parameters and independent variable are used as inputs to the output neural network. The output neural network is trained using reduced sets of training and testing data generated around the space-mapped nominal solution. We illustrate the accuracy and efficiency of our technique through the design and statistical analysis of a classical synthetic problem and a microstrip notch filter with mitered bends. Index Terms—Computer-aided design (CAD), electromagnetic (EM)-based design, EM-based yield prediction, microstrip filters, Monte Carlo analysis, neural modeling, space mapping, statistical analysis, surrogate models.

I. INTRODUCTION

S

TATISCAL analysis and yield estimations of RF and microwave circuits are crucial steps for manufacturability-driven design. Reliable yield prediction typically requires massive amounts of accurate simulations to cover the entire statistic of possible outcomes of a given manufacturing process. Performing Monte Carlo yield analysis by directly using high-fidelity full-wave electromagnetic (EM) simulations is not feasible for most practical problems. Innovative methods have been devised to incorporate field solvers in statistical analysis and design. EM-based yield optimization was proposed in [1] and [2] by using multidimensional quadratic models. Other approaches aim at avoiding redundant Monte Carlo simulations using techniques such as Latin hypercube sampling [3]. Artificial neural networks (ANNs) have also been employed to perform efficient EM-based statistical analysis and design.

Manuscript received March 30, 2006; revised August 15, 2006. This work was supported in part by the Consejo Nacional de Ciencia y Tecnología, Mexican Government under Grant I39341A and Grant C02-42930A-1. The work of V. Gutiérrez-Ayala was supported under the CONACYT-182533 Scholarship. The authors are with the Department of Electronics, Systems and Informatics, Instituto Tecnológico y de Estudios Superiores de Occidente (ITESO), Tlaquepaque, Jalisco 45090, Mexico (e-mail: [email protected]). Color versions of Figs. 1, 3, 8, 9–15, and 17–23 are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2006.885902

The most basic approach consists of training an ANN over a certain region of interest and then applying Monte Carlo analysis and yield optimization techniques to the computationally inexpensive, but accurate neuromodel, as in [4] and [5]. The use of input space-mapped neural models in the frequency domain was demonstrated in [6] for efficient EM-based statistical analysis and yield optimization. In this paper, we describe a method for efficient and highly accurate EM-based statistical analysis and yield prediction using a linear-input neural-output space-mapped model. The main contributions of our study [7] are as follows. 1) The nominal solution is obtained after applying a constrained Broyden-based linear input mapping approach to design (the use of constraints avoids the typical instability of the Broyden method [8]). 2) In contrast with other output mapping approaches ([9], [10]), we propose a neural output mapping modeling process in which not only the responses, but the design parameters and independent variable are used as inputs to the ANN, which gives an extremely powerful interpolating capability to the resultant surrogate. 3) We propose a Frobenius formulation (matrix form) for training the output neural network, in contrast to the typical Euclidean formulation in vector form [11]. We extend our study in [7] by describing the algorithms for automated generation of suitable learning and testing data, by explicitly formulating the statistical analysis problem under different scenarios, by testing the extrapolation ability of the output neural mapping, and by applying our technique to the design and statistical analysis of a second example, i.e., a microstrip notch filter with mitered bends. II. LINEAR-INPUT NEURAL-OUTPUT SPACE-MAPPING METHOD As in any other space-mapping-based optimization algorithm [12], we assume that there are at least two models available for the device to be designed: a fine model, which is very accurate, but computationally expensive, and a coarse model, which is less accurate, but computationally efficient. The linear-input neural-output space-mapping strategy is iland represent the design palustrated in Fig. 1. Vectors rameters of the coarse and fine models, respectively ( , , whose corresponding model responses are in vectors and . Scalar contains the independent variable according to the kind of simulation (frequency, time, etc.). is found In our approach, the linear mapping function first through an algorithmic design process that simultaneously

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Fig. 1. Linear-input neural-output space mapping. From [7].

reveals the fine model parameters that makes the fine model response close enough (from a practical engineering perspective) to a target response, which is given by , where is the the optimal coarse model response vector containing the optimal coarse model parameters. Ideally, the resultant input mapped coarse model could be used as an inexpensive vehicle to estimate the fine . In most practical cases, however, model yield around slightly deviates from due to an inherent residual that cannot be eliminated through an input mapping , making any yield prediction using unreliable, especially when the design specifications are tight. To overcome this problem, an output neural model whose internal free-parameters are in vector is trained around to eliminate the typical residual between and , as illustrated in Fig. 1. Our linear-input neural-output space-mapping method consists of three sub-processes, which are: 1) find a target response by optimizing the coarse model; 2) find and through a linear input space-mapping optimization; and 3) develop a suitable neural model valid in a tolerance region . Once is available, we use the linear-input around neural-output mapped coarse model to perform inexpensive, but highly accurate statistical analysis and yield calculations. A. Coarse Model Optimization We directly optimize the coarse model using classical optimization methods (1) is the objective function expressed in where is the vector of opterms of the design specifications and timal coarse model parameters. In our implementation we solve (1) using the sequential quadratic programming (SQP) method available in the MATLAB Optimization Toolbox.1 B. Linear Input Space Mapping A linear input space-mapping optimization algorithm is formulated to find an approximate root of the system of nonlinear

Fig. 2. Algorithm for constrained Broyden-based linear input space mapping. From [7].

equations (2) where the input nonlinear multidimensional vector function is evaluated through a local alignment of the two models at the current iterate (3a) where is the number of points of the independent variable and the th parameter extraction error vector is given by (3b) aligning the complete set of characterizing responses, denoted by and , respectively, as described in [7]. Predicting the next iterate can be realized following a linear inverse space-mapping approach to design (as in [13]) or a linear “direct” space-mapping approach. In this paper, we follow the later using an enhanced Broyden-based “direct” space-mapping algorithm, avoiding instabilities [8] by constraining the fine model parameters within user-defined limits and , as shown in Fig. 2. When the next candidate falls outside these limits, the step size is decreased in the same quasi-Newton direction. This simple improvement has been confirmed extremely effective, and avoids the need of extra fine model evaluations, as in the case of trust region methodologies. In our current implementation, we set the , but other values of between 0.2–0.8 shrinking factor where tested, yielding similar results. When exiting the algorithm in Fig. 2, we not only have the space-mapped solution available, but also the linear input mapping between the two models (4)

1MATLAB

Optimization Toolbox, ver. 7.0.1 (R14), The MathWorks Inc., Natick, MA, 2004.

where

and

.

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C. Developing the Output Neural Model The neuromapping is developed in a tolerance region around . If properly trained, eliminates the residual between the fine model and the input mapped obtained in the previous step. coarse model Training the output neuromapping aims at finding an opsuch that timal vector of weighting factors (5) for all and in the training region. Contrasting with other output mapping techniques [9], [10], we use as inputs for not only for the mapped coarse model responses, but also the fine model design parameters and the independent variable (see Fig. 1), which gives an extremely powerful interpolating capability to . The problem of training is formulated as

Fig. 3. Learning base points (2n + 1) in a star distribution around a spacemapped solution x 2 < , and testing base points (2n) in a rotated star distribution. From [7].

(6) where of

denotes the Frobenius norm of a matrix learning base points and samples for given by (7)

Matrix stores all the fine model learning responses, where is the number of characterizing responses and , in the circuit (e.g., the real and imaginary parts of ). Matrix is organized as follows:

Fig. 4. Algorithm for generating the learning base points in a star distribution around the space-mapped solution x .

(8) where matrix th learning base point

has the fine model outputs at the

.. .

(9) Fig. 5. Algorithm for generating the testing base points in a rotated star distribution with respect to the learning base points.

Similarly, in the learning set

contains all the outputs of the ANN

(10) and base point

has the outputs of the ANN at the th learning as follows:

fine model simulations, we take in a star distribu, and in a rotated star distribution, as tion around . The learning and testing illustrated in Fig. 3 for the case and , base points are stored in matrices respectively, with (12a)

(11)

(12b)

To control the generalization performance while solving (6), we use testing base points not seen during training. Similarly, the corresponding matrices at the testing base points are de, . To keep a reduced amount of noted by

An algorithm for generating the learning base points with a contains star distribution is in Fig. 4, where vector the fractional tolerances for each of the design parameters. The rotated star distribution of testing base points is generated using the algorithm in Fig. 5.

.. .

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Fig. 7. Two-section impedance transformer test problem. (a) Coarse model. (b) Fine model.

Fig. 6. Algorithm for training the output neuromapping model and input mapped coarse model. From [7].

Q between the fine

The learning and testing errors before developing the output neuromapping are given by

where is the number of outcomes, and represents a random variation for the th outcome. The perturbations in follow some statistical distribution, typically uniform or normal (Gaussian). a fine model acceptance We associate with each outcome index defined by if

(13a) (13b) where and store all the input mapped coarse model responses in the learning and testing sets, respectively. It is seen that the ANN has outputs and inputs. As an ANN paradigm for we use a three-layer perceptron (3LP) with hidden neurons. In our study, (6) is solved as a nonlinear curve-fitting problem in the least squares sense using the Levenberg–Marquardt method available in the MATLAB Optimization Toolbox. The algorithm for training the output neuromapping is in Fig. 6. We first generate all the learning and testing data around . We next train a 3LP with hidden neurons and calculate the corresponding training and testing errors. We keep increasing the complexity of (the number of hidden neurons in the 3LP) until the generalization performance starts to deteriorate, i.e., until the current testing error is larger than the previous one and the current learning error is smaller than the current testing error.

(15) if with defined as in (1), but using the fine model. If is sufficiently large for statistical significance, we can approximate the at the nominal space-mapped solution fine model yield by using

(16) Evaluating (16) is unfeasible for most practical problems given its extremely high computational cost. B. Statistical Analysis Using the Linear-Input Mapped Coarse Model Now we associate with each outcome defined by index

an acceptance

if

III. STATISTICAL ANALYSIS AFTER LINEAR-INPUT NEURAL-OUTPUT SPACE MAPPING

(17) if

A. Statistical Analysis Using the Fine Model A statistical design requires taking into account that the parameter values of the device to be manufactured fluctuate around their nominal values according to their statistical distributions and tolerances. Here, we consider that the parameters of the th manufactured device, outcome , are spread around the nom. These parameters can be represented as inal solution (14)

with defined as in (1), but now using the linear-input mapped coarse model. We can approximate the corresponding linear at the nominal design by input space-mapped yield using (18) Calculating (18) is computationally inexpensive.

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Fig. 8. Coarse and fine model responses at the optimal coarse model solution for the 10 : 1 two-section impedance transformer.

Fig. 9. Results after applying the constrained Broyden-based space-mapping algorithm to the 10 : 1 two-section impedance transformer.

Fig. 10. Errors before training the output neuromapping for the two-section impedance transformer. (a) Errors in learning points. (b) Errors in testing points.

IV. CAPACITIVELY LOADED IMPEDANCE TRANSFORMER C. Statistical Analysis Using the Linear-Input Neural-Output Mapped Coarse Model Finally we associate with each outcome index defined by

an acceptance

if if (19) with defined as in (1), but now using the linear-input neuraloutput space-mapped coarse model. We can approximate the at the nominal design by using corresponding yield (20) Calculating (20) is also computationally inexpensive. should be a good approximation of the actual .

To verify the accuracy of our approach, consider the classical test problem of a capacitively loaded 10 : 1 two-section impedance transformer [14]. The coarse and fine models are shown in Fig. 7. The coarse model consists of ideal transmission lines, while the “fine” model consists of capacitively loaded pF. In this ideal transmission lines with synthetic problem, the fine model is, in fact, computationally inexpensive. This allows us to test the accuracy of our technique since we can afford calculating the actual fine model yield. for frequenThe design specifications are cies between 0.5–1.5 GHz. The electrical lengths of the two transmission lines at 1 GHz are selected as design parameters . The characteristic impedances are kept fixed and . Both at the values models were implemented in MATLAB.2 The optimal coarse (degrees). The coarse and fine solution is are shown in Fig. 8. The results after model responses at applying our constrained Broyden-based space-mapping algorithm are illustrated in Fig. 9. The space-mapped solution 2MATLAB,

ver. 7.0.1 (R14), The MathWorks Inc., Natick, MA, 2004.

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Fig. 12. Learning and testing errors during training of the output neuromapping for the two-section impedance transformer. From [7].

Fig. 11. Errors after training the output neuromapping for the two-section impedance transformer. (a) Errors in learning points. (b) Errors in testing points.

(in degrees) is found after only three fine model evaluations (three frequency sweeps). Using tolerances of 10% for the design parameters around , an output neuromapping was developed for this problem. The learning and testing errors before training the output neural mapping are shown in Fig. 10 (the magnitude of the difference between the fine model characterizing responses and the linear-input mapped coarse model characterizing responses at each sample of the independent variable). The corresponding errors after training are shown in Fig. 11. Fig. 12 shows the performance of the output neural mapping training algorithm. The best performance is achieved with . The linear-input neural-output mapped coarse model response at is compared in Fig. 13 with that one of the fine model and the input mapped coarse model. It is seen that output neural mapping effectively eliminates the residual between and , as expected. A comparison in the yield estimation around between , the linear-input mapped coarse the fine model , and the linear-input neural-output model is shown in mapped coarse model

Fig. 13. Results after developing the output neuromodel impedance transformer. From [7].

Q for the two-section

Fig. 14 using maximum deviations of 5% with respect to for 1000 outcomes with uniform statistical distributions. It is seen that the Monte Carlo responses around of the linear-input mapped coarse model approximately follow the corresponding fine model responses [compare Fig. 14(a) with Fig. 14(c)]. This is an indication that the linear-input mapped coarse model requires a small adjustment to match the fine and around that point. This adjustment is realized model at by the output neural mapping . It is also seen in Fig. 14 that the yield predicted by the linear-input mapped coarse model has a significant error with respect to the actual fine model yield. This error can be very large if the design specifications are hardly satisfied by the fine model. Finally, it is confirmed in Fig. 14 that the linear-input neural-output space-mapping model predicts with a very high accuracy the fine model yield , as expected, since the Monte Carlo analysis was around realized within the training region of the output neural mapping. To test the extrapolation ability of the output neural mapping, a second statistical analysis was realized using maximum for 1000 outcomes deviations of 20% with respect to with uniform statistical distributions. The results are shown in Fig. 15. An excellent performance of the linear-input neural-

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Fig. 14. Statistical analysis of the impedance transformer with maximum deviations of 5% around x (1000 outcomes with uniform statistical distributions) using: (a) the linear-input mapped coarse model, (b) the linear-input neural-output mapped coarse model, and (c) the fine model. From [7].

Fig. 15. Statistical analysis of the impedance transformer with maximum de(1000 outcomes with uniform statistical distriviations of 20% around x butions) using: (a) the linear-input mapped coarse model, (b) the linear-input neural-output mapped coarse model, and (c) the fine model.

output mapped coarse model is observed, although it is being used in a region much larger than the region used for training the output neural mapping . To achieve a similar accuracy in

the yield prediction as the one observed in Fig. 14, it would be using an expanded tolerance region of necessary to retrain 20% around .

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Fig. 16. Microstrip notch filter with mitered bends. Fig. 18. Microstrip notch filter as implemented in Sonnet.

Fig. 17. Microstrip notch filter as implemented in APLAC.

V. YIELD ESTIMATION FOR A MICROSTRIP NOTCH FILTER Consider the microstrip notch filter with mitered bends illustrated in Fig. 16 [15]. is the open stubs length, is the length is the separation gap. The width of the coupled lines, and is the same for all the sections, as well as for the input and output lines of length . A substrate with thickness and relative dielectric constant is used. . The remaining The design parameters are mil, mil, and parameter values are (RT Duroid 5880 with loss tangent ). in the stopband The design specifications are in the passbands, where the stopband lies beand tween 13.19–13.21 GHz, and the passband includes frequencies below 13 GHz and above 13.4 GHz. The coarse model is implemented in APLAC,3 as shown in Fig. 17. It uses the built-in microstrip circuit models available in APLAC for lines, coupled lines, and mitered bends with mil. The fine model implementation is in Sonnet,4 (see Fig. 18). It uses a very high resolution grid (cell size of 0.5 mil 0.5 mil) mil, , and . with 3APLAC, 4em

ver. 7.91, APLAC Solutions Corporation, Helsinki, Finland, 2004. Suite, ver. 10.52, Sonnet Software Inc., North Syracuse, NY, 2005.

Fig. 19. Coarse and fine model responses at the optimal coarse model solution for the notch filter.

The

optimal

coarse model solution is mil . The coarse and fine model reare shown in Fig. 19. The results after sponses at applying our constrained Broyden-based space-mapping algorithm are illustrated in Fig. 20. The space-mapped solution mil is found after only one additional fine model simulation. Each fine model simulation requires 39 min (using Sonnet’s adaptive frequency sweep) on a Pentium 4 at 3 GHz with 768-MB RAM. Using a tolerance region of 0.5 mil for the design parame, an output neuromapping was developed with ters around the performance shown in Fig. 21. The best results are obtained . when The linear-input neural-output mapped coarse model reis compared in Fig. 22 with that one of the sponse at fine model and the input mapped coarse model. It is again confirmed that output neural mapping effectively eliminates the residual between and . Finally, we show in Fig. 23 a comparison in the yield estimabetween the linear-input mapped coarse model tion around

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Fig. 20. Results after applying the constrained Broyden-based space-mapping algorithm to the notch filter.

Fig. 23. Statistical analysis of the microstrip notch filter with maximum deviations of 0.2 mil around (50 outcomes with uniform statistical distributions) using: (a) the linear-input mapped coarse model and (b) the linear-input neural-output mapped coarse model.

6

Fig. 21. Learning and testing errors during training of the output neuromapping

Q for the microstrip notch filter.

x

tistical distributions. This example clearly shows that the linearinput mapped coarse model can produce very inaccurate yield predictions due to the typical residual between and . The problem is alleviated by the linear-input neural-output mapped coarse model. VI. CONCLUSION

Fig. 22. Results after developing the output neuromodel notch filter.

Q for the microstrip

and the linear-input neural-output mapped coarse using maximum deviations of model 0.2 mil with respect to for 50 outcomes with uniform sta-

We have described a method for highly accurate EM-based statistical analysis and yield estimation of RF and microwave circuits. It consists of applying a constrained Broyden-based linear-input space-mapping approach to design, followed by a neural-output space-mapping approach to modeling, in which the responses, design parameters, and independent variable are mapped. The output neuromodel is trained using reduced sets of learning and testing samples, which are algorithmically generated within the tolerance region. The resultant linear-input neural-output space-mapped model is used as a very efficient vehicle for accurate statistical analysis and yield prediction. Our technique is illustrated through the design and statistical analysis of a two-section impedance transformer and a microstrip notch filter with mitered bends.

RAYAS-SÁNCHEZ AND GUTIÉRREZ-AYALA: EM-BASED MONTE CARLO ANALYSIS AND YIELD PREDICTION OF MICROWAVE CIRCUITS

ACKNOWLEDGMENT The authors thank Dr. J. C. Rautio, Sonnet Software, Inc., Liverpool, NY, for making em available. The authors also thank M. Kaitera, APLAC Solutions Corporation, Helsinki, Finland, for making APLAC available. REFERENCES [1] J. W. Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny, and S. Ye, “Yield-driven electromagnetic optimization via multilevel multidimensional models,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 12, pp. 2269–2278, Dec. 1993. [2] J. W. Bandler, R. M. Biernacki, S. H. Chen, and P. A. Grobelny, “A CAD environment for performance and yield driven circuit design employing electromagnetic field simulators,” in Proc. IEEE Int. Circuits Syst. Symp., London, U.K., 1994, vol. 1, pp. 145–148. [3] J. F. Swidzinski and K. Chang, “Nonlinear statistical modeling and yield estimation technique for use in Monte Carlo simulations,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2316–2324, Dec. 2000. [4] A. H. Zaabab, Q. J. Zhang, and M. S. Nakhla, “A neural network modeling approach to circuit optimization and statistical design,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 6, pp. 1349–1358, Jun. 1995. [5] P. Burrascano, M. Dionigi, C. Fancelli, and M. Mongiardo, “A neural network model for CAD and optimization of microwave filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, Jun. 1998, pp. 13–16. [6] J. W. Bandler, J. E. Rayas-Sánchez, and Q. J. Zhang, “Yield-driven electromagnetic optimization via space mapping-based neuromodels,” Int. J. RF Microw. Comput.-Aided Eng., vol. 12, pp. 79–89, Jan. 2002. [7] J. E. Rayas-Sánchez and V. Gutiérrez-Ayala, “EM-based statistical analysis and yield estimation using linear-input and neural-output space mapping,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1597–1600. [8] J. E. Rayas-Sánchez, F. Lara-Rojo, and E. Martínez-Guerrero, “A linear inverse space mapping (LISM) algorithm to design linear and nonlinear RF and microwave circuits,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 960–968, Mar. 2005. [9] J. W. Bandler, Q. Cheng, D. H. Gebre-Mariam, K. Madsen, F. Pedersen, and J. Sondergaard, “EM-based surrogate modeling and design exploiting implicit, frequency and output space mappings,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 1003–1006. [10] J. W. Bandler, D. M. Hailu, K. Madsen, and F. A. Pedersen, “Space-mapping interpolating surrogate algorithm for highly optimized EM-based design of microwave devices,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2593–2600, Nov. 2004. [11] Q. J. Zhang and K. C. Gupta, Neural Networks for RF and Microwave Design. Norwood, MA: Artech House, 2000. [12] J. W. Bandler, Q. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr, K. Madsen, and J. Søndergaard, “Space mapping: The state of the art,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 337–361, Jan. 2004. [13] J. E. Rayas-Sánchez, F. Lara-Rojo, and E. Martínez-Guerrero, “A linear inverse space mapping algorithm for microwave design in the frequency and transient domains,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, Jun. 2004, pp. 1847–1850. [14] J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, and Q. J. Zhang, “Neural inverse space mapping for EM-based microwave design,” Int. J. RF Microw. Comput.-Aided Eng., vol. 13, pp. 136–147, Mar. 2003.

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[15] M. S. Narayana and N. Gogia, “Accurate design of a notch filter using electromagnetic simulator,” Appl. Microw. Wireless J., vol. 12, pp. 44–48, Nov. 2000. José Ernesto Rayas-Sánchez (S’88–M’89–SM’95) was born in Guadalajara, Jalisco, Mexico, on December 27, 1961. He received the B.Sc. degree in electronics engineering from the Instituto Tecnológico y de Estudios Superiores de Occidente (ITESO), Guadalajara, Mexico, in 1984, the Masters degree in electrical engineering from the Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM), Monterrey, Mexico, in 1989, and the Ph.D. degree in electrical engineering from McMaster University, Hamilton, ON, Canada, in 2001. Since 1989, he has been Full Professor with the Department of Electronics, Systems and Informatics, ITESO. In 1997, he began a sabbatical leave with the Simulation Optimization Systems Research Laboratory, McMaster University. In 2001, he returned to ITESO. He currently leads the Research Group on Computer-Aided Engineering of Circuits and Systems (CAECAS), ITESO. Since May 2005, he has been a Profesor Numerario (honorary distinction) with ITESO. He currently develops research in collaboration with the Universidad Politécnica de Valencia, as well as with Intel Guadalajara. He is a member of the Mexican National System of Researchers, Level I. His research focuses on the development of novel methods and techniques for computer-aided and knowledge-based modeling, design and optimization of high-speed electronic circuits and devices (including RF, microwave and wireless circuits), exploiting highly accurate but computationally expensive simulators. Dr. Rayas-Sánchez serves on the Editorial Boards of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and on the IEEE Latin America Transactions. He is also a member of the Technical Program Committee of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). During 2004 and 2005 he was the IEEE Mexican Council chair, as well as the IEEE Region 9 treasurer. He was the recipient of a 1997–2000 Consejo Nacional de Ciencia y Tecnología (CONACYT) Scholarship presented by the Mexican Government, as well as a 2000–2001 Ontario Graduate Scholarship (OGS) presented by the Ministry of Training for Colleges and Universities in Ontario. He was the recipient of a 2001–2003 CONACYT Repatriation and Installation Grant presented by the Mexican Government. He was also the recipient of a 2004–2007 SEP-CONACYT Fundamental Scientific Research Grant presented by the Mexican Government.

Vladimir Gutiérrez-Ayala (S’06) was born in Los Mochis, Sinaloa, Mexico, on August 11, 1977. He received the B.Sc. degree in communications and electronics engineering from the University of Colima, Colima, Mexico, in 2000, and the Masters degree in industrial electronics from the Instituto Tecnológico y de Estudios Superiores de Occidente (ITESO), Guadalajara, Mexico, in 2006. He is with the Research Group on Computer-Aided Engineering of Circuits and Systems (CAECAS), ITESO, where he collaborates as a Research Assistant in a project funded by Intel Guadalajara. His research interests include design and optimization of high-frequency electronics circuits exploiting space mapping and ANNs. He was the recipient of a 2002–2004 Consejo Nacional de Ciencia y Tecnología (CONACYT) Scholarship presented by the Mexican Government.

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A 10-Gb/s Reconfigurable CMOS Equalizer Employing a Transition Detector-Based Output Monitoring Technique for Band-Limited Serial Links Franklin Bien, Student Member, IEEE, Hyoungsoo Kim, Student Member, IEEE, Youngsik Hur, Member, IEEE, Moonkyun Maeng, Member, IEEE, Jeongwon Cha, Student Member, IEEE, Soumya Chandramouli, Student Member, IEEE, Edward Gebara, Member, IEEE, and Joy Laskar, Fellow, IEEE

Abstract—Limitations in data transmission caused by band limitation in broadband communication links can be improved significantly by using equalization techniques. In this paper, a reconfigurable feed-forward equalizer employing a transition detector (TD)-based calibration technique that provides a universal channel compensation solution is presented. Moreover, the newly proposed TD-based calibration technique monitors the channel output for further adjustments over time in order to provide optimum compensation in performance. The reconfigurable equalizer is implemented in a 0.18- m CMOS technology. The prototype successfully demonstrates the feasibility of the TD-based calibration technique for output monitoring. Index Terms—Band-limited serial links, finite-impluse (FIR) filter, output monitoring, reconfigurable equalization, 10 Gb/s, transition detector (TD), 0.18- m CMOS.

I. INTRODUCTION

T

HE ever-increasing demand for higher data rates in the multigigabit/s range has resulted in a need for wider bandwidth over existing band-limited channels such as copper and fiber. Transmission of multimedia content such as audio and video streams, for example, has pushed the need for higher computing power and data throughputs. Recently, 10-Gb/s serial data transmission over FR-4–based backplanes, which were originally designed for 1-Gbit Ethernet applications, has been reported [1], [2]. Moreover, the advances in optical links and the supporting electronics have dramatically increased the speed and amount of data traffic handled by a network system. However, the band-limited links are not keeping pace with these technical improvements for multigigabit serial data communication and are becoming a critical bottleneck. Interconnects can range from several inches to hundreds of miles, through copper, fiber, cable, etc. The limited bandwidth of the interconnect channel results in a loss in power of the highManuscript received April 12, 2006; revised June 26, 2006. F. Bien, H. Kim, J. Cha, S. Chandramouli, E. Gebara, and J. Laskar are with the Georgia Electronic Design Center, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]). Y. Hur is with the Samsung RFIC Design Center, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]). M. Maeng is with the Intel Corporation, Folsom, CA 95630 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2006.884660

frequency components of the transmitted signal. This causes dispersion of the signal, which results in inter-symbol interference (ISI). This ISI can be addressed by using a channel-compensation technique, namely, equalization [3], [4]. Previously, digital equalization techniques have been used to reduce ISI in band-limited wire-line applications. However, such techniques require high-resolution analog-to-digital converters with sampling rates at or above the symbol rate. The increased circuit complexity and power consumption required to apply this technique to high-speed serial data transmission are prohibitive at the considered data rates. Hence, analog or mixed-signal equalization techniques are attractive alternatives for multigigabit per second serial transmission [3]. The finite impulse response (FIR) filter architecture is one of the most common types of analog equalizer used in practice to compensate ISI. An equalizer using an FIR filter for 10-Gb/s backplane applications was reported [5], [6]. In this structure, the delay elements were implemented using an on-chip passive delay line, which offers the bandwidth benefit. However, this passive component-based equalizer cannot provide adjustable compensation for diverse channel characteristics. Therefore, an adjustable active delay line approach would be desirable to compensate diverse channels [7], [8]. In this paper, an equalizer with adjustable delay elements utilizing an active inductance peaking approach is introduced. This is the first analog feed-forward equalizer (FFE) implemented in a 0.18- m CMOS, which utilizes a tunable active delay-line approach for 10-Gb/s data communication to achieve a universal equalization solution for a wide range of band-limited channels. Moreover, a new output-monitoring scheme employing a transition detector (TD) is proposed. This scheme does not require clock and data recovery (CDR) circuitry resulting in reduced complexity for easier implementation. II. BAND-LIMITED DISPERSIVE SERIAL LINKS When a signal goes through a band-limited dispersive channel with an impulse response, as illustrated in Figs. 1(b) or 2(b), its output signal power spreads in time. This spreading of signal power causes ISI. In other words, transmitting a square pulse through such a dispersive channel results in a widened and flattened pulse at the far end. This implies that each data bit of information overlaps with its adjacent bits. This overlap can cause major distortions of the signal. At high data rates and in

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Fig. 1. Optical link system simulation. (a) Schematic. (b) Channel response. (c) Eye diagram after 25-km SMF with 10-Gb/s NRZ signal input.

long channels, the ISI can be so severe that it becomes impossible to recover the original transmitted data. This is a major phenomenon limiting data transmission and must be addressed for multigigabit/s serial data communications over band-limited channels. Therefore, it is necessary to analyze the impact of channel characteristics on signal integrity in order to compensate for the degradation caused by each channel. Here, optical fiber links and backplane channels are investigated in more detail. A. Fiber Optical Link The major concern in fiber-optic communications is pulse dispersion resulting in ISI. The ISI becomes more severe as data rate and distances are increased. Here, three different types of dispersion are briefly reviewed. In a multimode fiber (MMF), the numerous guided modes travel at different speeds, resulting in pulse dispersion at the receiver. This is called differential-modal delay (DMD) and results in ISI. Due to DMD and the resulting ISI, MMF usage is limited to short-haul applications at 10 Gb/s up to 300 m with nonreturn to zero (NRZ) serial data [5], [8]. In a single-mode fiber (SMF), polarization-mode dispersion (PMD) and chromatic dispersion (CD) cause ISI. PMD is created when two polarization modes experience slightly different conditions, as a result of a generic imperfect circular symmetry of fibers and other external stress on the fibers, and travel along the fibers at different speeds. CD is created by the variation of the speed of light through the fiber depending on a wavelength. The CD is the sum of two quantities, dispersion inherent to the material and dispersion arising from the structure of the waveguide. PMD and CD are the main dispersion factors in SMF [9].

Fig. 2. Forward transmission of eight 20-in FR4 backplane traces. (a) Frequency responses. (b) Impulse responses. (c) Eye diagrams over 20-in FR-4 backplane channel.

An optical system for the characterization of 25-km SMF is shown in Fig. 1(a). The optical signal is transmitted with a continuous-wave laser module, and received with a pin diode, forming a two-port network. The corresponding impulse response of the optical link is plotted in Fig. 1(b). As expected, the channel is dispersive. As shown in Fig. 1(c), the signal integrity of the transmitted 10-Gb/s signal has been severely degraded and the original information is unrecoverable without compensation [10]. As illustrated above, fiber optical links introduce dispersion in signals, which results in degraded signal integrity. As data rate and/or link distance increases, dispersion in the fiber optical links becomes more severe and contributes to ISI. Thus, it is necessary to compensate this degradation. Moreover, a fixed compensation for degraded signals cannot cover different types of channels and it is necessary to include a method to flexibly adapt to variations in data rate, types of fiber, and link distance. B. Backplane Multigigabit per Second Data Interface Channel loss is an important electrical parameter that affects the channel response and influences the design of various com-

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ponents in a backplane link. The channel loss is composed of conductor loss and dielectric loss. Both conductor and dielectric losses are directly proportional to frequency and, thus, become severe in the microwave frequency range (i.e., beyond 1 GHz) for FR4 dielectric-based components such as backplanes. This channel loss induces dispersion and degrades signal integrity severely. The channel loss is a major impediment in multigigabit per second backplane signaling [11]. At low frequency around dc, the conductor loss depends on the resistivity of the conductor and total area over which current is flowing. Since the dielectric material in printed circuit boards (PCBs) is not a perfect insulator, there is dc loss associated with flowing current through the dielectric material between a signal conductor and a reference plane. However, the conductor loss at dc for commercial PCB substrates is usually very negligible and can be ignored. However, as frequency increases, skin effect comes into play. The skin effect is a physical phenomenon in which current flowing in a conductor migrates toward the periphery of “skin” of the conductor as frequency increases. With increasing frequency, the nonuniform current distribution in the transmission line causes the resistance of a conductor to increase with the square root of frequency. Thus, high-frequency components experience more loss than low-frequency components [12]. Fig. 2(a) shows the system setup to characterize backplane channels. Two line cards are connected by transmission lines on of the neta backplane, forming a two-port network, and work has been measured for 8- and 20-in channels. The line card can be inserted at different separation length via connectors resulting in various overall trace lengths. Fig. 2(b) shows the impulse response of the corresponding channels. As expected, they behave like low-pass filters, depressing high-frequency components, thus causing dispersion for longer trace length. Fig. 2(c) shows the eye diagram of a 10-Gb/s NRZ signal at the output of a 20-in FR4 backplane channel. As shown in Fig. 2(c), the output signal is severely degraded for the 20-in case such that the signal cannot be recovered. It clearly illustrates the need for compensation to maximize the link distance while maintaining signal integrity. Furthermore, different board materials with unique dielectric constants show different characteristics. This implies that the compensation should be adjustable or reconfigurable to cover these variations. As illustrated above, communications through both fiber and backplane copper channels distort the transmitted signal, causing considerable ISI. As a result, it becomes impossible to communicate at high speeds beyond a certain distance using existing infrastructure. In Section III, system-level design details on electronic compensation solutions, which can maximize data throughput and link distance for given band-limited channels, are covered. III. SYSTEM-LEVEL DESIGN DETAIL A. Reconfigurable FFE Channel bandwidth limitation and modal dispersion can be addressed by using a channel-compensation technique, namely, equalization at the transmitter and/or receiver side [13]. An equalization technique compensates the frequency-dependent channel loss characteristics. The band-limited channel has a

Fig. 3. Frequency responses of three example channels and the corresponding optimal equalizer responses.

Fig. 4. System simulation result: (a) before equalization over 8-in backplane, (b) equalization over 8-in backplane, and (c) 20-in backplane.

low-pass frequency response, as shown in Fig. 3. The larger loss in the high-frequency range causes the signal power to smear into the neighboring symbols. The equalization technique restores the high-frequency component of the original transmitted signal. Thus, the frequency response of the equalizer has larger gain values for the high frequencies compared to low frequencies around dc, as shown in Fig. 3. Meanwhile, the equalization can be interpreted as a process to sharpen the channel impulse response. The width of the channel impulse response corresponds to the degree of signal power dispersion in the time domain for a given pulsewidth. Therefore, the equalizer can be regarded as a spectrum shaping filter that shortens the channel impulse response to bring it back to its original transmission width. Meanwhile, an equalizer can be incorporated at the transmitter or the receiver. The transmitter equalizer, which is called a pre-emphasis equalizer, is easier to realize than a receiver equalizer since the FIR filter can be built digitally. However, the pre-emphasis increases the near-end crosstalk (Xtalk) by boosting the high-frequency components for high-speed chip-to-chip interconnections [14]. Moreover, the pre-emphasis requires the information gathered at the receiver to dynamically update the tap coefficients of the FIR filter at the transmitter. Also, since the maximum signal swing at the transmitter is limited by the system constraints and the IC process technology, it is necessary to have additional gain at the receiver to compensate the high-frequency loss as the channel loss increases. For these reasons, the equalizer at the receiver is considered for the proposed work. The equalizer at the receiver can be realized with an analog FIR filter structure, which can be implemented as a zero forcing-linear equalizer (ZF LE) or as a minimum mean squared error-linear equalizer (MMSE LE) depending on the

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Fig. 5. Functional block diagram of the proposed reconfigurable FFE with TD-based output monitoring.

tap coefficient calculation principles [15]. As the transfer function of the ZF LE is the reciprocal of the channel transfer function, ISI caused by the frequency-dependent channel loss can be removed. However, the high-frequency Xtalk noise can also be amplified. In contrast, MMSE LE can ameliorate this noise enhancement problem since its tap coefficients are calculated to minimize overall signal degradation caused by both ISI and Xtalk noise. Frequency responses of the band-limited channel and the corresponding MMSE LE are shown in Fig. 3 [16]. Fig. 4 illustrates the simulated eye diagram of a 10-Gb/s signal before and after equalization over a 8- and 20-in backplane, respectively. An 8- and 20-in backplane required two taps with a 50-ps ( ) delay and four taps with a 33-ps ( ) delay, respectively. In other words, optimal equalizer system requirement varies for different channel configurations, demonstrating the need for a reconfigurable equalization technique to adjust over various band-limited signaling environments. In order to make the system adjustable to various channel environments, a reconfigurable FIR filter is integrated at the receiver, as illustrated in Fig. 5. The FIR filter consists of variable tap gain amplifiers (VTGAs) and tunable tap delay lines. Based on the measured channel response, system simulation is performed to derive the optimal number of taps, tap delay values, and tap coefficients. In order to ameliorate the noise enhancement problem, the minimum mean-squared error algorithm is used for calculation of the tap coefficients [17]. Fig. 5 shows the functional block diagram of the FIR filter at the receiver for data communications over band-limited links. The four-tap FIR filter is utilized to equalize the received signal. The FIR provides enough speed for 1–10-Gb/s communications using a relatively simple architecture. The FIR filter creates a frequency response for MMSE LE, as shown in Fig. 3. For optimum performance of the equalizer, system simulations were performed with 25-, 33-, and 50-ps tap spacing and were also investigated with two-, three-, and four-tap quantities. The largest eye opening with a minimum number of taps is chosen for a given channel to minimize power consumption. In the system simulation, practical implementation limitation, such as the 3–dB bandwidth of each tunable delay line and VTGA, is included.

B. TD-Based Output Monitoring Channel monitoring is critical to provide the appropriate adjustment for reconfigurable channel-compensation solutions. Previously, eye-monitoring schemes were suggested for channel output monitoring [7], [8]. However, this approach requires 10-Gb/s comparators that can be challenging for certain processes. Therefore, a new approach for channel output monitoring is proposed that can achieve a 10-Gb/s data rate and is easy to integrate with the reconfigurable FFE. In this study, a TD-based output monitoring technique is suggested for channel output monitoring to adjust the tap coefficients for optimal performance. Since the channel transfer function is not changing in real time, the proposed TD-based output monitoring technique employs a simple architecture for lower power consumption while achieving the targeted data throughput. To determine the equalization amount for reconfiguration of the system, it is necessary to know how well the FFE is performing. This can be achieved by measuring how much the output signal of the FFE has been dispersed. As detailed in Section II, the dispersion of the signal is mainly caused by the high-frequency component loss through the band-limited channel. This then causes ISI and closes the eye. Since the amount of the high-frequency components is proportional to the amount of the fast transitions, the performance of the FFE can be measured by measuring the amount of the fast transitions. The loss of high-frequency components makes the fast transitions of the signal, such as the edge of the square pulse, smoother and widened. In other words, the integrity of the received signal is improved as the high-frequency components of the transmitted signal experience less loss, letting more fast transitions of the signal occur. The transition signal can be detected by subtracting two delayed equalizer outputs. One path is delayed by and the other path is delayed by multiples of depending on the data rate. The differences of two delayed signals for the transmitted signal can be interpreted as the TD, as illustrated in Fig. 6. This difference will be squared and integrated over a certain period of time to generate a dc value that is proportional to the amount of transition detected. In other words, the amount of transition detected can be used as a figure-of-merit to assess the quality of

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Fig. 6. Conceptual illustration of TD.

the eye. This dc information enables reconfiguration of the FFE for optimal equalization with the optimizing algorithm implemented digitally. The system block diagram for this functionality is shown in Fig. 5. IV. CIRCUIT-LEVEL DESIGN DETAIL A. Reconfigurable Equalizer The key building blocks for the suggested reconfigurable equalizer integrated circuit (IC) are a wide-range tunable tap delay cell and a VTGA. The functional block diagram illustrated in Fig. 5 shows how these building blocks are connected. The channel output signal goes through the tap delay line. ( ps) up to ( ps) Fractional tap spacing of is determined by system simulation. These delayed signals are then multiplied by the tap weights given by system simulation. The resulting amplified signals are combined in the current domain. Finally, the output voltage signal swing is obtained with the total current applied to the common load that is illustrated as a summation node in Fig. 5. Since this signal processing is performed in the analog domain, the suggested analog equalizer consumes less power and provides broad bandwidth compared to the digital equalization approaches. The tunable active delay line consists of cascaded differential amplifiers, as shown in Fig. 7(a). The delay amount is determined by the RC response at the dominant pole that consists of the parasitic capacitance and the load impedance. These , values are highly sensitive to process variation. In order to ensure that the required delay range is covered over process variations, the delay line was designed with an ample margin to cover a range of 15 to 74 ps, as illustrated in Fig. 7(c). Such a wide range was achieved with three differential amplifiers stages cascaded to provide multiple signal paths. The delay weight between the two signal paths is controlled by a current-steering modified Gilbert cell, as illustrated in Fig. 7(a). This structure alleviates the headroom issue with reduced stacked devices [17]. The two differential inputs are connected to M1, M2 and M11, M12. Meanwhile, this delay line is inserted in series along the data path, as shown in Fig. 5. Therefore, the bandwidth of each delay line must be large enough for a 10-Gb/s data transfer. In order to enhance the bandwidth, an active inductance load with resistive feedback is used [18]. Fig. 7(b) shows the bandwidth for tap

Fig. 7. (a) Schematic, (b) bandwidth, and (c) tuning range performance of the proposed wide-range tunable delay.

delay settings at 25, 33, and 50 ps, respectively. While forward transmission gain is reduced by 0.2 dB over the tuning range, the overall bandwidth is maintained as a result of the zero located at the corner frequency. M3, M4, M7, M8, M13, and M14 along with RF represent such active inductance loads. In addition, M1, M2, M5, M6, and M9–M12 were interdigitated in the layout. In other words, the gates from positive inputs and negative inputs were cross-coupled in an alternating fashion to minimize parasitic capacitance for higher bandwidth operation, while achieving minimum phase-offset errors. connected to M15, the delay With control voltage amount can be varied. In other words, with maximum applied, and follows M1, M2, M5, M6, M9, and M10, resulting in a slow delay path. With minimum applied, and signals follow through only M11 and M12, resulting in a fast delay path. With analog control voltage applied, the delay value can vary continuously. Fig. 7(c) shows the performance of the tunable delay line for the designed fractional tap spacing. Wide tuning range is achieved from 15 ps (fast delay path) up to 74 ps (slow delay path) for control voltages from 0.6 to 1.75 V. From the system simulation results, the VTGA needs linear bipolar gain values from 1 to 1. The Gilbert-cell architecture is adopted to meet this requirement, as shown in Fig. 8(a). The proposed FFE has four VTGAs connected to the common load. Each amplifier flows dc current, resulting in four times the dc current flowing through the 50- resistor. This phenomenon

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Fig. 9. Schematic of the proposed fixed active delay line.

Fig. 8(c) shows the overall VTGA performance with gain changing from 1 to 1. Input and output dynamic range of 300 mV/p was achieved, while assuring wide linear range. Finally, the bandwidth performance of the proposed VTGA is shown in Fig. 8(b). It is illustrated over different control voltage settings showing bandwidth and gain relationship. The bandwidth of the proposed VTGA is maintained over 7 GHz across the gain value that is enough for 10-Gb/s data transmission. B. TD-Based Output Monitoring Block

Fig. 8. (a) Schematic, (b) bandwidth, and (c) tuning range performance of the proposed VTGA.

results in the voltage headroom issue. In order to ensure proper voltage headroom for each VTGA, a modified Gilbert cell structure was adopted with a current steering bias scheme. Instead of applying control voltage directly to the differential pair below and are the common source, control voltages applied to M5 and M6 to provide the bias currents proportional to the control input. In addition, both linearity and voltage headroom are enhanced by applying an active degeneration scheme between divided common source branches. The ML transistor pairs, as illustrated in Fig. 8(a), represent such active degeneration with M7, M8, and M10–M13 being the divided current sources.

As illustrated in the functional block diagram of Fig. 5, the TD block constantly monitors the equalized signal. To minimize the loading effect on the FFE output and maintain the bandwidth of the signal path, it is critical that the output sampling is performed with minimum gate size. Since the gate size of the summing circuit in Fig. 9 is larger than that of the delay circuit, an identical fixed delay block with minimum gate size is duplicated on both signal paths. The fixed delay block must provide more than 10 GHz of bandwidth for accurate sampling of the channel output. Fig. 9 depicts the fixed-delay schematic that incorporates active inductance peaking for maximum bandwidth [19]. Each delay block produces approximately 20-ps latency. Fixed-delay blocks are cascaded for transition amount control. Depending on the total delay from the second signal path, the total amount of overlap between the two signals varies. This overlap amount determines detected transition amount providing flexibility for various data rates. For complete operation of the TD between two differential signals, subtraction of the signals is needed. This subtracted waveform is converted to an absolute value for the integrator. Usually implementing those functions requires many transistors, resulting in degradation of high-frequency performance due to parasitic capacitances of MOS transistors. Thus, implementing this with a simple architecture that requires a small number of devices is critical. In this study, the error-detection and squaring functions are achieved at the same time by making use of a differential pair and the square relation between the gate voltages and drain current of the nMOS transistor. When two input signals are applied into the gate and the source of MOS transistor, the subtraction and squaring can be realized without additional components. Due to the inherent square law of the MOS transistor drain current in the saturation region, as follows, these two functions can be implemented

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Fig. 11. TD simulation.

is the bias current of the source follower and given by

(6)

Fig. 10. Schematic of the proposed subtract-and-square circuit.

using one circuit [20]. General MOS transistor’s square law is as follows:

Substituting

into

and

,

will be (7)

where (1) The squaring circuit of difference of two differential inputs and are shown in Fig. 10. Transistors M1, M2 act as the source followers and M3, M4 are squaring blocks. The aspect ratio of M1, M2 is much larger than that of M3, M4. All transistors are operating in the saturation region. At nodes A and is applied to the sources of M1 and M2 with a constant B, is the common-mode dc voltage for voltage drop. Assume two inputs, voltages at nodes A and B are and respectively. Output current (

(2) ) is given by

where

(3)

(4) and

(5)

(8)

The output current is the square of the difference between two input signals. Fig. 11 demonstrates the operation of the TD-based output-monitoring concept. When the output is unequalized, the detected transition amount is relatively small compared to when the output signal is equalized. By integrating this detected transition, it is possible to monitor the status of the equalizer’s output. Since the transition data is the subtraction between the original signal and delayed signal, it is a high-frequency signal. Therefore, the integrator requires a very high bandwidth. A conventional integrator with an op amp and switched capacitor cannot meet this requirement. Hence, in this study, an analog power integrator is implemented with a charge-pump architecture, as shown in Fig. 12(a). The proposed charge pump consists of two current sources: one for sourcing and the other for sinking currents. When the UP signal is active, source currents flow into M5. The gate–channel capacitance of the pMOS transistor acts as a hold capacitor. As a result, the output voltage rises. If the DOWN signal is active, source currents flow out of M5. Normally a charge pump charges up and down, as described. However, for this application, only charging up is needed for dc value. As shown in Fig. 12(a), the charge pump is modified to have only charge up at the output. To reset the dc value, an external control voltage is periodically applied to control the switch operation at M2 and reset the integrated value. When B is high, transistor M2 is on and all the charge will go to the ground.

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Fig. 14. FFE performance measurement setup over 8- and 20-in backplane trace lengths. (Color version available online at http://ieeexplore.ieee.org.)

Fig. 12. Charge-pump-based integrator. (a) Schematic. (b) Simulation result.

Fig. 15. Measured eye-diagram results. (a) Before equalization. (b) After equalization for 20-in backplane. (c) Over-equalized for 8-in backplane. (d) After 8-in backplane with reconfigured equalization.

Fig. 13. Bandwidth of the proposed reconfigurable FFE.

Fig. 12(b) illustrates the simulated operation of the proposed charge-pump-based integrator [21]. With unequalized input coming in, the integrator output increases slowly over time. Whereas when the input signal is equalized, the integrator receives more transition signals resulting in faster integrated output. This dc value is used at a digital control block, illustrated in Fig. 5, for optimal control based on the output monitor status. V. RESULTS For the fabrication of the equalizer, the 0.18- m CMOS technology provided by National Semiconductors, Santa Clara, CA, was used. This process has typical threshold voltage of 450 mV and cutoff frequency of 40 GHz. The bandwidth of the proposed equalizer is shown in Fig. 13. As can be seen from Fig. 13, the overall bandwidth is affected by four VTGAs as the primary load, and the serial data path limited by the three series of tunable delay. The solid line denotes bandwidth through all four taps, while the dashed line denotes bandwidth only through the first tap. The proposed equalizer is showing an ample 5.4-GHz overall bandwidth through all cases that is slightly higher than the Nyquist frequency of 5 GHz for 10-Gb/s data communications.

To demonstrate the reconfiguration option of the equalizer, the same equalizer is used to compensate 8- and 20-in backplanes trace lengths. Fig. 14 illustrates the measurement setup with pluggable daughter cards that vary the overall trace lengths. For the measurements, the HP70843B error performance analyzer and the HP70340A signal generator was used to generate 10-Gb/s pseudorandom bit sequences. After the proposed reconfigurable FFE mounted on a probe station, the Agilent 86100A wide-bandwidth oscilloscope was used to measure the output. For probing, seven dc probes and two ground–signal–signal–ground (GSSG) probes with the pitch of 150 nm were used. The 10-Gb/s signal after a 20-in backplane is shown in Fig. 15(a) with a completely closed eye diagram. No data information can be retrieved before equalization. Fig. 15(b) shows the eye diagram after equalization using delay. The eye diagram is open now and four taps and equalization is successful. The signal can now be recovered. Fig. 15(c) is the output waveform after an 8-in backplane and equalizer with settings for a 20-in backplane. As the channel configuration changes, signal integrity is impaired due to over-equalization. Fig. 15(d) shows the reconfigured FFE performance to correctly equalize the 8-in backplane with three delay. These test results demonstrates the need taps and for a reconfigurable equalizer IC, shown in Fig. 16. Fig. 17 is the simulation results that demonstrate the TD-based output monitoring technique. The first waveform is the transmitted data. After passing through a band-limited channel, the received data is severely degraded. The proposed FFE restores the signal as shown in the third waveform. The

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Fig. 16. Chip micrograph of the proposed reconfigurable equalizer.

Fig. 17. Simulation results that demonstrate the proposed TD-based output monitoring technique.

fourth waveform is a fixed-delayed waveform. Finally, the subtract-and-square circuit is able to take the difference and square the signal resulting in a positive signal ready for integration. As was illustrated in Fig. 12(b), the output of the integrator provides a dc signal that can be used for optimizing the equalizer tap coefficients. VI. CONCLUSION In this paper, a universal solution for compensating various band-limited channels has been proposed. A reconfigurable FFE IC has been implemented in a 0.18- m CMOS technology, which has a typical threshold voltage of 450 mV and cutoff frequency of 40 GHz. The proposed reconfigurable FFE successfully compensates various band-limited channels at 10 Gb/s. In addition, feasibility has been demonstrated for a new output monitoring technique that does not require any clocking information from a CDR. REFERENCES [1] G. Keiser, Optical Fiber Communications, 3rd ed. New York: McGraw-Hill, 2000. [2] C. Pelard, E. Gebara, A. J. Kim, M. Vrazel, E. Peddi, V. M. Hietala, S. Bajekal, S. Ralph, and J. Laskar, “Multilevel signaling and equalization over multimode fiber at 10 Gb/s,” in Proc. IEEE GaAs IC Symp., Nov. 2003, pp. 197–199. [3] H. Wu, J. A. Tierno, P. Pepeljugoski, J. Schaub, S. Gowda, J. A. Kash, and A. Hajimiri, “Integrated transversal equalizers in high-speed fiber-optic systems,” IEEE J. Solid-State Circuits, vol. 38, no. 12, pp. 2131–2137, Dec. 2003.

[4] L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “Increasing the bandwidth-distance product of multimode fiber using offset launch,” Electron. Lett., vol. 33, no. 3, pp. 232–233, Jan. 1997. [5] K. M. Patel and S. E. Ralph, “Multimode fiber link equalization by mode filtering via a multisegment photodetector,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, vol. 2, pp. 1343–1346. [6] Z. Haas and M. A. Santoro, “A mode-filtering scheme for improvement of the bandwidth-distance product of multimode fiber systems,” J. Lightw. Technol., vol. 11, no. 7, pp. 1125–1131, Jul. 1993. [7] F. Buchali, W. Baumert, and H. Bullow, “Adaptive 1 and 2 stage PMDcompensators for 40 Gbit/s transmission using eye monitor feedback,” in Opt. Fiber Conf., 2003, vol. 1, pp. 262–263. [8] B. Analui, A. Rylyakov, S. Rylov, M. Meghelli, and A. Hajimiri, “A 10-Gb/s two-dimensional eye-opening monitor in 0.13-m standard CMOS,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2689–2699, Dec. 2005. [9] X. Zhao and F. S. Choa, “Demonstration of 10-Gb/s transmission over a 1.5-km-long multimode fiber using equalization techniques,” IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1187–1189, Aug. 2002. [10] J. H. Winters and R. D. Gitlin, “Electrical signal processing techniques in long-haul, fiber-optic systems,” IEEE Trans. Commun., vol. 38, no. 9, pp. 1439–1453, Sep. 1990. [11] H. Bulow, “Electronic equalization of transmission impairments,” in Proc. Opt. Fiber Commun. Conf., Mar. 2002, pp. 24–25. [12] J. H. Winters and R. D. Gitlin, “Electrical signal processing techniques in long-haul, fiber-optic systems,” IEEE Trans. Commun., vol. 38, no. 9, pp. 1439–1453, Sep. 1990. [13] F. Krummenacher and N. Joehl, “A 4-MHz CMOS continuous-time filter with on-chip automatic tuning,” IEEE J. Solid-State Circuits, vol. 23, no. 6, pp. 750–758, Jun. 1988. [14] D. A. Watley, K. S. Farley, B. J. Shaw, W. S. Lee, G. Bordogna, A. P. Hadjifotiou, and R. E. Epworth, “Compensation of polarization-mode dispersion exceeding one bit period using single high-birefringence fiber,” Electron. Lett., vol. 35, no. 13, pp. 1094–1095, Jun. 1999. [15] I. Riant, S. Gurib, J. Gourhant, P. Sansonetti, C. Bungarzeanu, and R. Kashyap, “Chirped fiber Bragg gratings for WDM chromatic dispersion compensation in multispan 10-Gb/s transmission,” IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 5, pp. 1312–1324, Sep.–Oct. 1999. [16] J. G. Proakis, Digital Communications, 4th ed. New York: McGrawHill, 2001. [17] F. Bien, H. Kim, Y. Hur, M. Maeng, E. Gebara, and J. Laskar, “A reconfigurable 0.18-m CMOS equalizer IC with an improved tunable delay-line for 10-Gb/s backplane serial I/O links,” presented at the IEEE MTT-S Int. Microw. Symp., Jun. 2006. [18] Y. S. Hur, M. Maeng, C. Chun, F. Bien, H. Kim, S. Chandramouli, E. Gebara, and J. Laskar, “Equalization and near-end crosstalk (NEXT) noise cancellation for 20 Gb/s 4-PAM backplane serial I/O interconnections,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 246–255, Jan. 20051. [19] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits. Cambridge, U.K.: Cambridge Univ. Press, 1998. [20] H. Song and C. Kim, “An MOS four-quadrant analog multiplier using simple two-input squaring circuits with source followers,” IEEE J. Solid-State Circuits, vol. 25, no. 6, pp. 841–848, Jun. 1990. [21] M. Q. Le, P. J. Hurst, and K. C. Dyer, “An analog DFE for disk drives using a mixed-signal integrator,” IEEE J. Solid-State Circuits, vol. 34, no. 5, pp. 592–598, May 1999.

Franklin Bien (S’04) received the B.S. degree from Yonsei University, Seoul, Korea, in 1997, the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2000, and is currently working toward the Ph.D. degree at the Georgia Institute of Technology. From 2000 to 2002, he was with Agilent Technologies, as an Analog IC Design Engineer, where he developed transceiver ICs for enterprise segments. From 2003 to 2004, he was with Quellan Inc. as a Senior Design Engineer, where he developed ICs that improve the speed and reach of communication channels in consumer, broadcast, enterprise, and computing markets. His research interests include signal integrity improvement with alternate modulation schemes, Xtalk noise cancellation, and equalization techniques for 10 -Gb/s broadband communication applications.

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Hyoungsoo Kim (S’04) received the B.S. degree in electrical engineering from Yonsei University, Seoul, Korea in 2000, the M.S. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2004, and is currently working toward the Ph.D. degree at the Georgia Institute of Technology. His interests include CDR, equalization for pulse amplitude modulation (PAM) signals and mixed-circuit design.

Soumya Chandramouli (S’00) received the B.S. degree in electrical and computer engineering from Lafayette College, Easton, PA, in 1998, and is currently working toward the Ph.D. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta. Her research interests include CMOS circuit design for comparators and analog-to digital converters with applications in gigabit transceivers.

Youngsik Hur (S’04–M’06) received the B.S. and M.S. degrees in electrical engineering from Hanyang University, Seoul, Korea, in 1993 and 1995, respectively, and the Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2005. During his doctoral studies, he was involved with mixed-signal circuit implementation of equalization and noise-cancellation techniques for broadband wired and wireless communication applications. Prior to joining the Samsung RFIC Design Center, Georgia Institute of Technology, Atlanta, in 2006, he was with the Samsung Institute of Advanced Technology, Kiheung, Korea, and subsequently with Samsung Electronics, Suwon, Korea, from 1995 to 2001. During this period, he was involved with the development of an orthogonal frequency division multiplexing (OFDM) wireless communication system and a channel characterization of the 60-GHz indoor wireless channel. He subsequently lead the system development efforts of the Fiber-Optic Security Sensor System Project. His current research interests include developments of system and IC solutions enabling the convergence of digital broadcasting and broadband wireless data access. He is specifically focused on realizing cognitive radio (CR) technology as a promising coexistence solution of the unlicensed spectrum applications.

Edward Gebara (M’05) received the B.S. (with highest honors), M.S., and Ph.D. degrees in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 1996, 1999, and 2003, respectively. He is currently a Member of Technical Staff with Quellan Inc., Atlanta, GA, which develops high-performance analog semiconductors that improve the speed and reach of communication channels in consumer, broadcast, enterprise, computing, and wireless markets. He is also a research faculty member with the Georgia Institute of Technology, where he leads the Mixed Signal Team’s research efforts. The team’s research interest is to develop the foundation for alternate modulation schemes (quadrature amplitude modulation (QAM), optical subcarrier multiplexing (OSCM), etc.), equalization techniques, and Xtalk cancellation techniques on pure CMOS applied to next-generation wired and wireless communication. He has authored or coauthored over 50 publications

Moonkyun Maeng (S’03–A’05–M’06) received the B.S. degree from Kwangwoon University, Seoul, Korea, in 1999, and the M.S. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 2002 and 2005, respectively. He is currently an Analog IC Design Engineer with the Intel Corporation, Folsom, CA. Prior to joining the Intel Corporation, he was with National Semiconductor in 2003 for a summer internship, where he was involved with a gigabit interconnection project. In 2004, he joined the Intel Corporation for a summer internship, where he was involved in high-speed I/O interface circuit design. His research interests are CMOS mixed-signal IC design such as FFE, decision-feedback equalizers (DFEs), CDR, and gigabit transceivers for backplanes and fiber channels.

Jeongwon Cha (S’06) received the B.S. and M.S. degrees in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2004 and 2006, respectively, and is currently working toward the Ph.D. degree in electrical engineering from the Georgia Institute of Technology. For two years, he was a student with Korea University, Seoul, Korea, prior to joining the Georgia Institute of Technology. His current research interests include CDR, linearization of optical modulators, equalization of optical links, and mixed-circuit design.

Joy Laskar (S’84–M’85–SM’02–F’05) received the B.S. degree in computer engineering with math/physics minors (with highest honors) from Clemson University, Clemson, SC, in 1985, and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 1989 and 1991, respectively. Prior to joining the Georgia Institute of Technology in 1995, he held faculty positions with the University of Illinois at Urbana-Champaign and the University of Hawaii. With the Georgia Institute of Technology, he holds the Joseph M. Pettit Professorship of Electronics and is currently the Chair for the Electronic Design and Applications Technical Interest Group. He is also the Director of the Electronic Design Center, Georgia Institute of Technology. and the System Research Leader for the NSF Packaging Research Center. His research has produced numerous patents and transfer of technology to industry. Most recently, his research has resulted in the formation of two companies. In 1998, he co-founded the advanced wireless local area network (WLAN) IC Company RF Solutions, which is now part of Anadgics (Nasdaq: Anad). In 2001, he co-founded the next-generation interconnect company Quellan Inc., Atlanta, GA, which develops collaborative signal-processing solutions for enterprise applications. Prof. Laskar has been appointed an IEEE Distinguished Microwave Lecturer for the 2004–2006 term for “Recent Advances in High Performance Communication Modules and Circuits” seminar.

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CMOS Active Bandpass Filter Using Compacted Synthetic Quasi-TEM Lines at C -Band Ching-Kuang C. Tzuang, Fellow, IEEE, Hsien-Hung Wu, Student Member, IEEE, Hsien-Shun Wu, Member, IEEE, and Johnsea Chen

Abstract—This paper presents a fully monolithic transmission-line-based active bandpass filter (BPF) fabricated in a 0.18- m standard complementary metal–oxide–semiconductor (CMOS) technology. The half-wavelength resonators are realized by synthetic quasi-TEM complementary conducting-strip transmission lines (CCS TLs). To lower the insertion loss of the BPF, the differential nMOS cross-coupled pairs are combined with the parallel resonators. Besides, the active devices and CCS TLs are vertically integrated on the standard CMOS substrate. The -enhanced resonator, which is comprised of a CCS TL and an nMOS cross-coupled pair, is theoretically investigated. Simulation results indicate that the factor of the resonator can be increased from 3.4 to 84.0 at 6.53 GHz. Additionally, the prototype of the second-order BPF occupies an area of 1230 m 880 m, and the measured results demonstrate that the center frequency is 6.02 GHz with a bandwidth of 1.14 GHz. The 1dB and insertion loss are 15.2 dBm and 2.2 dB, respectively, when the BPF consumes 3.0 mA from a 1.8-V supply. A two-port noisy network is also reported to examine the noise figure (NF) of the proposed BPF. Theoretical results reveal that the NF is 11.38 dB at 6.0 GHz, with a difference of less than 7.2% among the measured data. Index Terms—Active bandpass filter (BPF), transmission line (TL).

-band, CMOS,

I. INTRODUCTION N-CHIP radio or RF systems-on-chip (RF SOCs) incorporating monolithic complementary metal–oxide–semiconductor (CMOS) bandpass filters (BPFs) have become increasingly attractive in the world of a congested frequency spectrum for personal communications service (PCS) band [1], wideband code-division multiple-access (WCDMA) receivers [2], and time-division-duplex (TDD) systems [3]. Elimination of off-chip filters often means adding RF performance, improving selectivity requirements, reducing noise pick-up, and lowering overall RF power consumption [2], [3]. On-chip CMOS passive resonators formed of transmission lines (TLs) typically have quality factors ( factors) proportional to the square root of the operating frequency. A carefully designed CMOS BPF at millimeter-wave frequency generally provides factor. Therefore, a passive BPF at 30 and an adequate

O

Manuscript received April 8, 2006; revised May 30, 2006. C.-K. C. Tzuang and H.-S. Wu are with the Graduate Institute of Communication Engineering, Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C. (e-mail: [email protected]). H.-H. Wu is with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C. (e-mail: [email protected]). J. Chen is with the Cadence Methodology Service Company, Taipei, Taiwan 116, R.O.C. Digital Object Identifier 10.1109/TMTT.2006.881507

40 GHz have been found to perform reasonably well [4], [5]. However, most wireless applications operate below -band (4–8 GHz) where the CMOS on-chip spiral inductor necessary for carrying out the resonator design has a fairly low factor, of typically 5 or below [6, Table I]. This paper presents the recent advance in the state-of-the-art CMOS active BPF design achieving a small size, low passband loss, high outband rejection, low power consumption, low noise figure (NF), and high input 1-dB compression point. The literature survey indicates that most active CMOS BPFs below the -band incorporate inductors for resonator designs, e.g., actively -enhanced coupled inductors [2], [7], emulated coupled inductors [6], energy-recovered spiral inductors [8], and -enhanced LC bandpass biquads [9]. This paper presents a novel approach based on a microwave filter design procedure incorporating low- half-wavelength resonators loaded by active circuits to compensate losses [10]. In contrast to the recently reported -band passive lumped-element filter [11], which was fabricated in a highly resistive silicon substrate with a resistivity 100 times that of a typical CMOS foundry wafer, the proposed design methodology adopts synthetic quasi-TEM TLs on a standard CMOS substrate, rendering a high-performance miniaturized active BPF design. The previously published research briefly reported the measurement results of the proposed active BPF [10]. However, this paper explores in detail the design of the active TL resonator based on a complementary conducting-strip transmission line (CCS TL) followed by the differential- and common-mode analyses on the active resonator in Section II. Section III then presents a practical example with the design parameters and experimental characterizations. Section IV then investigates the NF of the presented active BPF with a two-port noisy network. Conclusions are finally drawn in Section V. II. CMOS TL-BASED RESONATORS A. CMOS CCS TL Recently the synthetic quasi-TEM TL so-called CCS TL had experimentally demonstrated its application in [10], [12], [13]. The CCS TL is made of a unit cell, which has dimensions much smaller than the operating wavelength, typically one-thousandth. The unit cell consists of a mesh ground and a four-arm signal trace. The guiding characteristics of the CCS TL had been investigated intensively, showing the following features [12]–[14]. First, the characteristic impedance and propagation constant of the CCS TL can be controlled by the varying geometric parameters such as the width of the signal

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Fig. 1. Monolithic CCS TL of 7 vices.

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2 5 unit cells integrating above the active de-

trace and the mesh area of the mesh ground plane. Second, the real estate of the CCS TL-based passive circuit is proportional to the period of unit cell, which is scalable with advance in photolithography. Third, the mesh ground plane can provide good electromagnetic (EM) shields to avoid cross coupling of circuits integrated by the CCS TL. Fig. 1 reports for the first time that the CCS TL is right on top of transistor region. The inset of Fig. 1 shows the cross-sectional view of the CCS TL adopted in this paper, in which top metal forms a meandered signal path. M2 is applied to realize the mesh ground plane, which is sandwiched between the CCS TL and the first metal layer (M1) for interconnections between active devices. Such connections also include the biasing paths for the terminals (source, drain, and gate) in a MOS transistor backbone buses for paralleling the MOS transistors. The guiding characteristics of the CCS TL on the silicon substrate shown in Fig. 1 were investigated by performing full-wave EM simulations using Ansoft’s finite-element-based High-Frequency Structure Simulator (HFSS). The following material and structural parameters, which were defined in the EM simulations, were specified based on a typical 0.18- m CMOS 1P6M process. The thicknesses of M6 and M2 metal layers are 2.0 and 0.55 m, respectively. The relative dielectric constant and the thickness of inter-media-dielectric (IMD) sandwiched between M6 and M2 are 4.0 and 5.88 m, respectively. The thickness and conductivity of the silicon substrate are 482.6 m and 11 S/m, respectively. The linewidth (W) of the CCS TL is 30.0 m, the ) period (P) of the unit cell is 44 m and the mesh area ( is 40 m 40 m. The TL parameters, including complex characteristic impedances and propagation constants, were extracted from the twoport scattering analyses [12]. Fig. 2 shows the extracted results of the typical CCS TL design example of Fig. 1 based on the above-mentioned parameters. From 1.0 to 8.0 GHz, the real part of the characteristics impedance ( ), which is the solid line plotted in Fig. 2(a), nearly keeps at a constant value of 34.2 . The imaginary is capacitive, ranging from 11.7 to 2.04 . The part of normalized phase constant shown in solid line in Fig. 2(b) illustrates the value of 1.86 at the desired operating frequency.

Fig. 2. Guiding characteristics of the meandered compacted CMOS-based CCS TL of Fig. 1. (a) Complex characteristic impedance. (b) Normalized complex propagation constant. (c) factor.

Q

Therefore, we can estimate the physical length of a half-wavelength CCS TL at 6.0 GHz to be 13 210- m long and such TL can be compacted in the area of 792 m 792 m by using the meandered CCS unit cells with a period of 44.0 m. The normalized attenuation constant, which is plotted by the dotted symbol in Fig. 2(b), however, shows a relatively high loss aspect of the TL. In the low frequency limit (1 GHz), the metal thickness employed in the CCS TL is smaller than the skin depth, thus we observe larger attenuation losses. Fig. 2(c) plots the factor of the CCS TL against frequency, showing 2.19, 2.94, and 3.40 at 3.0, 5.0, and 6.53 GHz, respectively. factors employed in our design of an active resonator The

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Q

Fig. 3. -enhanced CCS half-wavelength resonator incorporating an nMOS cross-coupled pair.

are comparable, but smaller than those of inductor-based design [1]–[3], [6]–[9]. Since the factor of the CCS TL suffers from the process limitation, the losses of CCS-TL-based resonators need to be compensated. In Section II-B, a MOS-based active network is reported for elevating the factor of the CCS half-wavelength resonator. B.

Q

Fig. 4. Small-signal analyses of the -enhanced half-wavelength resonator. (a) Differential-mode analysis. (b) Common-mode analysis.

-Enhanced Monolithic Half-Wavelength Resonator

Fig. 3 shows the concept of a -enhanced complementary conducting-strip (CCS) half-wavelength resonator. A cross-coupled pair, which consists of two identical nMOS transistors, is integrated into a half-wavelength resonator. The drain terminal of N1 is directly connected to the gate terminal of N2 and vise versa. Two transistors are biased at the same dc potential ( ), and the drain terminals of both N1 and N2 are directly loaded with a CCS half-wavelength resonator forming a new composite resonator. Since the active resonator will be excited single endedly, not differentially, both common- and differential-mode signals will exit in the active resonator structure. Fig. 4(a) and (b) illustrates the equivalent circuits for differential- and common-mode excitations, respectively. When a differential-mode signal transmits into a cross-coupled nMOS transistors pair and establishes a positive feedback, a virtual ground is formed at the symmetric plane rendering a in Fig. 4(a) with magninegative differential resistance tude approximately equal to the inverse of transconductance of the cross-coupled pair [15]. On the other hand, the capacitance across the resonator is approximately half of the combined ca). pacitance ( Since the potentials on the drain and gate terminals of the nMOS are equal under a common-mode excitation, the nMOS acts as a gate–drain-connected diode. Therefore, two parallel RC networks are loaded with both sides of the half-wavelength resshown in Fig. 4(b) represents onator. The shunt resistance the small-signal resistive loss of the transistor operated in the saturation region. To make proper operation of the active BPF, the differential mode must prevail over the common mode in the passband. Since the cross-coupled pair can amplify the differential-mode signal and attenuate the common-mode signal, such a circuit characteristic can increase the common-mode rejection

of the proposed -enhanced resonator, and relax the issue on symmetrical layout of the resonator during the filter integration. The complex input impedance under differential-mode excitation was theoretically investigated by using Agilent’s ADS2004A software. Through the analysis, the length and width of the two transistors were set at 0.18 and 80 m, respectively. was isolated from the differential RF signal by an RF and were choke. The results illustrate that the value of nearly constant from 1.0 to 8.0 GHz, revealing a broadband characteristic of the equivalent active RC circuit. The total ) of the differentially driven active equivalent resistance ( resonator can be expressed by

(1) where represents the loss of the CCS half-wavelength resonator. Since the value of the frequency-dependent increases with increasing frequency, the active resonator tends to become more stable at frequency higher than the resonant is inversely proporfrequency. Furthermore, the value of tional to the drain current of the nMOS transistors [15]. Thus, can be applied to adjust proper negative as shown in Fig. 5, resistance for realizing a stable half-wavelength resonator. The inset in Fig. 6 depicts the schematic for extracting the factor of the active half-wavelength resonator unloaded shown in Fig. 3. Two tiny capacitors of 0.01 fF formed the EM coupling between the resonator and loads. Clearly the excitation was single ended. The size of the nMOS transistor was the same as that reported in Fig. 5, and the half-wavelength resonator was realized by using the meandered CCS of the CCS TL reported in Section II-A. The value of half-wavelength resonator and of the cross-coupled pair

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Fig. 7. Second-order CMOS TL-based BPF.

Fig. 5. Differential input impedance of a 0.18-m nMOS cross-coupled pair with length of 0.18 m and width of 80.0 m.

Fig. 8. Chip photograph of the prototype BPF in Fig. 7.

Fig. 6. Unloaded Q factor of Q-enhanced half-wavelength resonator incorporating a 0.18-m nMOS cross-coupled pair.

biased at 557 mV are 298.4 and 301.34 at 6.53 GHz, respectively. Therefore, according to (1), Fig. 6 illustrates a stable active half-wavelength resonator. The extracted factors shown in Fig. 6 follow the definition of the unloaded factor in [16]. Moreover, the magnitudes of the transducer gain of the weakly coupled active resonator are factor was only 3.40 for the also illustrated in Fig. 6. The passive CCS half-wavelength resonator. With the active -enhanced circuit biased at 525, 538, 549, and 557 mV, the enhanced factors were 9, 15, 39, and 84, respectively. Notably, the resonant frequency of the -enhanced resonator was slightly was increased. Such shifted from 6.633 to 6.531 GHz when shown in Fig. 5. frequency drift was caused by the increase of III. CMOS TL-BASED ACTIVE BPF Fig. 7 shows the complete schematic of a second-order BPF incorporating the -enhanced half-wavelength resonators [10]. The -inverters were realized by series capacitors , , and . The design procedure of the BPF is well documented in of the BPF was located at [16]. In this practical example, 6.02 GHz, and bandwidth (BW) was 1.0 GHz with a ripple of

0.2 dB. The order of the BPF was two and the reference impedances of two terminals ( and ) were 50 . The biasing provided biasing curand tuning networks controlled by rents for the nMOS cross-coupled pairs. These networks were isolated from the CCS TL resonators by the on-chip spiral inductors, as shown at the top of Fig. 8. Fig. 8 also illustrates the chip photograph of the prototype filter in Fig. 7. The entire active BPF, including the CCS TLs, capacitors, inductors, active networks, and pads were fully integrated in a chip area of 1230 m 880 m. The capacitor was realized with the so-called interdigital metal–oxide–metal (MoM) capacitors of was 380 fF with top-three metal layers. In the realizations, was 220 fF with an area of an area of 45.9 m 79.8 m, and 41.9 m 52.8 m, respectively. Additionally, the inductance of the on-chip spiral inductors was approximately 3.0 nH and occupied an area of 251 m 247 m. The small-signal experiments were performed after the on-wafer short-open-load-thru (SOLT) procedures had been conducted by the vector network analyzer (VNA) Agilent E5091A. In the measurements, the prototype shown in Fig. 7 ) of 1.8 V with a was biased by a supplying voltage ( current consumption of 3.0 mA. The value of and the power level of input signals were set at 1.0 V and 20 dBm, respectively. Additionally, the measured result was compared with simulations performed by Agilent’s ADS2004A. Before the simulation, all the passive components including capacitors, inductors, and CCS TL were characterized by Ansoft’s HFSS. The BSIM3 V3.2.4–based RF models used for active devices were provided by the foundry. Fig. 9(a) shows the comparisons

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Fig. 9. Transmission and reflection characteristics of the active BPF in Fig. 8. (a) Comparison of measured and simulated data over 5-GHz narrow BW. (b) Measured responses across 20-GHz broad BW for investigating spurious responses.

from 3.0 to 8.0 GHz, revealing good agreement between the simulated and measured data, except for the return loss at passband. The slight mismatch shows that the capacitive coupling between the two -enhanced half-wavelength resonators , and parasitic were well controlled through the -inverter coupling through the lossy substrate was not serious owing to the good EM shield from the meshed ground plane of the CCS TL. In other words, the CCS TL can effectively confine the EM propagations and eliminate the unwanted coupling of the adjacent signal lines in the compact layout. The measured results of two-port scattering parameters based on the 50- system lead the following observations. The center frequency of the second-order BPF is 6.02 GHz, and the insertion loss is approximately 2.2 dB from 5.38 to 6.65 GHz. The BW is approximately 1.14 GHz (5.26–6.40 GHz) with a return loss of 7.64 dB. Two reflection zeros are identified at 5.47 and 6.20 GHz. Additionally, the prototype can reject the low-side signal approximately 28.18 dB at 4.0 GHz and the high-side signal approximately 18.33 dB at 8.0 GHz. The spurious response of the prototype, which is observed in Fig. 9(b), is suppressed approximately 16.67 dB at 15.25 GHz. The nonlinear characteristics of the prototype had also been investigated by measuring the input third-order intermodulation ) and the 1-dB compression point ( ). intercept point ( For the measurement of , the signal generator Agilent

Fig. 10. Nonlinear characteristics of the active BPF in Fig. 8. (a) Input 1-dB ). (b) Input third-order intermodulation intercept point compression point (P (IIP ).

E8267D provided an input continuous wave (CW) at 6.02 GHz, and the spectrum analyzer Agilent E4440A was applied to observe the output signals of the prototype. For the measurement , two signal generators were applied to generate two of fundamental frequencies centered at 5.8 GHz with a separation of 10 MHz. The testing system, which includes the connectors and cables, were calibrated before the experiments. Additionally, the biasing conditions of the prototype were kept the same as those in the -parameter experiments. The measured results, as shown in Fig. 10, indicate the input power levels for and are 15.2 dBm and 9.6 dBm, respectively. IV. NOISE ANALYSES OF TL-BASED ACTIVE BPF Experimental results in Fig. 9(a) indicate that the prototype is a passive filter with an insertion loss of 2.2 dB in the passband. According to the textbook definition, the NF of a passive two-port network is equivalent to the inverse of its available power gain [17]. However, the proposed BPF, as depicted in Fig. 7, is comprised of a CCS TL and differential nMOS cross-coupled pairs. The cross-coupled pairs not only provide negative resistance to elevate the factor of the resonators, but also produce the noise simultaneously. Therefore, the noise contributions from the transistors need to be incorporated into the NF of the proposed BPF. Therefore, a noisy network is presented here to investigate the NF of the proposed BPF shown

TZUANG et al.: CMOS ACTIVE BPF USING COMPACTED SYNTHETIC QUASI-TEM LINES AT

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Fig. 11. Equivalent noisy two-port network of the prototype BPF in Fig. 7.

in Fig. 7. Fig. 11 illustrates the two-port network consists of an ideal amplifier and a noise current source. The gain of the ideal amplifier indicates the transmission coefficient of the BPF, and the noise current source at the output of the ideal amplifier represents the total noise current generated by the nMOS cross-coupled pairs. The noise characteristics of an nMOS cross-coupled pair had been well documented in [18] and [19]. The differential output noise current spectral density of an nMOS cross-coupled pair is equivalent to the summation of thermal noise generated in the channels of two nMOS transistors [19]. Furthermore, the channel noise of an nMOS transistor operating in saturation can be quantified by an equivalent noise current between the drain and source terminals

Fig. 12. NFs of the proposed BPF.

(2) and are the transconductance and channel noise where coefficient of an nMOS transistor, respectively [20], [21]. To demonstrate the feasibility of the proposed noisy network, the theoretical analyses were conducted with the two-port network illustrated in Fig. 11 and the transistor parameters reported derived according to the defin Section II-B. The value of inition in [21] was 8.872 mS. The value extracted from the small-signal noise analysis of the nMOS transistor was 1.012 at 6.0 GHz [21]. Thus, the total noise current spectrum denA Hz sity of the nMOS cross-couple pairs was at 298.15 K. The calculated NF of the proposed BPF after following the procedures described in [22] was 11.38 dB. Additionally, the calculation results from 5.5 to 6.0 GHz were compared with those of the simulations and experiments, as illustrated in Fig. 12, revealing a difference of less than 7.2% on the noise analyses. The measurements, which were undertaken using the Agilent NF analyzer N8974A, reveal that the NF of the prototype was approximately 12.36 dB at 5.5 GHz, which was slight decreased to 10.92 dB at 5.8 GHz. Simulation results indicate that the NF of the proposed bandpass filer was 12.30 and 11.40 dB at 5.5 and 6.0 GHz, respectively. These good agreements indicate that the proposed noisy network is valid for predicting the NF of the BPF shown in Fig. 7. Furthermore, the NF of the proposed BPF with different transistor width was also theoretically analyzed by following the same above-mentioned analytical procedures. Through the analyses, the characteristics of the BPF, including the insertion loss, reflection coefficient, and BW, were identical to those reported in Fig. 9(a).

Fig. 13. Theoretical predictions of noise performances for the proposed BPFs with different transistor widths. (a) g and . (b) NFs of the BPFs.

Fig. 13(a) and (b) plots the statistical results from which the following observations can be drawn. The value of , denoted by the curve with square symbols in Fig. 13(a), is highest at 1.63 with the smallest transistor width of 10.0 m. However, can be reduced and kept with a constant value of 1.10 when the is increased from width is larger than 80 m. Conversely, 5.52 to 11.12 mS, corresponding to the increase of transistor

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width from 10 to 160 m. Since the equivalent small-signal resistor between the drain and source terminals increases due to the nonquasi-static (NQS) effect [23], the higher value of is required to reduce the ohmic loss from the CCS TLs and the resistive loss in the channels of transistors. As revealed in (2), the noise current of the transistor is proportional to the product and . Consequently, the NF, denoted by the curve with of triangular symbols in Fig. 13(b), is 11.38 dB, corresponding to the transistor width of 10 m. Increasing the width of the transistor from 10 to 20 m causes the NF linearly reduced to its minimum value of 9.82 dB. However, using the transistor width larger than 20 m in the BPF increases the resultant NF. These observations demonstrate the design tradeoff for minimizing the NF of the proposed BPF. V. CONCLUSION A TL-based active BPF was realized by using standard 0.18- m CMOS 1P6M technology. The active BPF was constructed using the -enhanced half-wavelength resonators, which consisted of a differential nMOS cross-coupled pair and synthetic quasi-TEM CCS TL. In the CMOS process, the top metal (M6) and bottom metal (M1) formed the meandered traces and interconnections of the CCS TL and active devices. A mesh ground plane, located at M2, was sandwiched between M6 and M1, completing a vertical integrations for the proposed active BPF. The on-chip guiding characteristics of the CCS TL were theoretically extracted as the basic parameters for designing the -enhanced resonator. The circuit behaviors of the -enhanced resonator were theoretically investigated by conducting the differential- and common-mode analyses. The -enhanced resonator acted as a stable parallel resonator with -enhancement when the nMOS cross-coupled pair provided a negative resistance with an absolute value larger than that of a parallel resonator at the resonant frequency. The theoretical results indicate that the factor of the resonator was elevated from 3.4 to 84 at 6.53 GHz. This resonator was applied in designing a prototype of a second-order BPF at -band with a chip area of 1230 m 880 m. The comparisons between the on-wafer measurements and simulations reveal that the proposed active TL-based BPF is feasible. Drawing 3.0 mA from a 1.8-V supply, the prototype achieved 2.2-dB insertion loss and 7.64-dB return loss when operating with a 1.14-GHz BW at 6.02 GHz. The suppressions of spurious responses were 24 and 16.67 dB at 12.0 and 15.25 GHz, respectively. The high- and low-side rejections were 18.33 and 28.18 dB at 8.0 and 4.0 GHz, respectively. The input 1-dB compression point ) and third-order intermodulation intercept point ( ) ( were 15.2 dBm and 9.6 dBm, respectively. Additionally, a noisy two-port network was constructed to examine the NF of the proposed BPF. In the network, the total noise of the BPF consists of its transmission loss and the noise current produced by the nMOS cross-coupled pairs. The results of the analysis were compared with those of the simulations and experiments, revealing a difference among them of less than 7.2%. Such agreements validate the feasibility of the proposed noisy network. Furthermore, the NF of the active TL-based BPFs designed with different transistor widths

were theoretical analyzed using the proposed noisy network. A design curve demonstrating the tradeoff on minimizing the NF of the proposed active BPF was also reported. REFERENCES [1] D. Li and Y. Tsividis, “Design techniques for automatically tuned integrated gigahertz-range active LC filters,” IEEE J. Solid-State Circuits, vol. 37, no. 8, pp. 967–977, Aug. 2002. [2] T. Soorapanth and S. S. Wong, “A 0-dB IL 2140 30 MHz bandpass filter utilizing -enhanced spiral inductors in standard CMOS,” IEEE J. Solid-State Circuits, vol. 37, no. 5, pp. 579–586, May 2002. [3] X. He and W. B. Kuhn, “A 2.5-GHz low-power, high dynamic range, self-tuned -enhanced LC filter in SOI,” IEEE J. Solid-State Circuits, vol. 40, no. 8, pp. 1618–1628, Aug. 2005. [4] C. H. Doan, S. Emami, A. M. Niknejad, and R. W. Brodersen, “Design of CMOS for 60 GHz applications,” in IEEE Int. Solid-State Circuits Conf., San Francisco, CA, Feb. 2004, pp. 440–441. [5] H.-T. Tso and C.-N. Kuo, “40 GHz miniature bandpass filter design in standard CMOS process,” in Silicon Monolithic Integr. Circuits RF Syst. Top. Meeting, Atlanta, GA, Sep. 2004, pp. 239–242. [6] A. N. Mohieldin, E. Sanchez-Sinencio, and J. Silva-Martinez, “A 2.7-V 1.8-GHz fourth-order tunable LC bandpass filter based on emulation of magnetically coupled resonators,” IEEE J. Solid-State Circuits, vol. 38, no. 7, pp. 1172–1181, Jul. 2003. [7] S. Bantas and Y. Koutsoyannopoulos, “CMOS active-LC bandpass filters with coupled-inductor -enhancement and center frequency tuning,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 51, no. 2, pp. 69–76, Feb. 2004. [8] Y.-C. Wu and M. F. Chang, “On-chip RF spiral inductors and bandpass filters using active magnetic energy recovery,” in Proc. IEEE Custom Integr. Circuits Conf., Orlando, FL, May 2002, pp. 275–278. [9] F. Dulger, E. Sanchez-Sinencio, and J. Silva-Martinez, “A 1.3-V 5-mW fully integrated tunable bandpass filter at 2.1 GHz in 0.35 m CMOS,” IEEE J. Solid-State Circuits, vol. 38, no. 6, pp. 918–928, Jun. 2003. [10] C.-K. C. Tzuang, H.-H. Wu, H.-S. Wu, and J. Chen, “A CMOS miniaturized C -band active bandpass filter,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 772–775. [11] K. Entesari, T. Vaha-Heikkila, and G. M. Rebeiz, “Miniaturized differential filters for C - and Ku-band applications,” in Proc. Eur. Microw. Conf., Munich, Germany, 2003, pp. 227–230. [12] C.-C. Chen and C.-K. C. Tzuang, “Synthetic quasi-TEM meandered transmission lines for compacted microwave integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 6, pp. 1637–1647, Jun. 2004. [13] H.-S. Wu, H.-J. Yang, C.-J. Peng, and C.-K. Tzuang, “Miniaturized microwave passive filter incorporating multilayer synthetic quasi-TEM transmission line,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2317–2720, Sep. 2005. [14] H.-H. Wu, H.-S. Wu, and C.-K. C. Tzuang, “Synthesized highimpedance CMOS thin-film transmission line,” in Silicon Monolithic Integr. Circuits RF Syst. Top. Meeting, Atlanta, GA, 2004, pp. 302–304. [15] R. Behzad, RF Microelectronics. Upper Saddle River, NJ: PrenticeHall, 1998, p. 228. [16] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 8. [17] G. D. Vendelin, A. M. Pavio, and U. L. Rohde, Microwave Circuit Design using Linear and Nonlinear Techniques. New York: Wiley, 1990, p. 103. [18] P. A. Layman and S. G. Chamberlain, “A compact thermal noise model for the investigation of soft error rates in MOS VLSI digital circuits,” IEEE J. Solid-State Circuits, vol. 24, no. 2, pp. 79–89, Feb. 1989. [19] E. Hegazi, H. Sjoland, and A. A. Abidi, “A filtering technique to lower LC oscillator phase noise,” IEEE J. Solid-State Circuits, vol. 36, no. 2, pp. 1921–1929, Feb. 2001. [20] D. K. Shaeffer and T. H. Lee, The Design and Implementation of Low-Power CMOS Radio Receivers. Norwell, MA: Kluwer, 1999, pp. 52–53. [21] B. Razavi, Design of Analog CMOS Integrated Circuits. New York: McGraw-Hill, 2001, pp. 212–213. [22] G. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1997, ch. 4. [23] Y. Cheng and C. Hu, MOSFET Modeling & Bsim3 User’s Guide. Norwell, MA: Kluwer, 1999, ch. 10.

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Ching-Kuang C. Tzuang (S’80–M’80–SM’92– F’99) received the B.S. degree in electronic engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1977, the M.S. degree from the University of California at Los Angeles (UCLA), in 1980, and the Ph.D. degree in electrical engineering from The University of Texas at Austin, in 1986. From 1981 to 1984, he was with TRW, Redondo Beach, CA, where he was involved with analog and digital MMICs. Since 1986, he has been with the Institute of Communication Engineering, National Chiao Tung University. In February 2004, he joined the Graduate Institute of Communication Engineering, Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C., where he conducts research on advanced guiding structures for research and development of RF SOC, integrating active and passive microwave/millimeter-wave RF signal-processing components into a single chip. His research activities also involve the design and development of millimeter-wave and microwave active and passive circuits and the field theory analysis and design of various complex waveguide structures and large-array antennas. He has supervised 61 M.S. students and 21 Ph.D. students. Dr. Tzuang helped in the formation of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Taipei Chapter, and served as secretary, vice chairman, and chairman in 1988, 1989, and 1990, respectively. He recently served as the chairman of the Millimeter-Wave Industry Alliance, Taiwan Electrical and Electronic Manufacturers’ Association (TEEMA), an assisted interest group in promoting standardization and application of millimeter-wave technology.

Hsien-Hung Wu (S’04) received the B.S. and M.S. degrees in electronic engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1997 and 1999, and is currently working toward the Ph.D. degree in communication engineering at National Chiao Tung University. His research interests include RF integrated circuits and computer-aided design (CAD) methodologies.

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Hsien-Shun Wu (S’97–M’05) received the B.S. degree in electronic engineering from National Taipei University of Technology, Taipei, Taiwan, R.O.C. in 1999, and the M.S. and Ph.D. degrees in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C. in 2001, and 2005, respectively. He is currently a Post-Doctoral Research Fellow with the Graduate Institute of Communication Engineering, National Taiwan University. His research interests include the design of wireless system modules and the development of synthetic waveguides for RF circuits.

Johnsea Chen received the B.S. degree in materials science and engineering from National Tsing Hua University, Hsinchu, Taiwan, R.O.C., in 1977, and the M.S. and Ph.D. degrees in materials science from the University of Southern California, Los Angeles, in 1982 and 1985, respectively. From 1985 to 1991, he was with Rockwell International, Science Center, Thousand Oaks, CA, where he was involved with II–VI compound semiconductors. In 1991, he cofounded the 4 GaAs Research and Manufacturing Corporation, Hsinchu, Taiwan, R.O.C. It was the first III–V compound semiconductor IC design and fabrication facility in Taiwan, R.O.C. In 1996, he joined Etron Technologies Inc., a silicon-based integrated circuit (IC) design company, as the Senior Executive involved with development and business-oriented operations. Early in 2002, he joined the Cadence Methodology Service Company (CMSC), Taipei, Taiwan, R.O.C., a wholly owned subsidiary of Cadence Design Systems, which is the world leading electronic design automation (EDA) developer and supplier. He helped to develop RF related materials and devices in Taiwan, R.O.C., over the past 15 years. His recent research interests focus on the development of RF SOC chips using advance CMOS-based silicon processes.

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Testing High-Frequency Electronic Signals With Reflection-Mode Electroabsorption Modulators Rory L. Van Tuyl, Fellow, IEEE, Gloria E. Höfler, Robert G. Ritter, Todd S. Marshall, Member, IEEE, Jintian Zhu, Luca Billia, George M. Clifford, William Gong, and David P. Bour, Fellow, IEEE

Abstract—Remote testing of microwave signals to 25 GHz and digital signals to 12.5 Gb/s is demonstrated through fiber-optic cables. Reflection-mode electroabsorption modulators are used as high-impedance transducers to measure voltage and inject current. Transducers are imbedded in wafer probes, printed circuit probes and microwave packages for various applications including sensing incident and reflected microwave signals, probing serial data streams on printed circuit boards, probing digital and microwave monolithic integrated circuits, and performing time-domain reflectometry. Principal advantages of this technology are that it allows test equipment to be located at large distances from the devices being tested and that broadband signals can be remotely observed with little distortion. Index Terms—Digital measurements, electric variables measurement, electroabsorption, integrated-circuit (IC) measurements, pulse measurements, scattering parameters measurement, time-domain reflectometry, transducer.

I. INTRODUCTION

M

ICROWAVE AND high-speed digital signals are normally conveyed between test equipment and devicesunder-test via a coaxial cable, but the dispersive properties of a coaxial cable can contribute objectionable frequency-dependent loss and broadband waveform distortion over even short cables of less than 1-m length. This paper describes a method for overcoming the coaxial cable problem by using a bidirectional fiber-optic link that employs a reflection-mode electroabsorption modulator as an optical-to-electrical (O-E) and electrical-to-optical (E-O) transducer [1]. The reflection-mode electroabsorption modulator is a miniature opto-electronic chip based on multiquantum-well (MQW) device technology [2]. It linearly converts applied voltage to reflected optical power. It also functions as a photodetector Manuscript received March 12, 2006; revised August 12, 2006. R. L. Van Tuyl and T. S. Marshall are with Agilent Technologies, Santa Clara, CA 95051 USA (e-mail: [email protected]). G. E. Höfler was with Agilent Technologies, Palo Alto, CA 94304 USA. She is now with Argos Technologies, Santa Clara, CA 95051 USA. R. G. Ritter was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with Avago Technologies, San Jose, CA 95131 USA. J. Zhu was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with the Santur Corporation, Fremont, CA 94538 USA. L. Billia was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with Pressac, Turin, Italy. G. M. Clifford was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with Gen3 Solar Inc., Hayward, CA 94544 USA. W. Gong was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with Pelikan Technologies, Palo Alto, CA 94303 USA. D. P. Bour was with Agilent Technologies, Palo Alto, CA 94304 USA. He is now with the Bridgelux Inc., Sunnyvale, CA 94089 USA. Digital Object Identifier 10.1109/TMTT.2006.884668

and can thus inject current into a circuit under test. Complete switching from the fully reflective state to fully absorbing state can be accomplished with less than 5 V. Previous systems for testing electronic signals with optics have been based on reflection-mode electrooptic modulators [3]–[5], which are principally used as electric field sensors. Due to their small size ( 1 mm), these modulators may require thousands of volts for compete switching from the reflective to nonreflective state and are, thus, not sensitive enough for many voltage-sensing applications. (Traveling-wave electrooptic modulators can switch in less than 10 V, but are centimeters in length). In addition, electrooptic transducers are E-O converters only. In this paper, we describe the reflection-mode electroabsorption modulator, explain how it is used for remote sensing through fiber-optic links, and present experimental results for microwave transducers, high-speed digital and analog probes, and time-domain reflectometry. II. REFLECTION-MODE ELECTROABSORPTION MODULATOR A. Device Description The reflection-mode electroabsorption modulator (see Fig. 1) is a transducer that reflects light into a single optical fiber in proportion to applied voltage. By using the reflection mode (instead of the transmission mode commonly used in optical communication devices), each transducer can be accessed with a single optical fiber, thus leaving the opposite end of the transducer chip free for electrical connections. Electroabsorption modulators [2] can be made much smaller than electrooptic modulators and are thus preferred for applications where high electrical input impedance and minimum input capacitance are desired, as in the cases of high-frequency remote probing and sensing. An additional advantage of the reflection mode is that it allows for a double pass of light through the modulation region, thus, for a given absorption efficiency, a reflection modulator has only half the capacitance of a transmission modulator. Our reflection-mode electroabsorption modulator is a waveguide optical device built on a semi-insulating InP substrate. ) and Cleaved facets are coated with antireflection ( HR ( ) dielectric films. The active absorption section is a p-i-n diode with an MQW i-region configured as an optical waveguide. The active absorption region is 50- m long, a length chosen to be just long enough for nearly complete absorption and which has a small intrinsic capacitance (50–70 fF). Since the size of the absorbing region is so small, and because

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VAN TUYL et al.: TESTING HIGH-FREQUENCY ELECTRONIC SIGNALS WITH REFLECTION-MODE ELECTROABSORPTION MODULATORS

Fig. 1. Top view of reflection-mode electroabsorption modulator chip (300 m 300 m). Light enters (right) through an antireflective (AR) coating, travels through a passive waveguide (250-m long) to the MQW electroabsorptive waveguide section (50-m long), reflects from the high reflection (HR) coating to complete a double pass through the quantum-well region, then exits the chip through the passive waveguide. Voltage applied to the pads modulates the absorption of the quantum-well region, causing the reflection coefficient of the modulator to vary with applied voltage.

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parts handling demands a chip at least 300 m 300 m in size, it was necessary to incorporate a passive nonabsorbing waveguide onto the chip to convey light from the input facet to the absorbing region. The input and reflecting facets are 300 m apart. Electrical connections to the anode and cathode of the reflection-mode electroabsorption modulator are made through metal pads located near the reflecting facet. B. Device Material and Process The active region of the modulator consists of a strain-compensated MQW region composed of nine compressively strained quantum wells with a photoluminescence absorption edge at 1.48 m. The InGaAsP strained MQW structures and related overgrowths were done in a low-pressure MOVPE reactor with a close-coupled showerhead injector. Trimethyl indium, trimethyl gallium, and triethyl gallium were used for the MQW layers only. Tertiary butylarsine was used for the InGaAsP passive waveguide. Arsine, phosphine, diethyl zinc, and disilane (0.01% in H ) were used as precursors. An Si-doped InP buffer layer with doping concentration about cm was first deposited to define bias resistors used in the reflection-mode electroabsorption modulator circuits, then followed by growth of the active region. The active region growth was capped with 400 nm of p-type InP. An SiNx film was deposited and patterned to define the modulator length (50 m). The p-type InP and the active region around the masked area were removed by inductively coupled plasma etching. With the mask still in place, the passive waveguide layer was formed by selectively growing 0.3- m InGaAsP (bandgap wavelength m) covered with undoped InP 0.5- m thick. To complete the buried heterostructure (BH) lateral waveguide, a 1.5- m mesa was defined by a standard etching process, and this was followed by selective

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Fig. 2. Drawing of modulator-fiber assembly. A lensed fiber is mounted in a V-groove silicon mount to form a fiber subassembly. The modulator chip is first attached to a silicon submount, then the fiber subassembly is actively aligned using detected current and reflected power as a guide. After alignment, the V-groove fiber mount is attached to the silicon submount.

regrowth of iron-doped InP around the mesa. Once the mask was removed, the 1.5- m p-type cladding layer and ohmic contact layers were grown. A 3.3- m-thick polyimide layer was used under the anode bonding pad to minimize parasitic capacitance. After cleaving rows of devices into bars, high- and low-reflection dielectric coatings are applied to the entrance and reflecting )/SiO facets. The antireflection coating is a TiO ( ( ) stack with both layers deposited under O rich conditions. Reflectivity is . The high-reflectivity coating is )/SiO ( ) double stack with SiO dean Si ( posited under O rich conditions. Reflectivity is 94%. Devices are dc characterized under illumination at this point, and good devices are selected. After final cleaving into chips, the reflection-mode electroabsorption modulators are ready for assembly. C. Device Assembly To achieve a low-loss coupling of optical fiber to reflectionmode electroabsorption modulator, a semiautomatic assembly process with machine vision alignment is used. First, the reflection-mode electroabsorption modulator is die-attached to a silicon submount and the polarization-maintaining (PM) fiber is rotationally oriented and attached to an etched V-groove silicon part. Second, the fiber and reflection-mode electroabsorption modulator are actively aligned in three axes using a detected photocurrent and reflected power as alignment indicators. The machine vision system records the relative height and position of fiducial marks for the V-groove and reflection-mode electroabsorption modulator. The two parts are then separated in order to apply solder to the silicon submount for subsequent attachment to the V-groove part. Finally, the two silicon parts are returned to their previously recorded position and soldered together (active alignment is not possible at soldering temperatures). The completed assembly is shown in Fig. 2. The reflection-mode electroabsorption modulator optical waveguide is nominally 0.3- m high ( ) and 1.5- m wide ( ). Detected current plotted in an – alignment scan indicates that an elliptical mode approximately 1.1- m high

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Fig. 3. Detected current and reflected power versus fiber-to-modulator alignment in the horizontal transverse (X ) direction. Although the photocurrent collection versus displacement has a 1.25-m half-width, the reflected power falls to half at only 0.5 m of misalignment. An alignment tolerance of 0.25 m is required to achieve coupling efficiency equal to 94% of peak.

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Fig. 5. Schematics of reflection-mode electroabsorption modulator circuit chips used in modulator-fiber assemblies. These simple OEICs are comprised of reflection-mode electroabsorption modulators, resistors, and diodes. Case (a) is a single-ended transducer and case (b) is a dc-coupled differential transducer. For the differential transducer, the required negative anode bias is set by two forward biased diodes connected between +V in and the modulator’s anode. Approximately 2-V bias is generated, allowing the signals +V in and V in to operate at identical average voltages. Reflection-mode electroabsorption modulator OEIC chips are 300 m 450 m in size.

0

2

Fig. 4. Reflected power and detected current for modulator-fiber assembly versus voltage applied from modulator cathode to modulator anode. Reflected power slope efficiency (dPr/dV) in this example is 200 W=V and dynamic conductance is 1.4 mS (714 ). Best bias for linear modulator operation is at point M, best bias for photodetection is point D.

( ) and 2.3- m wide ( ) propagates in this waveguide, but similar – scans show that reflected power is collected over a circular area approximately 1 m in diameter (see Fig. 3). This means that fiber-to-modulator misalignment must be kept to less than 0.25 m to maintain coupling efficiency to within 94% of peak value. We estimate fiber-to-modulator coupling losses to be 1.5–2.2 dB. The externally measured reflection coefficient of the modulator biased to transparency (0 V) is approximately 25% ( 6 dB). D. Reflection and Absorption Characteristics A plot of typical absorption and reflection characteristics for the reflection-mode electroabsorption modulator is shown in Fig. 4. When biased at point M, the modulator reflects power in linear response to applied signal voltage over a range of approximately 2 V pk-pk. When biased at point D, the modulator acts as a waveguide photodetector with maximum responsivity.

Note that at the bias point M, reflected power is reduced to about one-half its maximum value (which is obtained at 0-V bias). Typical reflection coefficients for modulators biased at point M are 0.125. Typical slope efficiency (dPr/dV) for bias at M and incident power of 6.3 mW is 0.7 mW/V. The bias voltage for linear modulation is sensitive to both device temperature and illumination wavelength. At constant wavelength, the bias voltage for constant reflected power changes by 24 mV C. To hold reflected power constant over temperature, the illumination wavelength must be changed 0.4 nm C. For critical applications, the bias point must be stabilized by: 1) holding temperature constant; 2) moving the bias point to hold modulator average current constant; and 3) changing the illumination wavelength to hold modulator current constant. E. Reflection-Mode Electroabsorption Modulator Opto-Electronic Integrated Circuit (OEIC) Chips In practice, reflection-mode electroabsorption modulator chips are simple OEICs, as shown in Fig. 5. ) sink the photocurrent Resistors to the negative supply ( required to maintain negative anode bias on the modulator. ) source current Resistors connected to the positive supply ( necessary to offset dc current drawn from the signal pads , ) so that no net dc current needs to be supplied by ( the circuit under test. Inclusion of resistors requires one additional epitaxial layer growth and one additional patterning step. The forward biased diodes are implemented using the same

VAN TUYL et al.: TESTING HIGH-FREQUENCY ELECTRONIC SIGNALS WITH REFLECTION-MODE ELECTROABSORPTION MODULATORS

Fig. 6. System for sensing a remote voltage or injecting a remote current with a reflection-mode electroabsorption modulator. CW or modulated light from a laser passes through an optical circulator in PM optical fiber to the modulator. Light is reflected from the modulator in proportion to the voltage presented to it from the device-under-test. This modulated reflected light passes through the optical circulator and an (optional) optical amplifier to a photodetector. The detected photocurrent containing the signal information is amplified by the (optional) electronic amplifier and presented as a voltage to a test instrument.

epitaxial layers and lithography steps as the reflection-mode electroabsorption modulator p-i-n diodes. The OEIC chips are 450 m 300 m in size. In operation, the anode of the single-ended device is capacitively coupled to signal ground and the input signal is directly or capacitively coupled to the modulator’s cathode. For the differential transducer, the anode and cathode are driven differentially and , which can be directly coupled from inputs from the device-under-test. Of course, one of the input terminals can be a dc reference voltage if desired. All results presented here are for the reflection-mode electroabsorption modulator OEIC chips. III. SENSING SYSTEM The reflection-mode electroabsorption modulator transducers are intended for use in the configuration illustrated in Fig. 6. Light from a 1550-nm distributed feedback (DFB) laser is conveyed via polarization maintaining fibers and an optical circulator to the reflection-mode electroabsorption modulator transducer. If the intention is to inject a signal to the device-under-test, the illuminating light is modulated by an optical modulator following the illuminating laser, and the modulator is biased to 5 V for best detection efficiency and bandwidth. Current is then injected into the device-under-test. Responsivity of the electroabsorption modulator as a photodetector is 0.77 A/W so a modulated power of 6.5 mW supplied to the photodetector produces injected current of 5 mA to the device-under-test. If, however, the object is to monitor the voltage in the test device, the illumination is continuous wave (CW) light and the modulator is biased to 2 V for best linear modulator operation. Light is reflected from the reflection-mode electroabsorption modulator in linear proportion to the voltage supplied by the device-under-test, and is directed by the PM optical circulator to a photodetector through an (optional) optical amplifier. For most applications, amplification is required, and can be provided by a pre-detection optical amplifier or post-detection electronic amplifier, or both.

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Fig. 7. Linearized electronic circuit model of the modulator-optical amplifierphotodetector link. Modulator and photodetector capacitances form the main bandwidth limitation. The transconductance depends on the modulator slope efficiency, optical amplifier gain, and photodetector responsivity. Voltage gain further depends on load resistance or receiver amplifier transimpedance. Output equivalent noise is generated by a combination of optical and electronic amplifier noise.

TABLE I SIMULATED BANDWIDTH OF A REFLECTION-MODE ELECTROABSORPTION MODULATOR FOR VARIOUS SOURCE IMPEDANCES

For voltage monitoring, it is useful to consider the transfer function of the system from the modulator input terminals to the photodetector output. The resulting low-frequency transconductance is given in (1) as follows: (1) where photodetector output current; power reflected from modulator; input voltage to modulator; gain of optical amplifier; responsivity of photodetector (A/W). The output current is then converted to voltage though a load resistor or transimpedance amplifier. Operation of the sensing system can be visualized using the electronic equivalent circuit of Fig. 7. System bandwidth is limited by the chip input capacitances and the source impedance of the test node, as well as the photodetector bandwidth. For typical measured values of 70-fF modulator junction capacitance and 15-fF pad capacitance, and using a reflectionmode electroabsorption modulator as photodetector operating into a 50- load, theoretical link bandwidths (in the absence of connection inductance) are shown in Table I. The overall link transfer function, ignoring the frequency response, is given by (2) as follows: (2)

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TABLE II PROPERTIES OF UNITY GAIN LINKS WITH OPTICAL AMPLIFIER OR ELECTRONIC TRANSIMPEDANCE AMPLIFIER

TABLE III CALCULATED REFLECTION-MODE ELECTORABSORPTION MODULATOR DYNAMIC RANGE BASED ON MEASURED NOISE AND DISTORTION

Fig. 8. Drawing of fiber-modulator subassembly mounted with Be–Cu probe tips as part of an IC wafer probe. Probe arrangement fits a particular monolithic IC pad configuration. Inductance associated with the 1-mm-long probe tips produces a significant bandwidth constraint. View is from bottom side of the probe.

and the equivalent noise input voltage is (3) as follows: (3) where noise bandwidth of link; detected optical noise current (A electrical noise current (A

Hz);

Hz).

From (2) and (3), we calculate the required optical or electronic gain required to realize a link gain . The voltage-sensing link cited in Table II has a voltage gain of 34 dB so, in practice, an amplifier is required. A transimpedance amplifier is the preferred receiver for digital signals, and for analog signals where the distortion is not a factor. However, transimpedance amplifiers add distortion and limit the bandwidth of the link to less than could be achieved with an optical amplifier and detector operating directly into a load resistor. Erbium-doped fiber amplifiers were used in this study because they have lower noise than semiconductor optical amplifiers and feature essentially infinite signal bandwidth and zero signal distortion. When optimally biased at point M (see Fig. 4), distortion due to the modulator’s nonlinear transfer characteristic is dominated by third harmonic distortion, which is typically below 30 dBc at 10 dBm (2 V pk-pk). Taking 10 dBm as the maximum signal limit, link dynamic range for various bandwidths can be read from Table III. IV. PROBES AND TRANSDUCERS Operation of reflection-mode electroabsorption modulator transducers has been demonstrated in several configurations, as will be outlined here.

Fig. 9. (a) 10-Gb/s 1010 output of a monolithic IC measured with single-ended OEIC probe (20%/80% rise time = 26:4 ps, fall time = 28:8 ps, amplitude = 400 mV pk-pk, trace taken with 64 averages). Estimated probe rise time is 11 ps. (b) 10-Gb/s pseudorandom bit sequence (PRBS) eye diagram of 800-mV pk-pk differential output IC measured with differential OEIC probe.

A. Wafer Probe High-impedance probing of integrated circuits (ICs) is accomplished with the reflection-mode electroabsorption modulator probe shown in Fig. 8. The IC probe combines a modulator-fiber assembly with four Be–Cu probe tips soldered to a sapphire substrate. The probes are 1-mm long and have a 150- m pitch. DC-bias wires and PM fiber enter the assembly through a mounting fixture attached to a wafer probe station. The relatively large physical size of the probe tips creates a series resonance at 32 GHz in conjunction with the modulator’s capacitance. The estimated rise time of the optical probing system is 11 ps. Fidelity of the optically measured pulses compared to the same pulses measured electrically in a 50-GHz bandwidth is excellent. With optical amplification, the link faithfully renders 10-Gb/s waveforms (see Fig. 9).

VAN TUYL et al.: TESTING HIGH-FREQUENCY ELECTRONIC SIGNALS WITH REFLECTION-MODE ELECTROABSORPTION MODULATORS

Fig. 10. Printed circuit board probe snaps into retention fixture to contact differential transmission lines on the printed circuit board. Probe tips are 0.75-mm long with 0.414-mm pitch. Contact compliance is furnished by unidirectionally conductive polymer film. Differential reflection-mode electroabsorption modulator chip is used.

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Fig. 11. Waveforms measured with a differential reflection-mode electroabsorption modulator printed circuit board probe. Receiver is a p-i-n detector with transimpedance amplifier (7-GHz bandwidth). No optical amplification was used in the link. In (a), electrical signal reflections are clearly visible on top and base of pulses, revealing impedance mismatches on the printed circuit board. In (b), an open 10-Gb/s PRBS eye diagram is displayed.

B. Printed Circuit Board Probe To probe 10-Gb/s differential signals on a printed circuit board, we use the differential OEIC mounted in the fixture of Fig. 10. The modulator-fiber assemblies are connected to a sapphire substrate with 0.75-mm-long probe traces of plated gold. The probe traces contact to the printed circuit board through a sheet of unidirectionally conducting polymer. The probes align to the printed circuit board traces with the aid of an alignment fixture mounted to the printed circuit board. The probe snaps into the alignment fixture to connect to a differential transmission line (356- m-wide traces on 482- m pitch). The printed circuit board probe link used electronic amplification only in the form of a commercial p-i-n transimpedance A W, , GHz). amplifier module ( The optical probe performs a type of time-domain reflectometry when the printed circuit board traces are driven with wide pulses. Impedance discontinuities and other reflections are clearly visible to the optical probe, as seen in Fig. 11(a). A clean 10-Gb/s eye diagram consistent with the receiver bandwidth is observed in Fig. 11(b). C. Time-Domain Reflectometry The reflection-mode electroabsorption modulator transducer can be used to view electrical reflections on transmission lines, as shown in Fig. 11(a). However, it is also possible to inject step inputs to electrical transmission lines using the modulator in the photodetector mode. In this case, an external optical modulator driven by a step generator produces a step increase in optical power at the detector. Fig. 12(a) shows an optically generated step with 17.2-ps rise time, as viewed with a 50-GHz bandwidth electronic sampler. This optical step generation was combined with optical sensing using two reflection-mode electroabsorption modulator transducers to both generate steps and measure

Fig. 12. Time-domain reflectometry. (a) Using the modulator in detector mode, a step current is injected onto a 50- microstrip line. As observed with a 50-GHz bandwidth electrical sampler, the rise time is 17.2 ps, overshoot is 5%, and a capacitive reflection of 18% is observed from a nearby discontinuity. In (b), the step is observed with a nearby reflection-mode electroabsorption modulator transducer, which shows multiple reflections with 26-ps rise time, including a 21% impedance step mismatch.

electrical reflections [see Fig. 12(b)]. One advantage of these transducers is their ability to inject and measure signals on differential transmission lines. D. Microwave Transducer A microwave-sensing link consisting of a 50- terminated reflection-mode electroabsorption modulator input, an optical

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Fig. 15. Microwave directional bridge built with two optical modulator voltage sensors attached to a 50- microstrip transmission through line. Transducers are located 6 mm apart. (From [6].) Fig. 13. Measured frequency response of a reflection-mode electroabsorption modulator transducer link. Transducer gain (S 21) is shown for a transducer in a 50- terminated fixture (effective source impedance driving the modulator is 25

). Rolloff in frequency response below 30 GHz is mainly due to the 25-GHz bandwidth photodetector.

Fig. 14. Directional bridge with reflection-mode electroabsorption modulator voltage sensors. By measuring RF voltage magnitudes and phase difference at two points on the through line, we can compute incident and reflected RF power and, thus, S -parameters. Calibration of the directional bridge with short, open, and load allows for measurement of the reflection coefficient  for a test device by a network analyzer located far from the device-under-test. (After [6].)

amplifier, 16 m of optical fiber, and a 50- terminated phoA W, GHz) was constructed. todetector ( frequency response of this link. The meaFig. 13 shows the sured bandwidth is 22 GHz and the link gain is 28.5 dB. From package measurements, it is inferred that the bandwidth due to capacitive loading by the transducer is 35 GHz. Additional frequency response rolloff below 30 GHz is attributable to the photodetector. Equivalent input noise voltage due to the optical amplifier is 60.2 nV Hz ( 131.4 dBm Hz), which is 39.4 dB in excess of the thermal noise of a terminated 50- source. E. Microwave Directional Bridge Since the reflection-mode electroabsorption modulator transducers can measure voltage at closely spaced points on a transmission line, it is possible to compute directional power flow and -parameters of remote loads from these vector voltage measurements (see Fig. 14) [6].

Fig. 16. S 11 of  = 0:5 network measured directly with a network analyzer (solid line) and remotely by a network analyzer through a reflection-mode electroabsorption modulator directional bridge (circles). Remote measurement is accurate from 2.0 to 6.9 GHz. (From [6].)

It can be shown [6] that

(4) where (5) and constants determined by calibration procedure In situ calibration with short, open, and load standards determines the constants , , and , making it possible to measure the reflection coefficient of an arbitrary load impedance [6]. This

VAN TUYL et al.: TESTING HIGH-FREQUENCY ELECTRONIC SIGNALS WITH REFLECTION-MODE ELECTROABSORPTION MODULATORS

depends, however, on and being independent of one another, a condition that is not met when the separation between the points where they are measured is equal to zero or to an integral number of half-wavelengths of the test frequency. Thus, the spacing between transducers determines the minimum and maximum useful frequencies of operation. A reflection-mode electroabsorption modulator microwave directional bridge was built in the form of a hybrid microcircuit, as shown in Fig. 15. For this device, the distance between transducers was 6 mm, and measurements could be taken from 0.5 to 9.5 GHz with best accuracy from 2 to 6.9 GHz. Accurate measurements of the reflection coefficient of a remote impedance were made from 2 to 6.9 GHz with this defor a load with reflection coeffivice. A measurement of cient magnitude of 0.5 is shown in Fig. 16. The microwave directional bridge can, in principle, be extended to higher frequencies by reducing the spacing between transducers.

V. CONCLUSION Practical sensors and probes made with reflection-mode electroabsorption modulator OEICs have been used in bidirectional high-frequency connections over optical fiber. Demonstrated applications included monitoring of microwave signals in coaxial cable, probing of 10-Gb/s data on printed circuit boards and ICs, and time-domain reflectometry of microstrip substrates and connectors. Future applications could include remote monitoring and test of electronic and microwave systems and diagnostic testing of electronic equipment via imbedded probes.

ACKNOWLEDGMENT The authors would like to thank the following Agilent Technologies colleagues for thier contributions to this project: S. Song and J. Norman, for fabrication and assembly, M. Powers for mechanical subassembly development, and S. Newton and W. Ishak for much appreciated management support.

REFERENCES [1] R. L. Van Tuyl, “Device for remotely stimulating and measuring electronic signals through a fiber optic cable,” U.S. Patent 20050185246, Aug. 25, 2005. [2] G. L. Li and P. K. L. Yu, “Optical intensity modulators for digital and analog applications,” J. Lightw. Technol., vol. 21, no. 9, pp. 2010–2030, Sep. 2003. [3] J. Valdmanis and G. Mourou, “Subpicosecond electrooptic sampling: Principles and applications,” IEEE J. Quantum Electron., vol. QE-22, pp. 69–78, Jan. 1986. [4] B. Kolner and D. Bloom, “Electrooptic sampling in GaAs integrated circuits,” IEEE J. Quantum Electron., vol. QE-22, pp. 79–93, Jan. 1986. [5] K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electric field mapping system using an optical-fiber-based electrooptic probe,” IEEE Microw. Wireless Compon. Lett., vol. 11, pp. 164–166, Apr. 2001. [6] T. S. Marshall and R. L. Van Tuyl, “A calibrated microwave directional bridge for remote network analysis through optical fiber,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 11–16, 2006, ThPK-2.

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Rory L. Van Tuyl (SM’77–F’94) received the B.S. and M.S. degrees in electrical engineering from the University of California at Berkeley, in 1965 and 1969, respectively. In 1969, he joined Hewlett-Packard (now Agilent Technologies), Palo Alto, CA, where he has been involved with microwave and high-speed digital IC design, III–V technology, as well as microwave and lightwave test instrumentation. In 1981, he and his group also reported the first production process for GaAs ICs. From 1988 to 1989, he was a Hewlett-Packard visiting faculty member with the University of California at Santa Barbara. He is currently an Engineer with Agilent Laboratories, Santa Clara CA, where he conducts research in the field of high-frequency test. Dr. Van Tuyl was the recipient of the 1980 Outstanding Contributed Paper Award presented at the International Solid State Circuits Conference for his paper entitled “A Monolithic GaAs IC Signal Generation Chip.”

Gloria E. Höfler received the Ph.D., M.S., and B.S. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 1993, 1989, and 1986, respectively. From 1992 to 1994, she was with the 3M Photonics Laboratory, where she was involved in the development of II–VI blue-green lasers. From 1994 to 2001, she has held various engineering and managerial positions with Hewlett-Packard and Lumileds in the area of III–V opto-electronics ranging from device design and fabrication to packaging. In 2001, she joined Agilent Technologies, Palo Alto, CA, where she was involved with the development of high-speed components for datacom, metro networks, and sensing applications. She is currently with Argos Technologies, Santa Clara, CA. She has authored or coauthored over 40 peer-reviewed publications. She holds several patents.

Robert G. Ritter received the Masters of Science degree in mechanical engineering from the University of California at Berkeley, in 1970. In 1970, he joined Hewlett-Packard (now Agilent Technologies), Palo Alto, CA, where he was involved with the company’s first disc drive. He was involved with several other disc drive projects and was a Project Manager for the mechanical design of the first “Winchester” technology drive in Hewlett-Packard. In 1979, he transferred to Hewlett-Packard Laboratories, where he was involved with the “moving paper” plotter project, robotic mechanisms, and robotic systems. He also contributed to modeling and simulation software for manufacturing systems and supply chains. In 1996, he became a Project Manager for automation technologies, where he has overseen development and transfer to production of several manufacturing automation systems. He is currently with Avago Technologies, San Jose, CA. Mr. Ritter is a member of the Society of Manufacturing Engineers/Robotics International and the Society of Photo-Optical Instrumentation Engineers.

Todd S. Marshall (S’97–M’00) received the B.S. degree in engineering physics, M.S. degree in electrical engineering, and Ph.D. degree in electrical engineering from the University of Colorado at Boulder, in 1992, 1996, and 2000, respectively. From 1992 to 1995, he was contracted by the National Renewable Energy Laboratory, Golden CO, to develop and implement computational models of textured solar cell light-trapping effects for efficiency optimization. In 2000, he joined Agilent Technologies, where he was involved with microwave design for 40-Gb/s test equipment. He is currently an Engineer with Agilent Laboratories, Santa Clara, CA, where he conducts research in the field of high-frequency testing. His research interests also include full-wave electromagnetic modeling and open GL visualization.

Jintian Zhu received the B.S. degree in semiconductor physics, M.S. degree in semiconductor device physics and Ph.D. degree in opto-electronics (1994) from Jilin University, Changchun, China, in 1986, 1989, and 1994, respectively. From 1994 to 1998, he was a Post-Doctoral Researcher with the University of California at San Diego, La Jolla, where he performed research on material growth by MOCVD for high-speed modulators. From September 1998 to October 1999, he was involved with material growth for opto-electronic devices with Multiplex Inc. In 1999, he joined Agilent Technologies, Palo Alto, CA, where he was involved with material growth and device design for various

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opto-electronic devices and OEICs, including the reflection-mode electroabsorption modulator. He is currently a Senior Member of Technical Staff with the Santur Corporation, Freemont, CA, where he conducts research on tunable DFB lasers.

Luca Billia received the M.S. degree in electrical engineering from the Politecnico di Torino, Turin, Italy, in 2002. From 2002 to 2004, he was with Agilent Technologies, Palo Alto, CA, and Turin Italy. He is currently with Pressac, Turin, Italy.

George M. Clifford received the B.S. and M.S. degrees in mechanical engineering from the University of California at Berkeley, in 1967 and 1971, respectively. In 1971, he joined Hewlett-Packard (now Agilent Technologies), Palo Alto, CA, where he has been involved with mechanical development for spectrometry, magnetic printing, moving paper plotting, magnetic recording, magnetooptic recording, and precision assembly. He is currently with Gen3 Solar Inc., Hayward, CA.

William Gong received the B.S. degree in electrical engineering from Cooper Union, New York City, NY, in 1971, and the M.S.E.E. degree from Columbia University, New York, NY, in 1973.

He was with the IBM Corporation, where he was involved with computer simulation of nMOS circuits in large-scale integration (LSI) chips. He was also with PMI Motors Inc., where he designed motor controllers and optical encoders, and served as an Applications Engineer. In 1977, he joined Hewlett-Packard (now Agilent Technologies), Palo Alto, CA, where he was involved in analog circuit design of power supplies and data-acquisition products, robotics, and precision assembly research and development. He is currently with Pelikan Technologies, Palo Alto, CA.

David P. Bour (S’83–M’84–SM’88–F’00) received the B.S. degree in physics from the Massachusetts Institute of Technology (MIT), Cambridge, in 1983, and the Ph.D. degree in electrical engineering from Cornell University, Ithaca, NY, in 1987. From 1987 to 1991, he was a Member of Technical Staff with the Sarnoff Corporation. From 1991 to 1999, he was a Principal Scientist with the Electronic Materials Laboratory, Palo Alto Research Center, Xerox, Palo Alto, CA, where he fabricated nitride blue laser diodes and phosphide red laser diodes for laser printing. From 1999 to 2005, he was an Agilent Fellow with the Photonics and Electronics Research Laboratory, Agilent Laboratories, Palo Alto, CA, where he was involved with lasers for communication, data storage and display, and electroabsorption modulators. He is currently with Bridgelux Inc., Sunnyvale, CA. He has authored or coauthored over 200 papers and several book chapters. He holds over 50 U.S. patents.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 12, DECEMBER 2006

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Very Compact High-Gain Broadband Low-Noise Amplifier in InP HEMT Technology Satoshi Masuda, Member, IEEE, Toshihiro Ohki, and Tatsuya Hirose, Member, IEEE

Abstract—This paper presents the practical design methodology of an InP high electron-mobility transistor broadband low-noise amplifier (LNA) using multilayer transmission lines. The LNA consists of high-pass reactive matching circuits and resistive-feedback circuits in order to achieve both low-noise and broadband characteristics. The fabricated five-stage LNA successfully delivered a 43-dB gain with a noise figure of 1.9 dB at 23 GHz, and a gain of more than 40 dB from 18 to 43 GHz. The maximum gain was 0.9 mm2 , re49.5 dB at 32 GHz and the chip size was only 1.8 2 sulting in a gain density of 30.5 dB/mm . To the best of our knowl-band edge, this gain density is the highest performance in any LNA reported to date. In addition, a more compact LNA using spiral inductors was also demonstrated. Index Terms—Gain density, InP high electron-mobility transistor (HEMT), low-noise amplifier (LNA), multilayer.

I. INTRODUCTION

HE MARKET for millimeter-wave applications such as broadband wireless communication systems and 24-GHz short-range sensors is set to drive growth in monolithic-microwave integrated-circuit (MMIC) technology. A low-noise amplifier (LNA) is a key component in the new generation of receiver modules for these systems. They requires high gain, low power dissipation, and compact size, as well as low noise. InP high electron-mobility transistor (HEMT) technology is promising for achieving these characteristics because of its high electron mobility and high sheet carrier density in comparison with competing technologies such as GaAs HEMT, SiGe bipolar, and Si CMOS devices. Several adequately performing LNAs at microwave and millimeter-wave frequencies, have been reported [1]–[3]. Pobanz et al. [2] reported a five-stage LNA with a gain of more than 40 dB and a 1.4-dB noise figure (NF) using InP HEMT and microstrip lines (MSLs). However, when integrating an LNA designed using conventional MSLs with digital circuits on the same chip in order to achieve low-cost high-performance receivers, analog circuits such as LNAs are too large in comparison to digital ones. This is because the MSLs need a large line space to avoid coupling between the signal lines due to the large thickness of the semiconductor substrates. This makes it difficult to achieve a high integration level. In addition, the difference in the structure of

T

Manuscript received March 30, 2006; revised July 7, 2006. The authors are with Fujitsu Laboratories Ltd., Atsugi 243-0197, Japan (e-mail: [email protected]). Color versions of Figs. 5, 13, and 17 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/TMTT.2006.882873

Fig. 1. Cross-sectional view of an In-based HEMT.

the transmission line between them complicates the circuit design. High-frequency analog circuits usually use MSLs formed with a dielectric layer of semiconductor materials, while digital circuits are formed with multilayer lines in material that has a low-dielectric constant to reduce the parasitic capacitance, circuit size, and to increase its operating speed. To overcome these problems, we developed a practical analog design technique based on the thin-film microstrip line (TMSL) structure [4], [5] that is compatible with the structure for digital circuits, and achieved a very compact LNA [6]. The fabricated LNA demonstrated a record gain density of 30.5 dB/mm and proved its applicability in the fabrication of single-chip receivers at millimeter-wave frequencies. Moreover, we fabricated an LNA using spiral inductors, as well as TMSLs to reduce circuit size, and discussed its circuit stability with electromagnetic analysis. II. InP HEMT TECHNOLOGY We fabricated an LNA using 0.13- m InAlAs/InGaAs/InP HEMT technology. The epitaxial layer of our InAlAs/InGaAs/InP HEMTs was grown by metal organic vapor phase epitaxial growth (MOVPE) on 3-in semi-insulating InP wafers. The layer structure consisted of an undoped InAlAs buffer layer, an undoped InGaAs channel layer, an undoped InAlAs spacer layer, an Si-doped InAlAs carrier-supply layer, a undoped InAlAs barrier layer, an undoped etch-stopper layer, and an Si-doped InGaAs cap layer, as shown in Fig. 1. We used the InP etch-stopper layer between the InAlAs barrier layer and the InGaAs cap layer to improve the device uniformity. Nonalloyed ohmic contacts were formed with Mo/Ti/Pt/Au on the heavy doped InGaAs layer. We used electron-beam lithography and selective wet chemical etching to form both the gate electrode and gate recess. The InP surface in the recess is covered with a thin SiN dielectric film by using a plasma-enhanced chemical-vapor-deposition (CVD) system. A gate electrode consisting of Ti/Pt/Au was vapor deposited onto the InP layer and lifted off [7], [8]. The gate length was 0.13 m, as shown in Fig. 2. The threshold voltage and transconductance were 0.31 V and 1500 mS/mm. The extrinsic and,

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Fig. 2. Cross section of Y-shaped gate HEMT.

Fig. 5. Thru-line characteristic of fabricated TMSL. The TMSL is 1.05-mm long.

Fig. 3. Current gain, MSG, and Mason’s unilateral gain of 0.13-m InP HEMT . with extrapolated f and f

The measured -parameters for the TEG are plotted in Fig. 5. was less than 20 dB up to 50 GHz, and the was The 0.22 dB, equal to a relatively high insertion loss of 0.21 dB/mm at 30 GHz. This comes from the conductor loss due to the narrow linewidth and the thin dielectric layer with BCB. The measured characteristic impedance and effective dielectric constant were and 2.4, respectively. We modeled the TMSLs using 54.4 these measured results for the LNA design. B. Low-Noise Matching

Fig. 4. Schematic cross-sectional view of multilayer MMIC.

were 175 and 360 GHz for a 40 m 2 device, as shown in Fig. 3. We formed NiCr resistors with a sheet resistance of 50 square and SiN metal–insulator–metal (MIM) capacitors.

III. LNA DESIGN Our MMIC has four metal interconnect layers and three layers of benzocyclobutene (BCB) film. This is the structure usually used in our high-speed digital circuits [9]. We designed the MMIC using TMSLs formed by the first ground (GND) layer and the top transmission layer, as indicated by the rectangular area outlined by dashed lines in Fig. 4. Passive components such as resistors and capacitors were fabricated on the InP substrate. A. TMSL Characteristics First we fabricated a through-line test element group (TEG) to evaluate the TMSL characteristics. A photograph of the TEG is shown in Fig. 5. This has a 12- m-wide transmission line with a 5- m-thick BCB layer. The TMSL is 1.05-mm long.

To yield a lower NF, simple input matching circuits are necessary to reduce the loss because TMSLs, as well as passive components in the MMIC, have a relatively high loss, as shown in Fig. 5. Furthermore, a smaller optimum source reflection cois required to obtain broad efficient for noise matching noise matching and to reduce the sensitivity of design accuracy and process variations. To achieve this purpose, we calculated and as a function of the gatewidth at 24 GHz. We used a scalable HEMT model based on the noise temperature is of Pospieszalski [10] in calculation. As shown in Fig. 6, different from in any gatewidth HEMTs. This means that designing the amplifiers for minimum noise degrades the input return loss. Accordingly, we employed source inductance to improve the input return loss with noise matching [11]–[15]. When a source inductor is added to the transistor using a simple equivalent field-effect transistor (FET) model, as shown in Fig. 7, the input impedance of the transistor is expressed as follows:

where and are the gate and channel resistances. Therenearer to fore, the gate input resistance can be increased to . We calculated and as a function of to invesincreased, approached , tigate the optimum . As when was 300 m with a gatewidth of coming closest to 20 m 6, as indicated by the solid lines in Fig. 6. In addition, were small and near 90 with a the magnitude and angle of quality factor ( ) of less than 1.1. Therefore, the input matching circuits can be easily designed using a single short-stub circuit, as shown in Fig. 6, and the length of the TMSL, which has a

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Fig. 8. Block diagram of the five-stage amplifier.

Fig. 6. Calculated S and 0 for the InP HEMT as a function of gatewidth (W ) and source inductance (L ) at 24 GHz. The solid circle and square are 0 and S , respectively. Solid and dotted lines indicate the calculation as a function of L and W , respectively. The track of the impedance matching transformer is also shown with arrows.

Fig. 9. Schematic of two-stage LNA.

Fig. 7. Simple equivalent FET model with source inductor.

high insertion loss, can be reduced. We employed a 300- m source inductance with a 20 m 6 gatewidth for LNA design to reduce the loss from TMSLs, as well as to achieve a broad matching. C. Resistive Feedback Amplifier for Broadband Matching The gain bandwidth of amplifiers, which are designed with a high-pass reactive matching configuration, is limited by the characteristics of active devices such as the maximum available gain (MAG) and maximum stable gain (MSG). This makes it difficult to achieve wide bandwidth and gain flatness. We designed a multistage LNA using resistive feedback topology for the gain stage to compensate the gain profile over a wide frequency range. However, the feedback circuits are noisy. is exWhen circuits are connected in cascade, the NF pressed as follows:

where and are the NF and gain of the th-stage circuit, respectively. Thus, the noise of the gain stage does not affect the noise performance of the multistage amplifier significantly

Fig. 10. Calculated MSG/MAG of resistive feedback amplifier cell as a function of R , L , and L expressed in Table I.

if the first-stage circuit has a high gain. We controlled the gain profile with resistive feedback amplifiers. The block diagram of our five-stage amplifier is displayed in Fig. 8. It consists of a two-stage LNA and a three-stage resistive feedback amplifier. We used high-pass reactive matching circuits for the first two-stage amplifier to secure low noise and high gain, as shown in Fig. 9. We used shunt RC networks in the bias circuits to ensure the unconditional stability of the circuits. We employed resistive feedback topology for the three-stage gain amplifier and flattened the gain profile. The basic cell of the and in the feedresistive feedback amplifier includes in the drain line, as indicated in Fig. 10. We back loop, and calculated the MSG/MAG of the cell, which was the gain profile

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TABLE I PARAMETERS OF RESISTIVE FEEDBACK TRANSISTOR

Fig. 12. Calculated isolation of coupled TMSL and conventional MSL in MMIC at 30 GHz. The coupled line length is 1=4 at 30 GHz.

Fig. 11. Schematic of resistive feedback amplifier.

of an amplifier completely matched to 50 , using the parameters in Table I. The transistor has a gatewidth of 20 m 6. flattens the gain profile, while generates the gain peaking and extends the bandwidth of the amplifier, as shown in Fig. 10. also influences the gain and bandwidth. First, we Moreover , , and as “No. D” determined the combination of in Table I and optimized them by designing input and output matching circuits. The amplifier schematic is shown in Fig. 11. We used open and short stubs for impedance matching. The bias circuits include RC networks to secure the circuit stability over all the frequency range.

Fig. 13. Photomicrograph of the fabricated LNA with TMSLs. Its size is 1.8 0.9 mm .

2

D. Isolation of Coupled TMSLs When designing the compact high-gain amplifiers, we focused on isolating the transmission lines on the MMIC because crosstalk causes feedback oscillation in the MMICs. We calculated the isolation of the coupled TMSLs and conventional MSLs using an electromagnetic simulator. In calculation, we assumed that the TMSL structure had a 5- m dielectric layer with BCB on an InP substrate, while the MSL was formed with a 50- m-thick InP substrate, as shown in Fig. 12. A large line spacing improves isolation; however, we need a line spacing larger than 120 m for the MSLs to obtain 30-dB isolation due to the large thickness of the InP substrates. In contrast, it is possible to achieve 30-dB isolation of coupled lines at 30 GHz with a line spacing of only 15 m with TMSLs. To reduce the circuit size, it is much more effective to use TMSLs than conventional MSLs. We used TMSLs with a design rule in which the line spacing was larger than 15 m for the LNA design.

Fig. 14. Comparison between measured and simulated S -parameters of LNA. Solid and dotted lines are measured and simulated results, respectively (V = 0:1 V, V = 0:8 V, and I = 45 mA).

0

IV. FABRICATED LNA A. LNA With TMSLs The fabricated five-stage LNA is shown in Fig. 13. The chip was covered with a layer of ground metal under the transmission lines to form TMSLs. The signal-line-to-ground spacing for the TMSL was 5 m. We designed an LNA to assess the design accuracy of the TMSL. The LNA had five stages with

MASUDA et al.: VERY COMPACT HIGH-GAIN BROADBAND LNA IN InP HEMT TECHNOLOGY

Fig. 15. Measured S -parameters and NF of LNA. Simulated NF is also plotted with a dotted line.

Fig. 16. Measured S -parameters of LNA (V 62 mA).

= 0 V, V

= 1 V, and I

=

Fig. 18. Measured S -parameters of LNA (V I = 45 mA).

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=

00 1 V, :

V

= 0:8 V, and

Fig. 19. Measured S -parameters of LNA using spiral inductors (V V = 1 V, and I = 62 mA). S was over 0 dB at 24 GHz.

= 0 V,

Fig. 17. Photomicrograph of the fabricated LNA with spiral inductors and TMSLs. Its size is 1.8 0.8 mm .

2

a 120- m gatewidth InP HEMT. The matching circuits were designed with TMSLs. The size of the LNA circuit was only 0.9 mm , which is half that of conventional MSL ampli1.8 fiers [2], [3]. The measured -parameters are plotted in Fig. 14. The RF performance from 0.25 to 50 GHz was measured using an HP8510C vector network analyzer (VNA). The dc bias was V, V, and mA, which set at corresponded to a power dissipation of only 36 mW. The fabricated amplifier achieved a gain of 43 dB at 23 GHz and it was over 40 dB from 21 to 26 GHz. The input return loss was better than 10 dB from 16 to 31 GHz. The simulation results, which are also plotted in Fig. 14, agreed well with the measured data. Fig. 15 shows the -parameters and NF of the fabricated LNA at 20–26 GHz. Minimum NF is 1.9 dB at 23 GHz, while gain

Fig. 20. Calculated isolation of coupled spiral inductors with and without a ground layer under inductor lines.

flatness is 1.5 dB at 22–26 GHz. We also plotted the simulated NF in Fig. 15. The profile of simulated NF was nearly the same as the measured one, while the measurement was larger than the simulation by 0.4 dB near 23 GHz. Further improvement in the design accuracy should be necessary in terms of modeling for TMSLs and HEMT devices. We measured the LNA at another bias point, which yielded a higher gain, as shown in Fig. 16. The dc bias was set at V, V, and mA. The LNA achieved a gain of

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TABLE II STATE-OF-THE-ART K - AND Ka-BAND LNAs THAT HAVE BEEN REPORTED TO DATE

over 40 dB from 18 to 43 GHz and 49.5 dB at 32 GHz, which represents a record gain density of 30.5 dB/mm at 32 GHz.

B. LNA With TMSLs and Spiral Inductors In order to reduce circuit size, we also fabricated another LNA using spiral inductors. We removed the ground layer under the spiral inductor in order to reduce the conductor loss. We extracted the model of spiral inductor by using an electromagnetic simulator for circuit design. The photograph of the LNA with spiral inductors is shown in Fig. 17. The LNA had five stages with a 120- m gatewidth InP HEMT. We used shunt RC networks in the bias circuits to ensure the unconditional stability of the circuits. The size of the LNA circuit was only 1.8 0.8 mm, which was smaller by 12% than one with only TMSLs. The was 38 dB at measured -parameter are plotted in Fig. 18. 24 GHz and the input return loss was better than 10 dB. However, its performance was less superior than that of the LNA without spiral inductors, shown in Fig. 13, with the same bias V, condition. We also measured for a bias condition of V, and mA, which produces a higher gain, as shown in Fig. 19. Though the gain increased up to 40 dB was over 0 dB. The LNA with the spiral inat 23 GHz, ductor tends to be unstable at high gain operation. To discuss a reason for this, we calculated the isolation of coupled spiral inductors with and without a ground layer under their transmission lines. Fig. 20 shows the isolation characteristics as a function of frequency. The spacing of the coupled spiral inductors was 100 m, which is typically used in a fabricated LNA. One port of each inductor was shorted to investigate the maximum crosstalk level. The isolation was defined as MAG to eliminate the difference of impedance mismatching for the two types of spiral inductors. The isolation of the spiral inductor without a ground layer was 5 dB worse than that with a ground layer. This came from the parallel-plate mode between the surface ground layer and the bottom ground layer of the InP substrate, which had a higher dielectric constant than that of BCB. In addition, its value was much larger than that of coupled TMSLs, as compared with Fig. 12. Securing isolation of coupled spiral inductors is important for fabricating high-gain blocks at this frequency range. -band LNAs are The details of the state-of-the-art - and listed in Table II. Our LNA had the highest gain density in the - and -bands. Our design using TMSL, which ensures isolation of the coupled lines, is a practical method of producing high-gain LNAs at millimeter-wave frequencies.

V. CONCLUSION A high-gain LNA MMIC has been developed with TMSLs formed with multilayer lines. The fabricated LNA with an area 0.8 mm achieved a record gain density of of only 1.8 30.5 dB/mm at 32 GHz and an NF of 1.9 dB at 23 GHz. To achieve a broadband gain profile, reactive matching and resistive feedback topology were implemented. As a result, a gain of more than 40 dB from 18 to 43 GHz was demonstrated. We also designed the LNA using spiral inductors and discussed its instability from the viewpoint of electromagnetic coupling. Our design technique is essential for fabricating compact chips that integrate both analog and digital circuits for millimeter-wave applications. ACKNOWLEDGMENT The authors would like to thank Y. Nakasha, Fujitsu Laboratories Ltd., Kanagawa, Japan, for his technical support, and H. Shigematsu, K. Joshin, and Y. Kajihara, all with Fujitsu Laboratories Ltd., for their encouragement. REFERENCES [1] S. Fujimoto, T. Katoh, T. Ishida, T. Oku, Y. Sasaki, T. Ishikawa, and Y. Mitsui, “Ka-band ultra low noise MMIC amplifier using pseudomorphic HEMTs,” in IEEE Radio Freq. Integr. Circuits Symp., 1997, pp. 169–172. [2] C. Pobanz, M. Matloubian, L. Nguyen, M. Case, M. Hu, M. Lui, C. Hooper, and P. Janke, “A high gain, low power MMIC LNA for Ka-band using InP HEMTs,” in IEEE Radio Freq. Integr. Circuits Symp., 1999, pp. 146–152. [3] Y. Mimino, M. Hirato, K. Nakamura, K. Sakamoto, Y. Aoki, and S. Kuroda, “High gain-density K -band p-HEMT LNA MMIC for LMDS and satellite communication,” in IEEE Radio Freq. Integr. Circuits Symp., 2000, pp. 209–212. [4] T. Tokumitsu, T. Hiraoka, H. Nakamoto, and T. Takenaka, “Multilayer MMIC using 3 m 3-layer dielectric film structure,” in IEEE MTT-S Int. Microw. Symp. Dig., 1991, pp. 831–834. [5] K. Nishikawa, K. Kamogawa, B. Piernas, M. Tokumitsu, S. Sugitani, I. Toyoda, and K. Araki, “Three-dimensional MMIC technology for low-cost millimeter-wave MMICs,” IEEE J. Solid-State Circuits, vol. 36, no. 9, pp. 1351–1359, Sep. 2001. [6] S. Masuda, T. Ohki, and T. Hirose, “Very compact high-gain broadband low-noise amplifier in InP HEMT Technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 77–80. [7] T. Takahashi, M. Nihei, K. Makiyama, M. Nishi, T. Suzuki, and N. Hara, “Stable and uniform InAlAs/InGaAs HEMT ICs for 40-Gbit/s optical communication systems,” in Proc. 13th Int. InP and Related Mater. Conf., 2001, pp. 614–617. [8] N. Hara, K. Makiyama, T. Takahashi, K. Sawada, T. Arai, T. Ohki, M. Nihei, T. Suzuki, Y. Nakasha, and M. Nishi, “Highly uniform InAlAs-InGaAs HEMT technology for high-speed optical communication system ICs,” IEEE Trans. Semicond. Manuf., vol. 16, no. 3, pp. 370–375, Aug. 2003. [9] T. Suzuki, T. Takahashi, T. Hirose, and M. Takigawa, “A 80-Gbit D-type flip-flop circuit using InP HEMT technology,” in GaAs IC Symp. Tech. Dig., 2003, pp. 165–168.

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[10] M. W. Pospieszalski, “Modeling of noise parameters of MESFET’s and MODFET’s and their frequency and temperature dependence,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 9, pp. 1340–1350, 1989. [11] R. E. Lehmann and D. D. Heston, “ -band monolithic series feedback LNA,” IEEE Trans. Microw. Theory Tech., vol. MTT-33, no. 12, pp. 1566–2316, Dec. 1985. [12] B. Hughes, “Designing FET’s for broadband noise circles,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 2, pp. 190–198, Feb. 1993. [13] B. Hughes, J. Perdomo, and H. Kondoh, “12 GHz low-noise MMIC amplifier designed with a noise model that scales with MODFET size and bias,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 12, pp. 2311–2316, Dec. 1993. [14] M. S. Gupta and P. T. Greiling, “Microwave noise characterization of GaAs MESFET’s: Determination of extrinsic noise parameters,” IEEE Trans. Microw. Theory Tech., vol. 36, no. 4, pp. 745–751, Apr. 1988. [15] M. S. Gupta, O. Pitzalis, S. E. Rosenbaum, and P. T. Greiling, “Microwave noise characterization of GaAs MESFET’s: Evaluation by on-wafer low-frequency output noise current measurement,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 12, pp. 1208–1218, Dec. 1987.

nents, Packaging, and Manufacturing Technology (CPMT) Japan Chapter, the European Microwave Conference (EuMC) Microwave Prize presented at the 34th European Microwave Conference (EuMC 2004), and the Young Scientists’ Prize of the Minister of Education, Culture, Sports, Science, and Technology in 2006.

Satoshi Masuda (M’99) was born in Tokyo, Japan, in 1971. He received the B.E. and M.E. degrees in electrical engineering from Waseda University, Tokyo, Japan, in 1995 and 1997, respectively. In 1997, he joined Fujitsu Laboratories, Kanagawa, Japan, where he has been engaged in research and development of millimeter-wave monolithic integrated circuits (ICs). His current research interests include modeling of active and passive components, millimeter-wave monolithic IC design, and flip-chip packaging. Mr. Masuda was the recipient of the Best Paper Award presented at the 2002 IEEE GaAs IC Symposium, the Young Award presented at the International Conference on Electronics Packaging (ICEP) 2004 from the IEEE Compo-

Tatsuya Hirose (M’02) received the B.E. degree from Tokyo Denki University, Tokyo, Japan, in 1987, the M.E. degree from Hokkaido University, Sapporo, Japan, in 1989, and the Ph.D. degree from Tohoku University, Sendai, Japan, in 2004. In 1989, he joined Fujitsu Laboratories Ltd., Kanagawa, Japan, where he has been engaged in research on design and modeling of HEMTs, and development of MMICs base on their technologies. His current research interest includes high-speed and high-frequency ICs for optical and wireless

X

Toshihiro Ohki was born in Chiba, Japan, in 1976. He received the B.E. and M.E. degrees in electrical engineering from Waseda University, Tokyo, Japan, in 1999 and 2001, respectively. Since 2001, he has been with Fujitsu Laboratories, Kanagawa, Japan, where he has been engaged in research and development of resonant tunneling diodes (RTDs) and HEMTs for high-speed ICs. Mr. Ohki is a member of the Japan Society of Applied Physics.

communication systems. Dr. Hirose was the recipient of the 2003 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Outstanding Young Engineer Award.

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Low-Loss Integrated-Waveguide Passive Circuits Using Liquid-Crystal Polymer System-on-Package (SOP) Technology for Millimeter-Wave Applications Ki Seok Yang, Member, IEEE, Stephane Pinel, Member, IEEE, Il Kwon Kim, Student Member, IEEE, and Joy Laskar, Fellow, IEEE

Abstract—In this paper, we show a low-loss integrated waveguide (IWG), microstrip line-to-IWG transition, IWG bandpass filter (BPF), and system-on-package (SOP) using a liquid-crystal polymer (LCP) substrate, which can be used toward SOP technology for millimeter-wave applications. The proposed IWG can be used as a low-loss millimeter-wave transmission line on this substrate. The measured insertion loss of the IWG is 0.12 dB/mm and the measured insertion loss of two microstrip line-to-IWG transitions is 0.14 dB at 60 GHz. The evaluated IWG filter is demonstrated as the pre-select filter for RF front-end modules at the millimeter-wave band. The fabricated three-pole BPF at a center frequency of 61.1 GHz has specifications: a 3-dB bandwidth of approximately 13.4% ( 8.4 GHz), an insertion loss of 1.8 dB at the center frequency of 61.1 GHz, and a rejection of 15 dB over the passband. The proposed IWG can also be used as a low-loss millimeter-wave feed-through transition and interconnection between the monolithic microwave integrated circuit and the module instead of the vertical via structure. In terms of a SOP on LCP for millimeter-wave applications, the top face of the IWG does not have any electromagnetic effects, and a package lid can be attached to provide a hermetic sealing. These low-loss IWG circuits on LCP can easily be used in many millimeter-wave packaging applications. Index Terms—Bandpass filter (BPF), integrated waveguide (IWG), liquid-crystal polymer (LCP), millimeter wave, packaging, system-on-package (SOP).

I. INTRODUCTION

A

S CONSUMERS request high-data rate (1–10 Gb/s) transmission for next-generation wireless communication systems, millimeter-wave frequencies are an attractive high-bandwidth resource. There are many millimeter-wave applications of interest such as indoor wireless personal area networks (WPANs), radio-over-fiber (ROF) communications, automotive radars, and gigabit backbone networks [1]. In terms of packaging material, low-temperature co-fired ceramic (LTCC) is an attractive material for multilayer circuit integration and hermetic packaging, but its cost is relatively high and its processing reliability can be critical at the millimeter-wave band. Liquid-crystal polymer (LCP) is considered

Manuscript received April 16, 2006; revised July 16, 2006. This work was supported by the Georgia Electronic Design Center. The authors are with the Georgia Electronic Design Center, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2006.886004

as an emerging packaging material that has a unique combination of features and performances. It has good electrical characteristics at the millimeter-wave band, very good moisture absorption, a low coefficient of thermal expansion (CTE), and low cost [2], [3]. The packaging concept of the millimeter-wave transceiver system should be considered to provide reliability, low cost, easy assembling, hermetic sealing to prevent outdoor environmental effects, and low-loss feed-through interconnection. Multilayer structures, three-dimensional (3-D) integration, and system-on-package (SOP) technology use traditional via structures as an interconnection technique [2]. However, via structures exhibit loss, parasitic effect, and resonance at very high frequencies [13], [14]. The integrated waveguides (IWGs) on an LCP substrate can use a potential signal transmission line in a wide frequency bandwidth (full -band) and a resonant-free interconnection at the millimeter-wave band, and can be easily connected to any circuits using the microstrip line-to-IWG transition from [4]. The microstrip line-to-IWG can also easily implement the bandpass filter (BPF) and other passive circuits in an IWG. This paper presents low-loss IWG passive circuits on an LCP substrate in terms of SOP technology for millimeter-wave applications. In Section II, an IWG design on the LCP substrate is first presented. Section III shows a microstrip line-to-IWG transition and characteristics, which are measured and simulated from a fabricated IWG according to the length of the IWG. Furthermore, Section IV presents the diverse passive circuit fabrications and a three-pole BPF, which has been fabricated, with the measurement results shown. In Section V, the monolithic-microwave integrated-circuit (MMIC) module packaging solution for millimeter-wave applications has been issued on the IWG structure as a feed-through interconnection. This structure can be mounted on the lid to have hermetic shielding characteristics, and can be utilized for SOP applications.

II. IWG ON LCP Many of the materials used for the SOP have some limitations at the millimeter-wave band. In comparison with the typically used laminated organic substrates, LCP is a promising material for millimeter-wave bands. LCP presents some advantages such as dense multilayer capabilities, good electrical characteristics, good hermeticity, production repeatability, and low-cost production.

0018-9480/$20.00 © 2006 IEEE

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Fig. 1. IWG on LCP substrate.

Through the examination of LCP specifications, it could be speculated as a useful substrate at the millimeter-wave band. The electrical properties of LCP have low dielectric constants: up to 3.16 0.05 at 31.53 104.60 GHz, and 97 GHz [5]. The temperature coefficient of the dielectric constant is 42 ppm C from 11 to 105 GHz [5]. As the water absorption rate of LCP is 0.04%, it can survive in some circumstances of rain and moisture. The LCP’s CTE is 17 ppm C at the - and -axes from 30 C to 150 C. This value is similar to that of ceramic. The IWG was designed using LCP manufacturing rules. Further simulation of the IWG was performed using a commercial three-dimensional (3-D) electromagnetic (EM) field solver. The IWG on the substrate is of similar structure to the dielectric-filled waveguide with a reduced height. The basic structure of the proposed IWG on LCP is shown in Fig. 1. This structure consists of two lines of thru via-holes in the LCP substrate with metallized top and bottom surfaces. The design parameters of the IWG are the width of the IWG and the thickness of the LCP substrate. We have determined the thickness (150 m) because the thickness of MMIC chips based on GaAs or SiGe is 127 m and the thickness of the epoxy pasted to attach the chips onto the substrate is approximately 5 20 m. As the thickness of the IWG is similar to the thickness of the MMIC chips, the length of wire bonding will be reduced and the loss can then be minimized. In terms of preventing power leakage on the IWG, the return loss is studied according to via pitch when the IWG width is 2.6 mm and via diameter is 200 m. The simulation results are shown in Fig. 2. A 600- m pitch is determined and these dimensions are compatible with standard printed circuit board (PCB) process design rules. In general, the waveguide has high-pass filter frequency response characteristics. The usual mode of transmission in rect. The IWG on LCP is filled angular waveguides is called using a medium material with a constant dielectric constant. The lower cutoff frequency is found from the following equation: (1) where is the cutoff frequency of the waveguide mode, is is the width of the IWG, and is the the speed of light, dielectric constant of LCP [6].

Fig. 2. Return loss of IWG according to via pitch on LCP substrate.

Fig. 3. Cutoff frequency according to width of IWG.

The cutoff frequency of the IWG is obtained through a commercial 3-D EM field simulation in terms of the width of IWG. Simulation results based on 3-D simulation and calculation results based on (1) are shown in Fig. 3. Both results agree approximately. Little difference between equation results and simulation results can be found in the realization of both sides of the wall in the IWG because via array is replaced as the prefect metal wall. Through these simulation results, the optimum width can be decided for the microstrip line-to-IWG transition and IWG BPF. As the wireless local area network (WLAN) application frequency band in the U.S. is 59–64 GHz, the upper cutoff frequency is exactly one octave above the lower. A sufficient width is also needed to design the BPF and microstrip line-to-IWG transition on the IWG and, thus, the width is decided as 2.6 mm. The simulation results for an optimum IWG structure are shown in Fig. 4 when the length of the IWG is

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Fig. 4. Simulation results of IWG with 2.6-mm width on LCP substrate.

Fig. 6. Simulated IWG impedance.

Fig. 7. Manufactured IWG with different lengths on LCP substrate.

Fig. 5. Microstrip line-to-IWG transition.

6.6 mm and the dielectric constant is 3.16. The frequency response is the cutoff frequency (34.75 GHz) and the return loss for the -band (50–75 GHz) is lower than 30 dB. III. MICROSTRIP LINE-TO-IWG TRANSITION It is difficult to directly connect between some MMICs and IWGs on LCP so the microstrip line-to-IWG transition is necessary to interface between some circuits. The configuration of the IWG on the LCP is shown in Fig. 5. A microstrip waveline-to-IWG transition is designed to excite the guide mode into the LCP substrate. This transition consists of a microstrip line, a conductor-backed coplanar waveguide (CBCPW), and short-circuited slots [7]. The CBCPW section acts as an impedance transformer to match the impedance of the microstrip line, 50 with that of the IWG. The simulated impedance of the IWG on LCP structure determined from Section II is shown in Fig. 6 and displays the frequency-dependent nature of the impedance. In terms of electrical field distribution, the quasi-TEM mode in the microstrip line is mode in the IWG through the CBCPW changed to the mode and slot-line mode in CBCPW and slot lines located mode in IWG, the maximum on both sides. Like the

electrical field strength is at the center of the CBCPW and the minimum electrical field strength is at the short-circuited slots extremities. The short-circuited slot lines help to make mode in the IWG. The radiation loss emitted into the the atmosphere due to the slot line is relatively minor because the electrical field is built between the top and bottom planes and the via array prevents power leakage emission. The manufactured IWGs having different lengths are shown in Fig. 7. The ground–signal–ground (GSG) probe pads are made to measure the characteristics of the IWG, and a GSG probe with a 250- m probe pitch is used because of the limitation of probe pad dimensions. Therefore, the GSG probe pad is attached on both sides of the IWG structure. To remove the effects of the probe pad and eliminate the effects of the feeding lines, a thru-reflect-line (TRL) calibration is performed with an open reflect, a thru, and seven delay lines. Multical calibration software made by the National Institute of Standards and Technology (NIST), Boulder, CO, is used in the calibration [8]. The measurements are done over the 50–70-GHz band using an Agilent 8510XF vector network analyzer (VNA) and Cascade Microtech 250- m-pitch GSG 110-GHz probes. The simulation and measurement results for the 0.6- and 6.0-mm IWGs with two transitions are shown in Fig. 8 [4]. The insertion loss and return loss for the 0.6-mm IWG are shown in Fig. 8(a). The return loss for both data is below 20 dB and the insertion loss is similar in the range of 50–70 GHz for simulation and measurement results. Fig. 8(b) shows the results for the 6.0-mm

YANG et al.: LOW-LOSS IWG PASSIVE CIRCUITS USING LCP SOP TECHNOLOGY FOR MILLIMETER-WAVE APPLICATIONS

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Fig. 9. Insertion loss according to the length of IWG.

TABLE I CHARACTERISTICS OF IWGS (AT 60 GHz)

IV. LOW-LOSS INTEGRATED BPF

Fig. 8. Comparison for simulation and measurement results for IWG structures of 0.6 and 6.0 mm with two transitions. (a) 0.6-mm IWG with two transitions. (b) 6.0-mm IWG with two transitions.

IWG. The return loss is less than 20 dB for both cases, but the insertion loss has a different value. The measured insertion loss is higher compared with the simulation result. The reason may be due to the dielectric loss and some signal leakage in the IWG. The measurement data have been used to extract the insertion loss per unit length. Inspection of the insertion loss at 60 GHz shows that it is 0.2 and 0.82 dB for the 0.6- and 6.0-mm IWGs, respectively, including the microstrip line-to-IWG transition according to the measurement results. These insertion-loss measurement results for the different lengths of IWG are shown in Fig. 9. The insertion loss contributed from the transition loss between the microstrip line-to-IWG and the single IWG can be estimated using the curve-fit function. The summarized results are reported in Table I [4]. The insertion loss for the IWG is 0.12 dB/mm, and the insertion loss for two transitions is 0.14 dB [4]. According to [5], the microstrip line losses at 60 GHz are 0.08 and 0.15 dB/mm for 5- and 2 mil-thick LCP substrates, respectively. It is seen that the IWG exhibits comparable loss performances.

The IWG structure on the LCP substrate is similar to the dielectric-filled waveguide so the shunt-inductance-coupled waveguide filter can be implemented in this structure [10]. The filter design method follows in a similar design procedure to a coupled-cavity filter design. The low-pass to bandpass transformation in [10] for the general filter can be applied to an IWG filter with a narrow and moderate bandwidth. An IWG BPF has been designed with a bandwidth of 59–64 GHz for a WLAN application. According to the filter design specifications, the three-pole BPF based on an 0.1-dB ripple Chebyshev prototype is implemented. The eleare determined as ment values of the low-pass prototype , , and . The external quality factor and inter-resonator coupling coefficient between the th and th factors are also calculated as the follow equations: and

(2)

where is the center frequency and is the bandwidth of the filter. For an odd number of resonators, the values are symmetric and the external quality factor of the input and output is . Through 3-D EM simulation the same, i.e., for the IWG coupled vertical via-holes and the IWG cavity, the is simply (3)

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Fig. 10. Fabricated three-pole IWG filter.

where the value of can be found from taking , the dif. ference in frequency between the 90 and 90 phase of is the resonance frequency of the coupled resonator at the 0 phase [11]. External coupling is determined from (2), which is , as determined by (2). related to the desired prototype is determined in Fig. 10. The internal coupling coefficient between the th and th factors is computed from (4) which is derived from the low-pass prototype. The coupling coefficient is defined from the two characteristic frequencies and , the frequencies of the peaks in the transmission response of the coupled structure when electric (or short-circuit) and magnetic (or open-circuit) walls are alternately placed at the plane of symmetry between the resonators. The relationship is shown in the following equation [12]: (5) Following the above commented filter theory, the initial dimensions of resonators in the bandpass were determined. To optimize the filter performance, the 3-D EM simulation was used. For an odd number of resonators, the lengths and widths m, of the symmetric filter structure are m, m, and m. The measurement and simulation results are shown in Fig. 11. To get the exact measured results and remove the effect of the input/output probe pad for the Cascade 200- m-pitch microprobe, the Multical calibration software provided by NIST is performed [8]. The implemented filter has an insertion loss of 1.8 dB, which is higher than the simulated value of 1 dB. The return loss is also less than 20 dB for both the simulated and measured results. In Fig. 11(b), the 3-dB bandwidth of the fabricated filter is approximately 13.4% ( 8.2 GHz) at a center frequency of 61.1 GHz. The simulated results give a 3-dB bandwidth of 13% ( 8 GHz) at a center frequency of 61.7 GHz. The center frequency of the fabricated filter shifts the lower frequency, and it is caused by the manufacturing tolerance in the mechanical dimension and the tolerance of the dielectric constant in the electrical parameter at the 60-GHz band. Through our filter design approach on the IWG, several passive circuits can be implemented as a waveguide type on the LCP substrate. V. SOP APPLICATION USING IWG Some surface mount device (SMD) packages have been developed up to 40 GHz [13], and a shielded LTCC vertical transi-

Fig. 11. Measured and simulated results of three-pole IWG filter. (a) Return loss of three-pole IWG filter. (b) Insertion loss of three-pole IWG filter.

tion is shown in [14]. However, beyond 50 GHz, vertical interconnections using via structures become very challenging to design because of resonances. To solve this problem, the IWG and microstrip line-to-IWG transition can be used. The microstrip line-to-IWG transition has a lower insertion loss in comparison with via structures in SMD packages [13] and can be designed for frequencies beyond 40 GHz. Fig. 12 shows the configurations of the IWG on the LCP [4]. Fig. 12(a) shows the general IWG with the microstrip line-to-IWG transition; however, Fig. 12(b) shows how the input and output ports can be placed on different planes so that the structure can replace a vertical via structure to transmit the signal from the top plane to the bottom plane with minimum insertion loss and good matching performance. The simulation results are shown in Fig. 13. Since the top face of the IWG does not have any electromagnetic effects, a package lid can also be attached to provide a hermetic sealing. These IWG characteristics can be used for many

YANG et al.: LOW-LOSS IWG PASSIVE CIRCUITS USING LCP SOP TECHNOLOGY FOR MILLIMETER-WAVE APPLICATIONS

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Fig. 12. Microstrip line-to-IWG transition according to the input and output port on LCP substrate. (a) Input and output port at top plane. (b) Input port at top plane and output port at bottom plane.

Fig. 13. Simulation results between input and output port at top plane, and input port at top plane and output port at bottom plane. Fig. 15. Test results with (WML) and without (WOML) the metal lid on the IWG (6.0 mm) with two microstrip line-to-IWG transitions. (a) Experiment configuration. (b) Measured results.

Fig. 14. Field distribution on the cross section of the IWG.

millimeter-wave packaging applications that require a hermetic sealing structure. In addition, Fig. 14 shows the field distribution for the cross section of the IWG. The high field strength is visible inside the IWG, and only weak field strength is visible outside of the IWG. This confirms that no electrical field is flowing on the top metal surface of the IWG. According to the simulation results, it is possible to implement a hermetic packaging solution. To confirm whether the lid has an effect on the performance of the IWG, a metal block is put on the top surface of the IWG during the measurement. Fig. 15(a) shows the experiment configuration and Fig. 15(b) shows the experimental results [4]. The measured return loss and insertion loss for both configurations (with and without the metal block) are similar. In both cases,

the return loss is lower than 20 dB, and the insertion loss is approximately 0.82 and 0.9 dB with and without the metal block, respectively. Through this experiment, the IWG can be utilized in the millimeter-wave packaging solution because of the low insertion loss and the simple structure. A hermetic millimeter-wave MMIC packaging solution using the developed IWG is presented in Fig. 16 [4]. The feed-through input and output ports of the package are implemented using the IWG structure. The MMIC (GaAs, SiGe, Si, ) chip sets are mounted in the center of the package and connected to the package by gold ribbons. To make the hermetic sealing, a metal pattern using via rows surrounds the MMIC and connects the ground plane of the input and output IWG feed-through. A metal lid can be soldered on the top of the LCP base substrate to provide a hermetic sealing solution. Through these millimeter-wave packaging solutions using IWG structures, millimeter-wave packaging modules having low-loss interconnection can be used reliably for wide bandwidths. For SOP technology of millimeter-wave applications, lowloss IWGs implemented in an LCP substrate are examined as a candidate of choice. The proposed IWG can be used as a low-loss millimeter-wave feed-through transition between the MMIC and module. The top face of the IWG does not have

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Fig. 16. Packaging structure with IWG interconnection on LCP substrate.

any electromagnetic effects. A package lid can be attached to provide a hermetic sealing. The measured insertion loss of the IWG is 0.12 dB/mm, and the measured insertion loss of two microstrip line-to-IWG transitions is 0.14 dB. This low-loss IWG on LCP can easily be used in many millimeter-wave packaging applications. VI. CONCLUSION In terms of SOP technology for millimeter-wave applications, an IWG, a microstrip line-to-IWG transition, a BPF, and a packaging structure with hermetic shielding on an LCP substrate have been designed, fabricated, and measured. The insertion loss of the IWG is 0.12 dB/mm and the insertion loss of two microstrip line-to-IWG transitions is 0.14 dB. The three-pole BPF has been fabricated and the measurement results are the in1.8 dB and the return loss of 20 dB at sertion loss of the center frequency of 61.1 GHz with a 3-dB bandwidth (13%). This IWG has been utilized as a feed-through interconnection technique to implement a low-loss low-cost hermetic packaging solution for millimeter-wave applications such as WLAN communications and automotive radars. It is promising for these passive circuits in an IWG using LCP to be applied to cost-effective millimeter-wave systems.

[6] D. C. Thompson, J. Papapolymerou, and M. M. Tentzeris, “High temperature dielectric stability of liquid crystal polymer at mm-wave frequencies,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 9, pp. 561–563, Sep. 2005. [7] S. Choi, K. Yang, K. Tokuda, and Y. Kim, “A V -band planar narrow bandpass filter using a new type integrated waveguide transition,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 12, pp. 545–547, Dec. 2004. [8] “Multical User’s Guide,” NIST, Boulder, CO, 1995. [9] M. Ito, K. Maruhashi, K. Ikuina, T. Hashiguchi, S. Iwanaga, and K. Ohata, “A 60-GHz-band planar dielectric waveguide filter for flip-chip modules,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2431–2436, Dec. 2001. [10] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. North Bergen, NJ: Bookmart, 1985. [11] L. Harle and L. P. B. Katehi, “A vertically integrated micromachined filter,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 9, pp. 2063–2068, Sep. 2002. [12] P. Blondy, A. R. Brown, D. Cros, and G. M. Rebeiz, “Low-loss micromachined filters for millimeter-wave communication,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2283–2288, Dec. 1998. [13] M. Heijnigen and G. Gauthier, “Low-cost millimeter-wave transceiver module using SMD packaged MMICs,” in Proc. Eur. Microw. Conf., Sep. 2004, pp. 1269–1272. [14] R. Valois, D. Baillargeat, S. Verdeyme, M. Lahti, and T. Jaakola, “High performances of shielded LTCC vertical transitions from DC up to 50 GHz,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 2026–2032, Jun. 2005.

Ki Seok Yang (M’05) was born is Seoul, Korea, in 1974. He received the B.S. degree from HanKuk Aviation University, Geonggi-do, Korea, in 1996, and the M.S. and Ph.D. degrees in mechatronics from Gwangju Institute of Science and Technology (GIST), Gwangju, Korea, in 1998 and 2005, respectively. Since 2005, he has been a member of the research faculty with the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, Atlanta. His research interests include microwave and millimeter-wave passive and active components design, CMOS millimeter-wave circuit design, low phase-noise oscillators, frequency synthesizers, millimeter-wave front-end module packaging using LCP, millimeter-wave propagation channels, and high-speed millimeter-wave communication systems for 60-GHz ROF application.

REFERENCES [1] D. Thompson, J. Papapolymerou, and M. Tentzeris, “High temperature dielectric stability of liquid crystal polymer at mm-wave frequencies,” in Plastics, J. Peters, Ed., 2nd ed. New York: McGraw-Hill, 1964, vol. 3, pp. 15–64. [2] M. M. Tentzeris, J. Laskar, J. Papapolymerou, S. Pinel, V. Palazzari, R. Li, G. DeJean, N. Papageorgiou, D. Thompson, R. Bairavasubamanian, S. Sarkar, and J. H. Lee, “3-D-integrated RF and millimeter-wave functions and modules using liquid-crystal polymer (LCP) system-onpackage technology,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 332–340, May 2004. [3] J. Lee, G. Dejean, S. Sairkar, S. Pinel, K. Lim, J. Papapolymerou, J. Laskar, and M. M. Tentzeris, “Highly integrated millimeter-wave passive components using 3-D LTCC system-on-package (SOP) technology,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 2220–2229, Jun. 2005. [4] K. Yang, S. Pinel, I. K. Kim, and J. Laskar, “Millimeter-wave lowloss integrated waveguide on liquid crystal polymer substrate,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 965–968. [5] D. C. Thompson, O. Tantot, H. Jallageas, G. E. Ponchak, M. M. Tentzeris, and J. Papapolymerou, “Characterization of liquid-crystal polymer (LCP) material and transmission lines on LCP substrates from 30 to 110 GHz,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1343–1352, Apr. 2004.

Stephane Pinel (M’05) received the B.S. degree from Paul Sabatier University, Toulouse, France, in 1997, and the Ph.D. degree in microelectronics and microsystems (with highest honors) from the Laboratoire d’Analyze et d’Architecture des Systemes, Centre National de la Recherche Scientifique, Toulouse, France, in 2000. For three years, he has been involved with an UltraThin Chip Stacking (UTCS) European Project. He is currently a Research Engineer with the Microwaves Applications Group, Georgia Institute of Technology, Atlanta. He has authored or coauthored over 115 journal and proceeding papers, two book chapters, and numerous invited talks. He holds four patents/invention disclosures. His research interests include advanced 3-D integration and packaging technologies, RF and millimeter-waves embedded passives design using organic and ceramic material, RF microelectromechanical systems (MEMS) and micromachining techniques, SOP for RF front-end modules, and system-on-insulator (SOI) RF circuit design. Dr. Pinel has participated and organized numerous workshops. He was the recipient of the First Prize Award presented at the 1998 Society of Electronic and Electro-technique (SEE), the Second Prize Award presented by the 1999 International Microelectronics and Packaging Society (IMAPS), and the Best Paper Award presented at the 2002 International Conference on Microwave and Millimeter-Wave Technology, Beijing, China.

YANG et al.: LOW-LOSS IWG PASSIVE CIRCUITS USING LCP SOP TECHNOLOGY FOR MILLIMETER-WAVE APPLICATIONS

Il Kwon Kim (S’02) received the B.S. degree in radio communication engineering and the M.S. and the Ph.D. degrees in electrical and computer engineering from Yonsei University, Seoul, Korea in 1999, 2001, and 2006, respectively. He is currently a Post-Doctoral Researcher with the Georgia Institute of Technology, Atlanta. He has been with the School of Electrical and Computer Engineering, Georgia Institute of Technology, as a Visiting Student (April 2004) and a Research Engineer (April 2005). His research interests include fractal structure application on microwave devices/antennas and antenna and passive device design on LCP/LTCC substrates for 60-GHz millimeter wave application.

Joy Laskar (S’84–M’85–SM’02–F’05) received the B.S. degree in computer engineering with math/physics minors (with highest honors) from Clemson University, Clemson, SC, in 1985, and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign, in 1989 and 1991, respectively. Prior to joining the Georgia Institute of Technology in 1995, he held faculty positions with the University of Illinois at Urbana-Champaign and the University of Hawaii. With the Georgia Institute of

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Technology, he holds the Joseph M. Pettit Professorship of Electronics and is currently the Chair for the Electronic Design and Applications Technical Interest Group. He is also the Director of the Electronic Design Center, Georgia Institute of Technology. and the System Research Leader for the NSF Packaging Research Center. His research has produced numerous patents and transfer of technology to industry. Most recently, his research has resulted in the formation of two companies. In 1998, he co-founded the advanced WLAN IC Company RF Solutions, which is now part of Anadgics (Nasdaq: Anad). In 2001, he co-founded the next-generation interconnect company Quellan Inc., Atlanta, GA, which develops collaborative signal-processing solutions for enterprise applications. Prof. Laskar has been appointed an IEEE Distinguished Microwave Lecturer for the 2004–2006 term for “Recent Advances in High Performance Communication Modules and Circuits” seminar.

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M. Calcatera C. Caloz C. Camacho-Penalosa E. Camargo R. Cameron S. Cammer C. Campbell M. Campovecchio F. Canavero J. Cao J. Capmany F. Capolino G. Carchon R. Carter N. Carvalho F. Casas J. Catala R. Caverly J. Cavers Z. Cendes B. Cetiner R. Chair H. Chaloupka A. Chambarel B. Chambers C.-H. Chan Y.-J. Chan C.-Y. Chang F. Chang G. Chang H.-C. Chang H.-R. Chang K. Chang E. Channabasappa H. Chapell W. Chappell M. Chatras S. Chaudhuri S. Chebolu C.-C. Chen C.-H. Chen H.-H. Chen J. Chen R. Chen W.-K. Chen Y.-J. Chen K.-K. Cheng Y.-C. Cheng W.-C. Chew C.-Y. Chi Y.-C. Chiang C.-F. Chiasserini I.-T. Chiang J. C. Chiao I. Chiba D. Chigrin A. Chin C.-C. Chiu Y. Cho C. Choi J. Choi M.-J. Choi C.-K. Chou Y.-H. Chou D. Choudhury K. Choumei Y. Chow C. Christodoulou C. Christopoulos H.-R. Chuang Y. Chung B. Chye R. Cicchetti C. Cismaru D. Citrin P. Civalleri A. Ciubotaru T. Clark R. Clarke J. Cloete E. Cohen F. Colomb B. Colpitts M. Condon D. Consonni J. Corral A. Constanzo I. Corbella E. Costamagna A. Coustou J. Craninckx J. Crescenzi S. Cripps D. Cros T. Crowe M. Cryan J. Culver C. Curry W. Curtice M. da Cunha W.-L. Dai T. Dahm G. Dambrine B. Danly F. Danneville N. Das M. Davidovich A. Davis C. Davis L. Davis H. Dayal F. De Flaviis H. De Los Santos A. De Lustrac P. De Maagt J. de Mingo R. De Roo L. de Vreede D. De Zutter B. Deal A. Dearn P. Debicki J. Deen A. Deleniv M. DeLisio S. Demir A. Deutsch V. Devabhaktuni Y. Deval A. Diet L. Ding A. Djermoun T. Djordjevic J. Dobrowolski D. Dolfi W. Dou M. Douglas P. Draxler A. Dreher F. Drewniak J. Drewniak D. Dubuc S. Dudorov L. Dunleavy V. Dunn A. Duzdar

S. Dvorak L. Dworsky M. Dydyk M. Edwards R. Ehlers H. Eisele G. Eisenstein G. Eleftheriades M. Elliott T. Ellis A. Elsherbeni R. Emrick N. Engheta A. Enokihara Y. Eo H. Eom C. Ernst M. Esashi L. Escotte I. Eshrah V. Esposti M. Essaaidi K. Esselle H. Estaban J. Esteban C. Fager J. Fan D.-G. Fang M. Farina W. Fathelbab A. Fathy J. Favennec A. Fazal E. Fear M. Feldman A. Fernandez A. Ferrero T. Fickenscher J. Fiedziuszko D. Filipovic A. Fliflet B. Floyd P. Focardi N. Fong K. Foster P. Foster B. Frank C. Free J. Freire M. Freire R. Freund F. Frezza I. Frigyes C. Froehly J. Fu R. Fujimoto T. Fujioka O. Fujiwara H. Fukuyama V. Fusco D. Gabbay N. Gagnon J. Gallego B. Galwas O. Gandhi B.-Q. Gao J. Gao J. Garcia R. Garver A. Gasiewski B. Geelen B. Geller V. Gelnovatch W. Geppert F. Gerecht J. Gering M. Gerken S. Gevorgian R. Geyer O. Ghandi F. Ghannouchi K. Gharaibeh G. Ghione D. Ghodgaonkar F. Giannini J. Gilb A. Glisson M. Goano E. Godshalk M. Goldfarb P. Goldsmith M. Golio N. Gomez X. Gong R. Gonzalo S. Gopalsami A. Gopinath R. Gordon A. Gorur K. Goverdhanam W. Grabherr L. Gragnani J. Grahn G. Grau A. Grebennikov T. Gregorzyk I. Gresham A. Griol D. R. Grischowsky C. Grossman E. Grossman T. Grzegorczyk A. Gupta K. Gupta M. Gupta R. Gutmann W. Gwarek J. Hacker M. Hafizi S. Hadjiloucas S. Hagness D. Haigh P. Hale D. Ham K. Hamaguchi S. Hamedi-Hagh J. Hand K. Hashimoto Q. Han T. Hancock A. Hanke V. Hanna Z. Hao S. Hara L. Harle A. Harish P. Harrison H. Hartnagel J. Haslett G. Hau R. Haupt S. Hay H. Hayashi J. Hayashi L. Hayden J. Heaton

P. Hedekvist W. Heinrich G. Heiter M. Helier R. Henderson F. Henkel J. Herren P. Herczfeld F. Herzel J. Hessler A. Hiatala C. Hicks M. Hieda A. Higgins M. Hikita W. Hioe Y. Hirachi T. Hiraota A. Hirata T. Hiratsuka Y.-C. Ho W. Hoefer K. Hoffmann R. Hoffmann J. Hong J.-S. Hong K. Horiguchi Y. Horii J. Horng J. Horton K. Hosoya R. Howald H. Howe H.-M. Hsu H.-T. Hsu J.-P. Hsu C.-W. Hsue C.-C. Huang C. Huang F. Huang H. Huang H.-C. Huang J. Huang T.-W. Huang P. Huggard H.-T. Hui D. Humphreys A. Hung C.-M. Hung H. Hung J.-J. Hung I. Hunter H.-Y. Hwang T. Idehara S. Iezekiel J.-Y. Ihm Y. Iida H. Iizuka P. Ikalainen Y. Ikeda P. Ikonen K. Ikossi M. Ilic J. Inatani K. Iniewski H. Inokawa A. Inoue M. Ishida A. Ishimaru T. Ishizaki S. Islam Y. Ismail Y. Isota M. Ito T. Itoh Y. Itoh T. Ivanov C. Iversen D. Iverson M. Iwamoto Y. Iyama H. Izumi D. Jachowski C. Jackson D. Jackson R. Jackson M. Jacob S. Jacobsen D. Jaeger B. Jagannathan N. Jain R. Jakoby G. James V. Jandhyala M. Janezic H. Jantunen B. Jarry P. Jarry A. Jastrzbeski E. Jeckein W. Jemison Y. Jeon J. Jeong Y.-H. Jeong G. Jerinic A. Jerng T. Jerse D. Jiao J.-M. Jin J. Joe L. Johansson T. Johnson A. Joseph K. Joshin J. Joubert P. Juodawlkis P. Kabos S.-T. Kahng T. Kaho D. Kajfez T. Kamel Y. Kamimura H. Kamitsuna K. Kamogawa S. Kanamaluru H. Kanaya M. Kanda P. Kangaslahtii V. Kaper M. Kärkkäinen A. Karpov U. Karthaus A. Karwowski T. Kashiwa R. Kaul K. Kawakami A. Kawalec T. Kawanishi S. Kawasaki H. Kayano M. Kazimierczuk R. Keam L. Kempel P. Kenington K. Kenneth S. Kenny

Digital Object Identifier 10.1109/TMTT.2006.888689

A. Kerr A. Khalil A. Khanifar J. Kiang Y.-W. Kiang P.-S. Kildal O. Kilic B. Kim H. Kim I. Kim J.-P. Kim M. Kim W. Kim B. Kimm K. Kimura S. Kimura A. Kirilenko V. Kisel S. Kishimoto A. Kishk T. Kitamura K. Kitayama T. Kitazawa W. Klaus E. Klumprink R. Knerr R. Knöchel L. Knockaert K. Kobayashi Y. Kogami B. Kolner S. Komaki M. Komaru J. Komiak A. Komijani G. Kompa A. Konczykowska Y. Konishi A. Koonen B. Kopp K. Kornegay M. Koshiba T. Kosmanis J. Kot Y. Kotsuka S. Koul V. Kourkoulos A. B. Kozyrev A. Krenitskiy N. Kriplani K. Krishnamurthy V. Krishnamurthy A. Kroenig C. Kromer C. Krowne V. Krozer W. Kruppa R. Kshetrimayum H. Ku H. Kubo E. Kuester Y. Kuga W. Kuhn T. Kuki M. Kumar M. Kunert J. Kuno M. Kunst C.-N. Kuo J.-T. Kuo H. Kurebayashi T. Kuri F. Kuroki S. Kusunoki D. Kuylenstierna M. Kuzuhara I. Kwon Y.-W. Kwon R. Lai Y.-L. Lai P. Lampariello M. Lanagan M. Lancaster P. Lane U. Langmann Z. Lao G. Lapin L. Larson J. Laskar A. Lauer G. Lazzi Y. Le Coz Y. Le Guennec S. Le Maguer B. Lee C. Lee J.-F. Lee J.-W. Lee K. Lee R. Lee S.-G. Lee T. Lee Y.-C. Leong R. Leoni K.-W. Leung P. Leuchtmann G. Leuzzi A. Leven A. Levi R. Levy A. Lewandowski M. Lewis K. Li L.-W. Li X. Li Y. Li Y.-M. Li M. Liberti L. Ligthart S. Lim E. Limiti C. Lin J. Lin Y.-D. Lin Y.-S. Lin L. Lind S. Lindenmeier F. Ling A. Lipparini D. Lippens V. Litvinov C.-P. Liu Q.-H. Liu S.-I. Liu W. Liu O. Llopis D. Lo A. Loayssa R. Loison J. Long K. Lorincz U. Lott J.-H. Loui H.-C. Lu L.-H. Lu S. Lu

W.-T. Lu V. Lubecke G. Lucca S. Lucyszyn R. Luebbers L. Lunardi J. Luy S. Lyshevski J.-G. Ma Z. Ma S. Maas P. Maccarini G. Macchiarella P. Macchiarella J. Machac S. Maci J. Maciel M. Madihian B. Madhavan V. Madrangeas M. Magana S. Mahmoud S. Mahon I. Maio A. Majedi M. Majewski M. Makimoto J. Malherbe D. Malocha T. Manabe G. Manganaro T. Maniwa C. Mann H. Manohara R. Mansour D. Manstretta J. Mao S.-G. Mao S. Marchetti R. Marques J. Martens J. Marti F. Martin E. Martinez K. Maruhashi D. Masotti A. Massa S. Masuda A. Materka B. Matinpour M. Matsuo A. Matsushima A. Matsuzawa S. Matsuzawa G. Matthaei D. Matthews J.-P. Mattia J. Maurer J. Mayock J. Mazierska S. Mazumder G. Mazzarella K. McCarthy T. McKay J. McKinney R. McMillan D. McQuiddy P. Meany F. Medina S. Melle F. Mena C. Meng H.-K. Meng W. Menzel F. Mesa A. Metzger P. Meyer C. Mias K. Michalski G. Michel E. Michielssen A. Mickelson R. Miles D. Miller R. Minasian B. Minnis D. Mirshekar J. Mitchell O. Mitomi R. Mittra M. Miyakawa R. Miyamoto M. Miyazaki K. Mizuno S. Mizushina M. Mohamed S. Mohammadi A. Mohammadian M. Mongiardo J. Morente M. Morgan K. Mori A. Morini N. Morita E. Moros A. Morris J. Morsey H. Mosallaei M. Mrozowski J.-E. Mueller M. Muraguchi K. Murata H. Muthali T. Nagatsuma P. Nagel K. Naishadham T. Nakagawa M. Nakajima N. Nakajima J. Nakayama M. Nakayama M. Nakhla J. Nallatamby S. Nam S. Narahashi A. Natarajan J. Nath B. Nauwelaers J. Navarro I. Nefedovlgor H.-C. Neitzert B. Nelson S. Nelson A. Neri H. Newman D. Ngo E. Ngoya C. Nguyen K. Niclas E. Niehenke P. Nikitin A. Niknejad N. Nikolova T. Nirmalathas K. Nishikawa T. Nishikawa

K. Nishimura T. Nishino K. Nishizawa G. Niu W. Ng S. Nogi K. Noguchi T. Nojima A. Nosich B. Notaros K. Noujeim D. Novak T. Nozokido T. Nurgaliev D. Oates J. Obregon J. O’Callahan M. O’Droma M. Odyneic I. Ogawa M. Ogusu K. Oh M. Ohawa T. Ohira I. Ohta M. Ohtsuka S. Oikawa K. Okada Y. Okano H. Okazaki V. Okhmatovski A. Oki M. Okoniewski A. Oliner J. Olsson F. Olyslager A. Omar M. Omiya K. Onodera B.-L. Ooi I. Oppermann R. Orta S. Ortiz J. Ou T. Owada M. Ozkar J. Page de la Pega W. Palmer G.-W. Pan A. Paolella C. Papanicolopoulos J. Papapolymerou B.-K. Park C.-S. Park W. Park A. Parker D. Parker T. Parker J. Pearce B. Pejcinovic S.-T. Peng R. Pengelly R. Penty J. Pereda B. Perlman L. Perregrini M. Petelin R. Petersen W. Petersen A. Peterson A. Petosa A.-V. Pham J. Phillips H. Pickett M. Pieraccini L. Pierce B. Piernas J. Pierro P. Pieters M. Piket-May L. Pileggi Z.-Y. Ping M. Pirola A. Platzker C. Plett C. Pobanz R. Pogorzelski R. Pokharel R. Pollard G. Ponchak M. Popovic J. Portilla M. Pospieszalski V. Postoyalko A. Pothier S. Prasad D. Prather D. Prescott A. Priou D. Purdy Y. Qian T. Quach C. Quendo R. Quere F. Raab V. Radisic K. Radhakrishnan T. Rahkonen C. Railton A. Raisanen K. Rajab O. Ramahi J. Randa R. Ranson T. Rappaport J. Rathmell C. Rauscher J. Rautio B. Rawat J. Rayas-Sanchez R. Reano G. Rebeiz J. Rebollar B. Redman-White M. Reddy R. Reid H.-M. Rein J. Reinert R. Remis K. Remley C. Rey L. Reynolds A. Rezazadeh E. Rezek A. Riddle B. Riddle J.-S. Rieh E. Rius I. Robertson R. Robertson A. Rodriguez R. Rogers H. Rogier U. Rohde N. Rolland R. Romanofsky

A. Rong Y. Rong D. Root L. Roselli A. Rosen U. Rosenberg L. Roy M. Royer J. Roychowdury T. Rozzi B. Rubin M. Rudolph P. Russer D. Rutledge T. Ruttan A. Rydberg T. Rylander D. Rytting C. Saavedra A. Safavi-Naeini A. Safwat M. Sagawa B. Sahu A. Saitou I. Sakagami K. Sakaguchi K. Sakakibara K. Sakamoto K. Sakoda M. Salazar-Palma C. Samori L. Samoska A. Sanada Y. Sanada M. Sanagi P. Sandhiva U. Sangawa A. Sangster K. Sano K. Sarabandi T. Sarkar C. Sarris H. Sato M. Sato S. Sato H. Sawada H. Sawaya A. Sawicki A. Sayed I. Scherbatko J. Schellenberg G. Schettini F. Schettino B. Schiek M. Schindler E. Schlecht E. Schmidhammer D. Schmitt J. Schneider J. Schoukens A. Schuchinsky R. Schuhmann J. Schultz J. Schutt-Aine A. Seeds Y. Segawa T. Seki S. Selberherr G. Semouchkin E. Semouchkina Y.-K. Seng R. Settaluri J. Sevic O. Sevimli Y. Segawa Z. Shao M. Shapiro A. Sharma S. Sharma T. Shen Z.-X. Shen Y. Shestopalov H. Shigesawa Y.-C. Shih H. Shimasaki S. Shinjo N. Shino N. Shinohara T. Shimozuma W. Shiroma K. Shogen N. Shuley M. Shur D. Sievenpiper A. Sihvola C. Silva M. Silveira M. Silveirinha M. Silveirinhao K. Silvonen G. Simin R. Simons B. Sinha F. Sinnesbichler J. Sinsky J. Sitch H.-J. Siweris R. Sloan A. Smith D. Smith G. Smith P. Smith R. Snyder H. Sobol A. Sochava M. Solano K. Solbach M. Solomon M. Sorolla Ayza R. Sorrentino C. Soukoulis N. Soveiko E. Sovero J. Sowers M. Soyuer R. Sparks P. Staecker D. Staiculescu S. Stapleton J. Staudinger P. Stauffer P. Steenson K. Stephan M. Steyaert S. Stitzer A. Stoehr B. Strassner M. Stubbs M. Stuchly A. Suarez G. Subramanyam R. Sudbury N. Suematsu M. Sugiyama D. Sullivan L. Sundstrom

Y. Suzuki J. Svacina D. Swanson D. Sweeney R. Syms B. Szendrenyi W. Tabbara M. Tabib-Azar A. Taflove M. Taghivand N. Taguchi Y. Tahara G. Tait Y. Tajima T. Takagi K. Takahashi S. Takayama Y. Takayama S. Takeda I. Takenaka M. Taki K. Takizawa S. Talisa N. Talwalkar B.-T. Tan C.-Y. Tan J. Tan C.-W. Tang W.-C. Tang S. Tanaka T. Tanaka Y. Tanaka M. Tani E. Taniguchi H. Tanimoto R. Tascone J. Taub J. Tauritz R. Tayrani D. Teeter F. Teixeira R. Temkin M. Tentzeris K. Thakur H. Thal W. Thiel H.-W. Thim B. Thompson D. Thompson M. Tiebout L. Tiemeijer H. Toda M.-R. Tofighi M. Togashi T. Tokumitsu R. Tomasiunas A. Tombak K. Tomiyasu I. Toyoda S. Tretyakov R. Trew A. Trifiletti C. Trueman A. Truitt C.-M. Tsai E. Tsai L. Tsang H.-Q. Tserng T. Tsiboukis J. Tsui M. Tsuji T. Tsujiguchi T. Tsukahara K. Tsukamoto K. Tsunoda H. Tsurumi S. Tu R. Tucker M. Tur C.-K. Tzuang H. Uchida S. Uebayashi T. Ueda S. Ueno J. Uher F. Uhlmann T. Ulrich T. Umeda Y. Umeda F. Urbani T. Uwano P. Vainikainen P. Valanju F. Van de Water P. van den Berg D. Van der Weide G. Vandenbosch A. Vander Vorst D. Vanhoenacker-Janvie J. Vankka F. Van Straten K. Varian G. Vasilecu A. Vegas-Garcia L. Vegni A. Verma R. Vernon J. Verspecht B. Vidal L. Vietzorreck A. Viitanen A. Vilches C. Vittoria S. Vitusevich D. Viveiros V. Volman K. Wada K. Wakino D. Walker R. Walker M. Wallis C. Walsh C. Wan S. Wane B.-Z. Wang C. Wang D. Wang E. Wang H. Wang J. Wang K.-C. Wang S. Wang T.-H. Wang W. Wang X. Wang K. Warnick P. Warr S. Wartenberg O. Watanabe S. Watanabe R. Waugh D. Webb K. Webb R. Webster S. Wedge C.-J. Wei

J. Weirt R. Weigel G. Weihs R. Weikle C. Weil D. Weile A. Weily S. Weinreb J. Weiss C. Weitzel T. Weller C.-P. Wen M.-H. Weng R.-M. Weng S. Wentworth J. Whelehan L. Whicker J. Whitaker N. Whitbread D. White I. White S. Whiteley A. Whittneben B. Widrow G. Wilkins J. Williams T. Williams A. Williamson B. Willen B. Wilson J. Wiltse T. Winslow J. Winters A. Wittneben M. Wnuk M.-F. Wong S. Wong W. Woo J. Wood R. C. Wood G. Woods D. Woolard B.-L. Wu C. Wu H. Wu K. Wu K.-L. Wu Q. Wu Y.-S. Wu J. Wuerfl M. Wurzer J. Wustenberg G. Xiao C. Xie H. Xin Y.-Z. Xiong J. Xu Y. Xu Q. Xue T. Yakabe K. Yamamo S. Yamamoto S. Yamashita K. Yamauchi F. Yang H.-Y. Yang K. Yang Y. Yang Y.-J. Yang Z. Yang S. Yanagawa F. Yanovsky H. Yao J. Yao J. Yap B. Yarman K. Yashiro H. Yasser K. Yasumoto S. Ye J. Yeo S.-P. Yeo A. Yilmaz W.-Y. Yin S. Yngvesson N. Yoneda T. Yoneyama C.-K. Yong J.-G. Yook J.-B. Yoon R. York I. Yoshida S. Yoshikado L. Young M. Yousefi J.-W. Yu M. Yu P.-K. Yu W. Yu S.-W. Yun P. Yue A. Zaghoul A. Zaghloul A. Zajic K. Zaki P. Zampardi J. Zapata L. Zappelli J. Zehentner L. Zhang Q.-J. Zhang R. Zhang S. Zhang W. Zhang Y. P. Zhang A. Zhao L. Zhao Y. Zhao F. Zhenghe W. Zhou A. Zhu L. Zhu N.-H. Zhu Y.-S. Zhu Z. Zhu R. Zhukavin D. Zimmermann R. Ziolkowski H. Zirath J. Zmuidzinas A. Zozaya

2006 Index IEEE Transactions on Microwave Theory and Techniques Vol. 54 This index covers all technical items — papers, correspondence, reviews, etc. — that appeared in this periodical during 2006, and items from previous years that were commented upon or corrected in 2006. Departments and other items may also be covered if they have been judged to have archival value. The Author Index contains the primary entry for each item, listed under the first author's name. The primary entry includes the coauthors’ names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination. The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author’s name, the publication abbreviation, month, and year, and inclusive pages. Subject cross-references are included to assist in finding items of interest. Note that the item title is found only under the primary entry in the Author Index.

AUTHOR INDEX

A Aaen, P.H., J.A. Pla, and C.A. Balanis. Modeling techniques suitable for CAD-based design of internal matching networks of high-power RF/microwave transistors; T-MTT Jul 06 3052-3059 Aaen, P.H., see Wood, J., T-MTT Aug 06 3163-3172 Abbaspour-Tamijani, A., see Chih-Chieh Cheng, T-MTT Dec 06 4498-4506 Abdel-Malek, H.L., A.-kS.O. Hassan, E.A. Soliman, and S.A. Dakroury. The ellipsoidal technique for design centering of microwave circuits exploiting space-mapping interpolating surrogates; T-MTT Oct 06 3731-3738 Abdipour, A., see Movahhedi, M., T-MTT Jun 06 2636-2645 Aberle, J.T., see Elshafiey, T.F., T-MTT Feb 06 513-521 Aberle, J. T., see Panaretos, A. H., T-MTT Dec 06 4237-4246 Abib, G.I., see Bensmida, S., T-MTT Jun 06 2707-2712 Abou-Rjeily, C., see Keignart, J., T-MTT Jun 06 1812-1819 Abou-Rjeily, C., see Denis, B., T-MTT Jun 06 1896-1911 Abraham, J.K., see Taeksoo Ji, T-MTT Mar 06 1131-1138 Abramowicz, A., see Krupka, J., T-MTT Jun 06 2329-2335 Ackerman, E.I., see Cox, C.H., III, T-MTT Feb 06 906-920 Adalev, A.S., N.V. Korovkin, M. Hayakawa, and J.B. Nitsch. Deembedding and unterminating microwave fixtures with the genetic algorithm; T-MTT Jul 06 3131-3140 Adesida, I., see Guang Chen, T-MTT Jul 06 2949-2953 Adrian Eng-Choon Tan, M.Y.-W. Chia, and S.-W. Leong. Sub-nanosecond pulse-forming network on SiGe BiCMOS for UWB communications; TMTT Mar 06 1019-1024 Aissat, H., L. Cirio, M. Grzeskowiak, J.-M. Laheurte, and O. Picon. Reconfigurable circularly polarized antenna for short-range communication systems; T-MTT Jun 06 2856-2863 Akalin, T., A. Treizebre, and B. Bocquet. Single-wire transmission lines at terahertz frequencies; T-MTT Jun 06 2762-2767 Akan, V., see Duyar, M., T-MTT Jun 06 1388-1395 Akhtar, M.J., L.E. Feher, and M. Thumm. A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials; T-MTT May 06 2011-2022 Akitsu, T., see Kato, H., T-MTT Nov 06 3960-3967 Aksun, M.I., see Onal, T., T-MTT Oct 06 3739-3745 Albero-Ortiz, A., see Requena-Perez, M.E., T-MTT Feb 06 615-624 Alford, N., see Krupka, J., T-MTT Nov 06 3995-4001 Allen, C.A., K.M.K.H. Leong, and T. Itoh. Design of microstrip resonators using balanced and unbalanced composite right/left-handed transmission lines; T-MTT Jul 06 3104-3112 Allstot, D.J., see Banerjee, G., T-MTT Jun 06 2336-2345 Alomainy, A., see Yan Zhao, T-MTT Jun 06 1827-1835 Alonso, J.I., see Gomez-Garcia, R., T-MTT Oct 06 3751-3764 Alouini, M., see Blanc, S., T-MTT Jan 06 402-411 Alping, A., see Karnfelt, C., T-MTT Jun 06 2593-2603 Althaus, F., see Zasowski, T., T-MTT Jun 06 1836-1845 Alvarez-Melcon, A., see Gomez-Tornero, J.L., T-MTT Sep 06 3534-3542

Aly, O.A.M., and A.S. Omar. Reconstructing stratified permittivity profiles using super-resolution techniques; T-MTT Jan 06 492-498 Amari, S., U. Rosenberg, and R. Wu. In-line pseudoelliptic band-reject filters with nonresonating nodes and/or phase shifts; T-MTT Jan 06 428-436 Amari, S., C. LeDrew, and W. Menzel. Space-mapping optimization of planar coupled-resonator microwave filters; T-MTT May 06 2153-2159 Amari, S., see Mokhtaari, M., T-MTT Nov 06 3940-3946 Ammann, M.J., see Junker, M., T-MTT Jun 06 1576-1581 An, D., see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Anakabe, A., see Mallet, A., T-MTT Dec 06 4353-4361 Anderson, J., see Bharathan, K., T-MTT Jun 06 1301-1307 Andersson, K., see Sudow, M., T-MTT Dec 06 4072-4078 Anding Zhu, J. C. Pedro, and T. J. Brazil. Dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers; T-MTT Dec 06 4323-4332 Angelov, I., see Karnfelt, C., T-MTT Jun 06 2887-2898 Anh Do Manh, see Kaixue Ma, T-MTT Mar 06 1113-1119 Anh Do Manh, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Antar, Y.M.M., see Hamed, K.W., T-MTT Jun 06 2527-2533 Antipov, S.V., see Ling Jiang, T-MTT Jul 06 2944-2948 Antonsen, T.M., Jr., see Safier, P.N., T-MTT Oct 06 3605-3615 Anttila, L., see Valkama, M., T-MTT Jun 06 2356-2366 Araneo, R. Extraction of broad-band passive lumped equivalent circuits of microwave discontinuities; T-MTT Jan 06 393-401 Arnould, J.-D., see Kaddour, D., T-MTT Jun 06 2367-2375 Arslan, H., see Jiang Liu, T-MTT Aug 06 3191-3196 Aryanfar, F., and K. Sarabandi. Compact Millimeter-wave filters using distributed capacitively loaded CPW resonators; T-MTT Mar 06 11611165 Asano, K., see Takenaka, I., T-MTT Dec 06 4513-4521 Asbeck, P.M., see Kimball, D.F., T-MTT Nov 06 3848-3856 Asbeck, P. M., see Feipeg Wang, T-MTT Dec 06 4086-4099 Asbeck, P. M., see Yu Zhao, T-MTT Dec 06 4479-4488 Atsumi, Y., see Shingo Tanaka, T-MTT Feb 06 938-944 Atsumi, Y., see Taguchi, N., T-MTT Feb 06 945-950 Atsumi, Y., see Shingo Tanaka, T-MTT Jun 06 1561-1568 Attygalle, M., see Lim, C., T-MTT May 06 2181-2187 Aubert, H., see Perret, E., T-MTT Sep 06 3594-3601 August, N.J., and Dong Sam Ha. Operation, system architectures, and physical Layer design considerations of distributed MAC protocols for UWB; T-MTT Jul 06 3001-3012 Austin, M.W., see Winnall, S.T., T-MTT Feb 06 868-872 Au-Yeung Chung-Fai, see Chung-Fai Au-Yeung, T-MTT Jan 06 4-9 B Babakhani, A., see Buckwalter, J. F., T-MTT Dec 06 4271-4280 Baccarelli, P., C. Di Nallo, S. Paulotto, and D.R. Jackson. A full-wave numerical approach for modal analysis of 1-D periodic microstrip structures; T-MTT Jun 06 1350-1362 Bachtold, W., see Negra, R., T-MTT Jun 06 2684-2690 Baek, C.-W., see Llamas-Garro, I., T-MTT Dec 06 4161-4168 Baek Ho Jung, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Bagga, S., A.V. Vorobyov, S.A.P. Haddad, A.G. Yarovoy, W.A. Serdijn, and J.R. Long. Codesign of an impulse generator and miniaturized antennas for IR-UWB; T-MTT Jun 06 1656-1666 Baginski, M.E., see Faircloth, D.L., T-MTT Mar 06 1201-1209 Baillargeat, D., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Baillargeat, D., see Lenoir, P., T-MTT Jul 06 3090-3097 Bailly, C., see Saib, A., T-MTT Jun 06 2745-2754 Bajon, D., see Wane, S., T-MTT Dec 06 4397-4411 Baker, A., see Hennings, A., T-MTT Mar 06 1253-1261 Baki, R.A., T.K.K. Tsang, and M.N. El-Gamal. Distortion in RF CMOS short-channel low-noise amplifiers; T-MTT Jan 06 46-56 Bakkaloglu, B., see Hedayati, H., T-MTT Oct 06 3654-3663 Bakr, M.H., see Nikolova, N.K., T-MTT Feb 06 670-681 Bakr, M.H., see Nikolova, N.K., T-MTT Jun 06 1598-1610

IEEE T-MTT 2006 INDEX — 2 Bakr, M.H., see Sabbagh, M.A.E., T-MTT Aug 06 3339-3351 Baks, C.W., see Zwick, T., T-MTT Mar 06 1001-1010 Balanis, C.A., see Aaen, P.H., T-MTT Jul 06 3052-3059 Balbin, I., see Karmakar, N.C., T-MTT May 06 2160-2168 Ball, J.A.R., see Wells, C.G., T-MTT Jul 06 3013-3018 Banai, A., see Nick, M., T-MTT Jul 06 2993-3000 Bandler, J.W., see Nikolova, N.K., T-MTT Feb 06 670-681 Bandler, J.W., see Koziel, S., T-MTT Jun 06 2410-2421 Bandler, J.W., see Sabbagh, M.A.E., T-MTT Aug 06 3339-3351 Bandler, J.W., see Koziel, S., T-MTT Oct 06 3721-3730 Bandler, J. W., see Koziel, S., T-MTT Dec 06 4316-4322 Banerjee, G., K. Soumyanath, and D.J. Allstot. Measurement and modeling errors in noise parameters of scaled-CMOS devices; T-MTT Jun 06 23362345 Bang Chul Jung, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Baojun Wei, see Simsek, E., T-MTT Jan 06 216-225 Baozhu Liu, see Xiupu Zhang, T-MTT Feb 06 929-937 Barataud, D., see Macraigne, F., T-MTT Aug 06 3219-3226 Barba, I., see Cabeceira, A.C.L., T-MTT Jun 06 2780-2789 Barel, A.R.F., see Mingxu Liu, T-MTT Jun 06 1698-1706 Barelaud, B., see Darfeuille, S., T-MTT Dec 06 4381-4396 Barker, N.S., see Qin Shen, T-MTT Jun 06 2646-2658 Barras, D., F. Ellinger, H. Jackel, and W. Hirt. Low-power ultra-wideband wavelets generator with fast start-up circuit; T-MTT May 06 2138-2145 Barras, D., F. Ellinger, H. Jackel, and W. Hirt. A robust front-end architecture for low-power UWB radio transceivers; T-MTT Jun 06 17131723 Basu, A., see Pathak, N.P., T-MTT Jan 06 173-179 Batchelor, J.C., see Das, A., T-MTT Aug 06 3426-3432 Bayrak, M., see Duyar, M., T-MTT Jun 06 1388-1395 Beasly, P.T., see Mahon, J., T-MTT May 06 2050-2060 Becuwe, S., see Cuyt, A., T-MTT May 06 2265-2274 Bednarz, L., see Saib, A., T-MTT Jun 06 2745-2754 Bekers, D.J., S.J.L. van Eijndhoven, A.A.F. van de Ven, P.-P. Borsboom, and A.G. Tijhuis. Eigencurrent analysis of resonant behavior in finite antenna arrays; T-MTT Jun 06 2821-2829 Bensmida, S., E. Bergeault, G.I. Abib, and B. Huyart. Power amplifier characterization: an active load-pull system based on six-port reflectometer using complex modulated carrier; T-MTT Jun 06 2707-2712 Bergeault, E., see Bensmida, S., T-MTT Jun 06 2707-2712 Bergman, J., see Ma, B. Y., T-MTT Dec 06 4448-4455 Bernardin, N., see Cresson, P.-Y., T-MTT Jan 06 302-308 Berroth, M., see Lei Wu, T-MTT Jan 06 278-284 Bertazzi, F., F. Cappelluti, S.D. Guerrieri, F. Bonani, and G. Ghione. Selfconsistent coupled carrier transport full-wave EM analysis of semiconductor traveling-wave devices; T-MTT Jun 06 1611-1618 Bessemoulin, A., see Mahon, J., T-MTT May 06 2050-2060 Betts, G.E., see Cox, C.H., III, T-MTT Feb 06 906-920 Beukema, T., see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Beyene, W.T., see Hao Shi, T-MTT Jan 06 360-372 Bharathan, K., W. Lawson, J. Anderson, E.S. Gouveia, B.P. Hogan, and I. Spassovsky. Design and cold testing of a radial extraction output cavity for a frequency-doubling gyroklystron; T-MTT Jun 06 1301-1307 Bhattacharya, P. K., see Lee, K.-Y., T-MTT Dec 06 4141-4148 Bian, E., see Fengyi Huang, T-MTT Jan 06 115-119 Bien, F., H. Kim, Y. Hur, M. Maeng, J. Cha, S. Chandramouli, E. Gebara, and J. Laskar. A 10-Gb/s reconfigurable CMOS equalizer employing a transition detector based output monitoring technique for band-limited serial links; T-MTT Dec 06 4538-4547 Bila, S., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Bila, S., see Lenoir, P., T-MTT Jul 06 3090-3097 Bilbro, L., see Trew, R.J., T-MTT May 06 2061-2067 Billia, L., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Billinger, R.L., see Randa, J., T-MTT Mar 06 1180-1189 Billonnet, L., see Darfeuille, S., T-MTT Dec 06 4381-4396 Billstrom, N., see Sudow, M., T-MTT Dec 06 4072-4078 Biondi, T., A. Scuderi, E. Ragonese, and G. Palmisano. Analysis and modeling of layout scaling in silicon integrated stacked transformers; TMTT May 06 2203-2210 Blagovic, K., see Stevanovic, I., T-MTT Oct 06 3688-3697 Blanc, S., M. Alouini, K. Garenaux, M. Queguiner, and T. Merlet. Optical multibeamforming network based on WDM and dispersion fiber in receive mode; T-MTT Jan 06 402-411 Blau, K., see Weber, J., T-MTT Jun 06 2733-2740

+ Check author entry for coauthors

Blockley, P.S., J.B. Scott, D. Gunyan, and A.E. Parker. Noise considerations when determining phase of large-signal microwave measurements; T-MTT Aug 06 3182-3190 Boag, A., and B. Livshitz. Adaptive nonuniform-grid (NG) algorithm for fast capacitance extraction; T-MTT Sep 06 3565-3570 Bocquet, B., see Akalin, T., T-MTT Jun 06 2762-2767 Bogdashov, A., G. Denisov, D. Lukovnikov, Y. Rodin, D. Sobolev, and J. L. Hirshfield. Oversized Ka-band traveling-wave window for a high-power transmission; T-MTT Dec 06 4130-4135 Bok-Hyung Lee, D. An, Mun-Kyo Lee, Byeong-Ok Lim, Jung-Hun Oh, S.-D. Kim, Jin-Koo Rhee, Jung-Dong Park, and Sang-Yong Yi. Low conversion loss and high LO-RF isolation 94-GHz active down converter; T-MTT Jun 06 2422-2430 Boll, G., see Fung, A., T-MTT Dec 06 4507-4512 Bonache, J., I. Gil, J. Garcia-Garcia, and F. Martin. Novel microstrip bandpass filters based on complementary split-ring resonators; T-MTT Jan 06 265-271 Bonache, J., see Garcia-Garcia, J., T-MTT Jun 06 2628-2635 Bonache, J., see Gil, I., T-MTT Jun 06 2665-2674 Bonache, J., see Garcia-Garcia, J., T-MTT Dec 06 4136-4140 Bonani, F., see Bertazzi, F., T-MTT Jun 06 1611-1618 Bond, E.J., see Converse, M., T-MTT May 06 2169-2180 Bongard, F., see Stevanovic, I., T-MTT Oct 06 3688-3697 Borgarino, M., see Traverso, P. A., T-MTT Dec 06 4341-4352 Borges Carvalho, N., K.A. Remley, and D.E. Root. Guest editorial [intro. to the mini-special issue]; T-MTT Aug 06 3161-3162 Borges Carvalho, N., see Martins, J. P., T-MTT Dec 06 4432-4439 Boria, V.E., see Carbonell, J., T-MTT Jun 06 1527-1533 Boric-Lubecke, O., see Yanming Xiao, T-MTT May 06 2023-2032 Bornemann, J., see Rambabu, K., T-MTT Aug 06 3333-3338 Bornemann, J., see Mokhtaari, M., T-MTT Nov 06 3940-3946 Borsboom, P.-P., see Bekers, D.J., T-MTT Jun 06 2821-2829 Bosisio, R.G., see Moldovan, E., T-MTT Feb 06 625-632 Bosisio, R.G., see Yanyang Zhao, T-MTT Jun 06 1707-1712 Bosisio, R.G., see Xinyu Xu, T-MTT Jul 06 2937-2943 Bosisio, R. G., see Moldovan, E., T-MTT Nov 06 4017 Bossavit, A., see Ouchetto, O., T-MTT Jun 06 2615-2619 Boumaiza, S., see Taijun Liu, T-MTT Jun 06 1340-1349 Boumaiza, S., see Helaoui, M., T-MTT Jun 06 1396-1404 Boumaiza, S., see Hammi, O., T-MTT Aug 06 3246-3254 Bour, D. P., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Boutros, K., see Darwish, A. M., T-MTT Dec 06 4456-4463 Bouttement, Y., see Tiemeijer, L.F., T-MTT Aug 06 3378-3386 Bozzi, M., Duochuan Li, S. Germani, L. Perregrini, and Ke Wu. Analysis of NRD components via the order-reduced volume-integral-equation method combined with the tracking of the matrix eigenvalues; T-MTT Jan 06 339347 Brar, B., see Ma, B. Y., T-MTT Dec 06 4448-4455 Brazil, T.J., see Kallfass, I., T-MTT Jun 06 2312-2320 Brazil, T. J., see Anding Zhu, T-MTT Dec 06 4323-4332 Brebels, S., see Zwick, T., T-MTT Mar 06 1001-1010 Breeze, J., see Krupka, J., T-MTT Nov 06 3995-4001 Brookes, M., see Chorti, A., T-MTT Aug 06 3301-3315 Brown, A.K., see Yongwei Zhang, T-MTT Jun 06 1675-1680 Brzezina, G., L. Roy, and L. MacEachern. Planar antennas in LTCC technology with transceiver integration capability for ultra-wideband applications; T-MTT Jun 06 2830-2839 Bucholtz, F., see Urick, V.J., T-MTT Jun 06 1458-1463 Bucholtz, F., see Urick, V.J., T-MTT Jul 06 3141-3145 Buckwalter, J. F., A. Babakhani, A. Komijani, and A. Hajimiri. An integrated subharmonic coupled-oscillator scheme for a 60-GHz phased array transmitter; T-MTT Dec 06 4271-4280 Buell, K., H. Mosallaei, and K. Sarabandi. A substrate for small patch antennas providing tunable miniaturization factors; T-MTT Jan 06 135146 Bumman Kim, see Young Yun Woo, T-MTT May 06 1969-1974 Bumman Kim, see Huijung Kim, T-MTT Jul 06 2917-2924 Byeong-Ha Park, see Woonyun Kim, T-MTT May 06 2098-2105 Byeong-Ok Lim, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Byoung Hwa Lee, Dong Seok Park, Sang Soo Park, and Min Cheol Park. Design of new three-line balun and its implementation using multilayer configuration; T-MTT Jun 06 1405-1414 Byung-Sung Kim, see Jinsung Park, T-MTT Dec 06 4372-4380 Byung-Wook Min, and G.M. Rebeiz. A low-loss silicon-on-silicon DC-110GHz resonance-free package; T-MTT Feb 06 710-716

IEEE T-MTT 2006 INDEX — 3 C Cabanillas, J., see Lopez-Villegas, J.M., T-MTT Jan 06 226-234 Cabeceira, A.C.L., A. Grande, I. Barba, and J. Represa. A time-domain modeling for EM wave propagation in bi-isotropic media based on the TLM method; T-MTT Jun 06 2780-2789 Cabral, P. M., see Martins, J. P., T-MTT Dec 06 4432-4439 Caddemi, A., see Crupi, G., T-MTT Oct 06 3616-3622 Cai, A., see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Calabrese, M.L., G. d'Ambrosio, R. Massa, and G. Petraglia. A highefficiency waveguide applicator for in vitro exposure of mammalian cells at 1.95 GHz; T-MTT May 06 2256-2264 Camacho-Penalosa, C., see Marquez-Segura, E., T-MTT Feb 06 748-754 Campos-Roca, Y., C. Schworer, A. Leuther, and M. Seelmann-Eggebert. Gband metamorphic HEMT-based frequency multipliers; T-MTT Jul 06 2983-2992 Cangellaris, A.C., see Lukashevich, D., T-MTT Oct 06 3712-3720 Canning, J., see Winnall, S.T., T-MTT Feb 06 868-872 Canos, A.J., J.M. Catala-Civera, F.L. Penaranda-Foix, and Edl. Reyes-Davo. A novel technique for deembedding the unloaded resonance frequency from measurements of microwave cavities; T-MTT Aug 06 3407-3416 Cao Qunsheng, see Qunsheng Cao, T-MTT Aug 06 3316-3326 Cao Yi, see Yi Cao, T-MTT Jun 06 2398-2409 Cappelluti, F., see Bertazzi, F., T-MTT Jun 06 1611-1618 Carbonell, J., L.J. Rogla, V.E. Boria, and D. Lippens. Design and experimental verification of backward-wave propagation in periodic waveguide structures; T-MTT Jun 06 1527-1533 Cardinali, R., Luca De Nardis, M.-G. Di Benedetto, and P. Lombardo. UWB ranging accuracy in high- and low-data-rate applications; T-MTT Jun 06 1865-1875 Carey-Smith, B.E., and P.A. Warr. Distortion mechanisms in varactor diodetuned microwave filters; T-MTT Sep 06 3492-3500 Carretti, E., see Peverini, O.A., T-MTT Jan 06 412-420 Carvalho, N.B., J.C. Pedro, W. Jang, and M.B. Steer. Nonlinear RF circuits and systems simulation when driven by several modulated signals; T-MTT Feb 06 572-579 Carvalho, N.B., J.C. Pedro, and J.P. Martins. A corrected microwave multisine waveform generator; T-MTT Jun 06 2659-2664 Casares-Miranda, F.P., see Marquez-Segura, E., T-MTT Feb 06 748-754 Catala-Civera, J.M., see Canos, A.J., T-MTT Aug 06 3407-3416 Cazaux, J.L., see Quere, R., T-MTT Jun 06 2567 Centeno, A., see Krupka, J., T-MTT Nov 06 3995-4001 Cha, J., see Bien, F., T-MTT Dec 06 4538-4547 Chan, E.H.W., and R.A. Minasian. Suppression of phase-induced intensity noise in optical delay-line signal processors using a differential-detection technique; T-MTT Feb 06 873-879 Chan Chi Hou, see Yum, T.Y., T-MTT Aug 06 3255-3266 Chandrakasan, A.P., see Wentzloff, D.D., T-MTT Jun 06 1647-1655 Chandramouli, S., see Bien, F., T-MTT Dec 06 4538-4547 Chandrasekhar, A., see Zwick, T., T-MTT Mar 06 1001-1010 Chang, S.-F.R., see Yng-Huey Jeng, T-MTT Feb 06 633-638 Chang, S.-F.R., see Yng-Huey Jeng, T-MTT May 06 2146-2152 Chang Chia-Chi, see To-Po Wang, T-MTT Jan 06 88-95 Chang Chia-Hung, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Chang Chi-Yang, see Chun-Hsiang Chi, T-MTT Jun 06 2478-2486 Chang Chun-Fu, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Chang Chung-Long, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Chang-Hasnain, C.J., see Chrostowski, L., T-MTT Feb 06 788-796 Chang-Ho Lee, see Yunseo Park, T-MTT Jun 06 1687-1697 Chang-Ho Lee, see Sen, P., T-MTT Jun 06 2604-2614 Chang-Ho Lee, see Jinsung Park, T-MTT Dec 06 4372-4380 Chang Hong-Yeh, see Pei-Si Wu, T-MTT Jan 06 10-19 Chang Hong-Yeh, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Chang Hong-Yeh, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Chang Hong-Yeh, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Chang Ik Soo, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Chang Kai, see Wen-Hua Tu, T-MTT Mar 06 1084-1089 Chang Kai, see Seungpyo Hong, T-MTT Jun 06 1370-1378 Chang Kai, see Yu-Jiun Ren, T-MTT Jun 06 1495-1502 Chang Kai, see Wen-Hua Tu, T-MTT Jun 06 2497-2502 Chang Kai, see Yu-Jiun Ren, T-MTT Jul 06 2970-2976 Chang Kai, see Wen-Hua Tu, T-MTT Oct 06 3786-3792 Chang-Soon Choi, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Chang-Soon Choi, see Shoji, Y., T-MTT Oct 06 3664-3674 Chang-Soo Park, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 + Check author entry for coauthors

Chang Tsung-Hui, see Tsung-Hui Chang, T-MTT Jun 06 1731-1744 Chang Yi-Hao, see Rong Jiang, T-MTT Jul 06 3060-3068 Chang Ying-Tang, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Chang Ying-Tang, see To-Po Wang, T-MTT Jan 06 88-95 Chang Yu-Jung, see Tsung-Hui Chang, T-MTT Jun 06 1731-1744 Changzhi Li, Yanming Xiao, and Jenshan Lin. Experiment and spectral analysis of a low-power Ka-band heartbeat detector measuring from four sides of a human body; T-MTT Dec 06 4464-4471 Chan Khee Meng, see Rambabu, K., T-MTT Aug 06 3333-3338 Chan-Kuen Sim, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Chao-Hsiung Tseng, and Tah-Hsiung Chu. Measurement of frequencydependent equivalent width of substrate integrated waveguide; T-MTT Jun 06 1431-1437 Chao-Huang Wu, Yo-Shen Lin, Chi-Hsueh Wang, and Chun Hsiung Chen. Novel microstrip coupled-line bandpass filters with shortened coupled sections for stopband extension; T-MTT Feb 06 540-546 Chao-Huang Wu, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Chao Lu, A.-V.H. Pham, and D. Livezey. Development of multiband phase shifters in 180-nm RF CMOS technology with active loss compensation; T-MTT Jan 06 40-45 Chao Shih-Fong, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Chappell, W. J., see Joshi, H., T-MTT Dec 06 4169-4177 Chazelas, J., see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Chee Piew-Yong, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Che Lai Chih, see Li, E.S., T-MTT Jan 06 464-472 Che-Ming Wang, see Wen-Bin Tang, T-MTT Oct 06 3641-3647 Chen, C.C.-P., see Rong Jiang, T-MTT Jul 06 3060-3068 Chen, J., see Tzuang, C.-K. C., T-MTT Dec 06 4548-4555 Chen, K.J., see Hualiang Zhang, T-MTT Mar 06 1090-1095 Chen, K.J., see Leung, L.L.W., T-MTT May 06 2249-2255 Chen, M.J., A.-V.H. Pham, N.A. Evers, C. Kapusta, J. Iannotti, W. Kornrumpf, J.J. Maciel, and N. Karabudak. Design and development of a package using LCP for RF/microwave MEMS switches; T-MTT Nov 06 4009-4015 Chen, P., see Ma, B. Y., T-MTT Dec 06 4448-4455 Chen, X. M., see Fan, X.C., T-MTT Apr 06 1631 Chen Chi-Chen, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Chen Chi-Feng, see Chi-Feng Chen, T-MTT Feb 06 755-762 Chen Chi-Feng, see Chi-Feng Chen, T-MTT May 06 1945-1952 Chen Chi-Feng, see Chi-Feng Chen, T-MTT Sep 06 3550-3558 Chen Chun Hsiung, see Pu-Hua Deng, T-MTT Feb 06 533-539 Chen Chun Hsiung, see Chao-Huang Wu, T-MTT Feb 06 540-546 Chen Chun Hsiung, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Chen Chun Hsiung, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Chen Chun Hsiung, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Chen Chun Hsiung, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Chen Chun Hsiung, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Chen Chun Hsiung, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Cheng, K.-K.M., see Chung-Fai Au-Yeung, T-MTT Jan 06 4-9 Cheng-Chia Tu, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Cheng Chih-Chieh, see Chih-Chieh Cheng, T-MTT Dec 06 4498-4506 Cheng Eisenhower, see Yi-Chyun Chiou, T-MTT Aug 06 3352-3358 Cheng Jui-Ching, see Li, E.S., T-MTT Jan 06 464-472 Cheng-Ken Pao, see Kaihui Lin, T-MTT Dec 06 4041-4048 Cheng Qiang, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Chen Guang, see Guang Chen, T-MTT Jul 06 2949-2953 Cheng-Wei Qiu, see Ouchetto, O., T-MTT Nov 06 3893-3898 Chen Hsiao-Chin, see Tao Wang, T-MTT Feb 06 580-588 Chen Hsin-Hung, see Chih-Hung Lin, T-MTT May 06 2118-2127 Chen Ji, see Dagang Wu, T-MTT Dec 06 4472-4478 Chen Jiunn-Tsair, see Chih-Hung Lin, T-MTT May 06 2118-2127 Chen Ji Xin, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Chen Sheng-Bing, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Chen Sin-Ting, see Tzong-Lin Wu, T-MTT Aug 06 3398-3406 Chen Xiangfei, see Xiangfei Chen, T-MTT Feb 06 804-809 Chen Yi-Ming, see Yng-Huey Jeng, T-MTT May 06 2146-2152 Chen Zhi Ning, see Chu Gao, T-MTT Jun 06 1519-1526 Chen Zhi Ning, see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Cheol Park Min, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Cheol-Sig Pyo, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Cheol-Sig Pyo, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Cheong Pedro, see Si-Weng Fok, T-MTT May 06 2033-2041 Chern, J.G.J., see Hong-Yeh Chang, T-MTT Jan 06 20-30 Chia, B., see Hao Shi, T-MTT Jan 06 360-372 Chia, M.Y.-W., see Adrian Eng-Choon Tan, T-MTT Mar 06 1019-1024

IEEE T-MTT 2006 INDEX — 4 Chia, M.Y.W., see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Chia, M.Y.-W., Teck-Hwee Lim, Jee-Khoi Yin, Piew-Yong Chee, SiewWeng Leong, and Chan-Kuen Sim. Electronic beam-steering design for UWB phased array; T-MTT Jun 06 2431-2438 Chia, M.Y.-W., see Rambabu, K., T-MTT Aug 06 3333-3338 Chia, M.Y.-W., see Tan, A.E.-C., T-MTT Nov 06 3821-3827 Chia-Chi Chang, see To-Po Wang, T-MTT Jan 06 88-95 Chia-Hung Chang, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Chiang Yi-Chyun, see Yi-Chyun Chiang, T-MTT Nov 06 3947-3953 Chi-Chen Chen, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Chi Chong-Yung, see Tsung-Hui Chang, T-MTT Jun 06 1731-1744 Chi Chun-Hsiang, see Chun-Hsiang Chi, T-MTT Jun 06 2478-2486 Chien-Lin Wang, Guang-Hwa Shiue, Wei-Da Guo, and Ruey-Beei Wu. A systematic design to suppress wideband ground bounce noise in high speed circuits by electromagnetic-bandgap-enhanced split powers; T-MTT Dec 06 4209-4217 Chien-Min Lin, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Chi-Feng Chen, Ting-Yi Huang, and Ruey-Beei Wu. Novel compact net-type resonators and their applications to microstrip bandpass filters; T-MTT Feb 06 755-762 Chi-Feng Chen, Ting-Yi Huang, Chi-Ping Chou, and Ruey-Beei Wu. Microstrip diplexers design with common resonator sections for compact size, but high isolation; T-MTT May 06 1945-1952 Chi-Feng Chen, Ting-Yi Huang, and Ruey-Beei Wu. Design of dual- and triple-passband filters using alternately cascaded multiband resonators; TMTT Sep 06 3550-3558 Chih Che Lai, see Li, E.S., T-MTT Jan 06 464-472 Chih-Chieh Cheng, and A. Abbaspour-Tamijani. Study of 2-bit antennafilter-antenna elements for reconfigurable millimeter-wave lens arrays; TMTT Dec 06 4498-4506 Chih-Hung Lin, Hsin-Hung Chen, Yung-Yi Wang, and Jiunn-Tsair Chen. Dynamically optimum lookup-table spacing for power amplifier predistortion linearization; T-MTT May 06 2118-2127 Chih-Kai Wu, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Chih-Ming Lin, see Jui-Chieh Chiu, T-MTT Sep 06 3521-3525 Chih-Ming Tsai, and Hong-Ming Lee. The effects of component Q distribution on microwave filters; T-MTT Jun 06 1545-1553 Chi Hou Chan, see Yum, T.Y., T-MTT Aug 06 3255-3266 Chi-Hsueh Wang, see Pu-Hua Deng, T-MTT Feb 06 533-539 Chi-Hsueh Wang, see Chao-Huang Wu, T-MTT Feb 06 540-546 Chi-Hsueh Wang, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Chi-Hsueh Wang, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Chih-Yuan Tsai, see Kuo, J.-T., T-MTT Mar 06 1107-1112 Chilton, R.A., and R. Lee. Chirping unit cell length to increase frozen-mode bandwidth in nonreciprocal MPCs; T-MTT Jan 06 473-480 Chinchun Meng, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Ching-Wen Hsue, Lin-Chuan Tsai, and Yi-Hsien Tsai. Time-constant control of microwave integrators using transmission lines; T-MTT Mar 06 10431047 Ching-Wen Tang, and Sheng-Fu You. Design methodologies of LTCC bandpass filters, diplexer, and triplexer with transmission zeros; T-MTT Feb 06 717-723 Ching-Wen Tang, Sheng-Fu You, and I-Chung Liu. Design of a dual-band bandpass filter with low-temperature co-fired ceramic technology; T-MTT Aug 06 3327-3332 Chin Hsia, see Kimball, D.F., T-MTT Nov 06 3848-3856 Chin-Shen Lin, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Chiou Yi-Chyun, see Yi-Chyun Chiou, T-MTT Aug 06 3352-3358 Chi-Ping Chou, see Chi-Feng Chen, T-MTT May 06 1945-1952 Chirala, M. K., and C. Nguyen. Multilayer design techniques for extremely miniaturized CMOS microwave and millimeter-wave distributed passive circuits; T-MTT Dec 06 4218-4224 Chiu Hung-Wei, see Tao Wang, T-MTT Feb 06 580-588 Chiu Jui-Chieh, see Jui-Chieh Chiu, T-MTT Sep 06 3521-3525 Chiu Leung, see Yum, T.Y., T-MTT Aug 06 3255-3266 Chi-Yang Chang, see Chun-Hsiang Chi, T-MTT Jun 06 2478-2486 Choa Sung-Hoon, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Cho Choon Sik, see Choon Sik Cho, T-MTT Nov 06 3968-3974 Choi, C.T.M., and Shu-Hai Sun. Numerical performance and applications of the envelope ADI-FDTD method; T-MTT Jan 06 256-264 Choi Chang-Soon, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Choi Chang-Soon, see Shoji, Y., T-MTT Oct 06 3664-3674 Choi Jinsung, see Huijung Kim, T-MTT Jul 06 2917-2924 Choi Kwang-Seong, see Jeha Kim, T-MTT Feb 06 780-787 Choi Min-Ki, see Hongjoon Kim, T-MTT Dec 06 4178-4184 + Check author entry for coauthors

Choi Moon-Soon, see Piqueras, M.A., T-MTT Feb 06 887-899 Choi Mun-Ho, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Choi Sung Tae, see Sung Tae Choi, T-MTT May 06 1953-1960 Choi Won-Kyu, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Choi Woo-Young, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Cho Kyoung-Joon, see Wan-Jong Kim, T-MTT Sep 06 3469-3478 Cho Ming-Hsiang, see Ming-Hsiang Cho, T-MTT Mar 06 1296-1297 Chongcheawchamnan, M., see Phromloungsri, R., T-MTT Sep 06 3571-3582 Chong Jo Woon, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Chong-Yung Chi, see Tsung-Hui Chang, T-MTT Jun 06 1731-1744 Choon Sik Cho, J.W. Lee, and Jaeheung Kim. Dual- and triple-mode branchline ring resonators and harmonic suppressed half-ring resonators; T-MTT Nov 06 3968-3974 Choo Wooseung, see Woonyun Kim, T-MTT May 06 2098-2105 Chorti, A., and M. Brookes. On the effects of memoryless nonlinearities on M-QAM and DQPSK OFDM signals; T-MTT Aug 06 3301-3315 Cho Seonghwan, see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Chou Chi-Ping, see Chi-Feng Chen, T-MTT May 06 1945-1952 Christ, A., A. Klingenbock, T. Samaras, C. Goiceanu, and N. Kuster. The dependence of electromagnetic far-field absorption on body tissue composition in the frequency range from 300 MHz to 6 GHz; T-MTT May 06 2188-2195 Chrostowski, L., Xiaoxue Zhao, and C.J. Chang-Hasnain. Microwave performance of optically injection-locked VCSELs; T-MTT Feb 06 788796 Chuang Yu-Ju, see Jie-Wei Lai, T-MTT Feb 06 599-607 Chuang Yu-Ju, see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Chuanyi Yang, see Gope, D., T-MTT Jun 06 2453-2464 Chueh Yu-Zhi, see Shau-Gang Mao, T-MTT Sep 06 3543-3549 Chuen Ong Ling, see Yong-Xin Guo, T-MTT Mar 06 1196-1200 Chu Gao, Zhi Ning Chen, Yun Yi Wang, Ning Yang, and Xian Ming Qing. Study and suppression of ripples in passbands of series/parallel loaded EBG filters; T-MTT Jun 06 1519-1526 Chul Dong Kim, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Chul Jung Bang, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Chun-Fu Chang, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Chung-Fai Au-Yeung, and K.-K.M. Cheng. IMD reduction in CMOS double-balanced mixer using multibias dual-gate transistors; T-MTT Jan 06 4-9 Chung-Hwam Kim, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Chung-Hwan Kim, see Dong-Woo Kang, T-MTT Jan 06 294-301 Chung-Long Chang, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Chung Ming-An, see Yi-Chyun Chiang, T-MTT Nov 06 3947-3953 Chung-Ryul Kim, see Yun, Y., T-MTT Oct 06 3805-3817 Chung Shyh-Jong, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Chung Yong-Duck, see Jeha Kim, T-MTT Feb 06 780-787 Chung Yong-Duck, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Chung Yujin, see Huijung Kim, T-MTT Jul 06 2917-2924 Chun-Hsiang Chi, and Chi-Yang Chang. A new class of wideband multisection 180° hybrid rings using vertically installed planar couplers; T-MTT Jun 06 2478-2486 Chun Hsiung Chen, see Pu-Hua Deng, T-MTT Feb 06 533-539 Chun Hsiung Chen, see Chao-Huang Wu, T-MTT Feb 06 540-546 Chun Hsiung Chen, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Chun Hsiung Chen, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Chun Hsiung Chen, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Chun Hsiung Chen, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Chun Hsiung Chen, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Chun Hsiung Chen, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Chun Young-Hoon, see Young-Hoon Chun, T-MTT Feb 06 704-709 Chu Tah-Hsiung, see Chao-Hsiung Tseng, T-MTT Jun 06 1431-1437 Cimino, K., see Jie-Wei Lai, T-MTT Feb 06 599-607 Cimino, K., see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Cirio, L., see Aissat, H., T-MTT Jun 06 2856-2863 Claussen, T., see Krupka, J., T-MTT Nov 06 3995-4001 Clement, T.S., see Williams, D.F., T-MTT Jan 06 481-491 Clement, T.S., see Williams, D.F., T-MTT Mar 06 1210-1217 Clement, T.S., P.D. Hale, D.F. Williams, C.M. Wang, A. Dienstfrey, and D.A. Keenan. Calibration of sampling oscilloscopes with high-speed photodiodes; T-MTT Aug 06 3173-3181 Clement, T.S., see Dienstfrey, A., T-MTT Aug 06 3197-3208 Clifford, G. M., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Colantonio, P., F. Giannini, R. Giofre, E. Limiti, A. Serino, M. Peroni, P. Romanini, and C. Proietti. A C-band high-efficiency second-harmonic-

IEEE T-MTT 2006 INDEX — 5 tuned hybrid power amplifier in GaN technology; T-MTT Jun 06 27132722 Collado, A., see Georgiadis, A., T-MTT Nov 06 3864-3877 Collado, C., A. Grau, and F. De Flaviis. Dual-band planar quadrature hybrid with enhanced bandwidth response; T-MTT Jan 06 180-188 Collado, C., see Seron, D., T-MTT Mar 06 1154-1160 Coman, C.I., see Simeoni, M., T-MTT Jun 06 1503-1511 Comeau, J. P., see Morton, M. A., T-MTT Dec 06 4032-4040 Converse, M., E.J. Bond, B.D. Veen, and C. Hagness. A computational study of ultra-wideband versus narrowband microwave hyperthermia for breast cancer treatment; T-MTT May 06 2169-2180 Convert, E., see Mahon, J., T-MTT May 06 2050-2060 Corral, Juan.L., see Piqueras, M.A., T-MTT Feb 06 887-899 Cortiglioni, S., see Peverini, O.A., T-MTT Jan 06 412-420 Costantini, A., see Mahon, J., T-MTT May 06 2050-2060 Costanzo, A., see Rizzoli, V., T-MTT Dec 06 4149-4160 Cox, C.H., III, E.I. Ackerman, G.E. Betts, and J.L. Prince. Limits on the performance of RF-over-fiber links and their impact on device design; TMTT Feb 06 906-920 Craninckx, J., see Mingxu Liu, T-MTT Jun 06 1698-1706 Crespo-Cadenas, C., J. Reina-Tosina, and M.J. Madero-Ayora. IM3 and IM5 phase characterization and analysis based on a simplified Newton approach; T-MTT Jan 06 321-328 Crespo-Cadenas, C., J. Reina-Tosina, and M.J. Madero-Ayora. Evaluation of ACPR in mixers based on a parametric harmonic-balance approach; TMTT Jan 06 445-450 Crespo-Valero, P., see Stevanovic, I., T-MTT Jan 06 189-197 Crespo-Valero, P., see Perruisseau-Carrier, J., T-MTT Jan 06 383-392 Crespo-Valero, P., see Stevanovic, I., T-MTT Oct 06 3688-3697 Cressler, J.D., see Jongsoo Lee, T-MTT Mar 06 1262-1268 Cressler, J.D., see Yunseo Park, T-MTT Jun 06 1687-1697 Cressler, J. D., see Morton, M. A., T-MTT Dec 06 4032-4040 Cresson, P.-Y., C. Ricard, N. Bernardin, L. Dubois, and J. Pribetich. Design and modeling of a specific microwave applicator for the treatment of snoring; T-MTT Jan 06 302-308 Crowe, T.W., see Haiyong Xu, T-MTT Oct 06 3648-3653 Crupi, G., Dongping Xiao, D.M.M.-P. Schreurs, E. Limiti, A. Caddemi, W. De Raedt, and M. Germain. Accurate multibias equivalent-circuit extraction for GaN HEMTs; T-MTT Oct 06 3616-3622 Cui Tie Jun, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Cuyt, A., R.B. Lenin, S. Becuwe, and B. Verdonk. Adaptive multivariate rational data fitting with applications in electromagnetics; T-MTT May 06 2265-2274 D Dadello, A., see Mahon, J., T-MTT May 06 2050-2060 Dagang Wu, S. Shamsi, Ji Chen, and W. Kainz. Evaluations of specific absorption rate and temperature increase within pregnant female models in magnetic resonance imaging birdcage coils; T-MTT Dec 06 4472-4478 Dai, W., see Yu Du, T-MTT Mar 06 1287-1294 Dakroury, S.A., see Abdel-Malek, H.L., T-MTT Oct 06 3731-3738 d'Ambrosio, G., see Calabrese, M.L., T-MTT May 06 2256-2264 Daniel, J.E., see Padmanabhan, S., T-MTT Sep 06 3583-3593 Daniele, N., see Keignart, J., T-MTT Jun 06 1812-1819 Dan Keun Sung, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Dankov, P.I. Two-resonator method for measurement of dielectric anisotropy in multilayer samples; T-MTT Jun 06 1534-1544 Danly, B.G., see Safier, P.N., T-MTT Oct 06 3605-3615 Danneville, F., see Si Moussa, M., T-MTT Jun 06 2675-2683 Daoud, S.M., and P.N. Shastry. A novel wideband MMIC voltage controlled attenuator with a bandpass filter topology; T-MTT Jun 06 2576-2583 Darfeuille, S., J. Lintignat, R. Gomez-Garcia, Z. Sassi, B. Barelaud, L. Billonnet, B. Jarry, H. Marie, and P. Gamand. Silicon-integrated differential bandpass filters based on recursive and channelized principles and methodology to compute their exact noise figure; T-MTT Dec 06 4381-4396 Darwish, A. M., K. Boutros, B. Luo, B. D. Huebschman, E. Viveiros, and H. A. Hung. AlGaN/GaN Ka-band 5-W MMIC amplifier; T-MTT Dec 06 4456-4463 Das, A., A. Nkansah, N.J. Gomes, I.J. Garcia, J.C. Batchelor, and D. Wake. Design of low-cost multimode fiber-fed indoor wireless networks; T-MTT Aug 06 3426-3432 Daussin, R., see Saib, A., T-MTT Jun 06 2745-2754 Davidson, D.B., see Geschke, R.H., T-MTT Oct 06 3698-3705 + Check author entry for coauthors

Dawson, D., see Fung, A., T-MTT Dec 06 4507-4512 Dazhen Gu, see Randa, J., T-MTT Mar 06 1180-1189 Dazhen Gu, see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 De, A., see Mengtao Yuan, T-MTT Jun 06 2552-2563 Decoopman, T., A. Marteau, E. Lheurette, O. Vanbesien, and D. Lippens. Left-handed electromagnetic properties of split-ring resonator and wire loaded transmission line in a fin-line technology; T-MTT Jun 06 14511457 De Doncker, P., see Fort, A., T-MTT Jun 06 1820-1826 Deen, M.J., see Kouzaev, G.A., T-MTT Mar 06 1033-1042 De Flaviis, F., see Collado, C., T-MTT Jan 06 180-188 Degachi, L., and F.M. Ghannouchi. Systematic and rigorous extraction method of HBT small-signal model parameters; T-MTT Feb 06 682-688 DeJean, G., see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 de Lange, G., see Jackson, B.D., T-MTT Feb 06 547-558 Delaveaud, C., see Keignart, J., T-MTT Jun 06 1812-1819 Delic, H., see Guney, N., T-MTT Jun 06 1724-1730 De Nardis Luca, see Cardinali, R., T-MTT Jun 06 1865-1875 den Besten, J.H., see Piqueras, M.A., T-MTT Feb 06 887-899 Deng Pu-Hua, see Pu-Hua Deng, T-MTT Feb 06 533-539 Deng Pu-Hua, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Deng Pu-Hua, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Deng Pu-Hua, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Deng Zhichao, see Zhichao Deng, T-MTT Feb 06 763-767 Deng Zhichao, see Xiangfei Chen, T-MTT Feb 06 804-809 Denidni, A., see Djaiz, A., T-MTT May 06 1929-1936 Denidni, T.A., see Nedil, M., T-MTT Jan 06 499-507 Denis, B., J.-B. Pierrot, and C. Abou-Rjeily. Joint distributed synchronization and positioning in UWB ad hoc networks using TOA; T-MTT Jun 06 1896-1911 Denis, D., C.M. Snowden, and I.C. Hunter. Coupled electrothermal, electromagnetic, and physical modeling of microwave power FETs; TMTT Jun 06 2465-2470 Denisov, G., see Bogdashov, A., T-MTT Dec 06 4130-4135 Denning, A., see Fung, A., T-MTT Dec 06 4507-4512 De Raedt, W., see Crupi, G., T-MTT Oct 06 3616-3622 Derzakowski, K., see Krupka, J., T-MTT Jun 06 2329-2335 Deslandes, D., and Ke Wu. Accurate modeling, wave mechanisms, and design considerations of a substrate integrated waveguide; T-MTT Jun 06 2516-2526 Desset, C., see Fort, A., T-MTT Jun 06 1820-1826 Detrembleur, C., see Saib, A., T-MTT Jun 06 2745-2754 de Vreede, L. C. N., see Spirito, M., T-MTT Dec 06 4225-4236 Dexter, J.L., see Hunter, D.B., T-MTT Feb 06 861-867 Diaz, R. E., see Panaretos, A. H., T-MTT Dec 06 4237-4246 Diaz-Morcillo, A., see Requena-Perez, M.E., T-MTT Feb 06 615-624 Di Benedetto, M.-G., see Cardinali, R., T-MTT Jun 06 1865-1875 Di Donato, A., and T. Rozzi. A theory of multimode traveling-wave modulators for RF photonics; T-MTT Feb 06 724-734 Dienstfrey, A., see Williams, D.F., T-MTT Jan 06 481-491 Dienstfrey, A., see Clement, T.S., T-MTT Aug 06 3173-3181 Dienstfrey, A., P.D. Hale, D.A. Keenan, T.S. Clement, and D.F. Williams. Minimum-phase calibration of sampling oscilloscopes; T-MTT Aug 06 3197-3208 Di Giacomo, V., see Santarelli, A., T-MTT Dec 06 4021-4031 Di Nallo, C., see Baccarelli, P., T-MTT Jun 06 1350-1362 Ding Runtao, see Yi Cao, T-MTT Jun 06 2398-2409 Dionigi, M., see Ocera, A., T-MTT Jun 06 2568-2575 Djaiz, A., and A. Denidni. A new compact microstrip two-layer bandpass filter using aperture-coupled SIR-hairpin resonators with transmission zeros; T-MTT May 06 1929-1936 Doiron, T.A., see Kongpop U-yen, T-MTT Mar 06 1237-1244 Dolfi, D., see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Do Manh Anh, see Kaixue Ma, T-MTT Mar 06 1113-1119 Do Manh Anh, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Donell, M., see Franceschini, D., T-MTT Jun 06 1484-1494 Dong-Hyun Kim, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Dong-Jin Kim, see Dong-Won Kim, T-MTT Nov 06 3923-3930 Dong Kim Chul, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Dong Lee Hui, see Dong-Woo Kang, T-MTT Jan 06 294-301 Dong Park Jung, see Jung Dong Park, T-MTT Oct 06 3623-3629 Dongping Xiao, see Crupi, G., T-MTT Oct 06 3616-3622 Dong Sam Ha, see August, N.J., T-MTT Jul 06 3001-3012 Dong Seok Park, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Dong Tian Lin, see Hui Kan Liu, T-MTT Sep 06 3479-3485

IEEE T-MTT 2006 INDEX — 6 Dong-Won Kim, Dong-Jin Kim, and Jeong-Hae Lee. Compact partial Hplane filters; T-MTT Nov 06 3923-3930 Dong-Woo Kang, Hui Dong Lee, Chung-Hwan Kim, and Songcheol Hong. Ku-band MMIC phase shifter using a parallel resonator with 0.18-ȝm CMOS technology; T-MTT Jan 06 294-301 Dongying Li, see Nikolova, N.K., T-MTT Feb 06 670-681 Dong-Zo Kim, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 D'Orazio, W., and Ke Wu. Substrate-integrated-waveguide circulators suitable for millimeter-wave integration; T-MTT Oct 06 3675-3680 Draxler, P., see Kimball, D.F., T-MTT Nov 06 3848-3856 Dronov, V., see Safier, P.N., T-MTT Oct 06 3605-3615 Duan Yiwei, see Haiyong Xu, T-MTT Oct 06 3648-3653 Dubois, L., see Cresson, P.-Y., T-MTT Jan 06 302-308 Duchamp, J.-M., see Kaddour, D., T-MTT Jun 06 2367-2375 Duchamp, J.-M., see Pistono, E., T-MTT Jun 06 2790-2799 Duck-Hwan Kim, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Dufrene, B.M., see Sen, P., T-MTT Jun 06 2604-2614 Duixian Liu, see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Duk-Jae Woo, Taek-Kyung Lee, Jae-Wook Lee, Cheol-Sig Pyo, and WonKyu Choi. Novel U-slot and V-slot DGSs for bandstop filter with improved Q factor; T-MTT Jun 06 2840-2847 Dunleavy, L., see Padmanabhan, S., T-MTT Sep 06 3583-3593 Dunleavy, L.P., see Weatherspoon, M.H., T-MTT Feb 06 608-614 Dunleavy, L.P., see Jiang Liu, T-MTT Aug 06 3191-3196 Dunsmore, J.P., see Williams, D.F., T-MTT Mar 06 1210-1217 Duochuan Li, see Bozzi, M., T-MTT Jan 06 339-347 Duvillaret, L., see Pistono, E., T-MTT Jun 06 2790-2799 Duyar, M., V. Akan, E. Yazgan, and M. Bayrak. Analyses of elliptical coplanar coupled waveguides and coplanar coupled waveguides with finite ground width; T-MTT Jun 06 1388-1395 Duyn, J.H., see Shumin Wang, T-MTT May 06 2196-2202 Du Yu, see Yu Du, T-MTT Mar 06 1287-1294 E Edwards, D.J., see Pal, S., T-MTT Feb 06 768-775 Eghlidi, M. H., K. Mehrany, and B. Rashidian. Analytical approach for analysis of nonuniform lossy/lossless transmission lines and tapered microstrips; T-MTT Dec 06 4122-4129 Eisenhower Cheng, see Yi-Chyun Chiou, T-MTT Aug 06 3352-3358 Eleftheriades, G.V., see Kokkinos, T., T-MTT Jun 06 1619-1630 El-Gamal, M.N., see Baki, R.A., T-MTT Jan 06 46-56 Ellinger, F., see Sialm, G., T-MTT Jan 06 65-73 Ellinger, F., see Barras, D., T-MTT May 06 2138-2145 Ellinger, F., see Barras, D., T-MTT Jun 06 1713-1723 Ellis, T.J. Comments on "W-band multiport substrate-integrated waveguide Circuits"; T-MTT Nov 06 4016 El-Masry, E.I., see Elshurafa, A.M., T-MTT May 06 2211-2219 Elshafiey, T.F., and J.T. Aberle. Green's function for multilayer arbitrarily biased anisotropic structures-application to phase shifters, transducers, and magnetization angle effect; T-MTT Feb 06 513-521 Elshurafa, A.M., and E.I. El-Masry. Finite-element modeling of low-stress suspension structures and applications in RF MEMS parallel-plate variable capacitors; T-MTT May 06 2211-2219 Emrich, A., see Karnfelt, C., T-MTT Aug 06 3417-3425 Enard, A., see Piqueras, M.A., T-MTT Feb 06 887-899 Eng-Choon Tan Adrian, see Adrian Eng-Choon Tan, T-MTT Mar 06 10191024 Epp, L.W., D.J. Hoppe, and D.T. Kelley. A TE/TM modal solution for rectangular hard waveguides; T-MTT Mar 06 1048-1054 Eremenko, Z.E., and E.M. Ganapolskii. Resonant spherical hole in a high loss liquid at millimeter wavelengths; T-MTT May 06 2243-2248 Eric Rius, see Manchec, A., T-MTT Jun 06 2346-2355 Erkens, H., and H. Heuermann. Novel RF switch concepts for differential wireless communications frontends; T-MTT Jun 06 2376-2382 Erni, D., see Sialm, G., T-MTT Jan 06 65-73 Estebe, E., see Piqueras, M.A., T-MTT Feb 06 887-899 Eusebe, H., see Kaddour, D., T-MTT Jun 06 2367-2375 Evers, N.A., see Chen, M.J., T-MTT Nov 06 4009-4015 F Fairburn, M., see Lam, A.K.M., T-MTT Jan 06 240-246

+ Check author entry for coauthors

Faircloth, D.L., M.E. Baginski, and S.M. Wentworth. Complex permittivity and permeability extraction for multilayered samples using S-parameter waveguide measurements; T-MTT Mar 06 1201-1209 Fan, X.C., X. M. Chen, and X.Q. Liu. Corrections to "Complex-permittivity measurement on high-Q materials via combined numerical approaches" [Oct 05 3130-3134]; T-MTT Apr 06 1631 Farina, M., see Morini, A., T-MTT Sep 06 3515-3520 Farzaneh, F., see Nick, M., T-MTT Jul 06 2993-3000 Fathelbab, W.M., and M.B. Steer. Tapped marchand baluns for matching applications; T-MTT Jun 06 2543-2551 Fathy, A.E., Sung-Woo Lee, and D. Kalokitis. A simplified design approach for radial power combiners; T-MTT Jan 06 247-255 Fattorini, A., see Mahon, J., T-MTT May 06 2050-2060 Favennec, J.-F., see Manchec, A., T-MTT Jun 06 2346-2355 Fawal, A.E., and J.-Y. Le Boudec. A robust signal-detection method for ultrawideband networks with uncontrolled interference; T-MTT Jun 06 17691781 Fear, E.C., see Williams, T.C., T-MTT Jun 06 1308-1314 Feher, L.E., see Akhtar, M.J., T-MTT May 06 2011-2022 Feipeg Wang, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. Lie, P. M. Asbeck, and L. E. Larson. An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications; T-MTT Dec 06 4086-4099 Fel, N., see Si Moussa, M., T-MTT Jun 06 2675-2683 Feng, J., see Hao Shi, T-MTT Jan 06 360-372 Feng, M., see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Feng Milton, see Jie-Wei Lai, T-MTT Feb 06 599-607 Feng Xu, Ke Wu, and Wei Hong. Domain decomposition FDTD algorithm combined with numerical TL calibration technique and its application in parameter extraction of substrate integrated circuits; T-MTT Jan 06 329338 Fengyi Huang, Nan Jiang, and E. Bian. Characteristic-function approach to parameter extraction for asymmetric equivalent circuit of on-chip spiral inductors; T-MTT Jan 06 115-119 Fengyi Huang, see Jingxue Lu, T-MTT Jul 06 3155 Feresidis, A.P., see Goussetis, G., T-MTT Nov 06 3885-3892 Ferrand, P., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Ferrari, P., see Kaddour, D., T-MTT Jun 06 2367-2375 Ferrari, P., see Pistono, E., T-MTT Jun 06 2790-2799 Ferrari, P., see Safwat, A.M.E., T-MTT Sep 06 3559-3564 Ferrari, R.L., see Geschke, R.H., T-MTT Oct 06 3698-3705 Ferrero, A., and M. Pirola. Generalized mixed-mode S-parameters; T-MTT Jan 06 458-463 Filicori, F., see Santarelli, A., T-MTT Dec 06 4021-4031 Filicori, F., see Traverso, P. A., T-MTT Dec 06 4341-4352 Filipovic, D.S., see Vanhille, K.J., T-MTT Jun 06 2439-2446 Filipovic, S., see Lukic, M., T-MTT May 06 2068-2076 Florian, C., see Traverso, P. A., T-MTT Dec 06 4341-4352 Floyd, B.A., see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Fok Si-Weng, see Si-Weng Fok, T-MTT May 06 2033-2041 Fontaine, D.L., see Vanhille, K.J., T-MTT Jun 06 2439-2446 Formont, S., see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Fort, A., C. Desset, P. De Doncker, P. Wambacq, and L. Van Biesen. An ultra-wideband body area propagation channel Model-from statistics to implementation; T-MTT Jun 06 1820-1826 Franceschini, D., M. Donell, G. Franceschini, and A. Massa. Iterative image reconstruction of two-dimensional scatterers illuminated by TE waves; TMTT Jun 06 1484-1494 Franceschini, G., see Franceschini, D., T-MTT Jun 06 1484-1494 Fratticcioli, E., see Ocera, A., T-MTT Jun 06 2568-2575 Frederick Huang, see Guoyong Zhang, T-MTT Feb 06 559-563 Frederick Huang Quasi-dual-mode microstrip spiral filters using first and second harmonic resonances; T-MTT Feb 06 742-747 Free, C., see Kum Meng Lum, T-MTT Jun 06 2880-2886 Freundorfer, A.P., see Hamed, K.W., T-MTT Jun 06 2527-2533 Frigon, J.-F., see Yanyang Zhao, T-MTT Jun 06 1707-1712 Fritschi, R., see Perruisseau-Carrier, J., T-MTT Jan 06 383-392 Fuchs, B., O. Lafond, S. Rondineau, and M. Himdi. Design and characterization of half Maxwell fish-eye lens antennas in millimeter waves; T-MTT Jun 06 2292-2300 Fumeaux, C., see Sankaran, K., T-MTT Mar 06 1269-1276 Fumeaux, C., see Sankaran, K., T-MTT Dec 06 4297-4304 Fung, A., D. Dawson, L. Samoska, K. Lee, T. Gaier, P. Kangaslahti, C. Oleson, A. Denning, Yuenie Lau, and G. Boll. Two-port vector network

IEEE T-MTT 2006 INDEX — 7 analyzer measurements in the 218-344- and 356 500-GHz frequency bands; T-MTT Dec 06 4507-4512 Furuta, T., see Hirata, A., T-MTT May 06 1937-1944 Fuse, M., see Niiho, T., T-MTT Feb 06 980-989 Fu-Shun Zhang, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Fu-Yi Han, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Fu-Yi Han, Jian-Ming Wu, Tzyy-Sheng Horng, and Cheng-Chia Tu. A rigorous study of package and PCB effects on W-CDMA upconverter RFICs; T-MTT Oct 06 3793-3804

G Gaier, T., see Fung, A., T-MTT Dec 06 4507-4512 Galiere, J., see Piqueras, M.A., T-MTT Feb 06 887-899 Gamand, P., see Darfeuille, S., T-MTT Dec 06 4381-4396 Ganapolskii, E.M., see Eremenko, Z.E., T-MTT May 06 2243-2248 Gandhi, O.P., see Qing-Xiang Li, T-MTT Jul 06 3146-3154 Ganesan, S., E. Sanchez-Sinencio, and J. Silva-Martinez. A highly linear low-noise amplifier; T-MTT Dec 06 4079-4085 Gao, S., see Yi Qin, T-MTT Jun 06 2723-2732 Gao, S., see Yin Qin, T-MTT Jul 06 2910-2916 Gao Chu, see Chu Gao, T-MTT Jun 06 1519-1526 Gao Wei, see Wei Gao, T-MTT Mar 06 1055-1064 Garcia, I.J., see Das, A., T-MTT Aug 06 3426-3432 Garcia, J.P., F.Q. Pereira, D.C. Rebenaque, J.L.G. Tornero, and A.A. Melcon. A neural-network method for the analysis of multilayered shielded microwave circuits; T-MTT Jan 06 309-320 Garcia-Garcia, J., see Bonache, J., T-MTT Jan 06 265-271 Garcia-Garcia, J., J. Bonache, I. Gil, F. Martin, Md.C. Velazquez-Ahumada, and J. Martel. Miniaturized microstrip and CPW filters using coupled metamaterial resonators; T-MTT Jun 06 2628-2635 Garcia-Garcia, J., see Gil, I., T-MTT Jun 06 2665-2674 Garcia-Garcia, J., J. Bonache, and F. Martin. Application of electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-ofband performance; T-MTT Dec 06 4136-4140 Gard, K.G., see Walker, A., T-MTT May 06 1991-1999 Gard, K.G., see Gharaibeh, K.M., T-MTT Aug 06 3227-3236 Garenaux, K., see Blanc, S., T-MTT Jan 06 402-411 Gaucher, B., see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Gaucher, B.P., see Zwick, T., T-MTT Mar 06 1001-1010 Gebara, E., see Bien, F., T-MTT Dec 06 4538-4547 Georgiadis, A., A. Collado, and A. Suarez. New techniques for the analysis and design of coupled-oscillator systems; T-MTT Nov 06 3864-3877 Gerding, M., T. Musch, and B. Schiek. A novel approach for a high-precision multitarget-level measurement system based on time-domain reflectometry; T-MTT Jun 06 2768-2773 Gerecht, E., see Randa, J., T-MTT Mar 06 1180-1189 Gerecht, E., see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Germain, M., see Crupi, G., T-MTT Oct 06 3616-3622 Germani, S., see Bozzi, M., T-MTT Jan 06 339-347 Geschke, R.H., R.L. Ferrari, D.B. Davidson, and P. Meyer. The solution of waveguide scattering problems by application of an extended Huygens formulation; T-MTT Oct 06 3698-3705 Ghadam, A.S.H., see Valkama, M., T-MTT Jun 06 2356-2366 Ghannouchi, F.M., see Degachi, L., T-MTT Feb 06 682-688 Ghannouchi, F.M., see Taijun Liu, T-MTT Jun 06 1340-1349 Ghannouchi, F.M., see Helaoui, M., T-MTT Jun 06 1396-1404 Ghannouchi, F.M., see Hammi, O., T-MTT Aug 06 3246-3254 Gharaibeh, K.M., K.G. Gard, and M.B. Steer. In-band distortion of multisines; T-MTT Aug 06 3227-3236 Ghazel, A., see Helaoui, M., T-MTT Jun 06 1396-1404 Ghione, G., see Bertazzi, F., T-MTT Jun 06 1611-1618 Ghose, A., see Ruengwaree, A., T-MTT Jun 06 2774-2779 Giannini, F., see Colantonio, P., T-MTT Jun 06 2713-2722 Gil, I., see Bonache, J., T-MTT Jan 06 265-271 Gil, I., see Garcia-Garcia, J., T-MTT Jun 06 2628-2635 Gil, I., J. Bonache, J. Garcia-Garcia, and F. Martin. Tunable metamaterial transmission lines based on varactor-loaded split-ring resonators; T-MTT Jun 06 2665-2674 Ginzburg, N.S., see Rozental, R.M., T-MTT Jun 06 2741-2744 Giofre, R., see Colantonio, P., T-MTT Jun 06 2713-2722 Girbau, D., N. Otegi, L. Pradell, and A. Lazaro. Study of intermodulation in RF MEMS variable capacitors; T-MTT Mar 06 1120-1130 + Check author entry for coauthors

Glyavin, M.Y., see Rozental, R.M., T-MTT Jun 06 2741-2744 Goiceanu, C., see Christ, A., T-MTT May 06 2188-2195 Gol'tsman, G.N., see Ling Jiang, T-MTT Jul 06 2944-2948 Gomes, N.J., see Das, A., T-MTT Aug 06 3426-3432 Gomez, A., see Solano, M.A., T-MTT Mar 06 1297-1298 Gomez-Garcia, R., and J.I. Alonso. Systematic method for the exact synthesis of ultra-wideband filtering responses using high-pass and lowpass sections; T-MTT Oct 06 3751-3764 Gomez-Garcia, R., see Darfeuille, S., T-MTT Dec 06 4381-4396 Gomez-Tornero, J.L., S. Martinez-Lopez, and A. Alvarez-Melcon. Simple analysis and design of a new leaky-wave directional coupler in hybrid dielectric-waveguide printed-circuit technology; T-MTT Sep 06 3534-3542 Gong, W., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Gonzalez, O., J.A. Pereda, A. Herrera, and A. Vegas. An extension of the lumped-network FDTD method to linear two-port lumped circuits; T-MTT Jul 06 3045-3051 Gook-Ju Ihm, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Gope, D., A.E. Ruehli, Chuanyi Yang, and V. Jandhyala. (S)PEEC: Timeand frequency-domain surface formulation for modeling conductors and dielectrics in combined circuit electromagnetic simulations; T-MTT Jun 06 2453-2464 Goussard, Y., see Omrane, B., T-MTT Jun 06 1438-1450 Goussetis, G., A.P. Feresidis, and P. Kosmas. Efficient analysis, design, and filter applications of EBG waveguide with periodic resonant loads; T-MTT Nov 06 3885-3892 Gouveia, E.S., see Bharathan, K., T-MTT Jun 06 1301-1307 Grahn, J., see Sudow, M., T-MTT Dec 06 4072-4078 Grande, A., see Cabeceira, A.C.L., T-MTT Jun 06 2780-2789 Grau, A., see Collado, C., T-MTT Jan 06 180-188 Gravel, J.-F., and J.S. Wight. On the conception and analysis of a 12-GHz push-push phase-locked DRO; T-MTT Jan 06 153-159 Griso, G., see Ouchetto, O., T-MTT Jun 06 2615-2619 Grosskopf, G., see Piqueras, M.A., T-MTT Feb 06 887-899 Gruszczynski, S., K. Wincza, and K. Sachse. Design of compensated coupled-stripline 3-dB directional couplers, phase shifters, and magic-T'spart II: broadband coupled-line circuits; T-MTT Sep 06 3501-3507 Gruszczynski, S., K. Wincza, and K. Sachse. Design of compensated coupled-stripline 3-dB directional couplers, phase shifters, and magic-T'spart I: single-section coupled-line circuits; T-MTT Nov 06 3986-3994 Grzeskowiak, M., see Aissat, H., T-MTT Jun 06 2856-2863 Grzyb, J., see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Guang Chen, V. Kumar, R.S. Schwindt, and I. Adesida. A low gate bias model extraction technique for AlGaN/GaN HEMTs; T-MTT Jul 06 29492953 Guang-Hwa Shiue, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Guang-Hwa Shiue, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Guan Xin, see Xin Guan, T-MTT Aug 06 3278-3283 Gubner, J.A., and Kei Hao. A computable formula for the average bit error probability as a function of window size for the IEEE 802.15.3a UWB channel model; T-MTT Jun 06 1762-1768 Gu Dazhen, see Randa, J., T-MTT Mar 06 1180-1189 Gu Dazhen, see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Guerrieri, S.D., see Bertazzi, F., T-MTT Jun 06 1611-1618 Gug Lee Sang, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Guilin Sun, and C.W. Trueman. Efficient implementations of the CrankNicolson scheme for the finite-difference time-domain method; T-MTT May 06 2275-2284 Guney, N., H. Delic, and M. Koca. Robust detection of ultra-wideband signals in non-Gaussian noise; T-MTT Jun 06 1724-1730 Gunyan, D., see Blockley, P.S., T-MTT Aug 06 3182-3190 Guo Jyh-Chyurn, see Jyh-Chyurn Guo, T-MTT Nov 06 3975-3985 Guo Wei-Da, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Guo Wei-Da, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Guo Wei Huang, see Tao Wang, T-MTT Feb 06 580-588 Guo-Wei Huang, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Guo Yong-Xin, see Yong-Xin Guo, T-MTT Mar 06 1196-1200 Guoyong Zhang, M.J. Lancaster, and Frederick Huang. A high-temperature superconducting bandpass filter with microstrip quarter-wavelength spiral resonators; T-MTT Feb 06 559-563 Gutierrez-Ayala, V., see Rayas-Sanchez, J. E., T-MTT Dec 06 4528-4537 Guvenc, I., Z. Sahinoglu, and P.V. Orlik. TOA estimation for IR-UWB systems with different transceiver types; T-MTT Jun 06 1876-1886 Guyette, A.C., I.C. Hunter, and R.D. Pollard. The design of microwave bandpass filters using resonators with nonuniform Q; T-MTT Nov 06 3914-3922

IEEE T-MTT 2006 INDEX — 8 H Ha, S., see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Hacker, J. B., see Ma, B. Y., T-MTT Dec 06 4448-4455 Haddad, S.A.P., see Bagga, S., T-MTT Jun 06 1656-1666 Ha Dong Sam, see August, N.J., T-MTT Jul 06 3001-3012 Hagness, C., see Converse, M., T-MTT May 06 2169-2180 Haiyong Xu, Yiwei Duan, J.L. Hesler, T.W. Crowe, and R.M. Weikle, II. Subharmonically pumped millimeter-wave upconverters based on heterostructure barrier varactors; T-MTT Oct 06 3648-3653 Hajimiri, A., see Buckwalter, J. F., T-MTT Dec 06 4271-4280 Hale, P.D., see Williams, D.F., T-MTT Jan 06 481-491 Hale, P.D., see Williams, D.F., T-MTT Mar 06 1210-1217 Hale, P.D., see Clement, T.S., T-MTT Aug 06 3173-3181 Hale, P.D., see Dienstfrey, A., T-MTT Aug 06 3197-3208 Hallbjorner, P., see Karnfelt, C., T-MTT Jun 06 2593-2603 Ham, D., see Ricketts, D.S., T-MTT Jan 06 373-382 Hamada, Y., see Ito, M., T-MTT Dec 06 4522-4527 Hamaguchi, K., see Kawano, Y., T-MTT Dec 06 4489-4497 Hamed, K.W., A.P. Freundorfer, and Y.M.M. Antar. A new broadband monolithic passive differential coupler for K/ka-band applications; T-MTT Jun 06 2527-2533 Hammi, O., J. Sirois, S. Boumaiza, and F.M. Ghannouchi. Design and performance analysis of mismatched Doherty amplifiers using an accurate load-pull-based model; T-MTT Aug 06 3246-3254 Haneda, K., Jun-ichi Takada, and T. Kobayashi. A parametric UWB propagation channel estimation and its performance validation in an anechoic chamber; T-MTT Jun 06 1802-1811 Han Fu-Yi, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Han Fu-Yi, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Han Jeongwoo, see Jeongwoo Han, T-MTT Jan 06 285-293 Han Seok-Kyun, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Hansford, D. J., see Koulouridis, S., T-MTT Dec 06 4202-4208 Hao Kei, see Gubner, J.A., T-MTT Jun 06 1762-1768 Hao Shi, W.T. Beyene, J. Feng, B. Chia, and Xingchao Yuan. Properties of mixed-mode parameters of cascaded balanced networks and their applications in modeling of differential interconnects; T-MTT Jan 06 360372 Hao Yang, see Yan Zhao, T-MTT Jun 06 1827-1835 Harrison, R.G., see Kaddour, D., T-MTT Jun 06 2367-2375 Hartogh, P., see Villanueva, G.L., T-MTT Jun 06 1415-1424 Hartskeerl, D., see Spirito, M., T-MTT Dec 06 4225-4236 Harvey, J.T., see Mahon, J., T-MTT May 06 2050-2060 Hasegawa, K., see Takenaka, I., T-MTT Dec 06 4513-4521 Hashim, H.H., and S. Iezekiel. Traveling-wave microwave fiber-optic links; T-MTT Feb 06 951-958 Hassan, A.-kS.O., see Abdel-Malek, H.L., T-MTT Oct 06 3731-3738 Havens, R.J., see Tiemeijer, L.F., T-MTT Aug 06 3378-3386 Hayakawa, M., see Adalev, A.S., T-MTT Jul 06 3131-3140 Heck, H., see Simpson, J.J., T-MTT May 06 1983-1990 Hedayati, H., B. Bakkaloglu, and W. Khalil. Closed-loop nonlinear modeling of wideband Ȉǻ fractional-N frequency synthesizers; T-MTT Oct 06 36543663 Heeseon Shin, see Woonyun Kim, T-MTT May 06 2098-2105 Hein, M.A., see Weber, J., T-MTT Jun 06 2733-2740 Heino, P., see Kaija, T., T-MTT Mar 06 1295-1296 Heino, P., see Kaija, T., T-MTT May 06 1975-1982 Heinrich, W., see Zscheile, H., T-MTT May 06 2000-2010 Heinrich, W., see Rudolph, M., T-MTT Jul 06 2954-2961 Helaoui, M., S. Boumaiza, A. Ghazel, and F.M. Ghannouchi. Power and efficiency enhancement of 3G multicarrier amplifiers using digital signal processing with experimental validation; T-MTT Jun 06 1396-1404 Helszajn, J. Reflection angles of in-phase and split counter-rotating eigenvalues of the three-port circulator; T-MTT Mar 06 1076-1083 Hennings, A., E. Semouchkina, A. Baker, and G. Semouchkin. Design optimization and implementation of bandpass filters with normally fed microstrip resonators loaded by high-permittivity dielectric; T-MTT Mar 06 1253-1261 Herrera, A., see Gonzalez, O., T-MTT Jul 06 3045-3051 Herrera, J., see Piqueras, M.A., T-MTT Feb 06 887-899 Herrick, K.J., see Lahiji, R.R., T-MTT Jun 06 2699-2706 Hesler, J.L., see Haiyong Xu, T-MTT Oct 06 3648-3653 Hettak, K., G.A. Morin, and M.G. Stubbs. Size reduction of a MMIC direct up-converter at 44 GHz in multilayer CPW technology using thin-film microstrip stubs loading; T-MTT Sep 06 3453-3461 + Check author entry for coauthors

Heuermann, H., see Erkens, H., T-MTT Jun 06 2376-2382 Higashino, T., K. Tsukamoto, and S. Komaki. Proposal of photonic frequency-conversion method using bandpass sampling in multicarrier operated radio-on-fiber link; T-MTT Feb 06 973-979 Himdi, M., see Fuchs, B., T-MTT Jun 06 2292-2300 Himdi, M., see Zhadobov, M., T-MTT Jun 06 2534-2542 Hirata, A., T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta, H. Ito, H. Sugahara, Y. Sato, and T. Nagatsuma. 120-GHz-band millimeter-wave photonic wireless link for 10-Gb/s data transmission; TMTT May 06 1937-1944 Hiroe, A., see Saito, K., T-MTT Aug 06 3443-3449 Hirose, T., see Kawano, Y., T-MTT Dec 06 4489-4497 Hirose, T., see Masuda, S., T-MTT Dec 06 4565-4571 Hirshfield, J. L., see Bogdashov, A., T-MTT Dec 06 4130-4135 Hirt, W., see Barras, D., T-MTT May 06 2138-2145 Hirt, W., see Barras, D., T-MTT Jun 06 1713-1723 Hjelmgren, H., see Sudow, M., T-MTT Dec 06 4072-4078 Hock Kai Meng, see Kai Meng Hock, T-MTT Feb 06 648-659 Hofler, G. E., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Hogan, B.P., see Bharathan, K., T-MTT Jun 06 1301-1307 Ho-Jin Song, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Ho Jung Baek, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Holloway, C. L., and E. F. Kuester. Corrections to "Closed-form expressions for the current density on the ground plane of a microstrip line, with application to ground plane loss" [May 95 1204-1207]; T-MTT Nov 06 4018-4019 Holzman, E.L. Wideband measurement of the dielectric constant of an FR4 substrate using a parallel-coupled microstrip resonator; T-MTT Jul 06 3127-3130 Hong Jia-Sheng, see Young-Hoon Chun, T-MTT Feb 06 704-709 Hongjoon Kim, Sung-Jin Ho, Min-Ki Choi, A. B. Kozyrev, and D. W. van der Weide. Combined left- and right-handed tunable transmission lines with tunable passband and 0/sup°/ phase shift; T-MTT Dec 06 4178-4184 Hong-Ming Lee, see Chih-Ming Tsai, T-MTT Jun 06 1545-1553 Hong Seungpyo, see Seungpyo Hong, T-MTT Jun 06 1370-1378 Hong Songcheol, see Dong-Woo Kang, T-MTT Jan 06 294-301 Hongting Jia, and K. Yasumoto. Modal analysis of two-dimensional photonic-crystal waveguides formed by rectangular cylinders using an improved Fourier series method; T-MTT Feb 06 564-571 Hong Wei, see Feng Xu, T-MTT Jan 06 329-338 Hong-Yeh Chang, see Pei-Si Wu, T-MTT Jan 06 10-19 Hong-Yeh Chang, Pei-Si Wu, Tian-Wei Huang, Huei Wang, Chung-Long Chang, and J.G.J. Chern. Design and analysis of CMOS broad-band compact high-linearity modulators for gigabit microwave/millimeter-wave applications; T-MTT Jan 06 20-30 Hong-Yeh Chang, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Hong-Yeh Chang, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Hong Young-Pyo, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Hoon Kim Yong, see Sung Tae Choi, T-MTT May 06 1953-1960 Hoppe, D.J., see Epp, L.W., T-MTT Mar 06 1048-1054 Horiuchi, S., see Shingo Tanaka, T-MTT Jun 06 1561-1568 Horng Tzyy-Sheng, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Horng Tzyy-Sheng, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Horng Tzyy-Sheng, see Yu-Shun Tsai, T-MTT Dec 06 4412-4421 Hossein-Zadeh, M., and A.F.J. Levi. 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver; T-MTT Feb 06 821-831 Ho Sung-Jin, see Hongjoon Kim, T-MTT Dec 06 4178-4184 Hou Chan Chi, see Yum, T.Y., T-MTT Aug 06 3255-3266 Hoyos, S., and B.M. Sadler. Frequency-domain implementation of the transmitted-reference ultra-wideband receiver; T-MTT Jun 06 1745-1753 Hsia Chin, see Kimball, D.F., T-MTT Nov 06 3848-3856 Hsiao-Bin Liang, Yo-Sheng Lin, Chi-Chen Chen, Po-Feng Yeh, Yan-Ru Tzeng, Tao Wang, and Shey-Shi Lu. An analysis of perfect-magneticcoupling ultra-low-loss micromachined SMIS RF transformers for RFIC applications; T-MTT Dec 06 4256-14267 Hsiao-Chin Chen, see Tao Wang, T-MTT Feb 06 580-588 Hsiao-Kuang Lin, see Yng-Huey Jeng, T-MTT Feb 06 633-638 Hsieh Hsieh-Hung, see Liang-Hung Lu, T-MTT Sep 06 3462-3468 Hsieh-Hung Hsieh, see Liang-Hung Lu, T-MTT Sep 06 3462-3468 Hsieh Wei-Lin, see Yi-Chyun Chiang, T-MTT Nov 06 3947-3953 Hsin-Hung Chen, see Chih-Hung Lin, T-MTT May 06 2118-2127 Hsin Yue-Ming, see Wen-Bin Tang, T-MTT Oct 06 3641-3647 Hsiung Chen Chun, see Pu-Hua Deng, T-MTT Feb 06 533-539 Hsiung Chen Chun, see Chao-Huang Wu, T-MTT Feb 06 540-546 Hsiung Chen Chun, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018

IEEE T-MTT 2006 INDEX — 9 Hsiung Chen Chun, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Hsiung Chen Chun, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Hsiung Chen Chun, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Hsiung Chen Chun, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Hsiung Chen Chun, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Hsu, S. S. H., see Jun-De Jin, T-MTT Dec 06 4333-4340 Hsue Ching-Wen, see Ching-Wen Hsue, T-MTT Mar 06 1043-1047 Hu, R. Wide-band matched LNA design using transistor's intrinsic gate-drain capacitor; T-MTT Mar 06 1277-1286 Hualiang Zhang, and K.J. Chen. Miniaturized coplanar waveguide bandpass filters using multisection stepped-impedance resonators; T-MTT Mar 06 1090-1095 Huang, F., Ming Zhou, and Libin Yue. A narrowband superconducting filter using spirals with a reversal in winding direction; T-MTT Nov 06 39543959 Huang Fengyi, see Fengyi Huang, T-MTT Jan 06 115-119 Huang Fengyi, see Jingxue Lu, T-MTT Jul 06 3155 Huang Frederick, see Guoyong Zhang, T-MTT Feb 06 559-563 Huang Frederick, see Frederick Huang, T-MTT Feb 06 742-747 Huang Guo Wei, see Tao Wang, T-MTT Feb 06 580-588 Huang Guo-Wei, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Huang Ming-Feng, see Ming-Feng Huang, T-MTT Feb 06 660-669 Huang Tian-Wei, see Pei-Si Wu, T-MTT Jan 06 10-19 Huang Tian-Wei, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Huang Tian-Wei, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Huang Ting-Yi, see Chi-Feng Chen, T-MTT Feb 06 755-762 Huang Ting-Yi, see Chi-Feng Chen, T-MTT May 06 1945-1952 Huang Ting-Yi, see Ting-Yi Huang, T-MTT Jul 06 3038-3044 Huang Ting-Yi, see Chi-Feng Chen, T-MTT Sep 06 3550-3558 Huang Yu-Jen, see Yng-Huey Jeng, T-MTT May 06 2146-2152 Hua Zhu Ning, see Silvonen, K., T-MTT Jun 06 1464-1469 Huebschman, B. D., see Darwish, A. M., T-MTT Dec 06 4456-4463 Huei Wang, see Pei-Si Wu, T-MTT Jan 06 10-19 Huei Wang, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Huei Wang, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Huei Wang, see To-Po Wang, T-MTT Jan 06 88-95 Huei Wang, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Huei Wang, see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Huei Wang, see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Huei Wang, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Huei Wang, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Hui Dong Lee, see Dong-Woo Kang, T-MTT Jan 06 294-301 Huignard Jean-Pierre, see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Huijung Kim, Seonghan Ryu, Yujin Chung, Jinsung Choi, and Bumman Kim. A low phase-noise CMOS VCO with harmonic tuned LC tank; TMTT Jul 06 2917-2924 Hui Kan Liu, and Tian Lin Dong. Propagation characteristics for periodic waveguide based on generalized conservation of complex power technique; T-MTT Sep 06 3479-3485 Hui Lin Zhen, see Ling Jiang, T-MTT Jul 06 2944-2948 Hung, H. A., see Darwish, A. M., T-MTT Dec 06 4456-4463 Hung-Wei Chiu, see Tao Wang, T-MTT Feb 06 580-588 Hunter, D.B., M.E. Parker, and J.L. Dexter. Demonstration of a continuously variable true-time delay beamformer using a multichannel chirped fiber grating; T-MTT Feb 06 861-867 Hunter, D.B., and L.V.T. Nguyen. Widely tunable RF photonic filter using WDM and a multichannel chirped fiber grating; T-MTT Feb 06 900-905 Hunter, I.C., see Denis, D., T-MTT Jun 06 2465-2470 Hunter, I.C., see Guyette, A.C., T-MTT Nov 06 3914-3922 Huo Liu Qing, see Simsek, E., T-MTT Jan 06 216-225 Huo Liu Qing, see Simsek, E., T-MTT Nov 06 3878-3884 Hur, S., see Seungki Nam, T-MTT Jun 06 1315-1324 Hur, Y., see Bien, F., T-MTT Dec 06 4538-4547 Huyart, B., see Bensmida, S., T-MTT Jun 06 2707-2712 Huynen, I., see Saib, A., T-MTT Jun 06 2745-2754 Hu Zhirun, see Van Tuyen Vo, T-MTT Nov 06 3836-3842 Hwa Lee Byoung, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Hyeong Tae Jeong, Ik Soo Chang, and Chul Dong Kim. Compensation method for a nonlinear amplifier using the gain expansion phenomenon in a Doherty amplifier; T-MTT Jun 06 1425-1430 Hyunchol Shin, and Jongsik Kim. A 17-GHz push-push VCO based on output extraction from a capacitive common node in GaInP/GaAs HBT technology; T-MTT Nov 06 3857-3863

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Hyung-Mi Kim, and B. Lee. Bandgap and slow/fast-wave characteristics of defected ground structures (DGSs) including left-handed features; T-MTT Jul 06 3113-3120 I Iannotti, J., see Chen, M.J., T-MTT Nov 06 4009-4015 I-Chung Liu, see Ching-Wen Tang, T-MTT Aug 06 3327-3332 Idei, H., T. Shimozuma, M.A. Shapiro, T. Notake, S. Kubo, and R.J. Temkin. Experimental verification of phase retrieval of quasi-optical millimeterwave beams; T-MTT Nov 06 3899-3905 Iezekiel, S., see Hashim, H.H., T-MTT Feb 06 951-958 Ihm Gook-Ju, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Ikegami, T., see Ohno, K., T-MTT Jun 06 1782-1792 Ik Soo Chang, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Ingelstrom, P. A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes; T-MTT Jan 06 106-114 Inoue, R., Y. Odate, E. Tanabe, H. Kitano, and A. Maeda. Data analysis of the extraction of dielectric properties from insulating substrates utilizing the evanescent perturbation method; T-MTT Feb 06 522-532 In-Sang Song, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Isaksson, M., D. Wisell, and D. Ronnow. A comparative analysis of behavioral models for RF power amplifiers; T-MTT Jan 06 348-359 Ishikura, K., see Takenaka, I., T-MTT Dec 06 4513-4521 Ito, H., see Hirata, A., T-MTT May 06 1937-1944 Ito, K., see Saito, K., T-MTT Aug 06 3443-3449 Ito, M., S. Kishimoto, Y. Hamada, and K. Maruhashi. A 60-GHz-Band x 12 multiplier MMIC with reduced power consumption; T-MTT Dec 06 45224527 Itoh, T., see Allen, C.A., T-MTT Jul 06 3104-3112 Ivanov, E.N., and M.E. Tobar. Low phase-noise microwave oscillators with interferometric signal processing; T-MTT Aug 06 3284-3294 Iwamoto, M., see Yu Zhao, T-MTT Dec 06 4479-4488 Iwata, N., see Takenaka, I., T-MTT Dec 06 4513-4521 Iyer, M.K., see Jayabalan, J., T-MTT Jun 06 1331-1339 Iyer, N.M., see Mingxu Liu, T-MTT Jun 06 1698-1706 J Jaakola, T., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Jackel, H., see Sialm, G., T-MTT Jan 06 65-73 Jackel, H., see Barras, D., T-MTT May 06 2138-2145 Jackel, H., see Barras, D., T-MTT Jun 06 1713-1723 Jackson, B.D., G. de Lange, T. Zijlstra, M. Kroug, J.W. Kooi, J.A. Stern, and T.M. Klapwijk. Low-noise 0.8-0.96- and 0.96-1.12-THz superconductorinsulator-superconductor mixers for the herschel space observatory; TMTT Feb 06 547-558 Jackson, D.R., see Baccarelli, P., T-MTT Jun 06 1350-1362 Jackson, D. R., see Rodriguez-Berral, R., T-MTT Dec 06 4100-4110 Jackson, R.W. Rollett proviso in the stability of linear microwave circuits-a tutorial; T-MTT Mar 06 993-1000 Jaeger, N.A.F., see Lam, A.K.M., T-MTT Jan 06 240-246 Jaeheung Kim, see Choon Sik Cho, T-MTT Nov 06 3968-3974 Jaehoon Lee, see Seungki Nam, T-MTT Jun 06 1315-1324 Jae-Wook Lee, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Jaggard, D.L., see Wu, T.X., T-MTT Mar 06 1298 Jandhyala, V., see Gope, D., T-MTT Jun 06 2453-2464 Jang, H., see Seungki Nam, T-MTT Jun 06 1315-1324 Jang, W., see Carvalho, N.B., T-MTT Feb 06 572-579 Jantunen, H., see Kum Meng Lum, T-MTT Jun 06 2880-2886 Jarry, B., see Darfeuille, S., T-MTT Dec 06 4381-4396 Jayabalan, J., B.-L. Ooi, M.-S. Leong, and M.K. Iyer. Novel circuit model for three-dimensional geometries with multilayer dielectrics; T-MTT Jun 06 1331-1339 Jean-Pierre Huignard, see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Jee-Khoi Yin, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Jeha Kim, Young-Shik Kang, Yong-Duck Chung, and Kwang-Seong Choi. Development and RF characteristics of analog 60-GHz electroabsorption modulator module for RF/optic conversion; T-MTT Feb 06 780-787 Jeha Kim, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Jeng-Han Tsai, Hong-Yeh Chang, Pei-Si Wu, Yi-Lin Lee, Tian-Wei Huang, and Huei Wang. Design and analysis of a 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amplifiers; T-MTT Jun 06 2487-2496 Jeng Shyh-Kang, see Ming-Iu Lai, T-MTT Jan 06 160-168

IEEE T-MTT 2006 INDEX — 10 Jeng Shyh-Kang, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Jeng Yng-Huey, see Yng-Huey Jeng, T-MTT Feb 06 633-638 Jeng Yng-Huey, see Yng-Huey Jeng, T-MTT May 06 2146-2152 Jensen, L., see Krupka, J., T-MTT Nov 06 3995-4001 Jenshan Lin, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Jenshan Lin, see Changzhi Li, T-MTT Dec 06 4464-4471 Jen-Ti Peng, see Shry-Sann Liao, T-MTT Sep 06 3508-3514 Jen-Tsai Kuo, see Yi-Chyun Chiou, T-MTT Aug 06 3352-3358 Jeong-Hae Lee, see Dong-Won Kim, T-MTT Nov 06 3923-3930 Jeong Hyeong Tae, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Jeong Jichai, see Seungki Nam, T-MTT Jun 06 1315-1324 Jeong Jinho, see Kimball, D.F., T-MTT Nov 06 3848-3856 Jeongseon Lee, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Jeong Soon-Chul, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Jeongwoo Han, and C. Nguyen. On the development of a compact subnanosecond tunable monocycle pulse transmitter for UWB applications; TMTT Jan 06 285-293 Jeong Yoon-Ha, see Seung-Yup Lee, T-MTT Jan 06 451-457 Jeon Sanggeun, see Sanggeun Jeon, T-MTT Mar 06 1096-1106 Jeon Sanggeun, see Sanggeun Jeon, T-MTT Oct 06 3630-3640 Jerome, R., see Saib, A., T-MTT Jun 06 2745-2754 Jia Hongting, see Hongting Jia, T-MTT Feb 06 564-571 Jianbo Jin, M. Thumm, B. Piosczyk, and T. Rzesnicki. Theoretical investigation of an advanced launcher for a 2-MW 170-GHz TE34,19 coaxial cavity gyrotron; T-MTT Mar 06 1139-1145 Jiang Ling, see Ling Jiang, T-MTT Jul 06 2944-2948 Jiang Liu, L.P. Dunleavy, and H. Arslan. Large-signal behavioral modeling of nonlinear amplifiers based on load-pull AM-AM and AM-PM measurements; T-MTT Aug 06 3191-3196 Jiang Nan, see Fengyi Huang, T-MTT Jan 06 115-119 Jiang Rong, see Rong Jiang, T-MTT Jul 06 3060-3068 Jianguo Liu, see Simsek, E., T-MTT Nov 06 3878-3884 Jian-Guo Ma, see Kaixue Ma, T-MTT Mar 06 1113-1119 Jian-Guo Ma, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Jiang Zhu, see Nikolova, N.K., T-MTT Feb 06 670-681 Jian-Ming Wu, Fu-Yi Han, Tzyy-Sheng Horng, and Jenshan Lin. Directconversion quadrature modulator MMIC design with a new 90° phase shifter including package and PCB effects for W-CDMA applications; TMTT Jun 06 2691-2698 Jian-Ming Wu, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Jianping Yao, see Zhichao Deng, T-MTT Feb 06 763-767 Jianping Yao, see Xiangfei Chen, T-MTT Feb 06 804-809 Jianping Yao, see Xiupu Zhang, T-MTT Feb 06 929-937 Jiao Yong-Chang, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Jia-Sheng Hong, see Young-Hoon Chun, T-MTT Feb 06 704-709 Jichai Jeong, see Seungki Nam, T-MTT Jun 06 1315-1324 Ji Chen, see Dagang Wu, T-MTT Dec 06 4472-4478 Jie Wang, and Ke-Li Wu. A derived physically expressive circuit model for multilayer RF embedded passives; T-MTT May 06 1961-1968 Jie-Wei Lai, Yu-Ju Chuang, K. Cimino, and Milton Feng. Design of variable gain amplifier with gain-bandwidth product up to 354 GHz implemented in InP-InGaAs DHBT technology; T-MTT Feb 06 599-607 Jin, Y., see Rui Xu, T-MTT Aug 06 3271-3277 Jin-Fa Lee, see Venkatarayalu, N.V., T-MTT Jul 06 3019-3025 Jingxue Lu, and Fengyi Huang. Comments on "CMOS low-noise amplifier design optimization techniques"; T-MTT Jul 06 3155 Jinho Jeong, see Kimball, D.F., T-MTT Nov 06 3848-3856 Jinhwan Koh, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Jinhyuck Yu, see Woonyun Kim, T-MTT May 06 2098-2105 Jin Jianbo, see Jianbo Jin, T-MTT Mar 06 1139-1145 Jin Jun-De, see Jun-De Jin, T-MTT Dec 06 4333-4340 Jin-Koo Rhee, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Jinsung Choi, see Huijung Kim, T-MTT Jul 06 2917-2924 Jinsung Park, Chang-Ho Lee, Byung-Sung Kim, and J. Laskar. Design and analysis of low flicker-noise CMOS mixers for direct conversion receivers; T-MTT Dec 06 4372-4380 Jintian Zhu, see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Ji Taeksoo, see Taeksoo Ji, T-MTT Mar 06 1131-1138 Jiunn-Tsair Chen, see Chih-Hung Lin, T-MTT May 06 2118-2127 Ji-Won Jung, see Yun, Y., T-MTT Oct 06 3805-3817 Ji Xin Chen, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Jong-Gwan Yook, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Jong-Gwan Yook, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Jong-Heon Kim, see Wan-Jong Kim, T-MTT Sep 06 3469-3478

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Jong-Hoon Lee, N. Kidera, G. DeJean, S. Pinel, J. Laskar, and M.M. Tentzeris. A V-band front-end with 3-D integrated cavity filters/duplexers and antenna in LTCC technologies; T-MTT Jul 06 2925-2936 Jong-In Song, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Jongsik Kim, see Hyunchol Shin, T-MTT Nov 06 3857-3863 Jongsoo Lee, and J.D. Cressler. Analysis and design of an ultra-wideband low-noise amplifier using resistive feedback in SiGe HBT technology; TMTT Mar 06 1262-1268 Jong-Won Yu, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Joo Kim Wan, see Jung Dong Park, T-MTT Oct 06 3623-3629 Joon-Ho Lee, Tian Xiao, and Q.H. Liu. A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields; T-MTT Jan 06 437-444 Joon-Yong Lee, and Sungyul Yoo. Large error performance of UWB ranging in multipath and multiuser environments; T-MTT Jun 06 1887-1895 Joshi, H., and W. J. Chappell. Dual-band lumped-element bandpass filter; TMTT Dec 06 4169-4177 Joungho Kim, see Junwoo Lee, T-MTT Jun 06 1667-1674 Jo Woon Chong, Bang Chul Jung, and Dan Keun Sung. Statistical multiplexing-based hybrid FH-OFDMA system for OFDM-based UWB indoor radio access networks; T-MTT Jun 06 1793-1801 Ju-Ho Lee, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Jui-Chieh Chiu, Chih-Ming Lin, and Yeong-Her Wang. A 3-dB quadrature coupler suitable for PCB circuit design; T-MTT Sep 06 3521-3525 Jui-Ching Cheng, see Li, E.S., T-MTT Jan 06 464-472 Jun Cui Tie, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Jun-De Jin, S. S. H. Hsu, Ming-Ta Yang, and S. Liu. Low-loss differential semicoaxial interconnects in CMOS process; T-MTT Dec 06 4333-4340 Jung Baek Ho, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Jung Bang Chul, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Jung-Dong Park, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Jung Dong Park, and Wan Joo Kim. An efficient method of eliminating the range ambiguity for a low-cost FMCW radar using VCO tuning characteristics; T-MTT Oct 06 3623-3629 Jung-Hun Oh, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Jung Ji-Won, see Yun, Y., T-MTT Oct 06 3805-3817 Jung-Min Kim, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Jun-Hyuk Seo, Chang-Soon Choi, Young-Shik Kang, Yong-Duck Chung, Jeha Kim, and Woo-Young Choi. SOA-EAM frequency up/downconverters for 60-GHz bi-directional radio-on-fiber systems; T-MTT Feb 06 959-966 Jun-ichi Takada, see Haneda, K., T-MTT Jun 06 1802-1811 Junker, M., M.J. Ammann, A.T. Schwarzbacher, J. Klinger, K.-U. Lauterbach, and T. Schneider. A comparative test of Brillouin amplification and erbium-doped fiber amplification for the generation of millimeter waves with low phase noise properties; T-MTT Jun 06 15761581 Junwoo Lee, Young-Jin Park, Myunghoi Kim, C. Yoon, Joungho Kim, and Kwan-Ho Kim. System-on-package ultra-wideband transmitter using CMOS impulse generator; T-MTT Jun 06 1667-1674 Jun Yao Qi, see Ling Jiang, T-MTT Jul 06 2944-2948 Juodawlkis, P.W., see Seeds, A., T-MTT Feb 06 777-779 Jyh-Chyurn Guo, and Yi-Min Lin. A new lossy substrate model for accurate RF CMOS noise extraction and simulation with frequency and bias dependence; T-MTT Nov 06 3975-3985 K Kaddour, D., E. Pistono, J.-M. Duchamp, J.-D. Arnould, H. Eusebe, P. Ferrari, and R.G. Harrison. A compact and selective low-pass filter with reduced spurious responses, based on CPW tapered periodic structures; TMTT Jun 06 2367-2375 Kae-Oh Sun, and D. W. van der Weide. High-speed digital-to-analog converter using Schottky diode samplers; T-MTT Dec 06 4291-14296 Kai Chang, see Wen-Hua Tu, T-MTT Mar 06 1084-1089 Kai Chang, see Seungpyo Hong, T-MTT Jun 06 1370-1378 Kai Chang, see Yu-Jiun Ren, T-MTT Jun 06 1495-1502 Kai Chang, see Wen-Hua Tu, T-MTT Jun 06 2497-2502 Kai Chang, see Yu-Jiun Ren, T-MTT Jul 06 2970-2976 Kai Chang, see Wen-Hua Tu, T-MTT Oct 06 3786-3792 Kaihui Lin, Yuanxun Wang, Cheng-Ken Pao, and Yi-Chi Shih. A Ka-band FMCW radar front-end with adaptive leakage cancellation; T-MTT Dec 06 4041-4048 Kaija, T., and E.O. Ristolainen. An improved model for ground-shielded CMOS test fixtures; T-MTT Jan 06 82-87

IEEE T-MTT 2006 INDEX — 11 Kaija, T., and P. Heino. Comments on "A shield-based three-port deembedding method for microwave on-wafer characterization of deepsubmicrometer silicon MOSFETs"; T-MTT Mar 06 1295-1296 Kaija, T., and P. Heino. The optimization of on-wafer shield-based test fixture layout; T-MTT May 06 1975-1982 Kai Meng Hock Error correction for diffraction and multiple scattering in free-space microwave measurement of materials; T-MTT Feb 06 648-659 Kainz, W., see Dagang Wu, T-MTT Dec 06 4472-4478 Kaixue Ma, Jian-Guo Ma, Kiat Seng Yeo, and Manh Anh Do. A compact size coupling controllable filter with separate electric and magnetic coupling paths; T-MTT Mar 06 1113-1119 Kallfass, I., H. Schumacher, and T.J. Brazil. Multiple time constant modeling of dispersion dynamics in hetero field-effect transistors; T-MTT Jun 06 2312-2320 Kalokitis, D., see Fathy, A.E., T-MTT Jan 06 247-255 Kam-Weng Tam, see Si-Weng Fok, T-MTT May 06 2033-2041 Kanapady, R., see Qunsheng Cao, T-MTT Aug 06 3316-3326 Kangaslahti, P., see Fung, A., T-MTT Dec 06 4507-4512 Kang Dong-Woo, see Dong-Woo Kang, T-MTT Jan 06 294-301 Kang Young-Shik, see Jeha Kim, T-MTT Feb 06 780-787 Kang Young-Shik, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Kan Liu Hui, see Hui Kan Liu, T-MTT Sep 06 3479-3485 Kantartzis, N. V., see Sounas, D. L., T-MTT Dec 06 4111-4121 Kapusta, C., see Chen, M.J., T-MTT Nov 06 4009-4015 Karabudak, N., see Chen, M.J., T-MTT Nov 06 4009-4015 Karmakar, N.C., S.M. Roy, and I. Balbin. Quasi-static modeling of defected ground structure; T-MTT May 06 2160-2168 Karnfelt, C., P. Hallbjorner, H. Zirath, and A. Alping. High gain active microstrip antenna for 60-GHz WLAN/WPAN applications; T-MTT Jun 06 2593-2603 Karnfelt, C., R. Kozhuharov, H. Zirath, and I. Angelov. High-purity 60-GHzband single-chip u8 multipliers in pHEMT and mHEMT technology; TMTT Jun 06 2887-2898 Karnfelt, C., C. Tegnander, J. Rudnicki, J.P. Starski, and A. Emrich. Investigation of parylene-C on the performance of millimeter-wave circuits; T-MTT Aug 06 3417-3425 Kashyap, R., see Xiupu Zhang, T-MTT Feb 06 929-937 Katehi, L.P.B., see Lahiji, R.R., T-MTT Jun 06 2699-2706 Katehi, L. P. B., see Lee, K.-Y., T-MTT Dec 06 4141-4148 Kato, H., see Kato, H., T-MTT Nov 06 3960-3967 Kato, H., T. Kohori, E. Kondoh, T. Akitsu, and H. Kato. A noise-free and jitterless cavity system to distribute clocks over 10 GHz; T-MTT Nov 06 3960-3967 Kaurova, N.S., see Ling Jiang, T-MTT Jul 06 2944-2948 Kawano, Y., Y. Nakasha, K. Yokoo, S. Masuda, T. Takahashi, T. Hirose, Y. Oishi, and K. Hamaguchi. RF chipset for impulse UWB radar using 0.13ȝm InP-HEMT technology; T-MTT Dec 06 4489-4497 Kazimierczuk, M.K., see Kleismit, R.A., T-MTT Feb 06 639-647 Ke-Chiang Lin, Chun-Fu Chang, Min-Chung Wu, and Shyh-Jong Chung. Dual-bandpass filters with serial configuration using LTCC technology; TMTT Jun 06 2321-2328 Keenan, D.A., see Williams, D.F., T-MTT Jan 06 481-491 Keenan, D.A., see Clement, T.S., T-MTT Aug 06 3173-3181 Keenan, D.A., see Dienstfrey, A., T-MTT Aug 06 3197-3208 Keignart, J., C. Abou-Rjeily, C. Delaveaud, and N. Daniele. UWB SIMO channel measurements and simulations; T-MTT Jun 06 1812-1819 Kei Hao, see Gubner, J.A., T-MTT Jun 06 1762-1768 Ke-Li Wu, see Jie Wang, T-MTT May 06 1961-1968 Ke-Li Wu, see Lap Kun Yeung, T-MTT Jun 06 1512-1518 Ke-Li Wu, see Wei Meng, T-MTT Oct 06 3765-3771 Kelley, D.T., see Epp, L.W., T-MTT Mar 06 1048-1054 Kelly, M., see Masud, M.A., T-MTT Jun 06 2848-2855 Keun Sung Dan, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Ke Wu, see Feng Xu, T-MTT Jan 06 329-338 Ke Wu, see Bozzi, M., T-MTT Jan 06 339-347 Ke Wu, see Moldovan, E., T-MTT Feb 06 625-632 Ke Wu, see Xiupu Zhang, T-MTT Feb 06 929-937 Ke Wu, see Lin Li, T-MTT Jun 06 1470-1476 Ke Wu, see Yanyang Zhao, T-MTT Jun 06 1707-1712 Ke Wu, see Deslandes, D., T-MTT Jun 06 2516-2526 Ke Wu, see Patrovsky, A., T-MTT Jun 06 2872-2879 Ke Wu, see Xinyu Xu, T-MTT Jul 06 2937-2943 Ke Wu, see D'Orazio, W., T-MTT Oct 06 3675-3680 Ke Wu, see Moldovan, E., T-MTT Nov 06 4017

+ Check author entry for coauthors

Khalil, W., see Hedayati, H., T-MTT Oct 06 3654-3663 Khazaka, R., see Min Ma, T-MTT Dec 06 4305-4315 Khee Meng Chan, see Rambabu, K., T-MTT Aug 06 3333-3338 Khenissi, H., see Williams, D.F., T-MTT Mar 06 1210-1217 Khlifi, R., and P. Russer. Hybrid space-discretizing method - Method of moments for the analysis of transient interference; T-MTT Dec 06 44404447 Kiat Seng Yeo, see Kaixue Ma, T-MTT Mar 06 1113-1119 Kiat Seng Yeo, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Kidera, N., see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 Ki-Jin Kim, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Kikuchi, S., see Saito, K., T-MTT Aug 06 3443-3449 Kim, H., see Bien, F., T-MTT Dec 06 4538-4547 Kim, I. K., see Ki Seok Yang, T-MTT Dec 06 4572-4579 Kim, S.-D., see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Kim, Y., see Llamas-Garro, I., T-MTT Dec 06 4161-4168 Kim, Y.-K., see Llamas-Garro, I., T-MTT Dec 06 4161-4168 Ki-Man Kim, see Yun, Y., T-MTT Oct 06 3805-3817 Kimball, D.F., Jinho Jeong, Chin Hsia, P. Draxler, S. Lanfranco, W. Nagy, K. Linthicum, L.E. Larson, and P.M. Asbeck. High-efficiency envelopetracking W-CDMA base-station amplifier using GaN HFETs; T-MTT Nov 06 3848-3856 Kimball, D. F., see Feipeg Wang, T-MTT Dec 06 4086-4099 Kim Bumman, see Young Yun Woo, T-MTT May 06 1969-1974 Kim Bumman, see Huijung Kim, T-MTT Jul 06 2917-2924 Kim Byung-Sung, see Jinsung Park, T-MTT Dec 06 4372-4380 Kim Chul Dong, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Kim Chung-Hwam, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Kim Chung-Hwan, see Dong-Woo Kang, T-MTT Jan 06 294-301 Kim Chung-Ryul, see Yun, Y., T-MTT Oct 06 3805-3817 Kim Dong-Hyun, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Kim Dong-Jin, see Dong-Won Kim, T-MTT Nov 06 3923-3930 Kim Dong-Won, see Dong-Won Kim, T-MTT Nov 06 3923-3930 Kim Dong-Zo, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Kim Duck-Hwan, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Kim Hongjoon, see Hongjoon Kim, T-MTT Dec 06 4178-4184 Kim Huijung, see Huijung Kim, T-MTT Jul 06 2917-2924 Kim Hyung-Mi, see Hyung-Mi Kim, T-MTT Jul 06 3113-3120 Kim Jaeheung, see Choon Sik Cho, T-MTT Nov 06 3968-3974 Kim Jeha, see Jeha Kim, T-MTT Feb 06 780-787 Kim Jeha, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Kim Jong-Heon, see Wan-Jong Kim, T-MTT Sep 06 3469-3478 Kim Jongsik, see Hyunchol Shin, T-MTT Nov 06 3857-3863 Kim Joungho, see Junwoo Lee, T-MTT Jun 06 1667-1674 Kim Jung-Min, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Kim Ki-Jin, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Kim Ki-Man, see Yun, Y., T-MTT Oct 06 3805-3817 Kim Kwan-Ho, see Junwoo Lee, T-MTT Jun 06 1667-1674 Kim Myunghoi, see Junwoo Lee, T-MTT Jun 06 1667-1674 Kim Nae-Soo, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Kim Tae-Young, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Kimura, T., see Shingo Tanaka, T-MTT Feb 06 938-944 Kimura, T., see Taguchi, N., T-MTT Feb 06 945-950 Kimura, T., see Shingo Tanaka, T-MTT Jun 06 1561-1568 Kim Wan-Jong, see Wan-Jong Kim, T-MTT Sep 06 3469-3478 Kim Wan Joo, see Jung Dong Park, T-MTT Oct 06 3623-3629 Kim Won-Bae, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Kim Woonyun, see Woonyun Kim, T-MTT May 06 2098-2105 Kim Yong-Dae, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Kim Yonggyoo, see Seungki Nam, T-MTT Jun 06 1315-1324 Kim Yong Hoon, see Sung Tae Choi, T-MTT May 06 1953-1960 Kim Yonghoon, see Seungki Nam, T-MTT Jun 06 1315-1324 Kinayman, N., see Onal, T., T-MTT Oct 06 3739-3745 Kingsley, N., and J. Papapolymerou. Organic "Wafer-Scale" packaged miniature 4-bit RF MEMS phase shifter; T-MTT Mar 06 1229-1236 Kirby, P.L., see Padmanabhan, S., T-MTT Sep 06 3583-3593 Kirchoefer, S.W., see Rauscher, C., T-MTT Mar 06 1190-1195 Kirilenko, A.A., L.A. Rud, and V.I. Tkachenko. Nonsymmetrical H-plane corners for TE10-TEq0-mode conversion in rectangular waveguides; T-MTT Jun 06 2471-2477 Ki Seok Yang, see Sung Tae Choi, T-MTT May 06 1953-1960 Ki Seok Yang, S. Pinel, I. K. Kim, and J. Laskar. Low-loss integratedwaveguide passive circuits using liquid-crystal polymer system-onpackage (SOP) technology for millimeter-wave applications; T-MTT Dec 06 4572-4579

IEEE T-MTT 2006 INDEX — 12 Kishimoto, S., see Ito, M., T-MTT Dec 06 4522-4527 Kitano, H., see Inoue, R., T-MTT Feb 06 522-532 Kitayama, S., see Satoh, H., T-MTT Jan 06 210-215 Kitazawa, T., see Tsuji, M., T-MTT Jul 06 2962-2969 Kiziltas, G., see Koulouridis, S., T-MTT Dec 06 4202-4208 Klapwijk, T.M., see Jackson, B.D., T-MTT Feb 06 547-558 Kleismit, R.A., M.K. Kazimierczuk, and G. Kozlowski. Sensitivity and resolution of evanescent microwave microscope; T-MTT Feb 06 639-647 Klingenbock, A., see Christ, A., T-MTT May 06 2188-2195 Klinger, J., see Junker, M., T-MTT Jun 06 1576-1581 Knapp, P.F., see Urick, V.J., T-MTT Jun 06 1458-1463 Knochel, R.H., I. Oppermann, and A. Wittneben. Guest editorial [special issue intro. on ultra-wideband]; T-MTT Apr 06 1633-1636 Kobayashi, T., see Haneda, K., T-MTT Jun 06 1802-1811 Koca, M., see Guney, N., T-MTT Jun 06 1724-1730 Koers, G., J. Stiens, and R. Vounckx. Scalar calibration of quasi-optical reflection measurements; T-MTT Jul 06 3121-3126 Koh Jinhwan, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Kohori, T., see Kato, H., T-MTT Nov 06 3960-3967 Kokkinos, T., C.D. Sarris, and G.V. Eleftheriades. Periodic FDTD analysis of leaky-wave structures and applications to the analysis of negativerefractive-index leaky-wave antennas; T-MTT Jun 06 1619-1630 Kok-Yan Lee, see Sang-June Park, T-MTT Nov 06 3931-3939 Kollberg, E.L., and K.S. Yngvesson. Quantum-noise theory for terahertz hot electron bolometer mixers; T-MTT May 06 2077-2089 Komaki, S., see Murakoshi, A., T-MTT Feb 06 967-972 Komaki, S., see Higashino, T., T-MTT Feb 06 973-979 Komijani, A., see Buckwalter, J. F., T-MTT Dec 06 4271-4280 Kompa, G., see Ruengwaree, A., T-MTT Jun 06 2774-2779 Konaka, S., see Satoh, H., T-MTT Jan 06 210-215 Kondoh, E., see Kato, H., T-MTT Nov 06 3960-3967 Kongpop U-yen, E.J. Wollack, T.A. Doiron, J. Papapolymerou, and J. Laskar. A planar bandpass filter design with wide stopband using double split-end stepped-impedance resonators; T-MTT Mar 06 1237-1244 Kooi, J.W., see Jackson, B.D., T-MTT Feb 06 547-558 Kornrumpf, W., see Chen, M.J., T-MTT Nov 06 4009-4015 Korovkin, N.V., see Adalev, A.S., T-MTT Jul 06 3131-3140 Kosmas, P., and C.M. Rappaport. FDTD-based time reversal for microwave breast cancer Detection-localization in three dimensions; T-MTT Jun 06 1921-1927 Kosmas, P., see Goussetis, G., T-MTT Nov 06 3885-3892 Kosugi, T., see Hirata, A., T-MTT May 06 1937-1944 Koul, S.K., see Pathak, N.P., T-MTT Jan 06 173-179 Koulouridis, S., G. Kiziltas, Yijun Zhou, D. J. Hansford, and J. L. Volakis. Polymer-ceramic composites for microwave applications: Fabrication and performance assessment; T-MTT Dec 06 4202-4208 Kouzaev, G.A., M.J. Deen, N.K. Nikolova, and A.H. Rahal. Cavity models of planar components grounded by via-holes and their experimental verification; T-MTT Mar 06 1033-1042 Kozakowski, P., and M. Mrozowski. Quadratic programming approach to coupled resonator filter CAD; T-MTT Nov 06 3906-3913 Kozhuharov, R., see Karnfelt, C., T-MTT Jun 06 2887-2898 Koziel, S., J.W. Bandler, and K. Madsen. Space-mapping-based interpolation for engineering optimization; T-MTT Jun 06 2410-2421 Koziel, S., J.W. Bandler, and K. Madsen. A space-mapping framework for engineering Optimization-theory and implementation; T-MTT Oct 06 3721-3730 Koziel, S., J. W. Bandler, and K. Madsen. Theoretical justification of spacemapping-based modeling utilizing a database and on-demand parameter extraction; T-MTT Dec 06 4316-4322 Kozlowski, G., see Kleismit, R.A., T-MTT Feb 06 639-647 Kozyrev, A. B., see Hongjoon Kim, T-MTT Dec 06 4178-4184 Krishnamurthy, L., see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Krizhanovskii, V., see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Kromer, C., see Sialm, G., T-MTT Jan 06 65-73 Kroug, M., see Jackson, B.D., T-MTT Feb 06 547-558 Krupka, J., A. Abramowicz, and K. Derzakowski. Magnetically tunable filters for cellular communication terminals; T-MTT Jun 06 2329-2335 Krupka, J., J. Breeze, A. Centeno, N. Alford, T. Claussen, and L. Jensen. Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies; T-MTT Nov 06 3995-4001 Kuang Weiwei, see Trew, R.J., T-MTT May 06 2061-2067 Kubo, S., see Idei, H., T-MTT Nov 06 3899-3905 Kuester, E.F., see Se-Ho You, T-MTT May 06 2232-2242 Kuester, E. F., see Holloway, C. L., T-MTT Nov 06 4018-4019 + Check author entry for coauthors

Kuijk, M., see Mingxu Liu, T-MTT Jun 06 1698-1706 Kuk-Hyun Sunwoo, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Kumar, V., see Guang Chen, T-MTT Jul 06 2949-2953 Kum Meng Lum, T. Tick, C. Free, and H. Jantunen. Design and measurement data for a microwave dual-CP antenna using a new traveling-wave feed concept; T-MTT Jun 06 2880-2886 Kun Yeung Lap, see Lap Kun Yeung, T-MTT Jun 06 1512-1518 Kuo, C.J., see Ming-Feng Huang, T-MTT Feb 06 660-669 Kuo, J.-T., and Chih-Yuan Tsai. Periodic stepped-impedance ring resonator (PSIRR) bandpass filter with a miniaturized area and desirable upper stopband characteristics; T-MTT Mar 06 1107-1112 Kuo Jen-Tsai, see Yi-Chyun Chiou, T-MTT Aug 06 3352-3358 Kuo-Jung Sun, see To-Po Wang, T-MTT Jan 06 88-95 Kuo-Jung Sun, Zuo-Min Tsai, K.-Y. Lin, and Huei Wang. A noise optimization formulation for CMOS low-noise amplifiers with on-chip low-Q inductors; T-MTT Jun 06 1554-1560 Kuo-Jung Sun, see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Kuo Tsung-Nan, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Kuo Tsung-Nan, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Kurihara, T., see Takenaka, I., T-MTT Dec 06 4513-4521 Kurniawan, T., A. Nirmalathas, C. Lim, D. Novak, and R. Waterhouse. Performance analysis of optimized millimeter-wave fiber radio links; TMTT Feb 06 921-928 Kuster, N., see Christ, A., T-MTT May 06 2188-2195 Ku Yeonwoo, see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Kwang-Seong Choi, see Jeha Kim, T-MTT Feb 06 780-787 Kwan-Ho Kim, see Junwoo Lee, T-MTT Jun 06 1667-1674 Kwyro Lee, see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Kyoung-Hwan Oh, Tae-Young Kim, Sucbei Moon, Ho-Jin Song, Won-Bae Kim, Chang-Soo Park, and Jong-In Song. Characterization of uniplanar compact photonic-bandgap finite-width conductor-backed coplanar waveguide by using an electrooptic near-field mapping technique; T-MTT Feb 06 854-860 Kyoung-Joon Cho, see Wan-Jong Kim, T-MTT Sep 06 3469-3478 Kyung-Sik Lee, see Yun, Y., T-MTT Oct 06 3805-3817 L Lafond, O., see Fuchs, B., T-MTT Jun 06 2292-2300 Lager, I.E., see Simeoni, M., T-MTT Jun 06 1503-1511 Laheurte, J.-M., see Aissat, H., T-MTT Jun 06 2856-2863 Lahiji, R.R., K.J. Herrick, Yongshik Lee, A. Margomenos, S. Mohammadi, and L.P.B. Katehi. Multiwafer vertical interconnects for three-dimensional integrated circuits; T-MTT Jun 06 2699-2706 Lahti, M., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Lai Chih Che, see Li, E.S., T-MTT Jan 06 464-472 Lai Jie-Wei, see Jie-Wei Lai, T-MTT Feb 06 599-607 Lai Ming-Iu, see Ming-Iu Lai, T-MTT Jan 06 160-168 Lai Ming-Iu, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Lakshminarayanan, B., and T.M. Weller. Design and modeling of 4-bit slow-wave MEMS phase shifters; T-MTT Jan 06 120-127 Lam, A.K.M., M. Fairburn, and N.A.F. Jaeger. Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique; T-MTT Jan 06 240-246 Lancaster, M.J., see Guoyong Zhang, T-MTT Feb 06 559-563 Lanfranco, S., see Kimball, D.F., T-MTT Nov 06 3848-3856 Lap Kun Yeung, and Ke-Li Wu. An LTCC balanced-to-unbalanced extracted-pole bandpass filter with complex load; T-MTT Jun 06 15121518 Larson, L.E., see Kimball, D.F., T-MTT Nov 06 3848-3856 Larson, L. E., see Feipeg Wang, T-MTT Dec 06 4086-4099 Larson, L. E., see Ranjan, M., T-MTT Dec 06 4422-4431 Laskar, J., see Kongpop U-yen, T-MTT Mar 06 1237-1244 Laskar, J., see Sarkar, S., T-MTT Mar 06 1245-1252 Laskar, J., see Yunseo Park, T-MTT Jun 06 1687-1697 Laskar, J., see Sen, P., T-MTT Jun 06 2604-2614 Laskar, J., see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 Laskar, J., see Jinsung Park, T-MTT Dec 06 4372-4380 Laskar, J., see Bien, F., T-MTT Dec 06 4538-4547 Laskar, J., see Ki Seok Yang, T-MTT Dec 06 4572-4579 Latrach, M., see Zbitou, J., T-MTT Jan 06 147-152 Laurin, J.-J., see Omrane, B., T-MTT Jun 06 1438-1450 Lauterbach, K.-U., see Junker, M., T-MTT Jun 06 1576-1581 Lau Yuenie, see Fung, A., T-MTT Dec 06 4507-4512 Lawrence, B.G., see Mahon, J., T-MTT May 06 2050-2060

IEEE T-MTT 2006 INDEX — 13 Lawson, W., see Bharathan, K., T-MTT Jun 06 1301-1307 Lazaro, A., see Girbau, D., T-MTT Mar 06 1120-1130 Le Boudec, J.-Y., see Fawal, A.E., T-MTT Jun 06 1769-1781 Le Coq, L., see Zhadobov, M., T-MTT Jun 06 2534-2542 LeDrew, C., see Amari, S., T-MTT May 06 2153-2159 Lee, B., see Hyung-Mi Kim, T-MTT Jul 06 3113-3120 Lee, J.W., see Choon Sik Cho, T-MTT Nov 06 3968-3974 Lee, K., see Fung, A., T-MTT Dec 06 4507-4512 Lee, K.-Y., S. Mohammadi, P. K. Bhattacharya, and L. P. B. Katehi. Compact models based on transmission-line concept for integrated capacitors and inductors; T-MTT Dec 06 4141-4148 Lee, R., see Chilton, R.A., T-MTT Jan 06 473-480 Lee Bok-Hyung, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Lee Byoung Hwa, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Lee Chang-Ho, see Yunseo Park, T-MTT Jun 06 1687-1697 Lee Chang-Ho, see Sen, P., T-MTT Jun 06 2604-2614 Lee Chang-Ho, see Jinsung Park, T-MTT Dec 06 4372-4380 Lee Hong-Ming, see Chih-Ming Tsai, T-MTT Jun 06 1545-1553 Lee Hui Dong, see Dong-Woo Kang, T-MTT Jan 06 294-301 Lee Jaehoon, see Seungki Nam, T-MTT Jun 06 1315-1324 Lee Jae-Wook, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Lee Jeong-Hae, see Dong-Won Kim, T-MTT Nov 06 3923-3930 Lee Jeongseon, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Lee Jin-Fa, see Venkatarayalu, N.V., T-MTT Jul 06 3019-3025 Lee Jong-Hoon, see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 Lee Jongsoo, see Jongsoo Lee, T-MTT Mar 06 1262-1268 Lee Joon-Ho, see Joon-Ho Lee, T-MTT Jan 06 437-444 Lee Joon-Yong, see Joon-Yong Lee, T-MTT Jun 06 1887-1895 Lee Ju-Ho, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Lee Junwoo, see Junwoo Lee, T-MTT Jun 06 1667-1674 Lee Kok-Yan, see Sang-June Park, T-MTT Nov 06 3931-3939 Lee Kwyro, see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Lee Kyung-Sik, see Yun, Y., T-MTT Oct 06 3805-3817 Lee Mun-Kyo, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Lee Sang-Gug, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Lee Sang-Gug, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Lee Sang Gug, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Lee Seung-Yup, see Seung-Yup Lee, T-MTT Jan 06 451-457 Lee Shuenn-Yuh, see Ming-Feng Huang, T-MTT Feb 06 660-669 Lee Sung-Woo, see Fathy, A.E., T-MTT Jan 06 247-255 Lee Taek-Kyung, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Lee Wang-Sang, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Lee Yi-Lin, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Lee Yongshik, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Lee Yongshik, see Lahiji, R.R., T-MTT Jun 06 2699-2706 Lee Yong-Sub, see Seung-Yup Lee, T-MTT Jan 06 451-457 LeFevre, M., see Wood, J., T-MTT Aug 06 3163-3172 Legay, H., see Perret, E., T-MTT Sep 06 3594-3601 Lei Ming-Fong, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Lei Wu, Zengguang Sun, H. Yilmaz, and M. Berroth. A dual-frequency wilkinson power divider; T-MTT Jan 06 278-284 Le Minh, see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Lenin, R.B., see Cuyt, A., T-MTT May 06 2265-2274 Lenk, F., see Rudolph, M., T-MTT Jul 06 2954-2961 Lenoir, P., S. Bila, F. Seyfert, D. Baillargeat, and S. Verdeyme. Synthesis and design of asymmetrical dual-band bandpass filters based on equivalent network simplification; T-MTT Jul 06 3090-3097 Leong, K.M.K.H., see Allen, C.A., T-MTT Jul 06 3104-3112 Leong, M.-S., see Jayabalan, J., T-MTT Jun 06 1331-1339 Leong, S.-W., see Adrian Eng-Choon Tan, T-MTT Mar 06 1019-1024 Leong Siew-Weng, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Leung, L.L.W., and K.J. Chen. CAD equivalent-circuit modeling of attenuation and cross-coupling for edge-suspended coplanar waveguides on lossy silicon substrate; T-MTT May 06 2249-2255 Leung Chiu, see Yum, T.Y., T-MTT Aug 06 3255-3266 Leuther, A., see Campos-Roca, Y., T-MTT Jul 06 2983-2992 Levi, A.F.J., see Hossein-Zadeh, M., T-MTT Feb 06 821-831 Le Viet-Hoang, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Levush, B., see Safier, P.N., T-MTT Oct 06 3605-3615 Levy, R., R.V. Snyder, and Sanghoon Shin. Bandstop filters with extended upper passbands; T-MTT Jun 06 2503-2515 Lewandowski, A., see Williams, D.F., T-MTT Jan 06 481-491 Le-Wei Li, see Ouchetto, O., T-MTT Nov 06 3893-3898 Lheurette, E., see Decoopman, T., T-MTT Jun 06 1451-1457

+ Check author entry for coauthors

Li, E.S., Jui-Ching Cheng, and Chih Che Lai. Designs for broad-band microstrip vertical transitions using cavity couplers; T-MTT Jan 06 464472 Liang Hsiao-Bin, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Liang-Hung Lu, see To-Po Wang, T-MTT Jan 06 88-95 Liang-Hung Lu, Hsieh-Hung Hsieh, and Yu-Te Liao. A wide tuning-range CMOS VCO with a differential tunable active inductor; T-MTT Sep 06 3462-3468 Liao Shry-Sann, see Shry-Sann Liao, T-MTT Sep 06 3508-3514 Liao Yu-Te, see Liang-Hung Lu, T-MTT Sep 06 3462-3468 Libin Yue, see Huang, F., T-MTT Nov 06 3954-3959 Li Changzhi, see Changzhi Li, T-MTT Dec 06 4464-4471 Li Dongying, see Nikolova, N.K., T-MTT Feb 06 670-681 Li Duochuan, see Bozzi, M., T-MTT Jan 06 339-347 Lie, D. Y., see Feipeg Wang, T-MTT Dec 06 4086-4099 Li Le-Wei, see Ouchetto, O., T-MTT Nov 06 3893-3898 Li Lin, see Lin Li, T-MTT Jun 06 1470-1476 Lim, C., see Kurniawan, T., T-MTT Feb 06 921-928 Lim, C., M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse. Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links; T-MTT May 06 2181-2187 Lim Byeong-Ok, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Limiti, E., see Colantonio, P., T-MTT Jun 06 2713-2722 Limiti, E., see Crupi, G., T-MTT Oct 06 3616-3622 Lim Teck-Hwee, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Lim Wei Meng, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Lin, I. S., see McKinney, J. D., T-MTT Dec 06 4247-4255 Lin, J., see Xiuge Yang, T-MTT Jan 06 96-105 Lin, J., see Yanming Xiao, T-MTT May 06 2023-2032 Lin, J., see Verma, A., T-MTT Aug 06 3295-3300 Lin, K.-Y., see Mei-Chao Yeh, T-MTT Jan 06 31-39 Lin, K.-Y., see Zuo-Min Tsai, T-MTT May 06 2090-2097 Lin, K.-Y., see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Lin Chien-Min, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Lin Chih-Hung, see Chih-Hung Lin, T-MTT May 06 2118-2127 Lin Chih-Ming, see Jui-Chieh Chiu, T-MTT Sep 06 3521-3525 Lin Chin-Shen, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Lin-Chuan Tsai, see Ching-Wen Hsue, T-MTT Mar 06 1043-1047 Lin Dong Tian, see Hui Kan Liu, T-MTT Sep 06 3479-3485 Lindsay, A.C., see Winnall, S.T., T-MTT Feb 06 868-872 Ling Chuen Ong, see Yong-Xin Guo, T-MTT Mar 06 1196-1200 Ling Jiang, Wei Miao, Wen Zhang, Ning Li, Zhen Hui Lin, Qi Jun Yao, Sheng-Cai Shi, S.I. Svechnikov, Y.B. Vakhtomin, S.V. Antipov, B.M. Voronov, N.S. Kaurova, and G.N. Gol'tsman. Characterization of a quasioptical NbN superconducting HEB mixer; T-MTT Jul 06 2944-2948 Lin Hsiao-Kuang, see Yng-Huey Jeng, T-MTT Feb 06 633-638 Li Ning, see Ling Jiang, T-MTT Jul 06 2944-2948 Lin Jenshan, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Lin Jenshan, see Changzhi Li, T-MTT Dec 06 4464-4471 Lin Kaihui, see Kaihui Lin, T-MTT Dec 06 4041-4048 Lin Ke-Chiang, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Lin Li, and Ke Wu. Integrated planar spatial power combiner; T-MTT Jun 06 1470-1476 Lin Shih-Cheng, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Lin Shih-Cheng, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Lin Shih-Cheng, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Linthicum, K., see Kimball, D.F., T-MTT Nov 06 3848-3856 Lintignat, J., see Darfeuille, S., T-MTT Dec 06 4381-4396 Lin Xian Qi, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Lin Yi-Min, see Jyh-Chyurn Guo, T-MTT Nov 06 3975-3985 Lin Yo-Shen, see Pu-Hua Deng, T-MTT Feb 06 533-539 Lin Yo-Shen, see Chao-Huang Wu, T-MTT Feb 06 540-546 Lin Yo-Shen, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Lin Yo-Shen, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Lin Yo-Sheng, see Tao Wang, T-MTT Feb 06 580-588 Lin Yo-Sheng, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Lin Zhen Hui, see Ling Jiang, T-MTT Jul 06 2944-2948 Lippens, D., see Decoopman, T., T-MTT Jun 06 1451-1457 Lippens, D., see Carbonell, J., T-MTT Jun 06 1527-1533 Li Qing-Xiang, see Qing-Xiang Li, T-MTT Jul 06 3146-3154 Lissorgues-Bazin, G., see Martoglio, L., T-MTT Jul 06 3084-3089 Liu, Q.H., see Joon-Ho Lee, T-MTT Jan 06 437-444 Liu, S., see Jun-De Jin, T-MTT Dec 06 4333-4340 Liu, X.Q., see Fan, X.C., T-MTT Apr 06 1631 Liu Baozhu, see Xiupu Zhang, T-MTT Feb 06 929-937

IEEE T-MTT 2006 INDEX — 14 Liu Duixian, see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Liu Hui Kan, see Hui Kan Liu, T-MTT Sep 06 3479-3485 Liu I-Chung, see Ching-Wen Tang, T-MTT Aug 06 3327-3332 Liu Jiang, see Jiang Liu, T-MTT Aug 06 3191-3196 Liu Jianguo, see Simsek, E., T-MTT Nov 06 3878-3884 Liu Mingxu, see Mingxu Liu, T-MTT Jun 06 1698-1706 Liu Qing Huo, see Simsek, E., T-MTT Jan 06 216-225 Liu Qing Huo, see Simsek, E., T-MTT Nov 06 3878-3884 Liu Ren-Chieh, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Liu Ren-Chieh, see To-Po Wang, T-MTT Jan 06 88-95 Liu Ruo Peng, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Liu Taijun, see Taijun Liu, T-MTT Jun 06 1340-1349 Liu Yaxun, see Yaxun Liu, T-MTT Feb 06 689-703 Liu Yu, see Silvonen, K., T-MTT Jun 06 1464-1469 Liu Yueying, see Trew, R.J., T-MTT May 06 2061-2067 Liu Zhiyang, see Zhiyang Liu, T-MTT Jun 06 2447-2452 Liu Zhiyang, see Zhiyang Liu, T-MTT Jul 06 2977-2982 Livezey, D., see Chao Lu, T-MTT Jan 06 40-45 Livshitz, B., see Boag, A., T-MTT Sep 06 3565-3570 Li Xiaofeng, see Ricketts, D.S., T-MTT Jan 06 373-382 Li Yan, see Nikolova, N.K., T-MTT Jun 06 1598-1610 Li Ying, see Nikolova, N.K., T-MTT Jun 06 1598-1610 Llamas-Garro, I., Y. Kim, C.-W. Baek, and Y.-K. Kim. A planar high-Q micromachined monolithic half-coaxial transmission-line filter; T-MTT Dec 06 4161-4168 Llopis, O., see Rudolph, M., T-MTT Jul 06 2954-2961 Lombardo, P., see Cardinali, R., T-MTT Jun 06 1865-1875 Long, J.R., see Bagga, S., T-MTT Jun 06 1656-1666 Lonnqvist, A., J. Mallat, and A.V. Raisanen. Phase-hologram-based compact RCS test range at 310 GHz for scale models; T-MTT Jun 06 2391-2397 Lonnqvist, A., A. Tamminen, J. Mallat, and A.V. Raisanen. Monostatic reflectivity measurement of Radar absorbing materials at 310 GHz; TMTT Sep 06 3486-3491 Lopez, J., see Piqueras, M.A., T-MTT Feb 06 887-899 Lopez-Villegas, J.M., J.G. Macias-Montero, J.A. Osorio, J. Cabanillas, N. Vidal, and J. Samitier. BPSK to ASK signal conversion using injectionlocked oscillators-part II: experiment; T-MTT Jan 06 226-234 Lou Xudong, see Saib, A., T-MTT Jun 06 2745-2754 Lubecke, M., see Yanming Xiao, T-MTT May 06 2023-2032 Luca De Nardis, see Cardinali, R., T-MTT Jun 06 1865-1875 Lu Chao, see Chao Lu, T-MTT Jan 06 40-45 Lu Jingxue, see Jingxue Lu, T-MTT Jul 06 3155 Lukashevich, D., A.C. Cangellaris, and P. Russer. Oblique-oblique projection in TLM-MOR for high-Q structures; T-MTT Oct 06 3712-3720 Lukic, M., B. Rondineau, Z. Popovic, and S. Filipovic. Modeling of realistic rectangular ȝ-coaxial lines; T-MTT May 06 2068-2076 Lukovnikov, D., see Bogdashov, A., T-MTT Dec 06 4130-4135 Lu Liang-Hung, see To-Po Wang, T-MTT Jan 06 88-95 Lu Liang-Hung, see Liang-Hung Lu, T-MTT Sep 06 3462-3468 Lum Kum Meng, see Kum Meng Lum, T-MTT Jun 06 2880-2886 Luo, B., see Darwish, A. M., T-MTT Dec 06 4456-4463 Lu Shey-Shi, see Tao Wang, T-MTT Feb 06 580-588 Lu Shey-Shi, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 M Ma, B. Y., J. Bergman, P. Chen, J. B. Hacker, G. Sullivan, G. Nagy, and B. Brar. InAs/AlSb HEMT and its application to ultra-low-power wideband high-gain low-noise amplifiers; T-MTT Dec 06 4448-4455 Macchiarella, G., and S. Tamiazzo. Novel approach to the synthesis of microwave diplexers; T-MTT Dec 06 4281-4290 MacEachern, L., see Brzezina, G., T-MTT Jun 06 2830-2839 Macias-Montero, J.G., see Lopez-Villegas, J.M., T-MTT Jan 06 226-234 Maciel, J.J., see Chen, M.J., T-MTT Nov 06 4009-4015 Macraigne, F., T. Reveyrand, G. Neveux, D. Barataud, J.-M. Nebus, A. Soury, and E. NGoya. Time-domain envelope measurements for characterization and behavioral modeling of nonlinear devices with memory; T-MTT Aug 06 3219-3226 Madero-Ayora, M.J., see Crespo-Cadenas, C., T-MTT Jan 06 321-328 Madero-Ayora, M.J., see Crespo-Cadenas, C., T-MTT Jan 06 445-450 Madsen, K., see Koziel, S., T-MTT Jun 06 2410-2421 Madsen, K., see Koziel, S., T-MTT Oct 06 3721-3730 Madsen, K., see Koziel, S., T-MTT Dec 06 4316-4322 Maeda, A., see Inoue, R., T-MTT Feb 06 522-532 Maeng, M., see Bien, F., T-MTT Dec 06 4538-4547 + Check author entry for coauthors

Mahon, J., E. Convert, P.T. Beasly, A. Bessemoulin, A. Dadello, A. Costantini, A. Fattorini, M.G. McCulloch, B.G. Lawrence, and J.T. Harvey. Broadband integrated millimeter-wave up- and down-converter GaAs MMICs; T-MTT May 06 2050-2060 Ma Jian-Guo, see Kaixue Ma, T-MTT Mar 06 1113-1119 Ma Jian-Guo, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Ma Kaixue, see Kaixue Ma, T-MTT Mar 06 1113-1119 Maleki, L., see Rubiola, E., T-MTT Feb 06 816-820 Mallat, J., see Lonnqvist, A., T-MTT Jun 06 2391-2397 Mallat, J., see Lonnqvist, A., T-MTT Sep 06 3486-3491 Mallegol, S., and P. Queffelec. Extension and error analysis of the microstrip transmission-line method for the broad-band measurement of the permeability tensor; T-MTT Mar 06 1065-1075 Mallet, A., A. Anakabe, J. Sombrin, and R. Rodriguez. Multiport-amplifierbased architecture versus classical architecture for space telecommunication payloads; T-MTT Dec 06 4353-4361 Ma Min, see Min Ma, T-MTT Dec 06 4305-4315 Manchec, A., C. Quendo, J.-F. Favennec, Eric Rius, and C. Person. Synthesis of capacitive-coupled dual-behavior resonator (CCDBR) filters; T-MTT Jun 06 2346-2355 Manh Anh Do, see Kaixue Ma, T-MTT Mar 06 1113-1119 Manh Anh Do, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Mao Rui-Jie, see Rui-Jie Mao, T-MTT Sep 06 3526-3533 Mao Shau-Gang, see Shau-Gang Mao, T-MTT Sep 06 3543-3549 Marceaux, A., see Piqueras, M.A., T-MTT Feb 06 887-899 Margomenos, A., see Lahiji, R.R., T-MTT Jun 06 2699-2706 Marie, H., see Darfeuille, S., T-MTT Dec 06 4381-4396 Marietti, P., G. Scotti, A. Trifiletti, and G. Viviani. Stability criterion for two-port network with input and output terminations varying in elliptic regions; T-MTT Dec 06 4049-4055 Marques, R., see Plaza, G., T-MTT Jan 06 198-209 Marquez-Segura, E., F.P. Casares-Miranda, P. Otero, C. Camacho-Penalosa, and J.E. Page. Analytical model of the wire-bonded interdigital capacitor; T-MTT Feb 06 748-754 Marsh, E.D., see Reid, J.R., T-MTT Aug 06 3433-3442 Marshall, T. S., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Marteau, A., see Decoopman, T., T-MTT Jun 06 1451-1457 Martel, J., see Garcia-Garcia, J., T-MTT Jun 06 2628-2635 Marti, J., see Seeds, A., T-MTT Feb 06 777-779 Marti, J., see Piqueras, M.A., T-MTT Feb 06 887-899 Martin, F., see Bonache, J., T-MTT Jan 06 265-271 Martin, F., see Garcia-Garcia, J., T-MTT Jun 06 2628-2635 Martin, F., see Gil, I., T-MTT Jun 06 2665-2674 Martin, F., see Garcia-Garcia, J., T-MTT Dec 06 4136-4140 Martinez, J.M., see Piqueras, M.A., T-MTT Feb 06 887-899 Martinez-Lopez, A. G., see Martynyuk, A. E., T-MTT Dec 06 4056-4061 Martinez Lopez, J. I., see Martynyuk, A. E., T-MTT Dec 06 4056-4061 Martinez-Lopez, S., see Gomez-Tornero, J.L., T-MTT Sep 06 3534-3542 Martins, J.P., see Carvalho, N.B., T-MTT Jun 06 2659-2664 Martins, J.P., see Pedro, J.C., T-MTT Aug 06 3237-3245 Martins, J. P., P. M. Cabral, N. Borges Carvalho, and J. C. Pedro. A metric for the quantification of memory effects in power amplifiers; T-MTT Dec 06 4432-4439 Martins, R.P., see Si-Weng Fok, T-MTT May 06 2033-2041 Martoglio, L., E. Richalot, G. Lissorgues-Bazin, and O. Picon. Low-cost inverted line in silicon/glass technology for filter in the ka-band; T-MTT Jul 06 3084-3089 Martynyuk, A. E., A. G. Martinez-Lopez, and J. I. Martinez Lopez. 2-bit Xband reflective waveguide phase shifter with BCB-based bias circuits; TMTT Dec 06 4056-4061 Maruhashi, K., see Ito, M., T-MTT Dec 06 4522-4527 Masotti, D., see Rizzoli, V., T-MTT Dec 06 4149-4160 Massa, A., see Franceschini, D., T-MTT Jun 06 1484-1494 Massa, R., see Calabrese, M.L., T-MTT May 06 2256-2264 Masud, M.A., H. Zirath, and M. Kelly. A 45-dB variable-gain low-noise MMIC amplifier; T-MTT Jun 06 2848-2855 Masuda, K., see Niiho, T., T-MTT Feb 06 980-989 Masuda, S., see Kawano, Y., T-MTT Dec 06 4489-4497 Masuda, S., T. Ohki, and T. Hirose. Very compact high-gain broadband lownoise amplifier in InP HEMT technology; T-MTT Dec 06 4565-4571 Mateu, J., see Seron, D., T-MTT Mar 06 1154-1160 Ma Xikui, see Xikui Ma, T-MTT Jul 06 3026-3037 Mazlumi, F., S.H.H. Sadeghi, and R. Moini. Interaction of an open-ended rectangular waveguide probe with an arbitrary-shape surface crack in a lossy conductor; T-MTT Oct 06 3706-3711

IEEE T-MTT 2006 INDEX — 15 McCulloch, M.G., see Mahon, J., T-MTT May 06 2050-2060 McKinney, J.D., and A.M. Weiner. Compensation of the effects of antenna dispersion on UWB waveforms via optical pulse-shaping techniques; TMTT Jun 06 1681-1686 McKinney, J. D., I. S. Lin, and A. M. Weiner. Shaping the power spectrum of ultra-wideband radio-frequency signals; T-MTT Dec 06 4247-4255 Medina, F., see Plaza, G., T-MTT Jan 06 198-209 Mehrany, K., see Eghlidi, M. H., T-MTT Dec 06 4122-4129 Mei-Chao Yeh, Zuo-Min Tsai, Ren-Chieh Liu, K.-Y. Lin, Ying-Tang Chang, and Huei Wang. Design and analysis for a miniature CMOS SPDT switch using body-floating technique to improve power performance; T-MTT Jan 06 31-39 Mei-Chao Yeh, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Mei Sun, see Yue Ping Zhang, T-MTT Oct 06 3779-3785 Melcon, A.A., see Garcia, J.P., T-MTT Jan 06 309-320 Mellberg, A., and J. Stenarson. An evaluation of three simple scalable MIM capacitor models; T-MTT Jan 06 169-172 Melville, R., see Suarez, A., T-MTT Mar 06 1166-1179 Mencarelli, D., see Rozzi, T., T-MTT Feb 06 797-803 Meng Chan Khee, see Rambabu, K., T-MTT Aug 06 3333-3338 Meng Chinchun, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Meng Hock Kai, see Kai Meng Hock, T-MTT Feb 06 648-659 Meng Lim Wei, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Meng Lum Kum, see Kum Meng Lum, T-MTT Jun 06 2880-2886 Meng Miao, and C. Nguyen. On the development of an integrated CMOSbased UWB tunable-pulse transmit module; T-MTT Oct 06 3681-3687 Mengtao Yuan, T.K. Sarkar, and M. Salazar-Palma. A direct discrete complex image method from the closed-form Green's functions in multilayered media; T-MTT Mar 06 1025-1032 Mengtao Yuan, A. De, T.K. Sarkar, Jinhwan Koh, and Baek Ho Jung. Conditions for generation of stable and accurate hybrid TD-FD MoM solutions; T-MTT Jun 06 2552-2563 Meng Wei, see Wei Meng, T-MTT Oct 06 3765-3771 Menzel, W., see Amari, S., T-MTT May 06 2153-2159 Merlet, T., see Blanc, S., T-MTT Jan 06 402-411 Mesa, F., see Rodriguez-Berral, R., T-MTT Dec 06 4100-4110 Metzger, A. G., see Yu Zhao, T-MTT Dec 06 4479-4488 Meyer, G., see Zasowski, T., T-MTT Jun 06 1836-1845 Meyer, P., see Geschke, R.H., T-MTT Oct 06 3698-3705 Mezzanotte, P., see Ocera, A., T-MTT Jun 06 2383-2390 Miao Meng, see Meng Miao, T-MTT Oct 06 3681-3687 Miao Wei, see Ling Jiang, T-MTT Jul 06 2944-2948 Miara, B., see Ouchetto, O., T-MTT Jun 06 2615-2619 Milano, R., see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Milton Feng, see Jie-Wei Lai, T-MTT Feb 06 599-607 Mina, E.F., see Sen, P., T-MTT Jun 06 2604-2614 Minasian, R.A. Photonic signal processing of microwave signals; T-MTT Feb 06 832-846 Minasian, R.A., see Chan, E.H.W., T-MTT Feb 06 873-879 Minasian, Robert.A., see Yi, X., T-MTT Feb 06 880-886 Min Byung-Wook, see Byung-Wook Min, T-MTT Feb 06 710-716 Min Cheol Park, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Min-Chung Wu, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Ming-An Chung, see Yi-Chyun Chiang, T-MTT Nov 06 3947-3953 Ming-Da Tsai, see Pei-Si Wu, T-MTT Jan 06 10-19 Ming-Da Tsai, see To-Po Wang, T-MTT Jan 06 88-95 Ming-Feng Huang, C.J. Kuo, and Shuenn-Yuh Lee. A 5.25-GHz CMOS folded-cascode even-harmonic mixer for low-voltage applications; T-MTT Feb 06 660-669 Ming-Fong Lei, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Ming-Hsiang Cho Author's reply [to comments on "A shield-based three-port de-embedding method for microwave on-wafer characterization of deepsubmicrometer silicon MOSFETs"]; T-MTT Mar 06 1296-1297 Ming-Iu Lai, and Shyh-Kang Jeng. Compact microstrip dual-band bandpass filters design using genetic-algorithm techniques; T-MTT Jan 06 160-168 Ming-Iu Lai, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Ming Qing Xian, see Chu Gao, T-MTT Jun 06 1519-1526 Ming-Ta Yang, see Jun-De Jin, T-MTT Dec 06 4333-4340 Mingxu Liu, J. Craninckx, N.M. Iyer, M. Kuijk, and A.R.F. Barel. A 6.5-kV ESD-protected 3-5-GHz ultra-wideband BiCMOS low-noise amplifier using interstage gain roll-off compensation; T-MTT Jun 06 1698-1706 Ming Zhou, see Huang, F., T-MTT Nov 06 3954-3959 Minh Le, see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Min-Ki Choi, see Hongjoon Kim, T-MTT Dec 06 4178-4184

+ Check author entry for coauthors

Min Ma, and R. Khazaka. Sparse macromodeling for parametric nonlinear networks; T-MTT Dec 06 4305-4315 Min-Sou Wu, see Shau-Gang Mao, T-MTT Sep 06 3543-3549 Mitchell, A., see Winnall, S.T., T-MTT Feb 06 868-872 Mitchell, M., see Morton, M. A., T-MTT Dec 06 4032-4040 Mix, J.A., see Simpson, J.J., T-MTT May 06 1983-1990 Miyamoto, R.Y., see Shiroma, G.S., T-MTT Jan 06 128-134 Mi Yang Xin, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Mohammadi, S., see Lahiji, R.R., T-MTT Jun 06 2699-2706 Mohammadi, S., see Lee, K.-Y., T-MTT Dec 06 4141-4148 Moini, R., see Mazlumi, F., T-MTT Oct 06 3706-3711 Mokhtaari, M., J. Bornemann, K. Rambabu, and S. Amari. Coupling-matrix design of dual and triple passband filters; T-MTT Nov 06 3940-3946 Moldovan, E., R.G. Bosisio, and Ke Wu. W-band multiport substrateintegrated waveguide circuits; T-MTT Feb 06 625-632 Moldovan, E., R. G. Bosisio, and Ke Wu. Authors' reply [to comments on "W-Band multiport substrate-integrated waveguide circuits"]; T-MTT Nov 06 4017 Monari, J., see Peverini, O.A., T-MTT Jan 06 412-420 Monsterleet, A., see Tonda-Goldstein, S., T-MTT Feb 06 847-853 Monti, G., and L. Tarricone. Gaussian pulse expansion of modulated signals in a double-negative slab; T-MTT Jun 06 2755-2761 Monzo-Cabrera, J., see Requena-Perez, M.E., T-MTT Feb 06 615-624 Moon-Soon Choi, see Piqueras, M.A., T-MTT Feb 06 887-899 Moon Sucbei, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Moon-Su Yang, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Morf, T., see Sialm, G., T-MTT Jan 06 65-73 Morgan, J.M., see Williams, D.F., T-MTT Jan 06 481-491 Morin, G.A., see Hettak, K., T-MTT Sep 06 3453-3461 Morini, A., G. Venanzoni, and T. Rozzi. A new adaptive prototype for the design of side-coupled coaxial filters with close correspondence to the physical structure; T-MTT Mar 06 1146-1153 Morini, A., T. Rozzi, M. Farina, and G. Venanzoni. A new look at the practical design of compact diplexers; T-MTT Sep 06 3515-3520 Morton, M. A., J. P. Comeau, J. D. Cressler, M. Mitchell, and J. Papapolymerou. Sources of phase error and design considerations for silicon-based monolithic high-pass/low-pass microwave phase shifters; TMTT Dec 06 4032-4040 Mosallaei, H., see Buell, K., T-MTT Jan 06 135-146 Mosig, J.R., see Stevanovic, I., T-MTT Jan 06 189-197 Mosig, J.R., see Stevanovic, I., T-MTT Oct 06 3688-3697 Movahhedi, M., and A. Abdipour. Efficient numerical methods for simulation of high-frequency active devices; T-MTT Jun 06 2636-2645 Mrozowski, M., see Kozakowski, P., T-MTT Nov 06 3906-3913 Mukhopadhyay, R., see Sen, P., T-MTT Jun 06 2604-2614 Mun-Ho Choi, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Mun-Kyo Lee, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Murakoshi, A., K. Tsukamoto, and S. Komaki. High-performance RF signals transmission in SCM/WDMA radio-on-fiber bus link using optical FM method in presence of optical beat interference; T-MTT Feb 06 967-972 Murphy, E.K., and V.V. Yakovlev. RBF network optimization of complex microwave systems represented by small FDTD modeling data sets; TMTT Jul 06 3069-3083 Musch, T., see Gerding, M., T-MTT Jun 06 2768-2773 Myunghoi Kim, see Junwoo Lee, T-MTT Jun 06 1667-1674 N Nae-Soo Kim, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Nagatsuma, T., see Seeds, A., T-MTT Feb 06 777-779 Nagatsuma, T., see Hirata, A., T-MTT May 06 1937-1944 Nagy, G., see Ma, B. Y., T-MTT Dec 06 4448-4455 Nagy, W., see Kimball, D.F., T-MTT Nov 06 3848-3856 Nakajima, F., see Hirata, A., T-MTT May 06 1937-1944 Nakasha, Y., see Kawano, Y., T-MTT Dec 06 4489-4497 Nakaso, M., see Niiho, T., T-MTT Feb 06 980-989 Nam, I., see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Nam-Jin Oh, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Nam Seungki, see Seungki Nam, T-MTT Jun 06 1315-1324 Nanan, J.-C., see Wood, J., T-MTT Aug 06 3163-3172 Nan Jiang, see Fengyi Huang, T-MTT Jan 06 115-119 Nan Yu, see Rubiola, E., T-MTT Feb 06 816-820 Nardis Luca De, see Cardinali, R., T-MTT Jun 06 1865-1875 Nastos, N., and Y. Papananos. RF operation of MOSFETs under integrated inductors; T-MTT May 06 2106-2117

IEEE T-MTT 2006 INDEX — 16 Navarrini, A., and R.L. Plambeck. A turnstile junction waveguide orthomode transducer; T-MTT Jan 06 272-277 Ndagijimana, F., see Williams, D.F., T-MTT Mar 06 1210-1217 Nebus, J.-M., see Macraigne, F., T-MTT Aug 06 3219-3226 Nedil, M., T.A. Denidni, and L. Talbi. Novel butler matrix using CPW multilayer technology; T-MTT Jan 06 499-507 Negra, R., and W. Bachtold. Lumped-element load-network design for classE power amplifiers; T-MTT Jun 06 2684-2690 Neri, A., see Rizzoli, V., T-MTT Dec 06 4149-4160 Neveux, G., see Macraigne, F., T-MTT Aug 06 3219-3226 NGoya, E., see Macraigne, F., T-MTT Aug 06 3219-3226 Nguyen, C., see Jeongwoo Han, T-MTT Jan 06 285-293 Nguyen, C., see Rui Xu, T-MTT Aug 06 3271-3277 Nguyen, C., see Xin Guan, T-MTT Aug 06 3278-3283 Nguyen, C., see Meng Miao, T-MTT Oct 06 3681-3687 Nguyen, C., see Chirala, M. K., T-MTT Dec 06 4218-4224 Nguyen, L.V.T., see Hunter, D.B., T-MTT Feb 06 900-905 Nguyen Trung-Kien, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Nguyen Trung-Kien, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Nguyen Trung-Kien, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Nichols, C., see Vanhille, K.J., T-MTT Jun 06 2439-2446 Nicholson, J.J., see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Nick, M., A. Banai, and F. Farzaneh. Phase-noise measurement using two inter-injection-locked microwave oscillators; T-MTT Jul 06 2993-3000 Niiho, T., M. Nakaso, K. Masuda, H. Sasai, K. Utsumi, and M. Fuse. Transmission performance of multichannel wireless LAN system based on radio-over-fiber techniques; T-MTT Feb 06 980-989 Nikolova, N.K., Jiang Zhu, Dongying Li, M.H. Bakr, and J.W. Bandler. Sensitivity analysis of network parameters with electromagnetic frequency-domain simulators; T-MTT Feb 06 670-681 Nikolova, N.K., see Kouzaev, G.A., T-MTT Mar 06 1033-1042 Nikolova, N.K., Ying Li, Yan Li, and M.H. Bakr. Sensitivity analysis of scattering parameters with electromagnetic time-domain simulators; TMTT Jun 06 1598-1610 Nilsson, J., see Sudow, M., T-MTT Dec 06 4072-4078 Nilsson, P.A., see Sudow, M., T-MTT Dec 06 4072-4078 Ning Chen Zhi, see Chu Gao, T-MTT Jun 06 1519-1526 Ning Chen Zhi, see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Ning Hua Zhu, see Silvonen, K., T-MTT Jun 06 1464-1469 Ning Li, see Ling Jiang, T-MTT Jul 06 2944-2948 Ning Yang, see Chu Gao, T-MTT Jun 06 1519-1526 Nirmalathas, A., see Kurniawan, T., T-MTT Feb 06 921-928 Nirmalathas, A., see Lim, C., T-MTT May 06 2181-2187 Nishi, S., see Sung Tae Choi, T-MTT May 06 1953-1960 Nishikawa, K., K. Shintani, and S. Yamakawa. Characteristics of transmission lines fabricated by CMOS process with deep n-well implantation; T-MTT Feb 06 589-598 Nishikawa, T., see Tsuji, M., T-MTT Jul 06 2962-2969 Nitsch, J.B., see Adalev, A.S., T-MTT Jul 06 3131-3140 Nkansah, A., see Das, A., T-MTT Aug 06 3426-3432 Noori, B.H., see Wood, J., T-MTT Aug 06 3163-3172 Notake, T., see Idei, H., T-MTT Nov 06 3899-3905 Novak, D., see Kurniawan, T., T-MTT Feb 06 921-928 Novak, D., see Lim, C., T-MTT May 06 2181-2187 O O, K.K., see Seong-Mo Yim, T-MTT Jan 06 74-81 O, K.K., see Verma, A., T-MTT Aug 06 3295-3300 O'Callaghan, J.M., see Seron, D., T-MTT Mar 06 1154-1160 Ocera, A., R. Sorrentino, and P. Mezzanotte. Design of tunable phase shifters by the image-parameters method; T-MTT Jun 06 2383-2390 Ocera, A., M. Dionigi, E. Fratticcioli, and R. Sorrentino. A novel technique for complex permittivity measurement based on a planar four-port device; T-MTT Jun 06 2568-2575 Odate, Y., see Inoue, R., T-MTT Feb 06 522-532 Ogawa, H., see Shoji, Y., T-MTT Oct 06 3664-3674 Oh Jung-Hun, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Ohki, T., see Masuda, S., T-MTT Dec 06 4565-4571 Oh Kyoung-Hwan, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Oh Nam-Jin, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Ohno, K., and T. Ikegami. Interference mitigation study for UWB radio using template waveform processing; T-MTT Jun 06 1782-1792 Oishi, Y., see Kawano, Y., T-MTT Dec 06 4489-4497 Oleson, C., see Fung, A., T-MTT Dec 06 4507-4512 + Check author entry for coauthors

Olivieri, A., see Peverini, O.A., T-MTT Jan 06 412-420 Olivieri, A., see Peverini, O.A., T-MTT May 06 2042-2049 Omar, A.S., see Aly, O.A.M., T-MTT Jan 06 492-498 Omrane, B., J.-J. Laurin, and Y. Goussard. Subwavelength-resolution microwave tomography using wire grid models and enhanced regularization techniques; T-MTT Jun 06 1438-1450 Onal, T., M.I. Aksun, and N. Kinayman. An efficient full-wave simulation algorithm for multiple vertical conductors in printed circuits; T-MTT Oct 06 3739-3745 Ong Ling Chuen, see Yong-Xin Guo, T-MTT Mar 06 1196-1200 Ooi, B.-L., see Jayabalan, J., T-MTT Jun 06 1331-1339 Ooi, B.-L., and Ying Wang. Novel miniaturized open-square-loop resonator with inner split rings loading; T-MTT Jul 06 3098-3103 Oppermann, I., see Knochel, R.H., T-MTT Apr 06 1633-1636 Oppermann, I., see Stoica, L., T-MTT Jun 06 1637-1646 Oraizi, H., and A.-R. Sharifi. Design and optimization of broadband asymmetrical multisection wilkinson power divider; T-MTT May 06 22202231 Orlik, P.V., see Guvenc, I., T-MTT Jun 06 1876-1886 Orta, R., see Peverini, O.A., T-MTT Jan 06 412-420 Orta, R., see Peverini, O.A., T-MTT May 06 2042-2049 Osorio, J.A., see Lopez-Villegas, J.M., T-MTT Jan 06 226-234 Otegi, N., see Girbau, D., T-MTT Mar 06 1120-1130 Otero, P., see Marquez-Segura, E., T-MTT Feb 06 748-754 Ouchetto, O., S. Zouhdi, A. Bossavit, G. Griso, and B. Miara. Modeling of 3D periodic multiphase composites by homogenization; T-MTT Jun 06 2615-2619 Ouchetto, O., Cheng-Wei Qiu, S. Zouhdi, Le-Wei Li, and A. Razek. Homogenization of 3-D periodic bianisotropic metamaterials; T-MTT Nov 06 3893-3898 P Padmanabhan, S., L. Dunleavy, J.E. Daniel, A. Rodriguez, and P.L. Kirby. Broadband space conservative on-wafer network analyzer calibrations with more complex load and thru models; T-MTT Sep 06 3583-3593 Page, J.E., see Marquez-Segura, E., T-MTT Feb 06 748-754 Pagnoulle, C., see Saib, A., T-MTT Jun 06 2745-2754 Pal, S., C.J. Stevens, and D.J. Edwards. Compact parallel coupled HTS microstrip bandpass filters for wireless communications; T-MTT Feb 06 768-775 Palmisano, G., see Biondi, T., T-MTT May 06 2203-2210 Panaretos, A. H., J. T. Aberle, and R. E. Diaz. A three-dimensional finitedifference time-domain scheme based on a transversely extended-curl operator; T-MTT Dec 06 4237-4246 Pao Cheng-Ken, see Kaihui Lin, T-MTT Dec 06 4041-4048 Papananos, Y., see Nastos, N., T-MTT May 06 2106-2117 Papapolymerou, J., see Kingsley, N., T-MTT Mar 06 1229-1236 Papapolymerou, J., see Kongpop U-yen, T-MTT Mar 06 1237-1244 Papapolymerou, J., see Morton, M. A., T-MTT Dec 06 4032-4040 Parillaud, O., see Piqueras, M.A., T-MTT Feb 06 887-899 Parini, C., see Yan Zhao, T-MTT Jun 06 1827-1835 Park Byeong-Ha, see Woonyun Kim, T-MTT May 06 2098-2105 Park Chang-Soo, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Park Dong Seok, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Parker, A.E., see Blockley, P.S., T-MTT Aug 06 3182-3190 Parker, M.E., see Hunter, D.B., T-MTT Feb 06 861-867 Park Jinsung, see Jinsung Park, T-MTT Dec 06 4372-4380 Park Jung-Dong, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Park Jung Dong, see Jung Dong Park, T-MTT Oct 06 3623-3629 Park Min Cheol, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Park Sang-June, see Sang-June Park, T-MTT Nov 06 3931-3939 Park Sang Soo, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Park Young-Jin, see Junwoo Lee, T-MTT Jun 06 1667-1674 Park Yunseo, see Yunseo Park, T-MTT Jun 06 1687-1697 Pathak, N.P., A. Basu, and S.K. Koul. Full-wave nonlinear analysis of nonradiative dielectric guide circuits including lumped elements; T-MTT Jan 06 173-179 Patrovsky, A., and Ke Wu. Substrate integrated image guide (SIIG)-a planar dielectric waveguide technology for millimeter-wave applications; T-MTT Jun 06 2872-2879 Paulotto, S., see Baccarelli, P., T-MTT Jun 06 1350-1362 Pavageau, C., see Si Moussa, M., T-MTT Jun 06 2675-2683 Pedro, J.C., see Carvalho, N.B., T-MTT Feb 06 572-579 Pedro, J.C., see Carvalho, N.B., T-MTT Jun 06 2659-2664

IEEE T-MTT 2006 INDEX — 17 Pedro, J.C., and J.P. Martins. Amplitude and phase characterization of nonlinear mixing products; T-MTT Aug 06 3237-3245 Pedro, J. C., see Anding Zhu, T-MTT Dec 06 4323-4332 Pedro, J. C., see Martins, J. P., T-MTT Dec 06 4432-4439 Pedro Cheong, see Si-Weng Fok, T-MTT May 06 2033-2041 Pei-Si Wu, Hong-Yeh Chang, Ming-Da Tsai, Tian-Wei Huang, and Huei Wang. New miniature 15-20-GHz continuous-phase/amplitude control MMICs using 0.18-ȝm CMOS technology; T-MTT Jan 06 10-19 Pei-Si Wu, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Pei-Si Wu, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Pelk, M. J., see Spirito, M., T-MTT Dec 06 4225-4236 Penaranda-Foix, F.L., see Canos, A.J., T-MTT Aug 06 3407-3416 Peng Jen-Ti, see Shry-Sann Liao, T-MTT Sep 06 3508-3514 Peng Liu Ruo, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Peng Yu Xiao, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Pereda, J.A., see Gonzalez, O., T-MTT Jul 06 3045-3051 Pereira, F.Q., see Garcia, J.P., T-MTT Jan 06 309-320 Peroni, M., see Colantonio, P., T-MTT Jun 06 2713-2722 Perregrini, L., see Bozzi, M., T-MTT Jan 06 339-347 Perret, E., H. Aubert, and H. Legay. Scale-changing technique for the electromagnetic modeling of MEMS-controlled planar phase shifters; TMTT Sep 06 3594-3601 Perruisseau-Carrier, J., R. Fritschi, P. Crespo-Valero, and A.K. Skrivervik. Modeling of periodic distributed MEMS-application to the design of variable true-time delay lines; T-MTT Jan 06 383-392 Perruisseau-Carrier, J., and A.K. Skrivervik. Composite right/left-handed transmission line metamaterial phase shifters (MPS) in MMIC technology; T-MTT Jun 06 1582-1589 Person, C., see Manchec, A., T-MTT Jun 06 2346-2355 Petraglia, G., see Calabrese, M.L., T-MTT May 06 2256-2264 Peverini, O.A., R. Tascone, E. Carretti, G. Virone, A. Olivieri, R. Orta, S. Cortiglioni, and J. Monari. On-board calibration system for millimeterwave radiometers based on reference-polarized signal injection; T-MTT Jan 06 412-420 Peverini, O.A., R. Tascone, G. Virone, A. Olivieri, and R. Orta. Orthomode transducer for millimeter-wave correlation receivers; T-MTT May 06 2042-2049 Pfeiffer, U.R., and A. Valdes-Garcia. Millimeter-wave design considerations for power amplifiers in an SiGe process technology; T-MTT Jan 06 57-64 Pfeiffer, U.R., see Zwick, T., T-MTT Mar 06 1001-1010 Pfeiffer, U.R., J. Grzyb, Duixian Liu, B. Gaucher, T. Beukema, B.A. Floyd, and S.K. Reynolds. A chip-scale packaging technology for 60-GHz wireless chipsets; T-MTT Aug 06 3387-3397 Pham, A.-V.H., see Chao Lu, T-MTT Jan 06 40-45 Pham, A.-V.H., see Chen, M.J., T-MTT Nov 06 4009-4015 Phillips, M.D., and R.K. Settaluri. A novel toroidal inductor structure with through-hole vias in ground plane; T-MTT Jun 06 1325-1330 Phromloungsri, R., M. Chongcheawchamnan, and I.D. Robertson. Inductively compensated parallel coupled microstrip lines and their applications; T-MTT Sep 06 3571-3582 Picon, O., see Aissat, H., T-MTT Jun 06 2856-2863 Picon, O., see Martoglio, L., T-MTT Jul 06 3084-3089 Pierrot, J.-B., see Denis, B., T-MTT Jun 06 1896-1911 Piew-Yong Chee, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Piloto, A.J., see Yunchi Zhang, T-MTT Aug 06 3370-3377 Pinel, S., see Sarkar, S., T-MTT Mar 06 1245-1252 Pinel, S., see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 Pinel, S., see Ki Seok Yang, T-MTT Dec 06 4572-4579 Ping Zhang Yue, see Yue Ping Zhang, T-MTT Oct 06 3779-3785 Pintelon, R., see Rolain, Y., T-MTT Aug 06 3209-3218 Piosczyk, B., see Jianbo Jin, T-MTT Mar 06 1139-1145 Piqueras, M.A., G. Grosskopf, B. Vidal, J. Herrera, J.M. Martinez, P. Sanchis, V. Polo, Juan.L. Corral, A. Marceaux, J. Galiere, J. Lopez, A. Enard, J.-L. Valard, O. Parillaud, E. Estebe, N. Vodjdani, Moon-Soon Choi, J.H. den Besten, F.M. Soares, M.K. Smit, and J. Marti. Optically beamformed beam-switched adaptive antennas for fixed and mobile broad-band wireless access networks; T-MTT Feb 06 887-899 Pirola, M., see Ferrero, A., T-MTT Jan 06 458-463 Pistono, E., see Kaddour, D., T-MTT Jun 06 2367-2375 Pistono, E., M. Robert, L. Duvillaret, J.-M. Duchamp, A. Vilcot, and P. Ferrari. Compact fixed and tune-all bandpass filters based on coupled slow-wave resonators; T-MTT Jun 06 2790-2799 Pla, J.A., see Aaen, P.H., T-MTT Jul 06 3052-3059 Plambeck, R.L., see Navarrini, A., T-MTT Jan 06 272-277

+ Check author entry for coauthors

Plaza, G., R. Marques, and F. Medina. Quasi-TM MoL/MoM approach for computing the transmission-line parameters of lossy lines; T-MTT Jan 06 198-209 Podevin, F., see Safwat, A.M.E., T-MTT Sep 06 3559-3564 Po-Feng Yeh, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Pollard, R.D., see Guyette, A.C., T-MTT Nov 06 3914-3922 Polo, V., see Piqueras, M.A., T-MTT Feb 06 887-899 Popovic, Z., see Lukic, M., T-MTT May 06 2068-2076 Popovic, Z., see Vanhille, K.J., T-MTT Jun 06 2439-2446 Popp, J. D., see Feipeg Wang, T-MTT Dec 06 4086-4099 Pradell, L., see Girbau, D., T-MTT Mar 06 1120-1130 Pranger, H.J., see Tiemeijer, L.F., T-MTT Aug 06 3378-3386 Pratap, R.J., see Sen, P., T-MTT Jun 06 2604-2614 Pribetich, J., see Cresson, P.-Y., T-MTT Jan 06 302-308 Prince, J.L., see Cox, C.H., III, T-MTT Feb 06 906-920 Proietti, C., see Colantonio, P., T-MTT Jun 06 2713-2722 Pu-Hua Deng, Yo-Shen Lin, Chi-Hsueh Wang, and Chun Hsiung Chen. Compact microstrip bandpass filters with good selectivity and stopband rejection; T-MTT Feb 06 533-539 Pu-Hua Deng, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Pu-Hua Deng, Chi-Hsueh Wang, and Chun Hsiung Chen. Novel broadsidecoupled bandpass filters using both microstrip and coplanar-waveguide resonators; T-MTT Oct 06 3746-3750 Pu-Hua Deng, Ming-Iu Lai, Shyh-Kang Jeng, and Chun Hsiung Chen. Design of matching circuits for microstrip triplexers based on stepped impedance resonators; T-MTT Dec 06 4185-4192 Pyo Cheol-Sig, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Pyo Cheol-Sig, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Q Qiang Cheng, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Qi Jun Yao, see Ling Jiang, T-MTT Jul 06 2944-2948 Qi-Jun Zhang, see Yi Cao, T-MTT Jun 06 2398-2409 Qi Lin Xian, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Qing Huo Liu, see Simsek, E., T-MTT Jan 06 216-225 Qing Huo Liu, see Simsek, E., T-MTT Nov 06 3878-3884 Qing Sun, see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Qing-Xiang Li, and O.P. Gandhi. Thermal implications of the new relaxed IEEE RF safety standard for head exposures to cellular telephones at 835 and 1900 MHz; T-MTT Jul 06 3146-3154 Qing Xian Ming, see Chu Gao, T-MTT Jun 06 1519-1526 Qing Xianming, see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Qin Shen, and N.S. Barker. Distributed MEMS tunable matching network using minimal-contact RF-MEMS varactors; T-MTT Jun 06 2646-2658 Qin Yi, see Yi Qin, T-MTT Jun 06 2723-2732 Qin Yin, see Yin Qin, T-MTT Jul 06 2910-2916 Qiu, J.X., see Safier, P.N., T-MTT Oct 06 3605-3615 Qiu Cheng-Wei, see Ouchetto, O., T-MTT Nov 06 3893-3898 Quan Xue, see Yum, T.Y., T-MTT Aug 06 3255-3266 Queffelec, P., see Mallegol, S., T-MTT Mar 06 1065-1075 Queguiner, M., see Blanc, S., T-MTT Jan 06 402-411 Quendo, C., see Manchec, A., T-MTT Jun 06 2346-2355 Quere, R., and J.L. Cazaux. Guest editorial [35th European Microwave Conference special issue intro.]; T-MTT Jun 06 2567 Qunsheng Cao, R. Kanapady, and F. Reitich. High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics; T-MTT Aug 06 3316-3326 R Rabbachin, A., see Stoica, L., T-MTT Jun 06 1637-1646 Raffo, A., see Santarelli, A., T-MTT Dec 06 4021-4031 Ragonese, E., see Biondi, T., T-MTT May 06 2203-2210 Rahal, A.H., see Kouzaev, G.A., T-MTT Mar 06 1033-1042 Raisanen, A.V., see Lonnqvist, A., T-MTT Jun 06 2391-2397 Raisanen, A.V., see Lonnqvist, A., T-MTT Sep 06 3486-3491 Ramadan, O. Unconditionally stable Crank-Nicolson nearly PML algorithm for truncating linear Lorentz dispersive FDTD domains; T-MTT Jun 06 2807-2812 Rambabu, K., M.Y.-W. Chia, Khee Meng Chan, and J. Bornemann. Design of multiple-stopband filters for interference suppression in UWB applications; T-MTT Aug 06 3333-3338 Rambabu, K., see Tan, A.E.-C., T-MTT Nov 06 3821-3827 Rambabu, K., see Mokhtaari, M., T-MTT Nov 06 3940-3946

IEEE T-MTT 2006 INDEX — 18 Randa, J., E. Gerecht, Dazhen Gu, and R.L. Billinger. Precision measurement method for cryogenic amplifier noise temperatures below 5 K; T-MTT Mar 06 1180-1189 Ranjan, M., and L. E. Larson. Distortion analysis of ultra-wideband OFDM receiver front-ends; T-MTT Dec 06 4422-4431 Rappaport, C.M., see Kosmas, P., T-MTT Jun 06 1921-1927 Rashidian, B., see Eghlidi, M. H., T-MTT Dec 06 4122-4129 Raskin, J.-P., see Si Moussa, M., T-MTT Jun 06 2675-2683 Rauscher, C., and S.W. Kirchoefer. Miniature ridge-waveguide filter module employing moldable dielectric material; T-MTT Mar 06 1190-1195 Rayas-Sanchez, J. E., and V. Gutierrez-Ayala. EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping; T-MTT Dec 06 4528-4537 Razek, A., see Ouchetto, O., T-MTT Nov 06 3893-3898 Rebeiz, G.M., see Byung-Wook Min, T-MTT Feb 06 710-716 Rebeiz, G.M., see Sang-June Park, T-MTT Nov 06 3931-3939 Rebenaque, D.C., see Garcia, J.P., T-MTT Jan 06 309-320 Reid, J.R., E.D. Marsh, and R.T. Webster. Micromachined rectangularcoaxial transmission lines; T-MTT Aug 06 3433-3442 Reina-Tosina, J., see Crespo-Cadenas, C., T-MTT Jan 06 321-328 Reina-Tosina, J., see Crespo-Cadenas, C., T-MTT Jan 06 445-450 Reindl, L.M., see Villanueva, G.L., T-MTT Jun 06 1415-1424 Reitich, F., see Qunsheng Cao, T-MTT Aug 06 3316-3326 Remley, K.A., see Williams, D.F., T-MTT Mar 06 1210-1217 Remley, K.A., see Borges Carvalho, N., T-MTT Aug 06 3161-3162 Ren-Chieh Liu, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Ren-Chieh Liu, see To-Po Wang, T-MTT Jan 06 88-95 Renfors, M., see Valkama, M., T-MTT Jun 06 2356-2366 Ren Yu-Jiun, see Yu-Jiun Ren, T-MTT Jun 06 1495-1502 Ren Yu-Jiun, see Yu-Jiun Ren, T-MTT Jul 06 2970-2976 Represa, J., see Cabeceira, A.C.L., T-MTT Jun 06 2780-2789 Requena-Perez, M.E., A. Albero-Ortiz, J. Monzo-Cabrera, and A. DiazMorcillo. Combined use of genetic algorithms and gradient descent optmization methods for accurate inverse permittivity measurement; TMTT Feb 06 615-624 Reveyrand, T., see Macraigne, F., T-MTT Aug 06 3219-3226 Reyes-Davo, Edl., see Canos, A.J., T-MTT Aug 06 3407-3416 Reynolds, S.K., see Pfeiffer, U.R., T-MTT Aug 06 3387-3397 Rezazadeh, A.A., see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Rhee Jin-Koo, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Ricard, C., see Cresson, P.-Y., T-MTT Jan 06 302-308 Richalot, E., see Martoglio, L., T-MTT Jul 06 3084-3089 Ricketts, D.S., Xiaofeng Li, and D. Ham. Electrical soliton oscillator; T-MTT Jan 06 373-382 Rigaudeau, L., P. Ferrand, D. Baillargeat, S. Bila, S. Verdeyme, M. Lahti, and T. Jaakola. LTCC 3-D resonators applied to the design of very compact filters for Q-band applications; T-MTT Jun 06 2620-2627 Ristolainen, E.O., see Kaija, T., T-MTT Jan 06 82-87 Ritter, R. G., see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Rius Eric, see Manchec, A., T-MTT Jun 06 2346-2355 Rizzoli, V., A. Costanzo, D. Masotti, P. Spadoni, and A. Neri. Prediction of the end-to-end performance of a microwave/RF link by means of nonlinear/electromagnetic co-simulation; T-MTT Dec 06 4149-4160 Robert, M., see Pistono, E., T-MTT Jun 06 2790-2799 Robertson, I.D., see Phromloungsri, R., T-MTT Sep 06 3571-3582 Rodin, Y., see Bogdashov, A., T-MTT Dec 06 4130-4135 Rodriguez, A., see Padmanabhan, S., T-MTT Sep 06 3583-3593 Rodriguez, R., see Mallet, A., T-MTT Dec 06 4353-4361 Rodriguez-Berral, R., F. Mesa, and D. R. Jackson. A high-frequency circuit model for the gap excitation of a microstrip line; T-MTT Dec 06 41004110 Rodriguez-Morales, F., K.S. Yngvesson, R. Zannoni, E. Gerecht, Dazhen Gu, Xin Zhao, N. Wadefalk, and J.J. Nicholson. Development of integrated HEB/MMIC receivers for near-range terahertz imaging; T-MTT Jun 06 2301-2311 Rogge, M.S., see Urick, V.J., T-MTT Jun 06 1458-1463 Rogge, M.S., see Urick, V.J., T-MTT Jul 06 3141-3145 Rogla, L.J., see Carbonell, J., T-MTT Jun 06 1527-1533 Rolain, Y., W. Van Moer, R. Pintelon, and J. Schoukens. Experimental characterization of the nonlinear behavior of RF amplifiers; T-MTT Aug 06 3209-3218 Romanini, P., see Colantonio, P., T-MTT Jun 06 2713-2722 Romme, J., and K. Witrisal. Transmitted-reference UWB systems using weighted autocorrelation receivers; T-MTT Jun 06 1754-1761 Rondineau, B., see Lukic, M., T-MTT May 06 2068-2076 + Check author entry for coauthors

Rondineau, S., see Fuchs, B., T-MTT Jun 06 2292-2300 Rong Jiang, Yi-Hao Chang, and C.C.-P. Chen. ICCAP-a linear time sparsification and reordering algorithm for 3-D BEM capacitance extraction; T-MTT Jul 06 3060-3068 Ronnow, D., see Isaksson, M., T-MTT Jan 06 348-359 Root, D.E., see Borges Carvalho, N., T-MTT Aug 06 3161-3162 Rorsman, N., see Sudow, M., T-MTT Dec 06 4072-4078 Rosenberg, U., see Amari, S., T-MTT Jan 06 428-436 Roste, T., see Safari, N., T-MTT Jun 06 2813-2820 Roy, L., see Brzezina, G., T-MTT Jun 06 2830-2839 Roy, S.M., see Karmakar, N.C., T-MTT May 06 2160-2168 Rozental, R.M., N.S. Ginzburg, M.Y. Glyavin, and A.S. Sergeev. Novel source of the chaotic microwave radiation based on the gyro-backwardwave oscillator; T-MTT Jun 06 2741-2744 Rozzi, T., see Di Donato, A., T-MTT Feb 06 724-734 Rozzi, T., and D. Mencarelli. Application of algebraic invariants to full-wave simulators - rigorous analysis of the optical properties of nanowires; TMTT Feb 06 797-803 Rozzi, T., see Morini, A., T-MTT Mar 06 1146-1153 Rozzi, T., see Morini, A., T-MTT Sep 06 3515-3520 Rubiola, E., E. Salik, Nan Yu, and L. Maleki. Flicker noise in high-speed p-in photodiodes; T-MTT Feb 06 816-820 Rud, L.A., see Kirilenko, A.A., T-MTT Jun 06 2471-2477 Rudnicki, J., see Karnfelt, C., T-MTT Aug 06 3417-3425 Rudolph, M., F. Lenk, O. Llopis, and W. Heinrich. On the simulation of lowfrequency noise upconversion in InGaP/GaAs HBTs; T-MTT Jul 06 29542961 Ruehli, A.E., see Gope, D., T-MTT Jun 06 2453-2464 Ruengwaree, A., A. Ghose, and G. Kompa. A novel UWB rugby-ball antenna for near-range microwave Radar system; T-MTT Jun 06 2774-2779 Ruey-Beei Wu, see Chi-Feng Chen, T-MTT Feb 06 755-762 Ruey-Beei Wu, see Chi-Feng Chen, T-MTT May 06 1945-1952 Ruey-Beei Wu, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Ruey-Beei Wu, see Ting-Yi Huang, T-MTT Jul 06 3038-3044 Ruey-Beei Wu, see Chi-Feng Chen, T-MTT Sep 06 3550-3558 Ruey-Beei Wu, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Rui-Jie Mao, and Xiao-Hong Tang. Novel dual-mode bandpass filters using hexagonal loop resonators; T-MTT Sep 06 3526-3533 Rui Xu, Y. Jin, and C. Nguyen. Power-efficient switching-based CMOS UWB transmitters for UWB communications and Radar systems; T-MTT Aug 06 3271-3277 Runtao Ding, see Yi Cao, T-MTT Jun 06 2398-2409 Runton, D., see Wood, J., T-MTT Aug 06 3163-3172 Ruo Peng Liu, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Russat, J., see Si Moussa, M., T-MTT Jun 06 2675-2683 Russer, P., see Lukashevich, D., T-MTT Oct 06 3712-3720 Russer, P., see Khlifi, R., T-MTT Dec 06 4440-4447 Rutledge, D.B., see Sanggeun Jeon, T-MTT Mar 06 1096-1106 Rutledge, D.B., see Sanggeun Jeon, T-MTT Oct 06 3630-3640 Ryu Seonghan, see Huijung Kim, T-MTT Jul 06 2917-2924 Rzesnicki, T., see Jianbo Jin, T-MTT Mar 06 1139-1145 S Sabbagh, M.A.E., M.H. Bakr, and J.W. Bandler. Adjoint higher order sensitivities for fast full-wave optimization of microwave filters; T-MTT Aug 06 3339-3351 Sachse, K., see Gruszczynski, S., T-MTT Sep 06 3501-3507 Sachse, K., see Gruszczynski, S., T-MTT Nov 06 3986-3994 Sadeghi, S.H.H., see Mazlumi, F., T-MTT Oct 06 3706-3711 Sadler, B.M., see Hoyos, S., T-MTT Jun 06 1745-1753 Safari, N., J.P. Tanem, and T. Roste. A block-based predistortion for high power-amplifier linearization; T-MTT Jun 06 2813-2820 Safier, P.N., V. Dronov, T.M. Antonsen, Jr., J.X. Qiu, B.G. Danly, and B. Levush. From frequency-domain physics-based simulation to time-domain modeling of traveling-wave tube amplifiers for high data-rate communication applications; T-MTT Oct 06 3605-3615 Safwat, A.M.E., F. Podevin, P. Ferrari, and A. Vilcot. Tunable bandstop defected ground structure resonator using reconfigurable dumbbell-shaped coplanar waveguide; T-MTT Sep 06 3559-3564 Sahinoglu, Z., see Guvenc, I., T-MTT Jun 06 1876-1886 Saib, A., L. Bednarz, R. Daussin, C. Bailly, Xudong Lou, J.-M. Thomassin, C. Pagnoulle, C. Detrembleur, R. Jerome, and I. Huynen. Carbon nanotube composites for broadband microwave absorbing materials; T-MTT Jun 06 2745-2754

IEEE T-MTT 2006 INDEX — 19 Saito, K., A. Hiroe, S. Kikuchi, M. Takahashi, and K. Ito. Estimation of heating performances of a coaxial-slot antenna with endoscope for treatment of bile duct carcinoma; T-MTT Aug 06 3443-3449 Salazar-Palma, M., see Mengtao Yuan, T-MTT Mar 06 1025-1032 Salik, E., see Rubiola, E., T-MTT Feb 06 816-820 Samaras, T., see Christ, A., T-MTT May 06 2188-2195 Sambell, A., see Yi Qin, T-MTT Jun 06 2723-2732 Sambell, A., see Yin Qin, T-MTT Jul 06 2910-2916 Sam Ha Dong, see August, N.J., T-MTT Jul 06 3001-3012 Samitier, J., see Lopez-Villegas, J.M., T-MTT Jan 06 226-234 Samoska, L., see Fung, A., T-MTT Dec 06 4507-4512 Sanada, Y., see Takeuchi, Y., T-MTT Jun 06 1858-1864 Sanchez-Sinencio, E., see Ganesan, S., T-MTT Dec 06 4079-4085 Sanchis, P., see Piqueras, M.A., T-MTT Feb 06 887-899 Sang-Chul Sul, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Sanggeun Jeon, A. Suarez, and D.B. Rutledge. Analysis and elimination of hysteresis and noisy precursors in power amplifiers; T-MTT Mar 06 10961106 Sanggeun Jeon, A. Suarez, and D.B. Rutledge. Nonlinear design technique for high-power switching-mode oscillators; T-MTT Oct 06 3630-3640 Sang-Gug Lee, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Sang-Gug Lee, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Sang Gug Lee, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Sanghoon Shin, see Levy, R., T-MTT Jun 06 2503-2515 Sang-June Park, Kok-Yan Lee, and G.M. Rebeiz. Low-loss 5.15-5.70-GHz RF MEMS switchable filter for wireless LAN applications; T-MTT Nov 06 3931-3939 Sang Soo Park, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Sang-Yong Yi, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Sankaran, K., C. Fumeaux, and R. Vahldieck. Cell-centered finite-volumebased perfectly matched Layer for time-domain Maxwell system; T-MTT Mar 06 1269-1276 Sankaran, K., C. Fumeaux, and R. Vahldieck. Uniaxial and radial anisotropy models for finite-volume Maxwellian absorber; T-MTT Dec 06 4297-4304 Santarelli, A., V. Di Giacomo, A. Raffo, P. A. Traverso, G. Vannini, and F. Filicori. A nonquasi-static empirical model of electron devices; T-MTT Dec 06 4021-4031 Sarabandi, K., see Buell, K., T-MTT Jan 06 135-146 Sarabandi, K., see Aryanfar, F., T-MTT Mar 06 1161-1165 Sarkar, S., D.A. Yeh, S. Pinel, and J. Laskar. 60-GHz direct-conversion gigabit modulator/demodulator on liquid-crystal polymer; T-MTT Mar 06 1245-1252 Sarkar, S., see Sen, P., T-MTT Jun 06 2604-2614 Sarkar, T.K., see Mengtao Yuan, T-MTT Mar 06 1025-1032 Sarkar, T.K., see Mengtao Yuan, T-MTT Jun 06 2552-2563 Sarris, C.D., see Yaxun Liu, T-MTT Feb 06 689-703 Sarris, C.D., see Kokkinos, T., T-MTT Jun 06 1619-1630 Sasai, H., see Niiho, T., T-MTT Feb 06 980-989 Sassi, Z., see Darfeuille, S., T-MTT Dec 06 4381-4396 Sato, Y., see Hirata, A., T-MTT May 06 1937-1944 Satoh, H., N. Yoshida, S. Kitayama, and S. Konaka. Analysis of 2-D frequency converter utilizing compound nonlinear photonic-crystal structure by condensed node spatial network method; T-MTT Jan 06 210215 Sauleau, R., see Zhadobov, M., T-MTT Jun 06 2534-2542 Scheiblhofer, S., S. Schuster, and A. Stelzer. Signal model and linearization for nonlinear chirps in FMCW Radar SAW-ID tag request; T-MTT Jun 06 1477-1483 Schiek, B., see Gerding, M., T-MTT Jun 06 2768-2773 Schmuckles, F.J., see Zscheile, H., T-MTT May 06 2000-2010 Schneider, T., see Junker, M., T-MTT Jun 06 1576-1581 Schoukens, J., see Rolain, Y., T-MTT Aug 06 3209-3218 Schreurs, D.M.M.-P., see Crupi, G., T-MTT Oct 06 3616-3622 Schumacher, H., see Kallfass, I., T-MTT Jun 06 2312-2320 Schuster, S., see Scheiblhofer, S., T-MTT Jun 06 1477-1483 Schwarzbacher, A.T., see Junker, M., T-MTT Jun 06 1576-1581 Schwindt, R.S., see Guang Chen, T-MTT Jul 06 2949-2953 Schworer, C., see Campos-Roca, Y., T-MTT Jul 06 2983-2992 Scott, J.B., see Blockley, P.S., T-MTT Aug 06 3182-3190 Scotti, G., see Marietti, P., T-MTT Dec 06 4049-4055 Scuderi, A., see Biondi, T., T-MTT May 06 2203-2210 See, T.S.P., see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Seeds, A., P.W. Juodawlkis, J. Marti, and T. Nagatsuma. Guest editorial [intro. to the special issue on microwave photonics]; T-MTT Feb 06 777779 + Check author entry for coauthors

Seelmann-Eggebert, M., see Campos-Roca, Y., T-MTT Jul 06 2983-2992 Se-Ho You, and E.F. Kuester. Fast and direct coupled-micro strip interconnect reduced-order modeling based on the finite-element method; T-MTT May 06 2232-2242 Semouchkin, G., see Hennings, A., T-MTT Mar 06 1253-1261 Semouchkina, E., see Hennings, A., T-MTT Mar 06 1253-1261 Sen, P., W.H. Woods, S. Sarkar, R.J. Pratap, B.M. Dufrene, R. Mukhopadhyay, Chang-Ho Lee, E.F. Mina, and J. Laskar. Neuralnetwork-based parasitic modeling and extraction verification for RF/millimeter-wave integrated circuit design; T-MTT Jun 06 2604-2614 Seng Yeo Kiat, see Kaixue Ma, T-MTT Mar 06 1113-1119 Seng Yeo Kiat, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Seo Jun-Hyuk, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Seok-Kyun Han, see Trung-Kien Nguyen, T-MTT Dec 06 4062-4071 Seok Park Dong, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Seok Yang Ki, see Sung Tae Choi, T-MTT May 06 1953-1960 Seok Yang Ki, see Ki Seok Yang, T-MTT Dec 06 4572-4579 Seonghan Ryu, see Huijung Kim, T-MTT Jul 06 2917-2924 Seonghwan Cho, see Yeonwoo Ku, T-MTT Jun 06 1363-1369 Seong-Mo Yim, and K.K. O. Switched resonators and their applications in a dual-band monolithic CMOS LC-tuned VCO; T-MTT Jan 06 74-81 Serdijn, W.A., see Bagga, S., T-MTT Jun 06 1656-1666 Sergeev, A.S., see Rozental, R.M., T-MTT Jun 06 2741-2744 Serino, A., see Colantonio, P., T-MTT Jun 06 2713-2722 Seron, D., C. Collado, J. Mateu, and J.M. O'Callaghan. Analysis and Simulation of distributed nonlinearities in ferroelectrics and superconductors for microwave applications; T-MTT Mar 06 1154-1160 Settaluri, R.K., see Phillips, M.D., T-MTT Jun 06 1325-1330 Seungki Nam, Yonggyoo Kim, Yonghoon Kim, H. Jang, S. Hur, B. Song, Jaehoon Lee, and Jichai Jeong. Performance analysis of signal vias using virtual islands with shorting vias in multilayer PCBs; T-MTT Jun 06 13151324 Seungpyo Hong, and Kai Chang. A 10-35-GHz six-channel microstrip multiplexer for wide-band communication systems; T-MTT Jun 06 13701378 Seung-Yup Lee, Yong-Sub Lee, and Yoon-Ha Jeong. A novel phase measurement technique for IM3 components in RF power amplifiers; TMTT Jan 06 451-457 Seyfert, F., see Lenoir, P., T-MTT Jul 06 3090-3097 Shamsi, S., see Dagang Wu, T-MTT Dec 06 4472-4478 Shapiro, M.A., see Idei, H., T-MTT Nov 06 3899-3905 Sharifi, A.-R., see Oraizi, H., T-MTT May 06 2220-2231 Shastry, P.N., see Daoud, S.M., T-MTT Jun 06 2576-2583 Shastry, P.N., see Sundaram, B., T-MTT Jun 06 2584-2592 Shau-Gang Mao, Min-Sou Wu, and Yu-Zhi Chueh. Design of composite right/left-handed coplanar-waveguide bandpass and dual-passband filters; T-MTT Sep 06 3543-3549 Shealy, J.B., see Trew, R.J., T-MTT May 06 2061-2067 Sheng-Bing Chen, Yong-Chang Jiao, Wei Wang, and Fu-Shun Zhang. Modified T-shaped planar monopole antennas for multiband operation; TMTT Aug 06 3267-3270 Sheng-Cai Shi, see Ling Jiang, T-MTT Jul 06 2944-2948 Sheng-Che Tseng, Chinchun Meng, Chia-Hung Chang, Chih-Kai Wu, and Guo-Wei Huang. Monolithic broadband Gilbert micromixer with an integrated marchand balun using standard silicon IC process; T-MTT Dec 06 4362-4371 Sheng-Fu You, see Ching-Wen Tang, T-MTT Feb 06 717-723 Sheng-Fu You, see Ching-Wen Tang, T-MTT Aug 06 3327-3332 Shen Qin, see Qin Shen, T-MTT Jun 06 2646-2658 Shey-Shi Lu, see Tao Wang, T-MTT Feb 06 580-588 Shey-Shi Lu, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Shigesawa, H., see Tsuji, M., T-MTT Jan 06 421-427 Shi Hao, see Hao Shi, T-MTT Jan 06 360-372 Shih-Cheng Lin, Pu-Hua Deng, Yo-Shen Lin, Chi-Hsueh Wang, and Chun Hsiung Chen. Wide-stopband microstrip bandpass filters using dissimilar quarter-wavelength stepped-impedance resonators; T-MTT Mar 06 10111018 Shih-Cheng Lin, Tsung-Nan Kuo, Yo-Shen Lin, and Chun Hsiung Chen. Novel coplanar-waveguide bandpass filters using loaded air-bridge enhanced capacitors and broadside-coupled transition structures for wideband spurious suppression; T-MTT Aug 06 3359-3369 Shih-Cheng Lin, see Tsung-Nan Kuo, T-MTT Oct 06 3772-3778 Shih-Fong Chao, Chao-Huang Wu, Zou-Ming Tsai, Huei Wang, and Chun Hsiung Chen. Electronically switchable bandpass filters using loaded stepped-impedance resonators; T-MTT Dec 06 4193-4201

IEEE T-MTT 2006 INDEX — 20 Shih Yi-Chi, see Kaihui Lin, T-MTT Dec 06 4041-4048 Shijun Xiao, and A.M. Weiner. Programmable photonic microwave filters with arbitrary ultra-wideband phase response; T-MTT Nov 06 4002-4008 Shimizu, S., see Sung Tae Choi, T-MTT May 06 1953-1960 Shimizu, Y., see Takeuchi, Y., T-MTT Jun 06 1858-1864 Shimozuma, T., see Idei, H., T-MTT Nov 06 3899-3905 Shingo Tanaka, N. Taguchi, T. Kimura, and Y. Atsumi. A predistortion-type equi-path linearizer designed for radio-on-fiber system; T-MTT Feb 06 938-944 Shingo Tanaka, see Taguchi, N., T-MTT Feb 06 945-950 Shingo Tanaka, S. Horiuchi, T. Kimura, and Y. Atsumi. Design and fabrication of multiband p-i-n diode switches with ladder circuits; T-MTT Jun 06 1561-1568 Shin Heeseon, see Woonyun Kim, T-MTT May 06 2098-2105 Shin Hyunchol, see Hyunchol Shin, T-MTT Nov 06 3857-3863 Shin Sanghoon, see Levy, R., T-MTT Jun 06 2503-2515 Shintani, K., see Nishikawa, K., T-MTT Feb 06 589-598 Shiroma, G.S., R.Y. Miyamoto, and W.A. Shiroma. A full-duplex dualfrequency self-steering array using phase detection and phase shifting; TMTT Jan 06 128-134 Shiroma, W.A., see Shiroma, G.S., T-MTT Jan 06 128-134 Shi Sheng-Cai, see Ling Jiang, T-MTT Jul 06 2944-2948 Shiue Guang-Hwa, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Shiue Guang-Hwa, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Shi Yongqiang, see Yongqiang Shi, T-MTT Feb 06 810-815 Shoji, Y., Chang-Soon Choi, and H. Ogawa. 70-GHz-band OFDM transceivers based on self-heterodyne scheme for millimeter-wave wireless personal area network; T-MTT Oct 06 3664-3674 Shry-Sann Liao, and Jen-Ti Peng. Compact planar microstrip branch-line couplers using the quasi-lumped elements approach with nonsymmetrical and symmetrical T-shaped structure; T-MTT Sep 06 3508-3514 Shuenn-Yuh Lee, see Ming-Feng Huang, T-MTT Feb 06 660-669 Shu-Hai Sun, see Choi, C.T.M., T-MTT Jan 06 256-264 Shumin Wang, and J.H. Duyn. A split-field iterative ADI method for simulating transverse-magnetic waves in lossy media; T-MTT May 06 2196-2202 Shyh-Jong Chung, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Shyh-Kang Jeng, see Ming-Iu Lai, T-MTT Jan 06 160-168 Shyh-Kang Jeng, see Pu-Hua Deng, T-MTT Dec 06 4185-4192 Sialm, G., C. Kromer, F. Ellinger, T. Morf, D. Erni, and H. Jackel. Design of low-power fast VCSEL drivers for high-density links in 90-nm SOI CMOS; T-MTT Jan 06 65-73 Siew-Weng Leong, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Sik Cho Choon, see Choon Sik Cho, T-MTT Nov 06 3968-3974 Silva-Martinez, J., see Ganesan, S., T-MTT Dec 06 4079-4085 Silvonen, K., Ning Hua Zhu, and Yu Liu. A 16-term error model based on linear equations of voltage and current variables; T-MTT Jun 06 14641469 Sim Chan-Kuen, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Simeoni, M., C.I. Coman, and I.E. Lager. Patch end-Launchers-a family of compact colinear coaxial-to-rectangular waveguide transitions; T-MTT Jun 06 1503-1511 Simon, P., see Si Moussa, M., T-MTT Jun 06 2675-2683 Si Moussa, M., C. Pavageau, P. Simon, F. Danneville, J. Russat, N. Fel, J.-P. Raskin, and D. Vanhoenacker-Janvier. Behavior of a traveling-wave amplifier versus temperature in SOI technology; T-MTT Jun 06 2675-2683 Simpson, J.J., A. Taflove, J.A. Mix, and H. Heck. Substrate integrated waveguides optimized for ultrahigh-speed digital interconnects; T-MTT May 06 1983-1990 Simsek, E., Qing Huo Liu, and Baojun Wei. Singularity subtraction for evaluation of Green's functions for multilayer media; T-MTT Jan 06 216225 Simsek, E., Jianguo Liu, and Qing Huo Liu. A spectral integral method and hybrid SIM/FEM for layered media; T-MTT Nov 06 3878-3884 Sin-Ting Chen, see Tzong-Lin Wu, T-MTT Aug 06 3398-3406 Sirois, J., see Hammi, O., T-MTT Aug 06 3246-3254 Si-Weng Fok, Pedro Cheong, Kam-Weng Tam, and R.P. Martins. A novel microstrip square-loop dual-mode bandpass filter with simultaneous size reduction and spurious response suppression; T-MTT May 06 2033-2041 Skrivervik, A.K., see Perruisseau-Carrier, J., T-MTT Jan 06 383-392 Skrivervik, A.K., see Perruisseau-Carrier, J., T-MTT Jun 06 1582-1589 Smit, M.K., see Piqueras, M.A., T-MTT Feb 06 887-899 Snowden, C.M., see Denis, D., T-MTT Jun 06 2465-2470 Snyder, R.V., see Levy, R., T-MTT Jun 06 2503-2515 Soares, F.M., see Piqueras, M.A., T-MTT Feb 06 887-899 + Check author entry for coauthors

Sobolev, D., see Bogdashov, A., T-MTT Dec 06 4130-4135 Solano, M.A., A. Vegas, and A. Gomez. Comments on "A comprehensive study of discontinuities in chirowaveguides"; T-MTT Mar 06 1297-1298 Soliman, E.A., see Abdel-Malek, H.L., T-MTT Oct 06 3731-3738 Sombrin, J., see Mallet, A., T-MTT Dec 06 4353-4361 Song, B., see Seungki Nam, T-MTT Jun 06 1315-1324 Songcheol Hong, see Dong-Woo Kang, T-MTT Jan 06 294-301 Song Ho-Jin, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Song In-Sang, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Song Jong-In, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Soo Chang Ik, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Soon-Chul Jeong, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Soo Park Sang, see Byoung Hwa Lee, T-MTT Jun 06 1405-1414 Sorrentino, R., see Ocera, A., T-MTT Jun 06 2383-2390 Sorrentino, R., see Ocera, A., T-MTT Jun 06 2568-2575 Soumyanath, K., see Banerjee, G., T-MTT Jun 06 2336-2345 Sounas, D. L., N. V. Kantartzis, and T. D. Tsiboukis. Focusing efficiency analysis and performance optimization of arbitrarily sized DNG metamaterial slabs with losses; T-MTT Dec 06 4111-4121 Soury, A., see Macraigne, F., T-MTT Aug 06 3219-3226 Spadoni, P., see Rizzoli, V., T-MTT Dec 06 4149-4160 Spassovsky, I., see Bharathan, K., T-MTT Jun 06 1301-1307 Spirito, M., M. J. Pelk, F. van Rijs, S. J. C. H. Theeuwen, D. Hartskeerl, and L. C. N. de Vreede. Active harmonic load-pull for on-wafer out-of-band device linearity optimization; T-MTT Dec 06 4225-4236 Stahl, J., see Sudow, M., T-MTT Dec 06 4072-4078 Stapleton, S.P., see Wan-Jong Kim, T-MTT Sep 06 3469-3478 Starski, J.P., see Karnfelt, C., T-MTT Aug 06 3417-3425 Steer, M., see Walker, A., T-MTT May 06 1991-1999 Steer, M.B. Editorial: Mini-special issue on radio frequency integrated circuits [special section intro.]; T-MTT Jan 06 3 Steer, M.B., see Carvalho, N.B., T-MTT Feb 06 572-579 Steer, M.B., see Fathelbab, W.M., T-MTT Jun 06 2543-2551 Steer, M.B., see Gharaibeh, K.M., T-MTT Aug 06 3227-3236 Stelzer, A., see Scheiblhofer, S., T-MTT Jun 06 1477-1483 Stenarson, J., see Mellberg, A., T-MTT Jan 06 169-172 Stephan, R., see Weber, J., T-MTT Jun 06 2733-2740 Stern, J.A., see Jackson, B.D., T-MTT Feb 06 547-558 Stevanovic, I., P. Crespo-Valero, and J.R. Mosig. An Integral-equation technique for solving thick irises in rectangular waveguides; T-MTT Jan 06 189-197 Stevanovic, I., P. Crespo-Valero, K. Blagovic, F. Bongard, and J.R. Mosig. Integral-equation analysis of 3-D metallic objects arranged in 2-D lattices using the Ewald transformation; T-MTT Oct 06 3688-3697 Stevens, C.J., see Pal, S., T-MTT Feb 06 768-775 Stiens, J., see Koers, G., T-MTT Jul 06 3121-3126 Stoica, L., A. Rabbachin, and I. Oppermann. A low-complexity noncoherent IR-UWB transceiver architecture with TOA estimation; T-MTT Jun 06 1637-1646 Stubbs, M.G., see Hettak, K., T-MTT Sep 06 3453-3461 Stuenkel, M., see Yu-Ju Chuang, T-MTT Nov 06 3843-3847 Suarez, A., see Sanggeun Jeon, T-MTT Mar 06 1096-1106 Suarez, A., and R. Melville. Simulation-assisted design and analysis of varactor-based frequency multipliers and dividers; T-MTT Mar 06 11661179 Suarez, A., see Sanggeun Jeon, T-MTT Oct 06 3630-3640 Suarez, A., see Georgiadis, A., T-MTT Nov 06 3864-3877 Sucbei Moon, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Sudow, M., K. Andersson, N. Billstrom, J. Grahn, H. Hjelmgren, J. Nilsson, P.A. Nilsson, J. Stahl, H. Zirath, and N. Rorsman. An SiC MESFETBased MMIC Process; T-MTT Dec 06 4072-4078 Sugahara, H., see Hirata, A., T-MTT May 06 1937-1944 Sullivan, G., see Ma, B. Y., T-MTT Dec 06 4448-4455 Sul Sang-Chul, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Sundaram, B., and P.N. Shastry. A novel electronically tunable active duplexer for wireless transceiver applications; T-MTT Jun 06 2584-2592 Sung Dan Keun, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Sung-Gi Yang, see Woonyun Kim, T-MTT May 06 2098-2105 Sung-Hoon Choa, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Sung-Jin Ho, see Hongjoon Kim, T-MTT Dec 06 4178-4184 Sung Tae Choi, Ki Seok Yang, S. Nishi, S. Shimizu, K. Tokuda, and Yong Hoon Kim. A 60-GHz point-to-multipoint millimeter-wave fiber-radio communication system; T-MTT May 06 1953-1960 Sun Guilin, see Guilin Sun, T-MTT May 06 2275-2284 Sung-Woo Lee, see Fathy, A.E., T-MTT Jan 06 247-255

IEEE T-MTT 2006 INDEX — 21 Sungyul Yoo, see Joon-Yong Lee, T-MTT Jun 06 1887-1895 Sun Kae-Oh, see Kae-Oh Sun, T-MTT Dec 06 4291-14296 Sun Kuo-Jung, see To-Po Wang, T-MTT Jan 06 88-95 Sun Kuo-Jung, see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Sun Kuo-Jung, see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Sun Mei, see Yue Ping Zhang, T-MTT Oct 06 3779-3785 Sun Qing, see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Sun Shu-Hai, see Choi, C.T.M., T-MTT Jan 06 256-264 Sunwoo Kuk-Hyun, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Sun Zengguang, see Lei Wu, T-MTT Jan 06 278-284 Svechnikov, S.I., see Ling Jiang, T-MTT Jul 06 2944-2948 Swingen, L., see Urick, V.J., T-MTT Jun 06 1458-1463 T Tae Choi Sung, see Sung Tae Choi, T-MTT May 06 1953-1960 Tae Jeong Hyeong, see Hyeong Tae Jeong, T-MTT Jun 06 1425-1430 Taek-Kyung Lee, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Taeksoo Ji, H. Yoon, J.K. Abraham, and V.K. Varadan. Ku-band antenna array feed distribution network with ferroelectric phase shifters on silicon; T-MTT Mar 06 1131-1138 Tae-Young Kim, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Taflove, A., see Simpson, J.J., T-MTT May 06 1983-1990 Taguchi, N., see Shingo Tanaka, T-MTT Feb 06 938-944 Taguchi, N., Shingo Tanaka, T. Kimura, and Y. Atsumi. Relative-intensitynoise reduction technique for frequency-converted radio-on-fiber system; T-MTT Feb 06 945-950 Tah-Hsiung Chu, see Chao-Hsiung Tseng, T-MTT Jun 06 1431-1437 Taijun Liu, S. Boumaiza, and F.M. Ghannouchi. Augmented hammerstein predistorter for linearization of broad-band wireless transmitters; T-MTT Jun 06 1340-1349 Takada Jun-ichi, see Haneda, K., T-MTT Jun 06 1802-1811 Takahashi, H., see Hirata, A., T-MTT May 06 1937-1944 Takahashi, H., see Takenaka, I., T-MTT Dec 06 4513-4521 Takahashi, M., see Saito, K., T-MTT Aug 06 3443-3449 Takahashi, T., see Kawano, Y., T-MTT Dec 06 4489-4497 Takenaka, I., K. Ishikura, H. Takahashi, K. Hasegawa, T. Ueda, T. Kurihara, K. Asano, and N. Iwata. A distortion-cancelled Doherty high-power amplifier using 28-V GaAs heterojunction FETs for W-CDMA base stations; T-MTT Dec 06 4513-4521 Takeuchi, Y., Y. Shimizu, and Y. Sanada. Examination of antenna combinations for UWB ranging system; T-MTT Jun 06 1858-1864 Talbi, L., see Nedil, M., T-MTT Jan 06 499-507 Tallo, J., see Yunchi Zhang, T-MTT Aug 06 3370-3377 Tamiazzo, S., see Macchiarella, G., T-MTT Dec 06 4281-4290 Tam Kam-Weng, see Si-Weng Fok, T-MTT May 06 2033-2041 Tamminen, A., see Lonnqvist, A., T-MTT Sep 06 3486-3491 Tan, A.E.-C., M.Y.-W. Chia, and K. Rambabu. Design of ultra-wideband monopulse receiver; T-MTT Nov 06 3821-3827 Tanabe, E., see Inoue, R., T-MTT Feb 06 522-532 Tan Adrian Eng-Choon, see Adrian Eng-Choon Tan, T-MTT Mar 06 10191024 Tanaka Shingo, see Shingo Tanaka, T-MTT Feb 06 938-944 Tanaka Shingo, see Taguchi, N., T-MTT Feb 06 945-950 Tanaka Shingo, see Shingo Tanaka, T-MTT Jun 06 1561-1568 Tanem, J.P., see Safari, N., T-MTT Jun 06 2813-2820 Tang Ching-Wen, see Ching-Wen Tang, T-MTT Feb 06 717-723 Tang Ching-Wen, see Ching-Wen Tang, T-MTT Aug 06 3327-3332 Tang Wen-Bin, see Wen-Bin Tang, T-MTT Oct 06 3641-3647 Tang Xiao-Hong, see Rui-Jie Mao, T-MTT Sep 06 3526-3533 Tao Wang, Hsiao-Chin Chen, Hung-Wei Chiu, Yo-Sheng Lin, Guo Wei Huang, and Shey-Shi Lu. Micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technology; T-MTT Feb 06 580-588 Tao Wang, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Tarricone, L., see Monti, G., T-MTT Jun 06 2755-2761 Tascone, R., see Peverini, O.A., T-MTT Jan 06 412-420 Tascone, R., see Peverini, O.A., T-MTT May 06 2042-2049 Teck-Hwee Lim, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Tegnander, C., see Karnfelt, C., T-MTT Aug 06 3417-3425 Temkin, R.J., see Idei, H., T-MTT Nov 06 3899-3905 Tentzeris, M.M., see Jong-Hoon Lee, T-MTT Jul 06 2925-2936 Theeuwen, S. J. C. H., see Spirito, M., T-MTT Dec 06 4225-4236 Thomassin, J.-M., see Saib, A., T-MTT Jun 06 2745-2754 Thouroude, D., see Zhadobov, M., T-MTT Jun 06 2534-2542 Thumm, M., see Jianbo Jin, T-MTT Mar 06 1139-1145 + Check author entry for coauthors

Thumm, M., see Akhtar, M.J., T-MTT May 06 2011-2022 Tian Lin Dong, see Hui Kan Liu, T-MTT Sep 06 3479-3485 Tian-Wei Huang, see Pei-Si Wu, T-MTT Jan 06 10-19 Tian-Wei Huang, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Tian-Wei Huang, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Tian Xiao, see Joon-Ho Lee, T-MTT Jan 06 437-444 Tick, T., see Kum Meng Lum, T-MTT Jun 06 2880-2886 Tie Jun Cui, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Tiemeijer, L.F., R.J. Havens, Y. Bouttement, and H.J. Pranger. Physics-based wideband predictive compact model for inductors with high amounts of dummy metal fill; T-MTT Aug 06 3378-3386 Tijhuis, A.G., see Bekers, D.J., T-MTT Jun 06 2821-2829 Ting-Yi Huang, see Chi-Feng Chen, T-MTT Feb 06 755-762 Ting-Yi Huang, see Chi-Feng Chen, T-MTT May 06 1945-1952 Ting-Yi Huang, and Ruey-Beei Wu. Steady-state response by finitedifference time-domain method and lanczos algorithm; T-MTT Jul 06 3038-3044 Ting-Yi Huang, see Chi-Feng Chen, T-MTT Sep 06 3550-3558 Tkachenko, V.I., see Kirilenko, A.A., T-MTT Jun 06 2471-2477 Tobar, M.E., see Ivanov, E.N., T-MTT Aug 06 3284-3294 Tokuda, K., see Sung Tae Choi, T-MTT May 06 1953-1960 Tonda-Goldstein, S., D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and Jean-Pierre Huignard. Optical signal processing in Radar systems; T-MTT Feb 06 847-853 Tong Yan, see Yuanjin Zheng, T-MTT Jun 06 1912-1920 To-Po Wang, Chia-Chi Chang, Ren-Chieh Liu, Ming-Da Tsai, Kuo-Jung Sun, Ying-Tang Chang, Liang-Hung Lu, and Huei Wang. A low-power oscillator mixer in 0.18-ȝm CMOS technology; T-MTT Jan 06 88-95 Tornero, J.L.G., see Garcia, J.P., T-MTT Jan 06 309-320 Toutain, S., see Zbitou, J., T-MTT Jan 06 147-152 Traverso, P. A., see Santarelli, A., T-MTT Dec 06 4021-4031 Traverso, P. A., C. Florian, M. Borgarino, and F. Filicori. An empirical bipolar device nonlinear noise modeling approach for large signal microwave circuit analysis; T-MTT Dec 06 4341-4352 Treizebre, A., see Akalin, T., T-MTT Jun 06 2762-2767 Trew, R.J., Yueying Liu, L. Bilbro, Weiwei Kuang, R. Vetury, and J.B. Shealy. Nonlinear source resistance in high-voltage microwave AlGaN/GaN HFETs; T-MTT May 06 2061-2067 Trifiletti, A., see Marietti, P., T-MTT Dec 06 4049-4055 Trueman, C.W., see Guilin Sun, T-MTT May 06 2275-2284 Trung-Kien Nguyen, Nam-Jin Oh, Viet-Hoang Le, and Sang-Gug Lee. A low-power CMOS direct conversion receiver with 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee standard; T-MTT Feb 06 735-741 Trung-Kien Nguyen, Chung-Hwam Kim, Gook-Ju Ihm, Moon-Su Yang, and Sang-Gug Lee. [Authors' reply to comments on "CMOS low-noise amplifier design optimization techniques"]; T-MTT Jul 06 3155-3156 Trung-Kien Nguyen, V. Krizhanovskii, Jeongseon Lee, Seok-Kyun Han, Sang Gug Lee, Nae-Soo Kim, and Cheol-Sig Pyo. A low-power RF directconversion receiver/transmitter for 2.4-GHz-band IEEE 802.15.4 standard in 0.18-ȝm CMOS technology; T-MTT Dec 06 4062-4071 Tsai Chih-Ming, see Chih-Ming Tsai, T-MTT Jun 06 1545-1553 Tsai Chih-Yuan, see Kuo, J.-T., T-MTT Mar 06 1107-1112 Tsai Jeng-Han, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Tsai Lin-Chuan, see Ching-Wen Hsue, T-MTT Mar 06 1043-1047 Tsai Ming-Da, see Pei-Si Wu, T-MTT Jan 06 10-19 Tsai Ming-Da, see To-Po Wang, T-MTT Jan 06 88-95 Tsai Yi-Hsien, see Ching-Wen Hsue, T-MTT Mar 06 1043-1047 Tsai Yu-Shun, see Yu-Shun Tsai, T-MTT Dec 06 4412-4421 Tsai Zou-Ming, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Tsai Zuo-Min, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Tsai Zuo-Min, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Tsai Zuo-Min, see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Tsai Zuo-Min, see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Tsang, T.K.K., see Baki, R.A., T-MTT Jan 06 46-56 Tseng Chao-Hsiung, see Chao-Hsiung Tseng, T-MTT Jun 06 1431-1437 Tseng Sheng-Che, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Tsiboukis, T. D., see Sounas, D. L., T-MTT Dec 06 4111-4121 Tsuji, M., S. Ueki, and H. Shigesawa. Significant contribution of nonphysical leaky mode to the field excited by a source; T-MTT Jan 06 421-427 Tsuji, M., T. Nishikawa, K. Wakino, and T. Kitazawa. Bi-directionally fed phased-array antenna downsized with variable impedance phase shifter for ISM band; T-MTT Jul 06 2962-2969 Tsukamoto, K., see Murakoshi, A., T-MTT Feb 06 967-972 Tsukamoto, K., see Higashino, T., T-MTT Feb 06 973-979

IEEE T-MTT 2006 INDEX — 22 Tsung-Hui Chang, Chong-Yung Chi, and Yu-Jung Chang. Space-time selective RAKE receiver with finger selection strategies for UWB overlay communications; T-MTT Jun 06 1731-1744 Tsung-Nan Kuo, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Tsung-Nan Kuo, Shih-Cheng Lin, and Chun Hsiung Chen. Compact ultrawideband bandpass filters using composite microstrip-coplanar-waveguide structure; T-MTT Oct 06 3772-3778 Tu Cheng-Chia, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Tu Wen-Hua, see Wen-Hua Tu, T-MTT Mar 06 1084-1089 Tu Wen-Hua, see Wen-Hua Tu, T-MTT Jun 06 2497-2502 Tu Wen-Hua, see Wen-Hua Tu, T-MTT Oct 06 3786-3792 Tuyen Vo Van, see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Tuyen Vo Van, see Van Tuyen Vo, T-MTT Nov 06 3836-3842 Tzeng Yan-Ru, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Tzong-Lin Wu, and Sin-Ting Chen. A photonic crystal power/ground layer for eliminating simultaneously switching noise in high-speed circuit; TMTT Aug 06 3398-3406 Tzuang, C.-K. C., H.-H. Wu, H.-S. Wu, and J. Chen. CMOS active bandpass filter using compacted synthetic quasi-TEM lines at C-band; T-MTT Dec 06 4548-4555 Tzyy-Sheng Horng, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Tzyy-Sheng Horng, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Tzyy-Sheng Horng, see Yu-Shun Tsai, T-MTT Dec 06 4412-4421 U Ueda, T., see Takenaka, I., T-MTT Dec 06 4513-4521 Ueki, S., see Tsuji, M., T-MTT Jan 06 421-427 Urick, V.J., M.S. Rogge, P.F. Knapp, L. Swingen, and F. Bucholtz. Wideband predistortion linearization for externally modulated long-haul analog fiber-optic links; T-MTT Jun 06 1458-1463 Urick, V.J., M.S. Rogge, F. Bucholtz, and K.J. Williams. The performance of analog photonic links employing highly compressed erbium-doped fiber amplifiers; T-MTT Jul 06 3141-3145 Utsumi, K., see Niiho, T., T-MTT Feb 06 980-989 U-yen Kongpop, see Kongpop U-yen, T-MTT Mar 06 1237-1244 V Vahldieck, R., see Sankaran, K., T-MTT Mar 06 1269-1276 Vahldieck, R., see Sankaran, K., T-MTT Dec 06 4297-4304 Vakhtomin, Y.B., see Ling Jiang, T-MTT Jul 06 2944-2948 Valard, J.-L., see Piqueras, M.A., T-MTT Feb 06 887-899 Valdes-Garcia, A., see Pfeiffer, U.R., T-MTT Jan 06 57-64 Valkama, M., A.S.H. Ghadam, L. Anttila, and M. Renfors. Advanced digital signal processing techniques for compensation of nonlinear distortion in wideband multicarrier radio receivers; T-MTT Jun 06 2356-2366 Vanbesien, O., see Decoopman, T., T-MTT Jun 06 1451-1457 Van Biesen, L., see Fort, A., T-MTT Jun 06 1820-1826 Vandenbosch, G.A.E., see Volski, V., T-MTT Jan 06 235-239 van der Weide, D. W., see Hongjoon Kim, T-MTT Dec 06 4178-4184 van der Weide, D. W., see Kae-Oh Sun, T-MTT Dec 06 4291-14296 van de Ven, A.A.F., see Bekers, D.J., T-MTT Jun 06 2821-2829 van Eijndhoven, S.J.L., see Bekers, D.J., T-MTT Jun 06 2821-2829 Vanhille, K.J., D.L. Fontaine, C. Nichols, D.S. Filipovic, and Z. Popovic. Quasi-planar high-Q millimeter-wave resonators; T-MTT Jun 06 24392446 Vanhoenacker-Janvier, D., see Si Moussa, M., T-MTT Jun 06 2675-2683 Van Moer, W., see Rolain, Y., T-MTT Aug 06 3209-3218 Vannini, G., see Santarelli, A., T-MTT Dec 06 4021-4031 van Rijs, F., see Spirito, M., T-MTT Dec 06 4225-4236 Van Tuyen Vo, L. Krishnamurthy, Qing Sun, and A.A. Rezazadeh. 3-D lowloss coplanar waveguide transmission lines in multilayer MMICs; T-MTT Jun 06 2864-2871 Van Tuyen Vo, and Zhirun Hu. Optimization and realization of planar isolated GaAs zero-biased planar doped barrier diodes for microwave/millimeter-wave power detectors/sensors; T-MTT Nov 06 3836-3842 Van Tuyl, R. L., G. E. Hofler, R. G. Ritter, T. S. Marshall, Jintian Zhu, L. Billia, G. M. Clifford, W. Gong, and D. P. Bour. Testing high-frequency electronic signals with reflection-mode electroabsorption modulators; TMTT Dec 06 4556-4564 Varadan, V.K., see Taeksoo Ji, T-MTT Mar 06 1131-1138 Veen, B.D., see Converse, M., T-MTT May 06 2169-2180 Vegas, A., see Solano, M.A., T-MTT Mar 06 1297-1298 + Check author entry for coauthors

Vegas, A., see Gonzalez, O., T-MTT Jul 06 3045-3051 Velazquez-Ahumada, Md.C., see Garcia-Garcia, J., T-MTT Jun 06 26282635 Venanzoni, G., see Morini, A., T-MTT Mar 06 1146-1153 Venanzoni, G., see Morini, A., T-MTT Sep 06 3515-3520 Vendelin, G.D., see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Venkatarayalu, N.V., and Jin-Fa Lee. Removal of spurious DC modes in edge element solutions for modeling three-dimensional resonators; T-MTT Jul 06 3019-3025 Verdeyme, S., see Rigaudeau, L., T-MTT Jun 06 2620-2627 Verdeyme, S., see Lenoir, P., T-MTT Jul 06 3090-3097 Verdonk, B., see Cuyt, A., T-MTT May 06 2265-2274 Verma, A., K.K. O, and J. Lin. A low-power up-conversion CMOS mixer for 22-29-GHz ultra-wideband applications; T-MTT Aug 06 3295-3300 Vetury, R., see Trew, R.J., T-MTT May 06 2061-2067 Vidal, B., see Piqueras, M.A., T-MTT Feb 06 887-899 Vidal, N., see Lopez-Villegas, J.M., T-MTT Jan 06 226-234 Vie, V., see Zhadobov, M., T-MTT Jun 06 2534-2542 Viet-Hoang Le, see Trung-Kien Nguyen, T-MTT Feb 06 735-741 Vilcot, A., see Pistono, E., T-MTT Jun 06 2790-2799 Vilcot, A., see Safwat, A.M.E., T-MTT Sep 06 3559-3564 Villanueva, G.L., P. Hartogh, and L.M. Reindl. A digital dispersive matching network for SAW devices in chirp transform spectrometers; T-MTT Jun 06 1415-1424 Virone, G., see Peverini, O.A., T-MTT Jan 06 412-420 Virone, G., see Peverini, O.A., T-MTT May 06 2042-2049 Viveiros, E., see Darwish, A. M., T-MTT Dec 06 4456-4463 Viviani, G., see Marietti, P., T-MTT Dec 06 4049-4055 Vodjdani, N., see Piqueras, M.A., T-MTT Feb 06 887-899 Volakis, J. L., see Koulouridis, S., T-MTT Dec 06 4202-4208 Volmer, C., see Weber, J., T-MTT Jun 06 2733-2740 Volski, V., and G.A.E. Vandenbosch. Modeling of a cavity filled with a plane multilayered dielectric using the method of auxiliary sources; T-MTT Jan 06 235-239 Vorobyov, A.V., see Bagga, S., T-MTT Jun 06 1656-1666 Voronov, B.M., see Ling Jiang, T-MTT Jul 06 2944-2948 Vounckx, R., see Koers, G., T-MTT Jul 06 3121-3126 Vo Van Tuyen, see Van Tuyen Vo, T-MTT Jun 06 2864-2871 Vo Van Tuyen, see Van Tuyen Vo, T-MTT Nov 06 3836-3842

W

Wadefalk, N., see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Wake, D., see Das, A., T-MTT Aug 06 3426-3432 Wakino, K., see Tsuji, M., T-MTT Jul 06 2962-2969 Walker, A., M. Steer, and K.G. Gard. A vector intermodulation analyzer applied to behavioral modeling of nonlinear amplifiers with memory; TMTT May 06 1991-1999 Wambacq, P., see Fort, A., T-MTT Jun 06 1820-1826 Wane, S., and D. Bajon. Full-wave analysis of inhomogeneous deep-trench isolation patterning for substrate coupling reduction and Q-factor improvement; T-MTT Dec 06 4397-4411 Wang, C.M., see Clement, T.S., T-MTT Aug 06 3173-3181 Wang, J.C.M., see Williams, D.F., T-MTT Jan 06 481-491 Wang, J.C.M., see Williams, D.F., T-MTT Mar 06 1210-1217 Wang Che-Ming, see Wen-Bin Tang, T-MTT Oct 06 3641-3647 Wang Chien-Lin, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Wang Chi-Hsueh, see Pu-Hua Deng, T-MTT Feb 06 533-539 Wang Chi-Hsueh, see Chao-Huang Wu, T-MTT Feb 06 540-546 Wang Chi-Hsueh, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Wang Chi-Hsueh, see Pu-Hua Deng, T-MTT Oct 06 3746-3750 Wang Feipeg, see Feipeg Wang, T-MTT Dec 06 4086-4099 Wang Huei, see Pei-Si Wu, T-MTT Jan 06 10-19 Wang Huei, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Wang Huei, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Wang Huei, see To-Po Wang, T-MTT Jan 06 88-95 Wang Huei, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Wang Huei, see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Wang Huei, see Zuo-Min Tsai, T-MTT Jun 06 1590-1597 Wang Huei, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Wang Huei, see Shih-Fong Chao, T-MTT Dec 06 4193-4201

IEEE T-MTT 2006 INDEX — 23 Wang Jie, see Jie Wang, T-MTT May 06 1961-1968 Wang-Sang Lee, Dong-Zo Kim, Ki-Jin Kim, and Jong-Won Yu. Wideband planar monopole antennas with dual band-notched characteristics; T-MTT Jun 06 2800-2806 Wang Shumin, see Shumin Wang, T-MTT May 06 2196-2202 Wang Tao, see Tao Wang, T-MTT Feb 06 580-588 Wang Tao, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Wang To-Po, see To-Po Wang, T-MTT Jan 06 88-95 Wang Wei, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Wang Yeong-Her, see Jui-Chieh Chiu, T-MTT Sep 06 3521-3525 Wang Ying, see Ooi, B.-L., T-MTT Jul 06 3098-3103 Wang Yuanxun, see Kaihui Lin, T-MTT Dec 06 4041-4048 Wang Yung-Yi, see Chih-Hung Lin, T-MTT May 06 2118-2127 Wang Yun Yi, see Chu Gao, T-MTT Jun 06 1519-1526 Wan-Jong Kim, Kyoung-Joon Cho, S.P. Stapleton, and Jong-Heon Kim. Piecewise pre-equalized linearization of the wireless transmitter with a Doherty amplifier; T-MTT Sep 06 3469-3478 Wan Joo Kim, see Jung Dong Park, T-MTT Oct 06 3623-3629 Warr, P.A., see Carey-Smith, B.E., T-MTT Sep 06 3492-3500 Waterhouse, R., see Kurniawan, T., T-MTT Feb 06 921-928 Waterhouse, R., see Lim, C., T-MTT May 06 2181-2187 Weatherspoon, M.H., and L.P. Dunleavy. Experimental validation of generalized equations for FET cold noise source design; T-MTT Feb 06 608-614 Weber, J., C. Volmer, K. Blau, R. Stephan, and M.A. Hein. Miniaturized antenna arrays using decoupling networks with realistic elements; T-MTT Jun 06 2733-2740 Webster, R.T., see Reid, J.R., T-MTT Aug 06 3433-3442 Wei Baojun, see Simsek, E., T-MTT Jan 06 216-225 Wei-Da Guo, Guang-Hwa Shiue, Chien-Min Lin, and Ruey-Beei Wu. Comparisons between serpentine and flat spiral delay lines on transient reflection/transmission waveforms and eye diagrams; T-MTT Jun 06 13791387 Wei-Da Guo, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Wei Gao, and Zhiping Yu. Scalable compact circuit model and synthesis for RF CMOS spiral inductors; T-MTT Mar 06 1055-1064 Wei Hong, see Feng Xu, T-MTT Jan 06 329-338 Wei Huang Guo, see Tao Wang, T-MTT Feb 06 580-588 Weikle, R.M., see Zhiyang Liu, T-MTT Jun 06 2447-2452 Weikle, R.M., II, see Zhiyang Liu, T-MTT Jul 06 2977-2982 Weikle, R.M., II, see Haiyong Xu, T-MTT Oct 06 3648-3653 Wei-Lin Hsieh, see Yi-Chyun Chiang, T-MTT Nov 06 3947-3953 Wei Meng, and Ke-Li Wu. Analytical diagnosis and tuning of narrowband multicoupled resonator filters; T-MTT Oct 06 3765-3771 Wei Meng Lim, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Wei Miao, see Ling Jiang, T-MTT Jul 06 2944-2948 Weiner, A.M., see McKinney, J.D., T-MTT Jun 06 1681-1686 Weiner, A.M., see Shijun Xiao, T-MTT Nov 06 4002-4008 Weiner, A. M., see McKinney, J. D., T-MTT Dec 06 4247-4255 Wei Wang, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Weiwei Kuang, see Trew, R.J., T-MTT May 06 2061-2067 Weller, T.M., see Lakshminarayanan, B., T-MTT Jan 06 120-127 Wells, C.G., and J.A.R. Ball. Attenuation of a shielded rectangular dielectric rod waveguide; T-MTT Jul 06 3013-3018 Wen-Bin Tang, Che-Ming Wang, and Yue-Ming Hsin. A new extraction technique for the complete small-signal equivalent-circuit model of InGaP/GaAs HBT including base contact impedance and AC current crowding effect; T-MTT Oct 06 3641-3647 Wen-Hua Tu, and Kai Chang. Wide-band microstrip-to-coplanar stripline/slotline transitions; T-MTT Mar 06 1084-1089 Wen-Hua Tu, and Kai Chang. Compact second harmonic-suppressed bandstop and bandpass filters using open stubs; T-MTT Jun 06 2497-2502 Wen-Hua Tu, and Kai Chang. Microstrip elliptic-function low-pass filters using distributed elements or slotted ground structure; T-MTT Oct 06 3786-3792 Wenjian Yu, see Zuochang Ye, T-MTT May 06 2128-2137 Wentworth, S.M., see Faircloth, D.L., T-MTT Mar 06 1201-1209 Wentzloff, D.D., and A.P. Chandrakasan. Gaussian pulse Generators for subbanded ultra-wideband transmitters; T-MTT Jun 06 1647-1655 Wen Zhang, see Ling Jiang, T-MTT Jul 06 2944-2948 Westwick, D.T., see Williams, T.C., T-MTT Jun 06 1308-1314 Wight, J.S., see Gravel, J.-F., T-MTT Jan 06 153-159 Williams, D.F., A. Lewandowski, T.S. Clement, J.C.M. Wang, P.D. Hale, J.M. Morgan, D.A. Keenan, and A. Dienstfrey. Covariance-based

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uncertainty analysis of the NIST electrooptic sampling system; T-MTT Jan 06 481-491 Williams, D.F., H. Khenissi, F. Ndagijimana, K.A. Remley, J.P. Dunsmore, P.D. Hale, J.C.M. Wang, and T.S. Clement. Sampling-oscilloscope measurement of a microwave mixer with single-digit phase accuracy; TMTT Mar 06 1210-1217 Williams, D.F., see Clement, T.S., T-MTT Aug 06 3173-3181 Williams, D.F., see Dienstfrey, A., T-MTT Aug 06 3197-3208 Williams, K.J., see Urick, V.J., T-MTT Jul 06 3141-3145 Williams, T.C., E.C. Fear, and D.T. Westwick. Tissue sensing adaptive Radar for breast cancer detection-investigations of an improved skin-sensing method; T-MTT Jun 06 1308-1314 Wincza, K., see Gruszczynski, S., T-MTT Sep 06 3501-3507 Wincza, K., see Gruszczynski, S., T-MTT Nov 06 3986-3994 Winnall, S.T., A.C. Lindsay, M.W. Austin, J. Canning, and A. Mitchell. A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system; TMTT Feb 06 868-872 Wisell, D., see Isaksson, M., T-MTT Jan 06 348-359 Witrisal, K., see Romme, J., T-MTT Jun 06 1754-1761 Wittneben, A., see Knochel, R.H., T-MTT Apr 06 1633-1636 Wittneben, A., see Zasowski, T., T-MTT Jun 06 1836-1845 Wollack, E.J., see Kongpop U-yen, T-MTT Mar 06 1237-1244 Won-Bae Kim, see Kyoung-Hwan Oh, T-MTT Feb 06 854-860 Won-Kyu Choi, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Wood, J., M. LeFevre, D. Runton, J.-C. Nanan, B.H. Noori, and P.H. Aaen. Envelope-domain time series (ET) behavioral model of a Doherty RF power amplifier for system design; T-MTT Aug 06 3163-3172 Woods, W.H., see Sen, P., T-MTT Jun 06 2604-2614 Woo Duk-Jae, see Duk-Jae Woo, T-MTT Jun 06 2840-2847 Woon Chong Jo, see Jo Woon Chong, T-MTT Jun 06 1793-1801 Woonyun Kim, Jinhyuck Yu, Heeseon Shin, Sung-Gi Yang, Wooseung Choo, and Byeong-Ha Park. A dual-b and RF front-end of direct conversion receiver for wireless CDMA cellular phones with GPS capability; T-MTT May 06 2098-2105 Wooseung Choo, see Woonyun Kim, T-MTT May 06 2098-2105 Woo-Young Choi, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Woo Young Yun, see Young Yun Woo, T-MTT May 06 1969-1974 Wu, H.-H., see Tzuang, C.-K. C., T-MTT Dec 06 4548-4555 Wu, H.-S., see Tzuang, C.-K. C., T-MTT Dec 06 4548-4555 Wu, R., see Amari, S., T-MTT Jan 06 428-436 Wu, T.X., and D.L. Jaggard. Authors' reply [to comments on "A comprehensive study of discontinuities in chirowaveguides"]; T-MTT Mar 06 1298 Wu Chao-Huang, see Chao-Huang Wu, T-MTT Feb 06 540-546 Wu Chao-Huang, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Wu Chih-Kai, see Sheng-Che Tseng, T-MTT Dec 06 4362-4371 Wu Dagang, see Dagang Wu, T-MTT Dec 06 4472-4478 Wu Jian-Ming, see Jian-Ming Wu, T-MTT Jun 06 2691-2698 Wu Jian-Ming, see Fu-Yi Han, T-MTT Oct 06 3793-3804 Wu Ke, see Feng Xu, T-MTT Jan 06 329-338 Wu Ke, see Bozzi, M., T-MTT Jan 06 339-347 Wu Ke, see Moldovan, E., T-MTT Feb 06 625-632 Wu Ke, see Xiupu Zhang, T-MTT Feb 06 929-937 Wu Ke, see Lin Li, T-MTT Jun 06 1470-1476 Wu Ke, see Yanyang Zhao, T-MTT Jun 06 1707-1712 Wu Ke, see Deslandes, D., T-MTT Jun 06 2516-2526 Wu Ke, see Patrovsky, A., T-MTT Jun 06 2872-2879 Wu Ke, see Xinyu Xu, T-MTT Jul 06 2937-2943 Wu Ke, see D'Orazio, W., T-MTT Oct 06 3675-3680 Wu Ke, see Moldovan, E., T-MTT Nov 06 4017 Wu Ke-Li, see Jie Wang, T-MTT May 06 1961-1968 Wu Ke-Li, see Lap Kun Yeung, T-MTT Jun 06 1512-1518 Wu Ke-Li, see Wei Meng, T-MTT Oct 06 3765-3771 Wu Lei, see Lei Wu, T-MTT Jan 06 278-284 Wu Min-Chung, see Ke-Chiang Lin, T-MTT Jun 06 2321-2328 Wu Min-Sou, see Shau-Gang Mao, T-MTT Sep 06 3543-3549 Wu Pei-Si, see Pei-Si Wu, T-MTT Jan 06 10-19 Wu Pei-Si, see Hong-Yeh Chang, T-MTT Jan 06 20-30 Wu Pei-Si, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Wu Ruey-Beei, see Chi-Feng Chen, T-MTT Feb 06 755-762 Wu Ruey-Beei, see Chi-Feng Chen, T-MTT May 06 1945-1952 Wu Ruey-Beei, see Wei-Da Guo, T-MTT Jun 06 1379-1387 Wu Ruey-Beei, see Ting-Yi Huang, T-MTT Jul 06 3038-3044 Wu Ruey-Beei, see Chi-Feng Chen, T-MTT Sep 06 3550-3558

IEEE T-MTT 2006 INDEX — 24 Wu Ruey-Beei, see Chien-Lin Wang, T-MTT Dec 06 4209-4217 Wu Tzong-Lin, see Tzong-Lin Wu, T-MTT Aug 06 3398-3406 X Xiangfei Chen, Zhichao Deng, and Jianping Yao. Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser; T-MTT Feb 06 804-809 Xian Ming Qing, see Chu Gao, T-MTT Jun 06 1519-1526 Xianming Qing, see Zhi Ning Chen, T-MTT Jun 06 1846-1857 Xian Qi Lin, Ruo Peng Liu, Xin Mi Yang, Ji Xin Chen, Xiao Xing Yin, Qiang Cheng, and Tie Jun Cui. Arbitrarily dual-band components using simplified structures of conventional CRLH TLs; T-MTT Jul 06 29022909 Xiao Dongping, see Crupi, G., T-MTT Oct 06 3616-3622 Xiaofeng Li, see Ricketts, D.S., T-MTT Jan 06 373-382 Xiao-Hong Tang, see Rui-Jie Mao, T-MTT Sep 06 3526-3533 Xiao Peng Yu, Manh Anh Do, Wei Meng Lim, Kiat Seng Yeo, and Jian-Guo Ma. Design and optimization of the extended true single-phase clockbased prescaler; T-MTT Nov 06 3828-3835 Xiao Shijun, see Shijun Xiao, T-MTT Nov 06 4002-4008 Xiao Tian, see Joon-Ho Lee, T-MTT Jan 06 437-444 Xiao Xing Yin, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Xiaoxue Zhao, see Chrostowski, L., T-MTT Feb 06 788-796 Xiao Yanming, see Yanming Xiao, T-MTT May 06 2023-2032 Xiao Yanming, see Changzhi Li, T-MTT Dec 06 4464-4471 Xikui Ma, Xintai Zhao, and Yanzhen Zhao. A 3-D precise integration timedomain method without the restraints of the courant-friedrich-levy stability condition for the numerical solution of Maxwell's equations; TMTT Jul 06 3026-3037 Xin Chen Ji, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Xingchao Yuan, see Hao Shi, T-MTT Jan 06 360-372 Xin Guan, and C. Nguyen. Low-power-consumption and high-gain CMOS distributed amplifiers using cascade of inductively coupled commonsource gain cells for UWB systems; T-MTT Aug 06 3278-3283 Xing Yin Xiao, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Xin Mi Yang, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Xintai Zhao, see Xikui Ma, T-MTT Jul 06 3026-3037 Xinyu Xu, R.G. Bosisio, and Ke Wu. Analysis and implementation of six-port software-defined radio receiver platform; T-MTT Jul 06 2937-2943 Xin Zhao, see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Xiuge Yang, and J. Lin. A digitally controlled constant envelope phase-shift modulator for low-power broad-band wireless applications; T-MTT Jan 06 96-105 Xiupu Zhang, Baozhu Liu, Jianping Yao, Ke Wu, and R. Kashyap. A novel millimeter-wave-band radio-over-fiber system with dense wavelengthdivision multiplexing bus architecture; T-MTT Feb 06 929-937 Xudong Lou, see Saib, A., T-MTT Jun 06 2745-2754 Xue Quan, see Yum, T.Y., T-MTT Aug 06 3255-3266 Xu Feng, see Feng Xu, T-MTT Jan 06 329-338 Xu Haiyong, see Haiyong Xu, T-MTT Oct 06 3648-3653 Xu Rui, see Rui Xu, T-MTT Aug 06 3271-3277 Xu Xinyu, see Xinyu Xu, T-MTT Jul 06 2937-2943 Y Yakovlev, V.V., see Murphy, E.K., T-MTT Jul 06 3069-3083 Yamaguchi, R., see Hirata, A., T-MTT May 06 1937-1944 Yamakawa, S., see Nishikawa, K., T-MTT Feb 06 589-598 Yang, A. H., see Feipeg Wang, T-MTT Dec 06 4086-4099 Yang Chuanyi, see Gope, D., T-MTT Jun 06 2453-2464 Yang Hao, see Yan Zhao, T-MTT Jun 06 1827-1835 Yang Ki Seok, see Sung Tae Choi, T-MTT May 06 1953-1960 Yang Ki Seok, see Ki Seok Yang, T-MTT Dec 06 4572-4579 Yang Ming-Ta, see Jun-De Jin, T-MTT Dec 06 4333-4340 Yang Moon-Su, see Trung-Kien Nguyen, T-MTT Jul 06 3155-3156 Yang Ning, see Chu Gao, T-MTT Jun 06 1519-1526 Yang Sung-Gi, see Woonyun Kim, T-MTT May 06 2098-2105 Yang Xin Mi, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Yang Xiuge, see Xiuge Yang, T-MTT Jan 06 96-105 Yang Youngoo, see Young Yun Woo, T-MTT May 06 1969-1974 Yan Li, see Nikolova, N.K., T-MTT Jun 06 1598-1610 Yanming Xiao, J. Lin, O. Boric-Lubecke, and M. Lubecke. Frequency-tuning technique for remote detection of heartbeat and respiration using low-

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power double-sideband transmission in the ka-band; T-MTT May 06 20232032 Yanming Xiao, see Changzhi Li, T-MTT Dec 06 4464-4471 Yan-Ru Tzeng, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Yan Tong, see Yuanjin Zheng, T-MTT Jun 06 1912-1920 Yanyang Zhao, J.-F. Frigon, Ke Wu, and R.G. Bosisio. Multi(Six)-port impulse radio for ultra-wideband; T-MTT Jun 06 1707-1712 Yan Zhao, Yang Hao, A. Alomainy, and C. Parini. UWB on-body radio channel modeling using ray theory and subband FDTD method; T-MTT Jun 06 1827-1835 Yanzhen Zhao, see Xikui Ma, T-MTT Jul 06 3026-3037 Yao Jianping, see Zhichao Deng, T-MTT Feb 06 763-767 Yao Jianping, see Xiangfei Chen, T-MTT Feb 06 804-809 Yao Jianping, see Xiupu Zhang, T-MTT Feb 06 929-937 Yao Qi Jun, see Ling Jiang, T-MTT Jul 06 2944-2948 Yarovoy, A.G., see Bagga, S., T-MTT Jun 06 1656-1666 Yasumoto, K., see Hongting Jia, T-MTT Feb 06 564-571 Yaxun Liu, and C.D. Sarris. Efficient modeling of microwave integratedcircuit geometries via a dynamically adaptive mesh Refinement-FDTD technique; T-MTT Feb 06 689-703 Yazgan, E., see Duyar, M., T-MTT Jun 06 1388-1395 Yeh, D.A., see Sarkar, S., T-MTT Mar 06 1245-1252 Yeh Mei-Chao, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Yeh Mei-Chao, see Zuo-Min Tsai, T-MTT May 06 2090-2097 Yeh Po-Feng, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Yeo Kiat Seng, see Kaixue Ma, T-MTT Mar 06 1113-1119 Yeo Kiat Seng, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Yeong-Her Wang, see Jui-Chieh Chiu, T-MTT Sep 06 3521-3525 Yeonwoo Ku, I. Nam, S. Ha, Kwyro Lee, and Seonghwan Cho. Close-in phase-noise enhanced voltage-controlled oscillator employing parasitic VNPN transistor in CMOS process; T-MTT Jun 06 1363-1369 Yeung Lap Kun, see Lap Kun Yeung, T-MTT Jun 06 1512-1518 Ye Zuochang, see Zuochang Ye, T-MTT May 06 2128-2137 Yi, X., and Robert.A. Minasian. Dispersion induced RF distortion of spectrum-sliced microwave-photonic filters; T-MTT Feb 06 880-886 Yi Cao, Runtao Ding, and Qi-Jun Zhang. State-space dynamic neural network technique for high-speed IC applications: modeling and stability analysis; T-MTT Jun 06 2398-2409 Yi-Chi Shih, see Kaihui Lin, T-MTT Dec 06 4041-4048 Yi-Chyun Chiang, Wei-Lin Hsieh, and Ming-An Chung. A method of synthesizing microwave bandpass filters constructed with symmetrical or asymmetrical compact microstrip resonators; T-MTT Nov 06 3947-3953 Yi-Chyun Chiou, Jen-Tsai Kuo, and Eisenhower Cheng. Broadband quasiChebyshev bandpass filters with multimode stepped-impedance resonators (SIRs); T-MTT Aug 06 3352-3358 Yi-Hao Chang, see Rong Jiang, T-MTT Jul 06 3060-3068 Yi-Hsien Tsai, see Ching-Wen Hsue, T-MTT Mar 06 1043-1047 Yijun Zhou, see Koulouridis, S., T-MTT Dec 06 4202-4208 Yi-Lin Lee, see Jeng-Han Tsai, T-MTT Jun 06 2487-2496 Yilmaz, H., see Lei Wu, T-MTT Jan 06 278-284 Yi-Ming Chen, see Yng-Huey Jeng, T-MTT May 06 2146-2152 Yi-Min Lin, see Jyh-Chyurn Guo, T-MTT Nov 06 3975-3985 Yim Seong-Mo, see Seong-Mo Yim, T-MTT Jan 06 74-81 Ying Li, see Nikolova, N.K., T-MTT Jun 06 1598-1610 Ying-Tang Chang, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Ying-Tang Chang, see To-Po Wang, T-MTT Jan 06 88-95 Ying Wang, see Ooi, B.-L., T-MTT Jul 06 3098-3103 Yin Jee-Khoi, see Chia, M.Y.-W., T-MTT Jun 06 2431-2438 Yin Qin, S. Gao, and A. Sambell. Broadband high-efficiency circularly polarized active antenna and array for RF front-end application; T-MTT Jul 06 2910-2916 Yin Xiao Xing, see Xian Qi Lin, T-MTT Jul 06 2902-2909 Yi Qin, S. Gao, and A. Sambell. Broadband high-efficiency linearly and circularly polarized active integrated antennas; T-MTT Jun 06 2723-2732 Yi Sang-Yong, see Bok-Hyung Lee, T-MTT Jun 06 2422-2430 Yi Wang Yun, see Chu Gao, T-MTT Jun 06 1519-1526 Yiwei Duan, see Haiyong Xu, T-MTT Oct 06 3648-3653 Yng-Huey Jeng, S.-F.R. Chang, and Hsiao-Kuang Lin. A high stopbandrejection LTCC filter with multiple transmission zeros; T-MTT Feb 06 633-638 Yng-Huey Jeng, S.-F.R. Chang, Yi-Ming Chen, and Yu-Jen Huang. A novel self-coupled dual-mode ring resonator and its applications to bandpass filters; T-MTT May 06 2146-2152 Yngvesson, K.S., see Kollberg, E.L., T-MTT May 06 2077-2089 Yngvesson, K.S., see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311

IEEE T-MTT 2006 INDEX — 25 Yokoo, K., see Kawano, Y., T-MTT Dec 06 4489-4497 Yong-Chang Jiao, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Yong-Dae Kim, Kuk-Hyun Sunwoo, Sang-Chul Sul, Ju-Ho Lee, Duck-Hwan Kim, In-Sang Song, Sung-Hoon Choa, and Jong-Gwan Yook. Highly miniaturized RF bandpass filter based on thin-film bulk acoustic-wave resonator for 5-GHz-band application; T-MTT Mar 06 1218-1228 Yong-Duck Chung, see Jeha Kim, T-MTT Feb 06 780-787 Yong-Duck Chung, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Yonggyoo Kim, see Seungki Nam, T-MTT Jun 06 1315-1324 Yong Hoon Kim, see Sung Tae Choi, T-MTT May 06 1953-1960 Yonghoon Kim, see Seungki Nam, T-MTT Jun 06 1315-1324 Yongqiang Shi Micromachined wide-band lithium-niobate electrooptic Modulators; T-MTT Feb 06 810-815 Yongshik Lee, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Yongshik Lee, see Lahiji, R.R., T-MTT Jun 06 2699-2706 Yong-Sub Lee, see Seung-Yup Lee, T-MTT Jan 06 451-457 Yongwei Zhang, and A.K. Brown. The discone antenna in a BPSK directsequence indoor UWB communication system; T-MTT Jun 06 1675-1680 Yong-Xin Guo, Zhen-Yu Zhang, and Ling Chuen Ong. Improved wide-band Schiffman phase shifter; T-MTT Mar 06 1196-1200 Yook Jong-Gwan, see Yong-Dae Kim, T-MTT Mar 06 1218-1228 Yook Jong-Gwan, see Young-Pyo Hong, T-MTT Jun 06 1569-1575 Yoon, C., see Junwoo Lee, T-MTT Jun 06 1667-1674 Yoon, H., see Taeksoo Ji, T-MTT Mar 06 1131-1138 Yoon-Ha Jeong, see Seung-Yup Lee, T-MTT Jan 06 451-457 Yoo Sungyul, see Joon-Yong Lee, T-MTT Jun 06 1887-1895 Yo-Sheng Lin, see Tao Wang, T-MTT Feb 06 580-588 Yo-Sheng Lin, see Hsiao-Bin Liang, T-MTT Dec 06 4256-14267 Yo-Shen Lin, see Pu-Hua Deng, T-MTT Feb 06 533-539 Yo-Shen Lin, see Chao-Huang Wu, T-MTT Feb 06 540-546 Yo-Shen Lin, see Shih-Cheng Lin, T-MTT Mar 06 1011-1018 Yo-Shen Lin, see Shih-Cheng Lin, T-MTT Aug 06 3359-3369 Yoshida, N., see Satoh, H., T-MTT Jan 06 210-215 Young-Hoon Chun, and Jia-Sheng Hong. Compact wide-band branch-line hybrids; T-MTT Feb 06 704-709 Young-Jin Park, see Junwoo Lee, T-MTT Jun 06 1667-1674 Youngoo Yang, see Young Yun Woo, T-MTT May 06 1969-1974 Young-Pyo Hong, Jung-Min Kim, Soon-Chul Jeong, Dong-Hyun Kim, MunHo Choi, Yongshik Lee, and Jong-Gwan Yook. S-band dual-path dualpolarized antenna system for satellite digital audio radio service (SDARS) application; T-MTT Jun 06 1569-1575 Young-Shik Kang, see Jeha Kim, T-MTT Feb 06 780-787 Young-Shik Kang, see Jun-Hyuk Seo, T-MTT Feb 06 959-966 Young Yun Woo, Youngoo Yang, and Bumman Kim. Analysis and experiments for high-efficiency class-F and inverse class-F power amplifiers; T-MTT May 06 1969-1974 You Se-Ho, see Se-Ho You, T-MTT May 06 2232-2242 You Sheng-Fu, see Ching-Wen Tang, T-MTT Feb 06 717-723 You Sheng-Fu, see Ching-Wen Tang, T-MTT Aug 06 3327-3332 Yuanjin Zheng, Yueping Zhang, and Yan Tong. A novel wireless interconnect technology using impulse radio for interchip communications; T-MTT Jun 06 1912-1920 Yuan Mengtao, see Mengtao Yuan, T-MTT Mar 06 1025-1032 Yuan Mengtao, see Mengtao Yuan, T-MTT Jun 06 2552-2563 Yuan Xingchao, see Hao Shi, T-MTT Jan 06 360-372 Yuanxun Wang, see Kaihui Lin, T-MTT Dec 06 4041-4048 Yu Du, and W. Dai. Capture high-frequency partial inductance more accurately by gauss quadrature integration with skin-effect model; T-MTT Mar 06 1287-1294 Yue Libin, see Huang, F., T-MTT Nov 06 3954-3959 Yue-Ming Hsin, see Wen-Bin Tang, T-MTT Oct 06 3641-3647 Yuenie Lau, see Fung, A., T-MTT Dec 06 4507-4512 Yueping Zhang, see Yuanjin Zheng, T-MTT Jun 06 1912-1920 Yue Ping Zhang, and Mei Sun. Dual-band microstrip bandpass filter using stepped-impedance resonators with new coupling schemes; T-MTT Oct 06 3779-3785 Yueying Liu, see Trew, R.J., T-MTT May 06 2061-2067 Yu-Jen Huang, see Yng-Huey Jeng, T-MTT May 06 2146-2152 Yujin Chung, see Huijung Kim, T-MTT Jul 06 2917-2924 Yu Jinhyuck, see Woonyun Kim, T-MTT May 06 2098-2105 Yu-Jiun Ren, and Kai Chang. 5.8-GHz circularly polarized dual-diode rectenna and rectenna array for microwave power transmission; T-MTT Jun 06 1495-1502

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Yu-Jiun Ren, and Kai Chang. New 5.8-GHz circularly polarized retrodirective rectenna arrays for wireless power transmission; T-MTT Jul 06 2970-2976 Yu Jong-Won, see Wang-Sang Lee, T-MTT Jun 06 2800-2806 Yu-Ju Chuang, see Jie-Wei Lai, T-MTT Feb 06 599-607 Yu-Ju Chuang, K. Cimino, M. Stuenkel, M. Feng, Minh Le, and R. Milano. A wideband InP DHBT true logarithmic amplifier; T-MTT Nov 06 38433847 Yu-Jung Chang, see Tsung-Hui Chang, T-MTT Jun 06 1731-1744 Yu Liu, see Silvonen, K., T-MTT Jun 06 1464-1469 Yum, T.Y., Leung Chiu, Chi Hou Chan, and Quan Xue. High-efficiency linear RF Amplifier - a unified circuit approach to achieving compactness and low distortion; T-MTT Aug 06 3255-3266 Yun, Y., Kyung-Sik Lee, Chung-Ryul Kim, Ki-Man Kim, and Ji-Won Jung. Basic RF characteristics of the microstrip line employing periodically perforated ground metal and its application to highly miniaturized on-chip passive components on GaAs MMIC; T-MTT Oct 06 3805-3817 Yu Nan, see Rubiola, E., T-MTT Feb 06 816-820 Yunchi Zhang, K.A. Zaki, A.J. Piloto, and J. Tallo. Miniature broadband bandpass filters using double-layer coupled stripline resonators; T-MTT Aug 06 3370-3377 Yung-Yi Wang, see Chih-Hung Lin, T-MTT May 06 2118-2127 Yunseo Park, Chang-Ho Lee, J.D. Cressler, and J. Laskar. The analysis of UWB SiGe HBT LNA for its noise, linearity, and minimum group delay variation; T-MTT Jun 06 1687-1697 Yun Woo Young, see Young Yun Woo, T-MTT May 06 1969-1974 Yun Yi Wang, see Chu Gao, T-MTT Jun 06 1519-1526 Yu-Shun Tsai, and Tzyy-Sheng Horng. A broadband single-stage equivalent circuit for modeling LTCC bandpass filters; T-MTT Dec 06 4412-4421 Yu-Te Liao, see Liang-Hung Lu, T-MTT Sep 06 3462-3468 Yu Wenjian, see Zuochang Ye, T-MTT May 06 2128-2137 Yu Xiao Peng, see Xiao Peng Yu, T-MTT Nov 06 3828-3835 Yu Zhao, A. G. Metzger, P. J. Zampardi, M. Iwamoto, and P. M. Asbeck. Linearity improvement of HBT-based Doherty power amplifiers based on a simple analytical model; T-MTT Dec 06 4479-4488 Yu-Zhi Chueh, see Shau-Gang Mao, T-MTT Sep 06 3543-3549 Yu Zhiping, see Wei Gao, T-MTT Mar 06 1055-1064 Yu Zhiping, see Zuochang Ye, T-MTT May 06 2128-2137 Z Zaki, K.A., see Yunchi Zhang, T-MTT Aug 06 3370-3377 Zampardi, P. J., see Yu Zhao, T-MTT Dec 06 4479-4488 Zannoni, R., see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Zasowski, T., G. Meyer, F. Althaus, and A. Wittneben. UWB signal propagation at the human head; T-MTT Jun 06 1836-1845 Zbitou, J., M. Latrach, and S. Toutain. Hybrid rectenna and monolithic integrated zero-bias microwave rectifier; T-MTT Jan 06 147-152 Zengguang Sun, see Lei Wu, T-MTT Jan 06 278-284 Zhadobov, M., R. Sauleau, V. Vie, M. Himdi, L. Le Coq, and D. Thouroude. Interactions between 60-GHz millimeter waves and artificial biological membranes: dependence on radiation parameters; T-MTT Jun 06 25342542 Zhang Fu-Shun, see Sheng-Bing Chen, T-MTT Aug 06 3267-3270 Zhang Guoyong, see Guoyong Zhang, T-MTT Feb 06 559-563 Zhang Hualiang, see Hualiang Zhang, T-MTT Mar 06 1090-1095 Zhang Qi-Jun, see Yi Cao, T-MTT Jun 06 2398-2409 Zhang Wen, see Ling Jiang, T-MTT Jul 06 2944-2948 Zhang Xiupu, see Xiupu Zhang, T-MTT Feb 06 929-937 Zhang Yongwei, see Yongwei Zhang, T-MTT Jun 06 1675-1680 Zhang Yueping, see Yuanjin Zheng, T-MTT Jun 06 1912-1920 Zhang Yue Ping, see Yue Ping Zhang, T-MTT Oct 06 3779-3785 Zhang Yunchi, see Yunchi Zhang, T-MTT Aug 06 3370-3377 Zhang Zhen-Yu, see Yong-Xin Guo, T-MTT Mar 06 1196-1200 Zhao Xiaoxue, see Chrostowski, L., T-MTT Feb 06 788-796 Zhao Xin, see Rodriguez-Morales, F., T-MTT Jun 06 2301-2311 Zhao Xintai, see Xikui Ma, T-MTT Jul 06 3026-3037 Zhao Yan, see Yan Zhao, T-MTT Jun 06 1827-1835 Zhao Yanyang, see Yanyang Zhao, T-MTT Jun 06 1707-1712 Zhao Yanzhen, see Xikui Ma, T-MTT Jul 06 3026-3037 Zhao Yu, see Yu Zhao, T-MTT Dec 06 4479-4488 Zheng Yuanjin, see Yuanjin Zheng, T-MTT Jun 06 1912-1920 Zhen Hui Lin, see Ling Jiang, T-MTT Jul 06 2944-2948 Zhen-Yu Zhang, see Yong-Xin Guo, T-MTT Mar 06 1196-1200

IEEE T-MTT 2006 INDEX — 26 Zhichao Deng, and Jianping Yao. Photonic generation of microwave signal using a rational harmonic mode-locked fiber ring laser; T-MTT Feb 06 763-767 Zhichao Deng, see Xiangfei Chen, T-MTT Feb 06 804-809 Zhi Ning Chen, see Chu Gao, T-MTT Jun 06 1519-1526 Zhi Ning Chen, A. Cai, T.S.P. See, Xianming Qing, and M.Y.W. Chia. Small planar UWB antennas in proximity of the human head; T-MTT Jun 06 1846-1857 Zhiping Yu, see Wei Gao, T-MTT Mar 06 1055-1064 Zhiping Yu, see Zuochang Ye, T-MTT May 06 2128-2137 Zhirun Hu, see Van Tuyen Vo, T-MTT Nov 06 3836-3842 Zhiyang Liu, and R.M. Weikle. A reflectometer calibration method resistant to waveguide flange misalignment; T-MTT Jun 06 2447-2452 Zhiyang Liu, and R.M. Weikle, II. High-order subharmonically pumped mixers using phased local oscillators; T-MTT Jul 06 2977-2982 Zhou Ming, see Huang, F., T-MTT Nov 06 3954-3959 Zhou Yijun, see Koulouridis, S., T-MTT Dec 06 4202-4208 Zhu Anding, see Anding Zhu, T-MTT Dec 06 4323-4332 Zhu Jiang, see Nikolova, N.K., T-MTT Feb 06 670-681 Zhu Jintian, see Van Tuyl, R. L., T-MTT Dec 06 4556-4564 Zhu Ning Hua, see Silvonen, K., T-MTT Jun 06 1464-1469 Zijlstra, T., see Jackson, B.D., T-MTT Feb 06 547-558 Zirath, H., see Karnfelt, C., T-MTT Jun 06 2593-2603 Zirath, H., see Masud, M.A., T-MTT Jun 06 2848-2855 Zirath, H., see Karnfelt, C., T-MTT Jun 06 2887-2898 Zirath, H., see Sudow, M., T-MTT Dec 06 4072-4078 Zouhdi, S., see Ouchetto, O., T-MTT Jun 06 2615-2619 Zouhdi, S., see Ouchetto, O., T-MTT Nov 06 3893-3898 Zou-Ming Tsai, see Shih-Fong Chao, T-MTT Dec 06 4193-4201 Zscheile, H., F.J. Schmuckles, and W. Heinrich. Finite-difference formulation accounting for field singularities; T-MTT May 06 2000-2010 Zuochang Ye, Wenjian Yu, and Zhiping Yu. Efficient 3-d capacitance extraction considering lossy substrate with multilayered green's function; T-MTT May 06 2128-2137 Zuo-Min Tsai, see Mei-Chao Yeh, T-MTT Jan 06 31-39 Zuo-Min Tsai, Mei-Chao Yeh, Hong-Yeh Chang, Ming-Fong Lei, K.-Y. Lin, Chin-Shen Lin, and Huei Wang. FET-integrated CPW and the application in filter synthesis design method on traveling-wave switch above 100 GHz; T-MTT May 06 2090-2097 Zuo-Min Tsai, see Kuo-Jung Sun, T-MTT Jun 06 1554-1560 Zuo-Min Tsai, Kuo-Jung Sun, G.D. Vendelin, and Huei Wang. A new feedback method for power amplifier with unilateralization and improved output return loss; T-MTT Jun 06 1590-1597 Zwick, T., A. Chandrasekhar, C.W. Baks, U.R. Pfeiffer, S. Brebels, and B.P. Gaucher. Determination of the complex permittivity of packaging materials at millimeter-wave frequencies; T-MTT Mar 06 1001-1010

SUBJECT INDEX

A Accelerator cavities radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 Accelerator RF systems oversized Ka-band traveling-wave window for a high-power transmission. Bogdashov, A., + , T-MTT Dec 06 4130-4135 Access protocols; cf. Code division multiple access Acoustic devices; cf. Bulk acoustic wave devices Acoustic filters; cf. Surface acoustic wave filters Acoustic resonator filters; cf. Surface acoustic wave resonator filters Active antennas 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603 broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 Active arrays broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 Active circuits matching appls., tapped marchand baluns. Fathelbab, W.M., + , T-MTT Jun 06 2543-2551

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simul. of HF act. devices, efficient num. methods. Movahhedi, M., + , TMTT Jun 06 2636-2645 Active filters electronically tunable act. duplexer for wireless transceiver appls. Sundaram, B., + , T-MTT Jun 06 2584-2592 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 silicon-integrated differential bandpass filters based on recursive and channelized principles and methodology to compute their exact noise figure. Darfeuille, S., + , T-MTT Dec 06 4381-4396 Active networks; cf. Active filters; Gyrators Adaptive arrays bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 Adaptive filters design of side-coupled coaxial filters, close correspondence, phys. struct., adaptive prototype. Morini, A., + , T-MTT Mar 06 1146-1153 Adaptive radar breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 Adaptive systems; cf. Adaptive filters Algebra algebraic invariants, full-wave simulators, rigorous anal. of opt. props. of nanowires. Rozzi, T., + , T-MTT Feb 06 797-803 Algebra; cf. Polynomials Alkali metal compounds; cf. Lithium compounds Alkaline earth compounds; cf. Barium compounds Alloys; cf. Germanium alloys; Silicon alloys Aluminum high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 Aluminum compounds filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 HV microwave AlGaN/GaN HFETs, nonlin. source resist. Trew, R.J., + , T-MTT May 06 2061-2067 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 low gate bias model extr. tech. for AlGaN/GaN HEMTs. Guang Chen, + , T-MTT Jul 06 2949-2953 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Amplifiers AlGaN/GaN Ka-band 5-W MMIC amplifier. Darwish, A. M., + , T-MTT Dec 06 4456-4463 highly linear low-noise amplifier. Ganesan, S., + , T-MTT Dec 06 40794085 nonlin. amps., load-pull AM-AM and AM-PM meas., large-sig. behavioral modeling. Jiang Liu, + , T-MTT Aug 06 3191-3196 pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898 power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications. Feipeg Wang, + , T-MTT Dec 06 4086-4099 Amplifiers; cf. Distributed amplifiers; Feedback amplifiers; Operational amplifiers; Power amplifiers; Traveling wave amplifiers; Wideband amplifiers Amplitude modulation low-power UWB radio transceivers, robust front-end archit. Barras, D., + , T-MTT Jun 06 1713-1723 Amplitude modulation; cf. Amplitude shift keying; Quadrature amplitude modulation Amplitude shift keying 60-GHz-Band x 12 -multiplier MMIC with reduced power consumption. Ito, M., + , T-MTT Dec 06 4522-4527 60-GHz wireless chipsets, CSP technol. Pfeiffer, U.R., + , T-MTT Aug 06 3387-3397 BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234

IEEE T-MTT 2006 INDEX — 27 Analog circuits stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 Analog circuits; cf. Analog integrated circuits Analog-digital conversion compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 UWB, Multi(Six)-port impulse radio. Yanyang Zhao, + , T-MTT Jun 06 1707-1712 Analog integrated circuits cryogenic amp. noise temps. below 5 K, precision meas. method. Randa, J., + , T-MTT Mar 06 1180-1189 Analog integrated circuits; cf. BiCMOS analog integrated circuits Angle modulation; cf. Frequency modulation; Phase modulation Antenna accessories EM modeling of MEMS-controlled planar phase shifters, scale-changing tech. Perret, E., + , T-MTT Sep 06 3594-3601 Antenna accessories; cf. Antenna feeds Antenna arrays full-duplex dual-freq. self-steering array, phase detect. and phase shifting. Shiroma, G.S., + , T-MTT Jan 06 128-134 miniaturized antenna arrays, decoupling nets., realistic elements. Weber, J., + , T-MTT Jun 06 2733-2740 reson. behavior, finite antenna arrays, eigencurrent anal. Bekers, D.J., + , T-MTT Jun 06 2821-2829 UWB SIMO channel meas. and simul. Keignart, J., + , T-MTT Jun 06 1812-1819 Antenna arrays; cf. Microwave antenna arrays; Millimeter wave antenna arrays Antenna feeds bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 impulse generator and miniaturized antennas for IR-UWB, codesign. Bagga, S., + , T-MTT Jun 06 1656-1666 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 microwave dual-CP antenna, TW feed concept, design and meas. data. Kum Meng Lum, + , T-MTT Jun 06 2880-2886 short-range commun. systs., reconfigurable circ. polarized antenna. Aissat, H., + , T-MTT Jun 06 2856-2863 Antenna radiation patterns bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 compact colinear coaxial-to-rect. waveguide transits., patch endLaunchers, family. Simeoni, M., + , T-MTT Jun 06 1503-1511 continuously variable true-time delay beamformer, multichannel chirped fiber grating, demons. Hunter, D.B., + , T-MTT Feb 06 861-867 effects of antenna dispers., UWB waveforms via opt. pulse-shaping techs., compensation. McKinney, J.D., + , T-MTT Jun 06 1681-1686 leaky-wave structs. and appls., anal. of neg.-refr.-index leaky-wave antennas, periodic FDTD anal. Kokkinos, T., + , T-MTT Jun 06 16191630 miniaturized antenna arrays, decoupling nets., realistic elements. Weber, J., + , T-MTT Jun 06 2733-2740 multiband operation, modified T-shaped planar monopole antennas. Sheng-Bing Chen, + , T-MTT Aug 06 3267-3270 proximity of human head, small planar UWB antennas. Zhi Ning Chen, + , T-MTT Jun 06 1846-1857 UWB on-body radio channel modeling, ray theory and subband FDTD method. Yan Zhao, + , T-MTT Jun 06 1827-1835 Antennas; cf. Active antennas; Antenna accessories; Antenna arrays; Antenna radiation patterns; Antenna theory; Directive antennas; Leaky wave antennas; Microwave antennas; Millimeter wave antennas; Monopole antennas; Multibeam antennas; Reflector antennas; Satellite antennas Antenna theory leaky-wave structs. and appls., anal. of neg.-refr.-index leaky-wave antennas, periodic FDTD anal. Kokkinos, T., + , T-MTT Jun 06 16191630 + Check author entry for coauthors

UWB phased array, electron. beam-steering design. Chia, M.Y.-W., + , TMTT Jun 06 2431-2438 Application specific integrated circuits; cf. Mixed analog-digital integrated circuits Approximation methods component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 nonlin. behavior of RF amps., expt. charactn. Rolain, Y., + , T-MTT Aug 06 3209-3218 unconditionally stable Crank-Nicolson nearly PML algm. for truncating lin. Lorentz dispers. FDTD domains. Ramadan, O., T-MTT Jun 06 28072812 Arrays; cf. Antenna arrays Array signal processing continuously variable true-time delay beamformer, multichannel chirped fiber grating, demons. Hunter, D.B., + , T-MTT Feb 06 861-867 WDM and dispers. fiber, receive mode, opt. multibeamforming net. Blanc, S., + , T-MTT Jan 06 402-411 Assembly low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 Attenuators wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583 B Backward wave oscillators chaotic microwave radiation, gyro-BWO, source. Rozental, R.M., + , TMTT Jun 06 2741-2744 Backward wave tubes; cf. Backward wave oscillators Baluns 3-line balun and implement., multilayer config., design. Byoung Hwa Lee, + , T-MTT Jun 06 1405-1414 gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 LTCC balanced-to-unbalanced extracted-pole bandpass filter, complex load. Lap Kun Yeung, + , T-MTT Jun 06 1512-1518 matching appls., tapped marchand baluns. Fathelbab, W.M., + , T-MTT Jun 06 2543-2551 monolithic broadband Gilbert micromixer with an integrated marchand balun using standard silicon IC process. Sheng-Che Tseng, + , T-MTT Dec 06 4362-4371 wide-band microstrip-to-CPS/slotline transits. Wen-Hua Tu, + , T-MTT Mar 06 1084-1089 Bandpass filters 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 asymmetrical dual-band bandpass filters, equiv. net. simplification, synthesis and design. Lenoir, P., + , T-MTT Jul 06 3090-3097 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 broadband single-stage equivalent circuit for modeling LTCC bandpass filters. Yu-Shun Tsai, + , T-MTT Dec 06 4412-4421 broadside-coupled bandpass filters, both microstrip and CPW resonators. Pu-Hua Deng, + , T-MTT Oct 06 3746-3750 CMOS active bandpass filter using compacted synthetic quasi-TEM lines at C-band. Tzuang, C.-K. C., + , T-MTT Dec 06 4548-4555 combined left- and right-handed tunable transmission lines. Hongjoon Kim, + , T-MTT Dec 06 4178-4184 compact fixed and tune-all bandpass filters, coupled slow-wave resonators. Pistono, E., + , T-MTT Jun 06 2790-2799 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168

IEEE T-MTT 2006 INDEX — 28 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 compact net-type resonators and their appls., microstrip bandpass filters. Chi-Feng Chen, + , T-MTT Feb 06 755-762 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 compact second harmonic-suppressed bandstop and bandpass filters, open stubs. Wen-Hua Tu, + , T-MTT Jun 06 2497-2502 compact size coupling controllable filter, separate elec. and mag. coupling paths. Kaixue Ma, + , T-MTT Mar 06 1113-1119 compact UWB bandpass filters, composite microstrip-CPW struct. TsungNan Kuo, + , T-MTT Oct 06 3772-3778 complementary split-ring resonators, microstrip bandpass filters. Bonache, J., + , T-MTT Jan 06 265-271 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 composite right/left-handed CPW bandpass and dual-passband filters, design. Shau-Gang Mao, + , T-MTT Sep 06 3543-3549 CPW bandpass filters, loaded air-bridge enhanced capacitors and broadside-coupled transit. structs. for wideband spurious suppression. Shih-Cheng Lin, + , T-MTT Aug 06 3359-3369 design of very compact filters for Q-band appls., LTCC 3D resonators applied. Rigaudeau, L., + , T-MTT Jun 06 2620-2627 dual- and triple-passband filters, alternately cascaded multiband resonators, design. Chi-Feng Chen, + , T-MTT Sep 06 3550-3558 dual and triple passband filters, coupling-matrix design. Mokhtaari, M., + , T-MTT Nov 06 3940-3946 dual-band bandpass filter, LTCC technol., design. Ching-Wen Tang, + , TMTT Aug 06 3327-3332 dual-band lumped-element bandpass filter. Joshi, H., + , T-MTT Dec 06 4169-4177 dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 dual-bandpass filters, serial config., LTCC technol. Ke-Chiang Lin, + , TMTT Jun 06 2321-2328 dual-mode bandpass filters, hexagonal loop resonators. Rui-Jie Mao, + , T-MTT Sep 06 3526-3533 electronically switchable bandpass filters using loaded stepped-impedance resonators. Shih-Fong Chao, + , T-MTT Dec 06 4193-4201 engng. Optimization-theory and implement., space-mapping framework. Koziel, S., + , T-MTT Oct 06 3721-3730 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 liq.-cryst. polymer, 60-GHz direct-conversion gigabit modulator/demodulator. Sarkar, S., + , T-MTT Mar 06 1245-1252 low-loss integrated-waveguide passive circuits using liquid-crystal polymer system-on-package technology for millimeter-wave applications. Ki Seok Yang, + , T-MTT Dec 06 4572-4579 LTCC balanced-to-unbalanced extracted-pole bandpass filter, complex load. Lap Kun Yeung, + , T-MTT Jun 06 1512-1518 LTCC bandpass filters, diplexer, triplexer, transm. zeros, design methodologies. Ching-Wen Tang, + , T-MTT Feb 06 717-723 microstrip coupled-line bandpass filters, shortened coupled sects. for stopband extension. Chao-Huang Wu, + , T-MTT Feb 06 540-546 microstrip diplexers design, common resonator sects. for compact size, high isolation. Chi-Feng Chen, + , T-MTT May 06 1945-1952 microstrip sq.-loop dual-mode bandpass filter, simultaneous size reduction and spurious response suppression. Si-Weng Fok, + , T-MTT May 06 2033-2041 microwave bandpass filters, resonators, nonuniform Q, design. Guyette, A.C., + , T-MTT Nov 06 3914-3922 microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 miniature broadband bandpass filters, double-layer coupled stripline resonators. Yunchi Zhang, + , T-MTT Aug 06 3370-3377 miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095 + Check author entry for coauthors

periodic stepped-impedance ring resonator (PSIRR) bandpass filter, miniaturized area and desirable upper stopband characts. Kuo, J.-T., + , T-MTT Mar 06 1107-1112 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 ripples, passbands of series/parallel loaded EBG filters, study and suppression. Chu Gao, + , T-MTT Jun 06 1519-1526 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 Si/glass technol. for filter, ka-band, low-cost inverted line. Martoglio, L., + , T-MTT Jul 06 3084-3089 silicon-integrated differential bandpass filters based on recursive and channelized principles and methodology to compute their exact noise figure. Darfeuille, S., + , T-MTT Dec 06 4381-4396 synthesizing microwave bandpass filters constructed, symm., asymmetrical compact microstrip resonators, method. Yi-Chyun Chiang, + , T-MTT Nov 06 3947-3953 syst.-on-package UWB transmitter, CMOS impulse generator. Junwoo Lee, + , T-MTT Jun 06 1667-1674 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 V-band front-end, 3D integr. cavity filters/duplexers and antenna, LTCC technols. Jong-Hoon Lee, + , T-MTT Jul 06 2925-2936 wide-band commun. systs., 10-35-GHz 6-channel microstrip MUX. Seungpyo Hong, + , T-MTT Jun 06 1370-1378 wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Bandstop filters bandstop filter, improved Q factor, U-slot/V-slot DGSs. Duk-Jae Woo, + , T-MTT Jun 06 2840-2847 bandstop filters, extended upper passbands. Levy, R., + , T-MTT Jun 06 2503-2515 compact second harmonic-suppressed bandstop and bandpass filters, open stubs. Wen-Hua Tu, + , T-MTT Jun 06 2497-2502 defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 multiple-stopband filters for interf. suppression, UWB appls., design. Rambabu, K., + , T-MTT Aug 06 3333-3338 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 ripples, passbands of series/parallel loaded EBG filters, study and suppression. Chu Gao, + , T-MTT Jun 06 1519-1526 synthesizing microwave bandpass filters constructed, symm., asymmetrical compact microstrip resonators, method. Yi-Chyun Chiang, + , T-MTT Nov 06 3947-3953 tunable bandstop defected ground struct. resonator, reconfigurable dumbbell-shaped CPW. Safwat, A.M.E., + , T-MTT Sep 06 3559-3564 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Band-stop filters; cf. Notch filters Barium compounds ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 Bayes procedures IR-UWB systs., different transceiver types, TOA estim. Guvenc, I., + , TMTT Jun 06 1876-1886 Beam handling equipment; cf. Accelerator cavities Bessel functions gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 BiCMOS analog integrated circuits 6.5-kV ESD-protected 3-5-GHz UWB BiCMOS LNA, interstage gain roll-off compensation. Mingxu Liu, + , T-MTT Jun 06 1698-1706 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024

IEEE T-MTT 2006 INDEX — 29 BiCMOS integrated circuits class-E power amps., lumped-element load-net. design. Negra, R., + , TMTT Jun 06 2684-2690 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 impulse generator and miniaturized antennas for IR-UWB, codesign. Bagga, S., + , T-MTT Jun 06 1656-1666 integrated subharmonic coupled-oscillator scheme for a 60-GHz phased array transmitter. Buckwalter, J. F., + , T-MTT Dec 06 4271-4280 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 monolithic broadband Gilbert micromixer with an integrated marchand balun using standard silicon IC process. Sheng-Che Tseng, + , T-MTT Dec 06 4362-4371 silicon-integrated differential bandpass filters based on recursive and channelized principles and methodology to compute their exact noise figure. Darfeuille, S., + , T-MTT Dec 06 4381-4396 BiCMOS integrated circuits; cf. BiCMOS analog integrated circuits Bifurcation hysteresis and noisy precursors, power amps., anal. and elimination. Sanggeun Jeon, + , T-MTT Mar 06 1096-1106 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 BIMOS integrated circuits; cf. BiCMOS integrated circuits Biological effects of electromagnetic radiation 60-GHz mm waves and artificial biol. membranes, interacts. Zhadobov, M., + , T-MTT Jun 06 2534-2542 EM far-field absorpt., body tissue comp., freq. range from 300 MHz, 6 GHz, depend. Christ, A., + , T-MTT May 06 2188-2195 relax. IEEE RF safety std. for head exposures, cellular telephones, 835 and 1900 MHz, thermal implications. Qing-Xiang Li, + , T-MTT Jul 06 3146-3154 Biological effects of radiation 60-GHz mm waves and artificial biol. membranes, interacts. Zhadobov, M., + , T-MTT Jun 06 2534-2542 Biological organs; cf. Brain Biological tissues; cf. Skin Biology; cf. Cardiology Biomechanics; cf. Gait analysis Biomedical communication; cf. Telemedicine Biomedical equipment heating performs. of coaxial-slot antenna, endoscope for treatment of bile duct carcinoma, estim. Saito, K., + , T-MTT Aug 06 3443-3449 Biomedical image processing microwave breast cancer Detection-localization, 3 dimens., FDTD-based time reversal. Kosmas, P., + , T-MTT Jun 06 1921-1927 Biomedical imaging breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 Biomedical monitoring UWB body area propag. channel Model-from stats., implement. Fort, A., + , T-MTT Jun 06 1820-1826 Biomembranes 60-GHz mm waves and artificial biol. membranes, interacts. Zhadobov, M., + , T-MTT Jun 06 2534-2542 Biothermics; cf. Hyperthermia Bipolar integrated circuits empirical bipolar device nonlinear noise modeling approach for large signal microwave circuit analysis. Traverso, P. A., + , T-MTT Dec 06 4341-4352 Bipolar transistor circuits UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 Bipolar transistors; cf. Heterojunction bipolar transistors; Microwave bipolar transistors Bolometers quasiopt. NbN supercond. HEB mixer, charactn. Ling Jiang, + , T-MTT Jul 06 2944-2948 terahertz hot electron bolometer mixers, quantum-noise theory. Kollberg, E.L., + , T-MTT May 06 2077-2089

+ Check author entry for coauthors

Boundary element methods efficient 3-d capacitance extr. considering lossy substr., multilayered green's fn. Zuochang Ye, + , T-MTT May 06 2128-2137 ICCAP, lin. time sparsification and reordering algm. for 3D BEM capacitance extr. Rong Jiang, + , T-MTT Jul 06 3060-3068 spectral integral method and hybrid SIM/FEM for layered media. Simsek, E., + , T-MTT Nov 06 3878-3884 Boundary value problems cavity filled, plane multilayered dielec., method of auxiliary sources, modeling. Volski, V., + , T-MTT Jan 06 235-239 Brain UWB sig. propag., human head. Zasowski, T., + , T-MTT Jun 06 18361845 Brain modeling proximity of human head, small planar UWB antennas. Zhi Ning Chen, + , T-MTT Jun 06 1846-1857 Brillouin scattering Brillouin amplif. and Er-doped fiber amplif. for gener. of mm waves, low phase noise props., comparative test. Junker, M., + , T-MTT Jun 06 1576-1581 Broadband amplifiers broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 InP DHBT true logarithmic amp. Yu-Ju Chuang, + , T-MTT Nov 06 38433847 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 wide-band matched LNA design, transistor's intrinsic gate-drain capacitor. Hu, R., T-MTT Mar 06 1277-1286 Broadband communication fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 Broadband networks dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers. Anding Zhu, + , T-MTT Dec 06 4323-4332 very compact high-gain broadband low-noise amplifier in InP HEMT technology. Masuda, S., + , T-MTT Dec 06 4565-4571 Bulk acoustic wave devices highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 Butterworth filters exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 C CAD EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping. Rayas-Sanchez, J. E., + , T-MTT Dec 06 4528-4537 high-frequency circuit model for the gap excitation of a microstrip line. Rodriguez-Berral, R., + , T-MTT Dec 06 4100-4110 stability criterion for two-port network with input and output terminations varying in elliptic regions. Marietti, P., + , T-MTT Dec 06 4049-4055 theoretical justification of space-mapping-based modeling utilizing a database and on-demand parameter extraction. Koziel, S., + , T-MTT Dec 06 4316-4322 Cadmium compounds uniplanar compact photonic-bandgap finite-width conductor-backed CPW by electrooptic near-field mapping tech., charactn. Kyoung-Hwan Oh, + , T-MTT Feb 06 854-860 Calibration broadband space conservative on-wafer NWA calibs., complex load and thru models. Padmanabhan, S., + , T-MTT Sep 06 3583-3593 diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245

IEEE T-MTT 2006 INDEX — 30 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 lin. eqns. of voltage and current variables, 16-term error model. Silvonen, K., + , T-MTT Jun 06 1464-1469 mm-wave radiometers, ref.-polarized sig. injection, on-board calib. syst. Peverini, O.A., + , T-MTT Jan 06 412-420 quasiopt. refl. meas., scalar calib. Koers, G., + , T-MTT Jul 06 3121-3126 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 waveguide flange misalignment, reflectometer calib. method resistant. Zhiyang Liu, + , T-MTT Jun 06 2447-2452 Capacitance defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 efficient 3-d capacitance extr. considering lossy substr., multilayered green's fn. Zuochang Ye, + , T-MTT May 06 2128-2137 fast capacitance extr., adaptive nonuniform-grid (NG) algm. Boag, A., + , T-MTT Sep 06 3565-3570 transm. lines fabricated by CMOS proc., deep n-well implant. Nishikawa, K., + , T-MTT Feb 06 589-598 Capacitance measurement ICCAP, lin. time sparsification and reordering algm. for 3D BEM capacitance extr. Rong Jiang, + , T-MTT Jul 06 3060-3068 Capacitors CPW bandpass filters, loaded air-bridge enhanced capacitors and broadside-coupled transit. structs. for wideband spurious suppression. Shih-Cheng Lin, + , T-MTT Aug 06 3359-3369 periodic distrib. MEMS-appl., design of variable true-time delay lines, modeling. Perruisseau-Carrier, J., + , T-MTT Jan 06 383-392 transmission-line concept for integrated capacitors and inductors. Lee, K.Y., + , T-MTT Dec 06 4141-4148 wire-bonded interdigital capacitor, anal. model. Marquez-Segura, E., + , T-MTT Feb 06 748-754 Capacitors; cf. Thin film capacitors; Varactors Cardiology spectral analysis of a low-power Ka-band heartbeat detector measuring from four sides of a human body. Changzhi Li, + , T-MTT Dec 06 44644471 Cardiology; cf. Electrocardiography Cascade circuits 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 Cavity resonators deembedding unloaded reson. freq. from meas. of microwave cavities, tech. Canos, A.J., + , T-MTT Aug 06 3407-3416 filled, plane multilayered dielec., method of auxiliary sources, modeling. Volski, V., + , T-MTT Jan 06 235-239 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 meas. of dielec. anisotropy, multilayer samples, 2-resonator method. Dankov, P.I., T-MTT Jun 06 1534-1544 noise-free and jitterless cavity syst., distribute clocks, 10 GHz. Kato, H., + , T-MTT Nov 06 3960-3967 planar components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 Ceramics 3-line balun and implement., multilayer config., design. Byoung Hwa Lee, + , T-MTT Jun 06 1405-1414 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 dual-bandpass filters, serial config., LTCC technol. Ke-Chiang Lin, + , TMTT Jun 06 2321-2328 polymer-ceramic composites for microwave applications. Koulouridis, S., + , T-MTT Dec 06 4202-4208 Chebyshev approximation gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 + Check author entry for coauthors

Chebyshev filters broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 compact net-type resonators and their appls., microstrip bandpass filters. Chi-Feng Chen, + , T-MTT Feb 06 755-762 complementary split-ring resonators, microstrip bandpass filters. Bonache, J., + , T-MTT Jan 06 265-271 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 narrowband multicoupled resonator filters, anal. diagnosis and tuning. Wei Meng, + , T-MTT Oct 06 3765-3771 Chirality; cf. Chirowaveguides Chirowaveguides discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 Circuit analysis 6.5-kV ESD-protected 3-5-GHz UWB BiCMOS LNA, interstage gain roll-off compensation. Mingxu Liu, + , T-MTT Jun 06 1698-1706 ACPR, mixers, parametric harmonic-bal. approach. Crespo-Cadenas, C., + , T-MTT Jan 06 445-450 capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 fast capacitance extr., adaptive nonuniform-grid (NG) algm. Boag, A., + , T-MTT Sep 06 3565-3570 hysteresis and noisy precursors, power amps., anal. and elimination. Sanggeun Jeon, + , T-MTT Mar 06 1096-1106 mismatched Doherty amps., accurate load-pull-based model, design and perform. anal. Hammi, O., + , T-MTT Aug 06 3246-3254 nonlin. amps., load-pull AM-AM and AM-PM meas., large-sig. behavioral modeling. Jiang Liu, + , T-MTT Aug 06 3191-3196 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 Circuit analysis computing; cf. Circuit simulation Circuit feedback; cf. Feedback amplifiers Circuit layout; cf. Integrated circuit layout; Printed circuit layout Circuit noise accurate RF CMOS noise extr. and simul., freq. and bias depend., lossy substr. model. Jyh-Chyurn Guo, + , T-MTT Nov 06 3975-3985 eliminating simultaneously switching noise, high-speed cct., photonic cryst. power/ground layer. Tzong-Lin Wu, + , T-MTT Aug 06 3398-3406 gen. eqns. for FET cold noise source design, expt. validation. Weatherspoon, M.H., + , T-MTT Feb 06 608-614 hysteresis and noisy precursors, power amps., anal. and elimination. Sanggeun Jeon, + , T-MTT Mar 06 1096-1106 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 sig. vias, virtual islands, shorting vias, multilayer PCBs, perform. anal. Seungki Nam, + , T-MTT Jun 06 1315-1324 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 wide-band matched LNA design, transistor's intrinsic gate-drain capacitor. Hu, R., T-MTT Mar 06 1277-1286 Circuit noise; cf. Integrated circuit noise Circuit optimization 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 CMOS LNA design optim. techs. Jingxue Lu, + , T-MTT Jul 06 3155 CMOS LNA design optim. techs. ). Trung-Kien Nguyen, + , T-MTT Jul 06 3155-3156 CMOS low-noise amps., on-chip low-Q inductors, noise optim. formulation. Kuo-Jung Sun, + , T-MTT Jun 06 1554-1560

IEEE T-MTT 2006 INDEX — 31 complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 design centering of microwave ccts. exploiting space-mapping interpolating surrogates, ellipsoidal tech. Abdel-Malek, H.L., + , T-MTT Oct 06 3731-3738 fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 high-power switching-mode oscillators, nonlin. design tech. Sanggeun Jeon, + , T-MTT Oct 06 3630-3640 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 on-wafer shield-based test fixture layout, optim. Kaija, T., + , T-MTT May 06 1975-1982 periodic stepped-impedance ring resonator (PSIRR) bandpass filter, miniaturized area and desirable upper stopband characts. Kuo, J.-T., + , T-MTT Mar 06 1107-1112 Circuit simulation envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 wire-bonded interdigital capacitor, anal. model. Marquez-Segura, E., + , T-MTT Feb 06 748-754 Circuit stability high-power switching-mode oscillators, nonlin. design tech. Sanggeun Jeon, + , T-MTT Oct 06 3630-3640 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 Circuit synthesis asymmetrical dual-band bandpass filters, equiv. net. simplification, synthesis and design. Lenoir, P., + , T-MTT Jul 06 3090-3097 capacitive-coupled dual-behavior resonator (CCDBR) filters, synthesis. Manchec, A., + , T-MTT Jun 06 2346-2355 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 design of side-coupled coaxial filters, close correspondence, phys. struct., adaptive prototype. Morini, A., + , T-MTT Mar 06 1146-1153 dual and triple passband filters, coupling-matrix design. Mokhtaari, M., + , T-MTT Nov 06 3940-3946 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 improved wide-band Schiffman phase shifter. Yong-Xin Guo, + , T-MTT Mar 06 1196-1200 LTCC bandpass filters, diplexer, triplexer, transm. zeros, design methodologies. Ching-Wen Tang, + , T-MTT Feb 06 717-723 miniature ridge-waveguide filter module employing moldable dielec. material. Rauscher, C., + , T-MTT Mar 06 1190-1195 mismatched Doherty amps., accurate load-pull-based model, design and perform. anal. Hammi, O., + , T-MTT Aug 06 3246-3254 narrowband multicoupled resonator filters, anal. diagnosis and tuning. Wei Meng, + , T-MTT Oct 06 3765-3771 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 synthesis of microwave diplexers. Macchiarella, G., + , T-MTT Dec 06 4281-4290 synthesizing microwave bandpass filters constructed, symm., asymmetrical compact microstrip resonators, method. Yi-Chyun Chiang, + , T-MTT Nov 06 3947-3953 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607

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Circuit testing high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 Circuit testing; cf. Integrated circuit testing; Printed circuit testing Circuit topology 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 capacitive-coupled dual-behavior resonator (CCDBR) filters, synthesis. Manchec, A., + , T-MTT Jun 06 2346-2355 class-E power amps., lumped-element load-net. design. Negra, R., + , TMTT Jun 06 2684-2690 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 dual and triple passband filters, coupling-matrix design. Mokhtaari, M., + , T-MTT Nov 06 3940-3946 highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 narrowband multicoupled resonator filters, anal. diagnosis and tuning. Wei Meng, + , T-MTT Oct 06 3765-3771 Circuit tuning C-band high-effic. second-harmonic-tuned hybrid power amp., GaN technol. Colantonio, P., + , T-MTT Jun 06 2713-2722 eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 tunable phase shifters by image-params. method, design. Ocera, A., + , TMTT Jun 06 2383-2390 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 Circular waveguides 2-bit X-band reflective waveguide phase shifter with BCB-based bias circuits. Martynyuk, A. E., + , T-MTT Dec 06 4056-4061 Circulators in-phase and split counter-rot. eigenvalues of 3-port circulator, refl. angles. Helszajn, J., T-MTT Mar 06 1076-1083 Circulators; cf. Millimeter wave circulators Clocks noise-free and jitterless cavity syst., distribute clocks, 10 GHz. Kato, H., + , T-MTT Nov 06 3960-3967 CMOS analog integrated circuits 0.18-ȝm CMOS technol., low-power oscillator mixer. To-Po Wang, + , TMTT Jan 06 88-95 broad-band compact high-linearity modulators for gigabit microwave/mmwave appls., design and anal. Hong-Yeh Chang, + , T-MTT Jan 06 20-30 digitally controlled const. envelope phase-shift modulator for low-power broad-band wireless appls. Xiuge Yang, + , T-MTT Jan 06 96-105 double-balanced mixer, multibias dual-gate transistors, IMD reduction. Chung-Fai Au-Yeung, + , T-MTT Jan 06 4-9 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 LNA design optim. techs. Jingxue Lu, + , T-MTT Jul 06 3155 LNA design optim. techs. ). Trung-Kien Nguyen, + , T-MTT Jul 06 31553156 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 miniature 15-20-GHz continuous-phase/amplit. control MMICs, 0.18-ȝm CMOS technol. Pei-Si Wu, + , T-MTT Jan 06 10-19 MOSFETs under integr. inductors, RF operation. Nastos, N., + , T-MTT May 06 2106-2117 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 noise params. of scaled-CMOS devices, meas. and modeling errors. Banerjee, G., + , T-MTT Jun 06 2336-2345 RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56

IEEE T-MTT 2006 INDEX — 32 syst.-on-package UWB transmitter, CMOS impulse generator. Junwoo Lee, + , T-MTT Jun 06 1667-1674 CMOS digital integrated circuits extended true single-phase clock-based prescaler, design and optim. Xiao Peng Yu, + , T-MTT Nov 06 3828-3835 ku-band MMIC phase shifter, parallel resonator, 0.18-ȝm CMOS technol. Dong-Woo Kang, + , T-MTT Jan 06 294-301 CMOS integrated circuits 10-Gb/s reconfigurable CMOS equalizer employing a transition detector based output monitoring technique for band-limited serial links. Bien, F., + , T-MTT Dec 06 4538-4547 22-29-GHz UWB appls., low-power up-conversion CMOS mixer. Verma, A., + , T-MTT Aug 06 3295-3300 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 accurate RF CMOS noise extr. and simul., freq. and bias depend., lossy substr. model. Jyh-Chyurn Guo, + , T-MTT Nov 06 3975-3985 close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 CMOS active bandpass filter using compacted synthetic quasi-TEM lines at C-band. Tzuang, C.-K. C., + , T-MTT Dec 06 4548-4555 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 inductors, high amounts of dummy metal fill, phys.-based wideband predictive compact model. Tiemeijer, L.F., + , T-MTT Aug 06 33783386 integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 low-loss differential semicoaxial interconnects in CMOS process. Jun-De Jin, + , T-MTT Dec 06 4333-4340 low-noise amps., on-chip low-Q inductors, noise optim. formulation. KuoJung Sun, + , T-MTT Jun 06 1554-1560 low phase-noise CMOS VCO, harmonic tuned LC tank. Huijung Kim, + , T-MTT Jul 06 2917-2924 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 low-power-consumption and high-gain CMOS distrib. amps., cascade of inductively coupled common-source gain cells for UWB systs. Xin Guan, + , T-MTT Aug 06 3278-3283 low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73 low-power RF direct-conversion receiver/transmitter for 2.4-GHz-band IEEE 802.15.4 standard in 0.18-ȝm CMOS technology. Trung-Kien Nguyen, + , T-MTT Dec 06 4062-4071 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 multilayer design techniques for extremely miniaturized CMOS microwave and millimeter-wave distributed passive circuits. Chirala, M. K., + , T-MTT Dec 06 4218-4224 scalable compact cct. model and synthesis for RF CMOS spiral inductors. Wei Gao, + , T-MTT Mar 06 1055-1064 transm. lines fabricated by CMOS proc., deep n-well implant. Nishikawa, K., + , T-MTT Feb 06 589-598 TWA vs. temp., SOI technol., behavior. Si Moussa, M., + , T-MTT Jun 06 2675-2683 UWB communs. and Radar systs., power-efficient switching-based CMOS UWB transmitters. Rui Xu, + , T-MTT Aug 06 3271-3277 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 wireless interconnect technol., impulse radio for interchip communs. Yuanjin Zheng, + , T-MTT Jun 06 1912-1920 CMOS integrated circuits; cf. CMOS analog integrated circuits; CMOS digital integrated circuits CMSO integrated circuits low flicker-noise CMOS mixers for direct-conversion receivers. Jinsung Park, + , T-MTT Dec 06 4372-4380 Coatings; cf. Epitaxial layers Coaxial transmission lines micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 realistic rect. ȝ-coaxial lines, modeling. Lukic, M., + , T-MTT May 06 2068-2076 + Check author entry for coauthors

Coaxial waveguides advanced launcher for 2-MW 170-GHz TE34,19 coaxial cavity gyrotron, theor. investig. Jianbo Jin, + , T-MTT Mar 06 1139-1145 compact colinear coaxial-to-rect. waveguide transits., patch endLaunchers, family. Simeoni, M., + , T-MTT Jun 06 1503-1511 design of side-coupled coaxial filters, close correspondence, phys. struct., adaptive prototype. Morini, A., + , T-MTT Mar 06 1146-1153 planar high-Q micromachined monolithic half-coaxial transmission-line filter. Llamas-Garro, I., + , T-MTT Dec 06 4161-4168 Code division multiaccess 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 ACPR, mixers, parametric harmonic-bal. approach. Crespo-Cadenas, C., + , T-MTT Jan 06 445-450 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 high-effic. envelope-tracking W-CDMA base-station amp., GaN HFETs. Kimball, D.F., + , T-MTT Nov 06 3848-3856 high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 IM3 components, RF power amps., phase meas. tech. Seung-Yup Lee, + , T-MTT Jan 06 451-457 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 multisines, in-band distortion. Gharaibeh, K.M., + , T-MTT Aug 06 32273236 nonlin. amp., gain expansion phenom., Doherty amp., compensation method. Hyeong Tae Jeong, + , T-MTT Jun 06 1425-1430 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Code division multiple access distortion-cancelled Doherty high-power amplifier using 28-V GaAs heterojunction FETs for W-CDMA base stations. Takenaka, I., + , TMTT Dec 06 4513-4521 linearity improvement of HBT-based Doherty power amplifiers based on a simple analytical model. Yu Zhao, + , T-MTT Dec 06 4479-4488 Coils specific absorption rate and temperature increase within pregnant female models in magnetic resonance imaging birdcage coils. Dagang Wu, + , T-MTT Dec 06 4472-4478 Coils; cf. Superconducting coils Communication systems multiport-amplifier-based architecture versus classical architecture for space telecommunication payloads. Mallet, A., + , T-MTT Dec 06 43534361 Comparators antenna combinations for UWB ranging syst., exam. Takeuchi, Y., + , TMTT Jun 06 1858-1864 Compensation multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 nonlin. amp., gain expansion phenom., Doherty amp., compensation method. Hyeong Tae Jeong, + , T-MTT Jun 06 1425-1430 Complexity theory efficient 3-d capacitance extr. considering lossy substr., multilayered green's fn. Zuochang Ye, + , T-MTT May 06 2128-2137 TLM-MOR for high-Q structs., oblique-oblique projection. Lukashevich, D., + , T-MTT Oct 06 3712-3720 UWB ad hoc nets., TOA, joint distrib. sync. and positioning. Denis, B., + , T-MTT Jun 06 1896-1911 Computer applications; cf. CAD Computer architecture; cf. Reconfigurable architectures Conductivity permitt., dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001

IEEE T-MTT 2006 INDEX — 33 Conductors multiple vert. conductors, PC, efficient full-wave simul. algm. Onal, T., + , T-MTT Oct 06 3739-3745 open-ended rect. waveguide probe, arbitrary-shape surface crack, lossy conductor, interact. Mazlumi, F., + , T-MTT Oct 06 3706-3711 (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 Control systems; cf. Reduced order systems Control theory; cf. Compensation Convergence of numerical methods; cf. Numerical stability Converters broadband integr. mm-wave up- and down-converter GaAs MMICs. Mahon, J., + , T-MTT May 06 2050-2060 high-speed digital-to-analog converter using Schottky diode samplers. Kae-Oh Sun, + , T-MTT Dec 06 4291-14296 Converters; cf. Driver circuits Coplanar transmission lines two-port vector network analyzer measurements in the 218-344- and 356 500-GHz frequency bands. Fung, A., + , T-MTT Dec 06 4507-4512 Coplanar waveguides 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 broadband space conservative on-wafer NWA calibs., complex load and thru models. Padmanabhan, S., + , T-MTT Sep 06 3583-3593 butler matrix, CPW multilayer technol. Nedil, M., + , T-MTT Jan 06 499507 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 compact UWB bandpass filters, composite microstrip-CPW struct. TsungNan Kuo, + , T-MTT Oct 06 3772-3778 composite right/left-handed CPW bandpass and dual-passband filters, design. Shau-Gang Mao, + , T-MTT Sep 06 3543-3549 ellipt. coplanar coupled waveguides and coplanar coupled waveguides, finite ground width, anals. Duyar, M., + , T-MTT Jun 06 1388-1395 filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 low-loss Si-on-Si DC-110-GHz reson.-free package. Byung-Wook Min, + , T-MTT Feb 06 710-716 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 multilayer MMICs, 3D low-loss CPW transm. lines. Van Tuyen Vo, + , TMTT Jun 06 2864-2871 PCB cct. design, 3-dB quadrature coupler suitable. Jui-Chieh Chiu, + , TMTT Sep 06 3521-3525 short-range commun. systs., reconfigurable circ. polarized antenna. Aissat, H., + , T-MTT Jun 06 2856-2863 single-wire transm. lines, terahertz freqs. Akalin, T., + , T-MTT Jun 06 2762-2767 tunable bandstop defected ground struct. resonator, reconfigurable dumbbell-shaped CPW. Safwat, A.M.E., + , T-MTT Sep 06 3559-3564 uniplanar compact photonic-bandgap finite-width conductor-backed CPW by electrooptic near-field mapping tech., charactn. Kyoung-Hwan Oh, + , T-MTT Feb 06 854-860 wide-band microstrip-to-CPS/slotline transits. Wen-Hua Tu, + , T-MTT Mar 06 1084-1089 Copper quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 Correlation nonlin. mixing products, amplit. and phase charactn. Pedro, J.C., + , TMTT Aug 06 3237-3245

+ Check author entry for coauthors

transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 UWB ranging, multipath and multiuser environments, large error perform. Joon-Yong Lee, + , T-MTT Jun 06 1887-1895 Correlation techniques large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 Corundum; cf. Sapphire Counting circuits extended true single-phase clock-based prescaler, design and optim. Xiao Peng Yu, + , T-MTT Nov 06 3828-3835 Coupled mode analysis discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 Coupling circuits 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 anal. and design of coupled-oscillator systs., techs. Georgiadis, A., + , TMTT Nov 06 3864-3877 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 compact size coupling controllable filter, separate elec. and mag. coupling paths. Kaixue Ma, + , T-MTT Mar 06 1113-1119 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part I, design. Gruszczynski, S., + , T-MTT Nov 06 3986-3994 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 CPW bandpass filters, loaded air-bridge enhanced capacitors and broadside-coupled transit. structs. for wideband spurious suppression. Shih-Cheng Lin, + , T-MTT Aug 06 3359-3369 deembedding unloaded reson. freq. from meas. of microwave cavities, tech. Canos, A.J., + , T-MTT Aug 06 3407-3416 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 microstrip coupled-line bandpass filters, shortened coupled sects. for stopband extension. Chao-Huang Wu, + , T-MTT Feb 06 540-546 miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095 Covariance matrices NIST electrooptic sampling syst., covariance-based uncertainty anal. Williams, D.F., + , T-MTT Jan 06 481-491 Crack detection open-ended rect. waveguide probe, arbitrary-shape surface crack, lossy conductor, interact. Mazlumi, F., + , T-MTT Oct 06 3706-3711 Cracks; cf. Crack detection Crosstalk serpentine and flat spiral delay lines, transient refl./transm. waveforms and eye diags., comparisons. Wei-Da Guo, + , T-MTT Jun 06 1379-1387 Cryogenic electronics amp. noise temps. below 5 K, precision meas. method. Randa, J., + , TMTT Mar 06 1180-1189 Cryogenics; cf. Cryogenic electronics Crystal filters; cf. Surface acoustic wave filters Crystals; cf. Epitaxial layers Current density capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 comput. transm.-line params. of lossy lines, Quasi-TM MoL/MoM approach. Plaza, G., + , T-MTT Jan 06 198-209 corrections to "Closed-form expressions for the current density on the ground plane of a microstrip line, with application to ground plane loss" (May 95 1204-1207). Holloway, C. L., + , T-MTT Nov 06 4018-4019 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Current distribution capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294

IEEE T-MTT 2006 INDEX — 34 Current supplies close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 CW radar eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 phase-hologram-based compact RCS test range, 310 GHz for scale models. Lonnqvist, A., + , T-MTT Jun 06 2391-2397 D Data communication SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 Data communication equipment; cf. Modems Data conversion 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 Data conversion; cf. Analog-digital conversion; Digital-analog conversion Data handling; cf. Table lookup Deconvolution sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 Delay circuits integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 Delay circuits; cf. Delay lines Delay lines compact sub-nanosecond tunable monocycle pulse transmitter for UWB appls. Jeongwoo Han, + , T-MTT Jan 06 285-293 periodic distrib. MEMS-appl., design of variable true-time delay lines, modeling. Perruisseau-Carrier, J., + , T-MTT Jan 06 383-392 serpentine and flat spiral delay lines, transient refl./transm. waveforms and eye diags., comparisons. Wei-Da Guo, + , T-MTT Jun 06 1379-1387 Delay lines; cf. Optical delay lines Demodulation low-power UWB radio transceivers, robust front-end archit. Barras, D., + , T-MTT Jun 06 1713-1723 SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 Demodulators; cf. Modems Design automation anal. of multilayered shielded microwave ccts., neural-net. method. Garcia, J.P., + , T-MTT Jan 06 309-320 atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 broadband asymmetrical multisection wilkinson power divider, design and optim. Oraizi, H., + , T-MTT May 06 2220-2231 CAD-based design of internal matching nets. of high-power RF/microwave transistors, modeling techs. suitable. Aaen, P.H., + , TMTT Jul 06 3052-3059 coupled resonator filter CAD, quadratic prog. approach. Kozakowski, P., + , T-MTT Nov 06 3906-3913 design centering of microwave ccts. exploiting space-mapping interpolating surrogates, ellipsoidal tech. Abdel-Malek, H.L., + , T-MTT Oct 06 3731-3738 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 wire-bonded interdigital capacitor, anal. model. Marquez-Segura, E., + , T-MTT Feb 06 748-754 Dielectric devices; cf. Capacitors; Dielectric resonators; Ferroelectric devices Dielectric liquids high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 Dielectric loaded waveguides rect. hard waveguides, TE/TM modal soln. Epp, L.W., + , T-MTT Mar 06 1048-1054

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Dielectric losses backward-wave propag., periodic waveguide structs., design and expt. verification. Carbonell, J., + , T-MTT Jun 06 1527-1533 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 Dielectric materials 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 broadband microwave absorbing materials, C nanotube composites. Saib, A., + , T-MTT Jun 06 2745-2754 complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 GA and gradient descent optmization methods for accurate inverse permitt. meas., combined. Requena-Perez, M.E., + , T-MTT Feb 06 615624 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 rect. hard waveguides, TE/TM modal soln. Epp, L.W., + , T-MTT Mar 06 1048-1054 (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450 Dielectric materials; cf. Dielectric liquids; Ferroelectric materials Dielectric measurement; cf. Permittivity measurement Dielectric measurements complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 meas. of dielec. anisotropy, multilayer samples, 2-resonator method. Dankov, P.I., T-MTT Jun 06 1534-1544 permitt., dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001 Dielectric properties; cf. Capacitance; Dielectric losses Dielectric resonator oscillators 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 low phase-noise microwave oscillators, interferometric sig. proc. Ivanov, E.N., + , T-MTT Aug 06 3284-3294 Dielectric resonators cavity filled, plane multilayered dielec., method of auxiliary sources, modeling. Volski, V., + , T-MTT Jan 06 235-239 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 permitt., dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 Dielectric resonators; cf. Dielectric resonator oscillators Dielectric waveguides GA and gradient descent optmization methods for accurate inverse permitt. meas., combined. Requena-Perez, M.E., + , T-MTT Feb 06 615624 leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 substr. integr. image guide (SIIG), planar dielec. waveguide technol. for mm-wave appls. Patrovsky, A., + , T-MTT Jun 06 2872-2879 Dielectric waveguides; cf. Nonradiative dielectric waveguides Difference equations lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 Differential equations; cf. Difference equations; Green's function methods Differentiating circuits SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024

IEEE T-MTT 2006 INDEX — 35 Digital-analog conversion high-speed digital-to-analog converter using Schottky diode samplers. Kae-Oh Sun, + , T-MTT Dec 06 4291-14296 Digital audio broadcasting satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 Digital circuits eliminating simultaneously switching noise, high-speed cct., photonic cryst. power/ground layer. Tzong-Lin Wu, + , T-MTT Aug 06 3398-3406 Digital circuits; cf. Digital filters; Switching circuits Digital filters 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 Digital radio; cf. Digital audio broadcasting Digital signal processing Ka-band FMCW radar front-end with adaptive leakage cancellation. Kaihui Lin, + , T-MTT Dec 06 4041-4048 Digital signal processors 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 SAW devices, chirp transform spectrometers, digital dispers. matching net. Villanueva, G.L., + , T-MTT Jun 06 1415-1424 Directional couplers broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 butler matrix, CPW multilayer technol. Nedil, M., + , T-MTT Jan 06 499507 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part I, design. Gruszczynski, S., + , T-MTT Nov 06 3986-3994 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 phase-hologram-based compact RCS test range, 310 GHz for scale models. Lonnqvist, A., + , T-MTT Jun 06 2391-2397 Directive antennas 5.8-GHz circ. polarized retrodirective rectenna arrays for wireless power transm. Yu-Jiun Ren, + , T-MTT Jul 06 2970-2976 bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 Directive antennas; cf. Horn antennas; Lens antennas Discrete Fourier transforms eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 Discrete transforms; cf. Discrete Fourier transforms Display instrumentation; cf. Oscilloscopes; Three-dimensional displays Distance measurement eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 Distortion measurement distortion analysis of ultra-wideband OFDM receiver front-ends. Ranjan, M., + , T-MTT Dec 06 4422-4431 Distributed amplifiers low-power-consumption and high-gain CMOS distrib. amps., cascade of inductively coupled common-source gain cells for UWB systs. Xin Guan, + , T-MTT Aug 06 3278-3283 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 Distributed feedback lasers radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 uniplanar compact photonic-bandgap finite-width conductor-backed CPW by electrooptic near-field mapping tech., charactn. Kyoung-Hwan Oh, + , T-MTT Feb 06 854-860 Distributed parameter circuits compact wide-band branch-line hybrids. Young-Hoon Chun, + , T-MTT Feb 06 704-709 Distributed parameter networks; cf. Distributed amplifiers Diversity methods self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674

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UWB SIMO channel meas. and simul. Keignart, J., + , T-MTT Jun 06 1812-1819 Dosimetry in vitro exposure of mammalian cells, 1.95 GHz, high-effic. waveguide applicator. Calabrese, M.L., + , T-MTT May 06 2256-2264 Driver circuits low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73 nonlin. amp., gain expansion phenom., Doherty amp., compensation method. Hyeong Tae Jeong, + , T-MTT Jun 06 1425-1430 Duality periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 Dynamic response; cf. Transient response E Eddy currents fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 Eigenvalues and eigenfunctions cavity filled, plane multilayered dielec., method of auxiliary sources, modeling. Volski, V., + , T-MTT Jan 06 235-239 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 in-phase and split counter-rot. eigenvalues of 3-port circulator, refl. angles. Helszajn, J., T-MTT Mar 06 1076-1083 nonphysical leaky mode, field excited by source, significant contrib. Tsuji, M., + , T-MTT Jan 06 421-427 NRD components via order-reduced vol.-integral-eqn. method combined, tracking of matrix eigenvalues. Bozzi, M., + , T-MTT Jan 06 339-347 periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 reson. behavior, finite antenna arrays, eigencurrent anal. Bekers, D.J., + , T-MTT Jun 06 2821-2829 spurious DC modes, edge element solns. for modeling 3D resonators, removal. Venkatarayalu, N.V., + , T-MTT Jul 06 3019-3025 Electrical conductivity; cf. Photoconductivity Electric current; cf. Current density; Current distribution; Eddy currents Electric fields waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Electric immittance; cf. Electric impedance Electric impedance electronically switchable bandpass filters using loaded stepped-impedance resonators. Shih-Fong Chao, + , T-MTT Dec 06 4193-4201 matching circuits for microstrip triplexers based on stepped-impedance resonators. Pu-Hua Deng, + , T-MTT Dec 06 4185-4192 Electric variables measurement; cf. Capacitance measurement; Phase measurement Electroabsorption 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 testing high-frequency electronic signals with reflection-mode electroabsorption modulators. Van Tuyl, R. L., + , T-MTT Dec 06 45564564 Electrocardiography rem. detect. of heartbeat and respiration, low-power DSB transm., kaband, freq.-tuning tech. Yanming Xiao, + , T-MTT May 06 2023-2032 Electromagnetic devices electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-of-band performance. Garcia-Garcia, J., + , T-MTT Dec 06 4136-4140 EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping. Rayas-Sanchez, J. E., + , T-MTT Dec 06 4528-4537

IEEE T-MTT 2006 INDEX — 36 end-to-end performance of a microwave/RF link by means of nonlinear/electromagnetic co-simulation. Rizzoli, V., + , T-MTT Dec 06 4149-4160 theoretical justification of space-mapping-based modeling utilizing a database and on-demand parameter extraction. Koziel, S., + , T-MTT Dec 06 4316-4322 Electromagnetic diffraction diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 Electromagnetic fields 3D periodic bianisotropic metamaterials, homogenization. Ouchetto, O., + , T-MTT Nov 06 3893-3898 3D periodic multiphase composites by homogenization, modeling. Ouchetto, O., + , T-MTT Jun 06 2615-2619 3D spectral-element method, mixed-order curl conforming vector basis fns. for EM fields. Joon-Ho Lee, + , T-MTT Jan 06 437-444 capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 FDTD method and lanczos algm., steady-state response. Ting-Yi Huang, + , T-MTT Jul 06 3038-3044 field singularities, finite-difference formulation accounting. Zscheile, H., + , T-MTT May 06 2000-2010 H(curl)-conforming hierarchical basis fns. for tetrahedral meshes, set. Ingelstrom, P., T-MTT Jan 06 106-114 Electromagnetic heating heating performs. of coaxial-slot antenna, endoscope for treatment of bile duct carcinoma, estim. Saito, K., + , T-MTT Aug 06 3443-3449 in vitro exposure of mammalian cells, 1.95 GHz, high-effic. waveguide applicator. Calabrese, M.L., + , T-MTT May 06 2256-2264 specific microwave applicator for treatment of snoring, design and modeling. Cresson, P.-Y., + , T-MTT Jan 06 302-308 Electromagnetic induction; cf. Inductance Electromagnetic interference design to suppress wideband ground bounce noise in high-speed circuits by electromagnetic-bandgap-enhanced split powers. Chien-Lin Wang, + , T-MTT Dec 06 4209-4217 eliminating simultaneously switching noise, high-speed cct., photonic cryst. power/ground layer. Tzong-Lin Wu, + , T-MTT Aug 06 3398-3406 MOSFETs under integr. inductors, RF operation. Nastos, N., + , T-MTT May 06 2106-2117 Electromagnetic propagation 2D freq. converter utilizing cpd. nonlin. photonic-cryst. struct. by condensed node spatial net. method. Satoh, H., + , T-MTT Jan 06 210215 3D spectral-element method, mixed-order curl conforming vector basis fns. for EM fields. Joon-Ho Lee, + , T-MTT Jan 06 437-444 biisotropic media, TLM method, time-domain modeling. Cabeceira, A.C.L., + , T-MTT Jun 06 2780-2789 comput. electromagnetics, high-order Runge-Kutta multiresolution timedomain methods. Qunsheng Cao, + , T-MTT Aug 06 3316-3326 reson. behavior, finite antenna arrays, eigencurrent anal. Bekers, D.J., + , T-MTT Jun 06 2821-2829 unconditionally stable Crank-Nicolson nearly PML algm. for truncating lin. Lorentz dispers. FDTD domains. Ramadan, O., T-MTT Jun 06 28072812 UWB body area propag. channel Model-from stats., implement. Fort, A., + , T-MTT Jun 06 1820-1826 Electromagnetic propagation in absorbing media far-field absorpt., body tissue comp., freq. range from 300 MHz, 6 GHz, depend. Christ, A., + , T-MTT May 06 2188-2195 Radar absorbing materials, 310 GHz, monostatic reflectivity meas. Lonnqvist, A., + , T-MTT Sep 06 3486-3491 Electromagnetic propagation in dispersive media 2D photonic-cryst. waveguides form. by rect. cylinders, improved Fourier series method, modal anal. Hongting Jia, + , T-MTT Feb 06 564-571 effects of antenna dispers., UWB waveforms via opt. pulse-shaping techs., compensation. McKinney, J.D., + , T-MTT Jun 06 1681-1686 EM wave propag., biisotropic media, TLM method, time-domain modeling. Cabeceira, A.C.L., + , T-MTT Jun 06 2780-2789 increase frozen-mode bandwidth, nonreciprocal MPCs, chirping unit cell length. Chilton, R.A., + , T-MTT Jan 06 473-480 modulated sigs., double-neg. slab, Gaussian pulse expansion. Monti, G., + , T-MTT Jun 06 2755-2761

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Electromagnetic radiation direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 rem. detect. of heartbeat and respiration, low-power DSB transm., kaband, freq.-tuning tech. Yanming Xiao, + , T-MTT May 06 2023-2032 specific microwave applicator for treatment of snoring, design and modeling. Cresson, P.-Y., + , T-MTT Jan 06 302-308 Electromagnetic reflection quasiopt. refl. meas., scalar calib. Koers, G., + , T-MTT Jul 06 3121-3126 Electromagnetic scattering 2D scatterers illum. by TE waves, iter. image reconstruction. Franceschini, D., + , T-MTT Jun 06 1484-1494 breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 envelope ADI-FDTD method, num. perform. and appls. Choi, C.T.M., + , T-MTT Jan 06 256-264 reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 simulating TM waves, lossy media, split-field iter. ADI method. Shumin Wang, + , T-MTT May 06 2196-2202 spectral integral method and hybrid SIM/FEM for layered media. Simsek, E., + , T-MTT Nov 06 3878-3884 waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Electromagnetic shielding; cf. Magnetic shielding Electromagnetic wave diffraction; cf. Geometrical theory of diffraction Electromagnetism; cf. Maxwell equations Electron device noise; cf. Semiconductor device noise Electron device testing; cf. Semiconductor device testing Electronic engineering; cf. Cryogenic electronics; Low-power electronics Electronic engineering computing; cf. SPICE Electronic equipment testing; cf. Circuit testing Electron microscopy evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 Electron wave tubes; cf. Traveling wave tubes Electro-optical effects; cf. Electroabsorption Electrooptic devices NIST electrooptic sampling syst., covariance-based uncertainty anal. Williams, D.F., + , T-MTT Jan 06 481-491 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 wide-band electrooptic intens. modulator freq. response meas., opt. heterodyne down-conversion tech. Lam, A.K.M., + , T-MTT Jan 06 240246 Electrooptic effects uniplanar compact photonic-bandgap finite-width conductor-backed CPW by electrooptic near-field mapping tech., charactn. Kyoung-Hwan Oh, + , T-MTT Feb 06 854-860 Electrooptic modulation 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 multimode TW modulators for RF photonics. Di Donato, A., + , T-MTT Feb 06 724-734 Electrostatic devices; cf. Capacitors Electrostatic discharges 6.5-kV ESD-protected 3-5-GHz UWB BiCMOS LNA, interstage gain roll-off compensation. Mingxu Liu, + , T-MTT Jun 06 1698-1706 Electrostatics; cf. Electric fields Elliptic filters in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 microstrip ellipt.-fn. low-pass filters, distrib. elements, slotted ground struct. Wen-Hua Tu, + , T-MTT Oct 06 3786-3792 miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095

IEEE T-MTT 2006 INDEX — 37 narrowband supercond. filter, spirals, reversal, winding direction. Huang, F., + , T-MTT Nov 06 3954-3959 Engineering facilities; cf. Test facilities Epitaxial layers planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 Equalizers wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Equations; cf. Integral equations; Nonlinear equations Equiripple filters; cf. Chebyshev filters; Elliptic filters Equivalent circuits 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 asymmetrical dual-band bandpass filters, equiv. net. simplification, synthesis and design. Lenoir, P., + , T-MTT Jul 06 3090-3097 atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 broad-band pass. lumped equiv. ccts. of microwave discontinuities, extr. Araneo, R., T-MTT Jan 06 393-401 broadband single-stage equivalent circuit for modeling LTCC bandpass filters. Yu-Shun Tsai, + , T-MTT Dec 06 4412-4421 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 compact wide-band branch-line hybrids. Young-Hoon Chun, + , T-MTT Feb 06 704-709 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 derived physically expressive cct. model for multilayer RF embedded passives. Jie Wang, + , T-MTT May 06 1961-1968 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 efficient anal., design, filter appls. of EBG waveguide, periodic reson. loads. Goussetis, G., + , T-MTT Nov 06 3885-3892 GaN HEMTs, accurate multibias equiv.-cct. extr. Crupi, G., + , T-MTT Oct 06 3616-3622 high-frequency circuit model for the gap excitation of a microstrip line. Rodriguez-Berral, R., + , T-MTT Dec 06 4100-4110 low gate bias model extr. tech. for AlGaN/GaN HEMTs. Guang Chen, + , T-MTT Jul 06 2949-2953 lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 mixed-mode params. of cascaded balanced nets. and their appls., modeling of differential interconnects, props. Hao Shi, + , T-MTT Jan 06 360-372 nonlin. RF ccts./systs. simul., driven by several modulated sigs. Carvalho, N.B., + , T-MTT Feb 06 572-579 NRD guide ccts. incl. lumped elements, full-wave nonlin. anal. Pathak, N.P., + , T-MTT Jan 06 173-179 param. extr. for asymmetric equiv. cct. of on-chip spiral inductors, charact.-fn. approach. Fengyi Huang, + , T-MTT Jan 06 115-119 planar components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 ripples, passbands of series/parallel loaded EBG filters, study and suppression. Chu Gao, + , T-MTT Jun 06 1519-1526 (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 toroidal inductor struct., through-hole vias, ground plane. Phillips, M.D., + , T-MTT Jun 06 1325-1330 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674

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Erbium Brillouin amplif. and Er-doped fiber amplif. for gener. of mm waves, low phase noise props., comparative test. Junker, M., + , T-MTT Jun 06 1576-1581 Error analysis 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 av. bit error probab., fn. of window size for IEEE 802.15.3a UWB channel model, computable formula. Gubner, J.A., + , T-MTT Jun 06 1762-1768 memoryless nonlinearities, M-QAM and DQPSK OFDM sigs., effects. Chorti, A., + , T-MTT Aug 06 3301-3315 microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 sources of phase error and design considerations for silicon-based monolithic high-pass/low-pass microwave phase shifters. Morton, M. A., + , T-MTT Dec 06 4032-4040 transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 UWB SIMO channel meas. and simul. Keignart, J., + , T-MTT Jun 06 1812-1819 Error correction diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 Error correction; cf. Forward error correction Errors; cf. Measurement errors Error statistics end-to-end performance of a microwave/RF link by means of nonlinear/electromagnetic co-simulation. Rizzoli, V., + , T-MTT Dec 06 4149-4160 Estimation multisines, in-band distortion. Gharaibeh, K.M., + , T-MTT Aug 06 32273236 Estimation theory; cf. Maximum likelihood estimation; Phase estimation; Recursive estimation Etching; cf. Sputter etching Evolutionary computation; cf. Genetic algorithms F Fast Fourier transforms; cf. Discrete Fourier transforms Fault currents; cf. Leakage currents FDTD methods 3D precise integrat. time-domain method without restraints of courantfriedrich-levy stabil. condition for num. soln. of Maxwell's eqns. Xikui Ma, + , T-MTT Jul 06 3026-3037 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 Crank-Nicolson scheme for FDTD method, efficient implementations. Guilin Sun, + , T-MTT May 06 2275-2284 domain decomp. FDTD algm. combined, num. TL calib. tech. and appl., param. extr. of substr. IC. Feng Xu, + , T-MTT Jan 06 329-338 eliminating simultaneously switching noise, high-speed cct., photonic cryst. power/ground layer. Tzong-Lin Wu, + , T-MTT Aug 06 3398-3406 EM far-field absorpt., body tissue comp., freq. range from 300 MHz, 6 GHz, depend. Christ, A., + , T-MTT May 06 2188-2195 envelope ADI-FDTD method, num. perform. and appls. Choi, C.T.M., + , T-MTT Jan 06 256-264 leaky-wave structs. and appls., anal. of neg.-refr.-index leaky-wave antennas, periodic FDTD anal. Kokkinos, T., + , T-MTT Jun 06 16191630 lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 method and lanczos algm., steady-state response. Ting-Yi Huang, + , TMTT Jul 06 3038-3044 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703

IEEE T-MTT 2006 INDEX — 38 microwave breast cancer Detection-localization, 3 dimens., FDTD-based time reversal. Kosmas, P., + , T-MTT Jun 06 1921-1927 nonphysical leaky mode, field excited by source, significant contrib. Tsuji, M., + , T-MTT Jan 06 421-427 sig. vias, virtual islands, shorting vias, multilayer PCBs, perform. anal. Seungki Nam, + , T-MTT Jun 06 1315-1324 simul. of HF act. devices, efficient num. methods. Movahhedi, M., + , TMTT Jun 06 2636-2645 time-domain Maxwell syst., cell-centered finite-vol.-based perfectly matched Layer. Sankaran, K., + , T-MTT Mar 06 1269-1276 unconditionally stable Crank-Nicolson nearly PML algm. for truncating lin. Lorentz dispers. FDTD domains. Ramadan, O., T-MTT Jun 06 28072812 UWB on-body radio channel modeling, ray theory and subband FDTD method. Yan Zhao, + , T-MTT Jun 06 1827-1835 UWB sig. propag., human head. Zasowski, T., + , T-MTT Jun 06 18361845 UWB vs. narrowband microwave hyperthermia for breast cancer treatment, comput. study. Converse, M., + , T-MTT May 06 2169-2180 Feedback amplifiers power amp., unilateralization and improved output return loss, feedback method. Zuo-Min Tsai, + , T-MTT Jun 06 1590-1597 wide-band matched LNA design, transistor's intrinsic gate-drain capacitor. Hu, R., T-MTT Mar 06 1277-1286 Feedback circuits SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 Feedforward neural nets; cf. Radial basis function networks Ferrite devices; cf. Ferrite filters; Ferrite isolators; Ferrite phase shifters Ferrite filters cellular commun. terminals, magnetically tunable filters. Krupka, J., + , TMTT Jun 06 2329-2335 Ferrite isolators multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 Ferrite phase shifters multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 Ferroelectric devices distrib. nonlinearities, ferroelectrics and superconds. for microwave appls., anal. and Simulation. Seron, D., + , T-MTT Mar 06 1154-1160 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 Ferroelectric materials distrib. nonlinearities, ferroelectrics and superconds. for microwave appls., anal. and Simulation. Seron, D., + , T-MTT Mar 06 1154-1160 FET switches filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 Fibers; cf. Optical fibers Field effect devices; cf. Field effect transistors; MIS devices Field effect transistor circuits; cf. HEMT circuits; MESFET circuits; MOSFET circuits Field effect transistors nonquasi-static empirical model of electron devices. Santarelli, A., + , TMTT Dec 06 4021-4031 Field effect transistors; cf. High electron mobility transistors Field programmable gate arrays high power-amp. linearization, block-based predistortion. Safari, N., + , TMTT Jun 06 2813-2820 UWB, Multi(Six)-port impulse radio. Yanyang Zhao, + , T-MTT Jun 06 1707-1712 Filters efficient anal., design, filter appls. of EBG waveguide, periodic reson. loads. Goussetis, G., + , T-MTT Nov 06 3885-3892 electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-of-band performance. Garcia-Garcia, J., + , T-MTT Dec 06 4136-4140 Filters; cf. Active filters; Adaptive filters; Band-pass filters; Butterworth filters; Digital filters; Ferrite filters; FIR filters; High-pass filters; Low-

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pass filters; Notch filters; Passive filters; Programmable filters; Resonator filters; Switched filters; Waveguide filters Finite difference methods field singularities, finite-difference formulation accounting. Zscheile, H., + , T-MTT May 06 2000-2010 net. params., EM freq.-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Feb 06 670-681 simulating TM waves, lossy media, split-field iter. ADI method. Shumin Wang, + , T-MTT May 06 2196-2202 Finite different methods specific absorption rate and temperature increase within pregnant female models in magnetic resonance imaging birdcage coils. Dagang Wu, + , T-MTT Dec 06 4472-4478 Finite different time-domain analysis 3-D finite-difference time-domain scheme based on a transversely extended-curl operator. Panaretos, A. H., + , T-MTT Dec 06 4237-4246 Finite element analysis; cf. Mesh generation Finite element methods 3D periodic multiphase composites by homogenization, modeling. Ouchetto, O., + , T-MTT Jun 06 2615-2619 3D spectral-element method, mixed-order curl conforming vector basis fns. for EM fields. Joon-Ho Lee, + , T-MTT Jan 06 437-444 algebraic invariants, full-wave simulators, rigorous anal. of opt. props. of nanowires. Rozzi, T., + , T-MTT Feb 06 797-803 broad-band microstrip vert. transits., cavity couplers, designs. Li, E.S., + , T-MTT Jan 06 464-472 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 increase frozen-mode bandwidth, nonreciprocal MPCs, chirping unit cell length. Chilton, R.A., + , T-MTT Jan 06 473-480 leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 low-stress suspen. structs. and appls., RF MEMS parallel-plate variable capacitors, finite-element modeling. Elshurafa, A.M., + , T-MTT May 06 2211-2219 mm-wave integrat., substr.-integr.-waveguide circulators suitable. D'Orazio, W., + , T-MTT Oct 06 3675-3680 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 realistic rect. ȝ-coaxial lines, modeling. Lukic, M., + , T-MTT May 06 2068-2076 self-consistent coupled carrier transport full-wave EM anal. of semicond. TW devices. Bertazzi, F., + , T-MTT Jun 06 1611-1618 spectral integral method and hybrid SIM/FEM for layered media. Simsek, E., + , T-MTT Nov 06 3878-3884 spurious DC modes, edge element solns. for modeling 3D resonators, removal. Venkatarayalu, N.V., + , T-MTT Jul 06 3019-3025 waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Finline split-ring resonator and wire loaded transm. line, fin-line technol., lefthanded EM props. Decoopman, T., + , T-MTT Jun 06 1451-1457 FIR digital filters widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 FIR filters 10-Gb/s reconfigurable CMOS equalizer employing a transition detector based output monitoring technique for band-limited serial links. Bien, F., + , T-MTT Dec 06 4538-4547 Flaw detection; cf. Crack detection Flicker noise low flicker-noise CMOS mixers for direct-conversion receivers. Jinsung Park, + , T-MTT Dec 06 4372-4380 Flip-chip devices parylene-C, perform. of mm-wave ccts. Karnfelt, C., + , T-MTT Aug 06 3417-3425 FM radar eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483

IEEE T-MTT 2006 INDEX — 39 Forward error correction self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 Frequency conversion 2D freq. converter utilizing cpd. nonlin. photonic-cryst. struct. by condensed node spatial net. method. Satoh, H., + , T-MTT Jan 06 210215 Brillouin amplif. and Er-doped fiber amplif. for gener. of mm waves, low phase noise props., comparative test. Junker, M., + , T-MTT Jun 06 1576-1581 extended true single-phase clock-based prescaler, design and optim. Xiao Peng Yu, + , T-MTT Nov 06 3828-3835 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 heterostruct. barrier varactors, subharmonically pumped mm-wave upconverters. Haiyong Xu, + , T-MTT Oct 06 3648-3653 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 Frequency division multiaccess OFDM-based UWB indoor radio access nets., stat. MUX-based hybrid FH-OFDMA syst. Jo Woon Chong, + , T-MTT Jun 06 1793-1801 Frequency division multiplexing high- and low-data-rate appls., UWB ranging accuracy. Cardinali, R., + , T-MTT Jun 06 1865-1875 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 Frequency division multiplexing; cf. OFDM modulation Frequency domain analysis dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 net. params., EM freq.-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Feb 06 670-681 nonlin. amps., load-pull AM-AM and AM-PM meas., large-sig. behavioral modeling. Jiang Liu, + , T-MTT Aug 06 3191-3196 reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 Frequency domain synthesis time-domain modeling of TWT amps. for high data-rate commun. appls., from freq.-domain phys.-based simul. Safier, P.N., + , T-MTT Oct 06 3605-3615 Frequency hop communication OFDM-based UWB indoor radio access nets., stat. MUX-based hybrid FH-OFDMA syst. Jo Woon Chong, + , T-MTT Jun 06 1793-1801 Frequency modulation SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 Frequency modulation; cf. FM radar Frequency response complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 in-phase and split counter-rot. eigenvalues of 3-port circulator, refl. angles. Helszajn, J., T-MTT Mar 06 1076-1083 microstrip diplexers design, common resonator sects. for compact size, high isolation. Chi-Feng Chen, + , T-MTT May 06 1945-1952 perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 wide-band electrooptic intens. modulator freq. response meas., opt. heterodyne down-conversion tech. Lam, A.K.M., + , T-MTT Jan 06 240246

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Frequency selective surfaces 3D metallic objs. arranged, 2D lattices, Ewald transform., integral-eqn. anal. Stevanovic, I., + , T-MTT Oct 06 3688-3697 Frequency synthesizers nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 SAW devices, chirp transform spectrometers, digital dispers. matching net. Villanueva, G.L., + , T-MTT Jun 06 1415-1424 wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 Function approximation; cf. Chebyshev approximation Functions; cf. Bessel functions; Green's function methods; Transfer functions; Transforms G Gait analysis very compact high-gain broadband low-noise amplifier in InP HEMT technology. Masuda, S., + , T-MTT Dec 06 4565-4571 Gallium compounds 45-dB variable-gain low-noise MMIC amp. Masud, M.A., + , T-MTT Jun 06 2848-2855 behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 broadband integr. mm-wave up- and down-converter GaAs MMICs. Mahon, J., + , T-MTT May 06 2050-2060 C-band high-effic. second-harmonic-tuned hybrid power amp., GaN technol. Colantonio, P., + , T-MTT Jun 06 2713-2722 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 GaN HEMTs, accurate multibias equiv.-cct. extr. Crupi, G., + , T-MTT Oct 06 3616-3622 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 high-effic. class-F and inverse class-F power amps., anal. and expts. Young Yun Woo, + , T-MTT May 06 1969-1974 high-effic. envelope-tracking W-CDMA base-station amp., GaN HFETs. Kimball, D.F., + , T-MTT Nov 06 3848-3856 HV microwave AlGaN/GaN HFETs, nonlin. source resist. Trew, R.J., + , T-MTT May 06 2061-2067 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 low gate bias model extr. tech. for AlGaN/GaN HEMTs. Guang Chen, + , T-MTT Jul 06 2949-2953 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 power amp. charactn. Bensmida, S., + , T-MTT Jun 06 2707-2712 power amp., unilateralization and improved output return loss, feedback method. Zuo-Min Tsai, + , T-MTT Jun 06 1590-1597 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 wideband InP DHBT true logarithmic amp. Yu-Ju Chuang, + , T-MTT Nov 06 3843-3847 wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583

IEEE T-MTT 2006 INDEX — 40 Gaussian channels av. bit error probab., fn. of window size for IEEE 802.15.3a UWB channel model, computable formula. Gubner, J.A., + , T-MTT Jun 06 1762-1768 Gaussian distributions advanced launcher for 2-MW 170-GHz TE34,19 coaxial cavity gyrotron, theor. investig. Jianbo Jin, + , T-MTT Mar 06 1139-1145 Gaussian noise UWB sigs., nonGaussian noise, robust detect. Guney, N., + , T-MTT Jun 06 1724-1730 Gaussian processes capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 modulated sigs., double-neg. slab, Gaussian pulse expansion. Monti, G., + , T-MTT Jun 06 2755-2761 Gaussian processes; cf. Gaussian channels; Gaussian noise Genetic algorithms compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 deembedding/unterminating microwave fixtures, GA. Adalev, A.S., + , TMTT Jul 06 3131-3140 GA and gradient descent optmization methods for accurate inverse permitt. meas., combined. Requena-Perez, M.E., + , T-MTT Feb 06 615624 Geometrical optics leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 Geometrical optics; cf. Ray tracing Geometrical theory of diffraction UWB on-body radio channel modeling, ray theory and subband FDTD method. Yan Zhao, + , T-MTT Jun 06 1827-1835 Germanium alloys behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 Global Positioning System direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 Gold evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 Green's function methods 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 3D metallic objs. arranged, 2D lattices, Ewald transform., integral-eqn. anal. Stevanovic, I., + , T-MTT Oct 06 3688-3697 anal. of multilayered shielded microwave ccts., neural-net. method. Garcia, J.P., + , T-MTT Jan 06 309-320 corrections to "Closed-form expressions for the current density on the ground plane of a microstrip line, with application to ground plane loss" (May 95 1204-1207). Holloway, C. L., + , T-MTT Nov 06 4018-4019 direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 efficient 3-d capacitance extr. considering lossy substr., multilayered green's fn. Zuochang Ye, + , T-MTT May 06 2128-2137 eval. of Green's fns. for multilayer media, singularity subtraction. Simsek, E., + , T-MTT Jan 06 216-225 modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521

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multiple vert. conductors, PC, efficient full-wave simul. algm. Onal, T., + , T-MTT Oct 06 3739-3745 Gyrators mm-wave integrat., substr.-integr.-waveguide circulators suitable. D'Orazio, W., + , T-MTT Oct 06 3675-3680 Gyrotrons advanced launcher for 2-MW 170-GHz TE34,19 coaxial cavity gyrotron, theor. investig. Jianbo Jin, + , T-MTT Mar 06 1139-1145 chaotic microwave radiation, gyro-BWO, source. Rozental, R.M., + , TMTT Jun 06 2741-2744 radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 H Harmonic distortion compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 HEMT circuits 60-GHz-Band x 12 -multiplier MMIC with reduced power consumption. Ito, M., + , T-MTT Dec 06 4522-4527 InAs/AlSb HEMT and its application to ultra-low-power wideband highgain low-noise amplifiers. Ma, B. Y., + , T-MTT Dec 06 4448-4455 RF chipset for impulse UWB radar using 0.13-ȝm InP-HEMT technology. Kawano, Y., + , T-MTT Dec 06 4489-4497 very compact high-gain broadband low-noise amplifier in InP HEMT technology. Masuda, S., + , T-MTT Dec 06 4565-4571 Hessian matrices fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 Heterojunction bipolar transistors active harmonic load-pull for on-wafer out-of-band device linearity optimization. Spirito, M., + , T-MTT Dec 06 4225-4236 behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 HBT small-sig. model params., systematic and rigorous extr. method. Degachi, L., + , T-MTT Feb 06 682-688 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 linearity improvement of HBT-based Doherty power amplifiers based on a simple analytical model. Yu Zhao, + , T-MTT Dec 06 4479-4488 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 wideband InP DHBT true logarithmic amp. Yu-Ju Chuang, + , T-MTT Nov 06 3843-3847 High electron mobility distortion-cancelled Doherty high-power amplifier using 28-V GaAs heterojunction FETs for W-CDMA base stations. Takenaka, I., + , TMTT Dec 06 4513-4521 High electron mobility transistors InAs/AlSb HEMT and its application to ultra-low-power wideband highgain low-noise amplifiers. Ma, B. Y., + , T-MTT Dec 06 4448-4455 RF chipset for impulse UWB radar using 0.13-ȝm InP-HEMT technology. Kawano, Y., + , T-MTT Dec 06 4489-4497 Higher order statistics corrected microwave multisine waveform generator. Carvalho, N.B., + , T-MTT Jun 06 2659-2664 High-frequency effects; cf. Skin effect High-pass filters compact UWB bandpass filters, composite microstrip-CPW struct. TsungNan Kuo, + , T-MTT Oct 06 3772-3778 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898

IEEE T-MTT 2006 INDEX — 41 High-temperature superconductors distrib. nonlinearities, ferroelectrics and superconds. for microwave appls., anal. and Simulation. Seron, D., + , T-MTT Mar 06 1154-1160 High-voltage engineering; cf. High-voltage techniques High-voltage techniques radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 Hilbert transforms sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 Holography phase-hologram-based compact RCS test range, 310 GHz for scale models. Lonnqvist, A., + , T-MTT Jun 06 2391-2397 Horn antennas effects of antenna dispers., UWB waveforms via opt. pulse-shaping techs., compensation. McKinney, J.D., + , T-MTT Jun 06 1681-1686 UWB monopulse receiver, design. Tan, A.E.-C., + , T-MTT Nov 06 38213827 Hot carriers terahertz hot electron bolometer mixers, quantum-noise theory. Kollberg, E.L., + , T-MTT May 06 2077-2089 Humidity parylene-C, perform. of mm-wave ccts. Karnfelt, C., + , T-MTT Aug 06 3417-3425 Hybrid integrated circuits dual-band planar quadrature hybrid, enhanced bandwidth response. Collado, C., + , T-MTT Jan 06 180-188 Hyperthermia heating performs. of coaxial-slot antenna, endoscope for treatment of bile duct carcinoma, estim. Saito, K., + , T-MTT Aug 06 3443-3449 UWB vs. narrowband microwave hyperthermia for breast cancer treatment, comput. study. Converse, M., + , T-MTT May 06 2169-2180 Hysteresis hysteresis and noisy precursors, power amps., anal. and elimination. Sanggeun Jeon, + , T-MTT Mar 06 1096-1106

I

IEEE standards av. bit error probab., fn. of window size for IEEE 802.15.3a UWB channel model, computable formula. Gubner, J.A., + , T-MTT Jun 06 1762-1768 high- and low-data-rate appls., UWB ranging accuracy. Cardinali, R., + , T-MTT Jun 06 1865-1875 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 low-power RF direct-conversion receiver/transmitter for 2.4-GHz-band IEEE 802.15.4 standard in 0.18-ȝm CMOS technology. Trung-Kien Nguyen, + , T-MTT Dec 06 4062-4071 relax. IEEE RF safety std. for head exposures, cellular telephones, 835 and 1900 MHz, thermal implications. Qing-Xiang Li, + , T-MTT Jul 06 3146-3154 UWB nets., uncontrolled interf., robust sig.-detect. method. Fawal, A.E., + , T-MTT Jun 06 1769-1781 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 IF amplifiers integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 Image processing; cf. Image reconstruction; Radar imaging Image reconstruction 2D scatterers illum. by TE waves, iter. image reconstruction. Franceschini, D., + , T-MTT Jun 06 1484-1494 Imaging; cf. Biomedical imaging; Magnetic resonance imaging; Microwave imaging; Radar imaging; Submillimeter wave imaging Immittance converters microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 Impedance broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 + Check author entry for coauthors

Impedance matching 3-line balun and implement., multilayer config., design. Byoung Hwa Lee, + , T-MTT Jun 06 1405-1414 analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 broadband asymmetrical multisection wilkinson power divider, design and optim. Oraizi, H., + , T-MTT May 06 2220-2231 distrib. MEMS tunable matching net., minimal-contact RF-MEMS varactors. Qin Shen, + , T-MTT Jun 06 2646-2658 highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 wide-band microstrip-to-CPS/slotline transits. Wen-Hua Tu, + , T-MTT Mar 06 1084-1089 Indium compounds complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 HV microwave AlGaN/GaN HFETs, nonlin. source resist. Trew, R.J., + , T-MTT May 06 2061-2067 integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 wideband InP DHBT true logarithmic amp. Yu-Ju Chuang, + , T-MTT Nov 06 3843-3847 Indoor radio communication BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 OFDM-based UWB indoor radio access nets., stat. MUX-based hybrid FH-OFDMA syst. Jo Woon Chong, + , T-MTT Jun 06 1793-1801 Inductance defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 inductors, high amounts of dummy metal fill, phys.-based wideband predictive compact model. Tiemeijer, L.F., + , T-MTT Aug 06 33783386 Inductors CMOS low-noise amps., on-chip low-Q inductors, noise optim. formulation. Kuo-Jung Sun, + , T-MTT Jun 06 1554-1560 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 high amounts of dummy metal fill, phys.-based wideband predictive compact model. Tiemeijer, L.F., + , T-MTT Aug 06 3378-3386 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 MOSFETs under integr. inductors, RF operation. Nastos, N., + , T-MTT May 06 2106-2117 param. extr. for asymmetric equiv. cct. of on-chip spiral inductors, charact.-fn. approach. Fengyi Huang, + , T-MTT Jan 06 115-119 scalable compact cct. model and synthesis for RF CMOS spiral inductors. Wei Gao, + , T-MTT Mar 06 1055-1064 toroidal inductor struct., through-hole vias, ground plane. Phillips, M.D., + , T-MTT Jun 06 1325-1330 transmission-line concept for integrated capacitors and inductors. Lee, K.Y., + , T-MTT Dec 06 4141-4148 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 Information theory; cf. Error statistics; Prediction theory

IEEE T-MTT 2006 INDEX — 42 Injection locked oscillators BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 phase-noise meas., 2 inter-injection-locked microwave oscillators. Nick, M., + , T-MTT Jul 06 2993-3000 Inorganic compounds; cf. Aluminum compounds; Cadmium compounds; Gallium compounds; Indium compounds; Silicon compounds Instrument amplifiers behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 Instrumentation large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 Instruments; cf. Clocks Integral equations 3D metallic objs. arranged, 2D lattices, Ewald transform., integral-eqn. anal. Stevanovic, I., + , T-MTT Oct 06 3688-3697 anal. of multilayered shielded microwave ccts., neural-net. method. Garcia, J.P., + , T-MTT Jan 06 309-320 capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 eval. of Green's fns. for multilayer media, singularity subtraction. Simsek, E., + , T-MTT Jan 06 216-225 fast capacitance extr., adaptive nonuniform-grid (NG) algm. Boag, A., + , T-MTT Sep 06 3565-3570 modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 NRD components via order-reduced vol.-integral-eqn. method combined, tracking of matrix eigenvalues. Bozzi, M., + , T-MTT Jan 06 339-347 solving thick irises, rect. waveguides, Integral-eqn. tech. Stevanovic, I., + , T-MTT Jan 06 189-197 spectral integral method and hybrid SIM/FEM for layered media. Simsek, E., + , T-MTT Nov 06 3878-3884 (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Integrated circuit design 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 6.5-kV ESD-protected 3-5-GHz UWB BiCMOS LNA, interstage gain roll-off compensation. Mingxu Liu, + , T-MTT Jun 06 1698-1706 CMOS LNA design optim. techs. Jingxue Lu, + , T-MTT Jul 06 3155 CMOS LNA design optim. techs. ). Trung-Kien Nguyen, + , T-MTT Jul 06 3155-3156 composite right/left-handed transm. line metamaterial phase shifters (MPS), MMIC technol. Perruisseau-Carrier, J., + , T-MTT Jun 06 1582-1589 domain decomp. FDTD algm. combined, num. TL calib. tech. and appl., param. extr. of substr. IC. Feng Xu, + , T-MTT Jan 06 329-338 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 neural-net.-based parasitic modeling and extr. verification for RF/mmwave IC design. Sen, P., + , T-MTT Jun 06 2604-2614 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 scalable compact cct. model and synthesis for RF CMOS spiral inductors. Wei Gao, + , T-MTT Mar 06 1055-1064 ultrahigh-speed digital interconnects, substr. integr. waveguides optimized. Simpson, J.J., + , T-MTT May 06 1983-1990 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 Integrated circuit design; cf. Integrated circuit layout Integrated circuit interconnections 3D IC, multiwafer vert. interconnects. Lahiji, R.R., + , T-MTT Jun 06 2699-2706

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direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 mixed-mode params. of cascaded balanced nets. and their appls., modeling of differential interconnects, props. Hao Shi, + , T-MTT Jan 06 360-372 ultrahigh-speed digital interconnects, substr. integr. waveguides optimized. Simpson, J.J., + , T-MTT May 06 1983-1990 wireless interconnect technol., impulse radio for interchip communs. Yuanjin Zheng, + , T-MTT Jun 06 1912-1920 Integrated circuit layout CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 layout scaling, Si integr. stacked transformers, anal. and modeling. Biondi, T., + , T-MTT May 06 2203-2210 on-wafer shield-based test fixture layout, optim. Kaija, T., + , T-MTT May 06 1975-1982 Integrated circuit measurements cryogenic amp. noise temps. below 5 K, precision meas. method. Randa, J., + , T-MTT Mar 06 1180-1189 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 noise params. of scaled-CMOS devices, meas. and modeling errors. Banerjee, G., + , T-MTT Jun 06 2336-2345 Integrated circuit modeling behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 composite right/left-handed transm. line metamaterial phase shifters (MPS), MMIC technol. Perruisseau-Carrier, J., + , T-MTT Jun 06 1582-1589 derived physically expressive cct. model for multilayer RF embedded passives. Jie Wang, + , T-MTT May 06 1961-1968 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 mixed-mode params. of cascaded balanced nets. and their appls., modeling of differential interconnects, props. Hao Shi, + , T-MTT Jan 06 360-372 neural-net.-based parasitic modeling and extr. verification for RF/mmwave IC design. Sen, P., + , T-MTT Jun 06 2604-2614 noise params. of scaled-CMOS devices, meas. and modeling errors. Banerjee, G., + , T-MTT Jun 06 2336-2345 power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 scalable compact cct. model and synthesis for RF CMOS spiral inductors. Wei Gao, + , T-MTT Mar 06 1055-1064 Integrated circuit noise close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 CMOS LNA design optim. techs. Jingxue Lu, + , T-MTT Jul 06 3155 CMOS LNA design optim. techs. ). Trung-Kien Nguyen, + , T-MTT Jul 06 3155-3156 CMOS low-noise amps., on-chip low-Q inductors, noise optim. formulation. Kuo-Jung Sun, + , T-MTT Jun 06 1554-1560 cryogenic amp. noise temps. below 5 K, precision meas. method. Randa, J., + , T-MTT Mar 06 1180-1189 Integrated circuit packaging 3D IC, multiwafer vert. interconnects. Lahiji, R.R., + , T-MTT Jun 06 2699-2706 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 Integrated circuits; cf. Analog integrated circuits; Hybrid integrated circuits; Integrated optoelectronics; Monolithic integrated circuits; Power integrated circuits; Radiofrequency integrated circuits Integrated circuit technology; cf. Integrated circuit interconnections; Integrated circuit packaging Integrated circuit testing ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 on-wafer shield-based test fixture layout, optim. Kaija, T., + , T-MTT May 06 1975-1982

IEEE T-MTT 2006 INDEX — 43 ultrahigh-speed digital interconnects, substr. integr. waveguides optimized. Simpson, J.J., + , T-MTT May 06 1983-1990 Integrated optics analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 microwave channelizer and spectroscope, integr. opt. Bragg-grating Fabry-Perot and integr. hybrid Fresnel lens syst. Winnall, S.T., + , TMTT Feb 06 868-872 Integrated optoelectronics Radar systs., opt. sig. proc. Tonda-Goldstein, S., + , T-MTT Feb 06 847853 w-band multiport substr.-integr. waveguide Circuits. Ellis, T.J., T-MTT Nov 06 4016 Integration (mathematics) direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 Integrators microwave integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , T-MTT Mar 06 1043-1047 Interconnections low-loss differential semicoaxial interconnects in CMOS process. Jun-De Jin, + , T-MTT Dec 06 4333-4340 Interconnections; cf. Integrated circuit interconnections; Optical interconnections Interface phenomena 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 Interference SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 space-time selective RAKE receiver, finger selection strategies for UWB overlay communs. Tsung-Hui Chang, + , T-MTT Jun 06 1731-1744 UWB nets., uncontrolled interf., robust sig.-detect. method. Fawal, A.E., + , T-MTT Jun 06 1769-1781 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 Interference (signal); cf. Crosstalk; Electromagnetic interference; Intersymbol interference Interference suppression compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 multiple-stopband filters for interf. suppression, UWB appls., design. Rambabu, K., + , T-MTT Aug 06 3333-3338 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 photonic freq.-conversion method, bandpass sampling, multicarrier operated radio-on-fiber link, proposal. Higashino, T., + , T-MTT Feb 06 973-979 ripples, passbands of series/parallel loaded EBG filters, study and suppression. Chu Gao, + , T-MTT Jun 06 1519-1526 transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Intermodulation; cf. Intermodulation distortion Intermodulation distortion analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 C-band high-effic. second-harmonic-tuned hybrid power amp., GaN technol. Colantonio, P., + , T-MTT Jun 06 2713-2722

+ Check author entry for coauthors

charactn. and behavioral modeling of nonlin. devices, memory, timedomain envelope meas. Macraigne, F., + , T-MTT Aug 06 3219-3226 CMOS double-balanced mixer, multibias dual-gate transistors, IMD reduction. Chung-Fai Au-Yeung, + , T-MTT Jan 06 4-9 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 multisines, in-band distortion. Gharaibeh, K.M., + , T-MTT Aug 06 32273236 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 RF MEMS variable capacitors. Girbau, D., + , T-MTT Mar 06 1120-1130 wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 Interpolation adaptive multivariate rational data fitting, appls., electromagnetics. Cuyt, A., + , T-MTT May 06 2265-2274 engng. optim., space-mapping-based interpolation. Koziel, S., + , T-MTT Jun 06 2410-2421 H(curl)-conforming hierarchical basis fns. for tetrahedral meshes, set. Ingelstrom, P., T-MTT Jan 06 106-114 Intersymbol interference transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 Ion implantation planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 Iterative methods 2D scatterers illum. by TE waves, iter. image reconstruction. Franceschini, D., + , T-MTT Jun 06 1484-1494 fast capacitance extr., adaptive nonuniform-grid (NG) algm. Boag, A., + , T-MTT Sep 06 3565-3570 FDTD method and lanczos algm., steady-state response. Ting-Yi Huang, + , T-MTT Jul 06 3038-3044 field singularities, finite-difference formulation accounting. Zscheile, H., + , T-MTT May 06 2000-2010 miniaturized antenna arrays, decoupling nets., realistic elements. Weber, J., + , T-MTT Jun 06 2733-2740 simulating TM waves, lossy media, split-field iter. ADI method. Shumin Wang, + , T-MTT May 06 2196-2202 Iterative methods; cf. Newton method K Klystrons radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 L Ladder circuits multiband p-i-n diode switches, ladder ccts., design and fab. Shingo Tanaka, + , T-MTT Jun 06 1561-1568 Land mobile radio cellular systems commun. terminals, magnetically tunable filters. Krupka, J., + , T-MTT Jun 06 2329-2335 relax. IEEE RF safety std. for head exposures, cellular telephones, 835 and 1900 MHz, thermal implications. Qing-Xiang Li, + , T-MTT Jul 06 3146-3154 Lanthanum compounds compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 Laplace transforms lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 Laser accessories low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73

IEEE T-MTT 2006 INDEX — 44 Laser applications uniplanar compact photonic-bandgap finite-width conductor-backed CPW by electrooptic near-field mapping tech., charactn. Kyoung-Hwan Oh, + , T-MTT Feb 06 854-860 Laser modes microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 Lasers; cf. Distributed feedback lasers; Ring lasers Laser tuning wide-band electrooptic intens. modulator freq. response meas., opt. heterodyne down-conversion tech. Lam, A.K.M., + , T-MTT Jan 06 240246 Lead bonding wire-bonded interdigital capacitor, anal. model. Marquez-Segura, E., + , T-MTT Feb 06 748-754 Leakage currents Ka-band FMCW radar front-end with adaptive leakage cancellation. Kaihui Lin, + , T-MTT Dec 06 4041-4048 Leaky wave antennas modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 structs. and appls., anal. of neg.-refr.-index leaky-wave antennas, periodic FDTD anal. Kokkinos, T., + , T-MTT Jun 06 1619-1630 Least squares methods 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 measuring complex permitt. tensor of uniaxial composite materials, waveguide-based 2-step approach. Akhtar, M.J., + , T-MTT May 06 2011-2022 UWB ad hoc nets., TOA, joint distrib. sync. and positioning. Denis, B., + , T-MTT Jun 06 1896-1911 Lens antennas half Maxwell fish-eye lens antennas, mm waves, design and charactn. Fuchs, B., + , T-MTT Jun 06 2292-2300 Lenses microwave channelizer and spectroscope, integr. opt. Bragg-grating Fabry-Perot and integr. hybrid Fresnel lens syst. Winnall, S.T., + , TMTT Feb 06 868-872 Level measurement high-precision multitarget-level meas. syst., TDR, approach. Gerding, M., + , T-MTT Jun 06 2768-2773 Linear accelerators radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 Linear algebra; cf. Eigenvalues and eigenfunctions Linear approximation CMOS double-balanced mixer, multibias dual-gate transistors, IMD reduction. Chung-Fai Au-Yeung, + , T-MTT Jan 06 4-9 externally modulated long-haul analog fiber-optic links, wide-band predistortion linearization. Urick, V.J., + , T-MTT Jun 06 1458-1463 high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 high power-amp. linearization, block-based predistortion. Safari, N., + , TMTT Jun 06 2813-2820 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 nonlin. amp., gain expansion phenom., Doherty amp., compensation method. Hyeong Tae Jeong, + , T-MTT Jun 06 1425-1430 nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 power amp. predistortion linearization, dynamically optimum lookup-table spacing. Chih-Hung Lin, + , T-MTT May 06 2118-2127 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Linear circuits broad-band pass. lumped equiv. ccts. of microwave discontinuities, extr. Araneo, R., T-MTT Jan 06 393-401 class-E power amps., lumped-element load-net. design. Negra, R., + , TMTT Jun 06 2684-2690 compact planar microstrip branch-line couplers, quasilumped elements approach, nonsymmetrical and symm. T-shaped struct. Shry-Sann Liao, + , T-MTT Sep 06 3508-3514 + Check author entry for coauthors

compact wide-band branch-line hybrids. Young-Hoon Chun, + , T-MTT Feb 06 704-709 lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 multiband p-i-n diode switches, ladder ccts., design and fab. Shingo Tanaka, + , T-MTT Jun 06 1561-1568 net. params., EM freq.-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Feb 06 670-681 NRD guide ccts. incl. lumped elements, full-wave nonlin. anal. Pathak, N.P., + , T-MTT Jan 06 173-179 stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 Liquid crystal devices low-loss integrated-waveguide passive circuits using liquid-crystal polymer system-on-package technology for millimeter-wave applications. Ki Seok Yang, + , T-MTT Dec 06 4572-4579 Liquid crystals organic Wafer-Scale packaged miniature 4-bit RF MEMS phase shifter. Kingsley, N., + , T-MTT Mar 06 1229-1236 package, LCP for RF/microwave MEMS switches, design and develop. Chen, M.J., + , T-MTT Nov 06 4009-4015 polymer, 60-GHz direct-conversion gigabit modulator/demodulator. Sarkar, S., + , T-MTT Mar 06 1245-1252 Liquids; cf. Dielectric liquids; Liquid crystals Lithium compounds 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 Lithography; cf. Photolithography Local area networks; cf. Wireless LAN Log normal distributions av. bit error probab., fn. of window size for IEEE 802.15.3a UWB channel model, computable formula. Gubner, J.A., + , T-MTT Jun 06 1762-1768 UWB body area propag. channel Model-from stats., implement. Fort, A., + , T-MTT Jun 06 1820-1826 Losses; cf. Dielectric losses; Optical losses Loss measurement complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 meas. of dielec. anisotropy, multilayer samples, 2-resonator method. Dankov, P.I., T-MTT Jun 06 1534-1544 permitt., dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001 Low-pass filters compact and selective low-pass filter, reduced spurious responses, CPW tapered periodic structs. Kaddour, D., + , T-MTT Jun 06 2367-2375 defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 microstrip ellipt.-fn. low-pass filters, distrib. elements, slotted ground struct. Wen-Hua Tu, + , T-MTT Oct 06 3786-3792 Low-power electronics InAs/AlSb HEMT and its application to ultra-low-power wideband highgain low-noise amplifiers. Ma, B. Y., + , T-MTT Dec 06 4448-4455 low-power RF direct-conversion receiver/transmitter for 2.4-GHz-band IEEE 802.15.4 standard in 0.18-ȝm CMOS technology. Trung-Kien Nguyen, + , T-MTT Dec 06 4062-4071 M Machining; cf. Micromachining Magnetic anisotropy multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 uniaxial and radial anisotropy models for finite-volume Maxwellian absorber. Sankaran, K., + , T-MTT Dec 06 4297-4304 Magnetic circuits perfect-magnetic-coupling ultra-low-loss micromachined SMIS RF transformers for RFIC applications. Hsiao-Bin Liang, + , T-MTT Dec 06 4256-14267

IEEE T-MTT 2006 INDEX — 45 Magnetic fields waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Magnetic layered films multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 Magnetic materials increase frozen-mode bandwidth, nonreciprocal MPCs, chirping unit cell length. Chilton, R.A., + , T-MTT Jan 06 473-480 small patch antennas providing tunable miniaturization factors, substr. Buell, K., + , T-MTT Jan 06 135-146 Magnetic resonance imaging specific absorption rate and temperature increase within pregnant female models in magnetic resonance imaging birdcage coils. Dagang Wu, + , T-MTT Dec 06 4472-4478 Magnetic shielding broadband microwave absorbing materials, C nanotube composites. Saib, A., + , T-MTT Jun 06 2745-2754 Magnetism; cf. Magnetic fields; Magnetic materials; Magnetic shielding Magnetization; cf. Magnetic anisotropy Magnetization processes small patch antennas providing tunable miniaturization factors, substr. Buell, K., + , T-MTT Jan 06 135-146 Masers microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 Materials; cf. Ceramics; Dielectric materials; Magnetic materials; Quartz; Semiconductor materials Materials testing evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 measuring complex permitt. tensor of uniaxial composite materials, waveguide-based 2-step approach. Akhtar, M.J., + , T-MTT May 06 2011-2022 Materials testing; cf. Nondestructive testing Mathematical analysis; cf. Bessel functions; Eigenvalues and eigenfunctions; Integral equations; Time-domain analysis; Transforms Mathematics; cf. Algebra Matrices butler matrix, CPW multilayer technol. Nedil, M., + , T-MTT Jan 06 499507 direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 fast capacitance extr., adaptive nonuniform-grid (NG) algm. Boag, A., + , T-MTT Sep 06 3565-3570 lin. eqns. of voltage and current variables, 16-term error model. Silvonen, K., + , T-MTT Jun 06 1464-1469 NRD components via order-reduced vol.-integral-eqn. method combined, tracking of matrix eigenvalues. Bozzi, M., + , T-MTT Jan 06 339-347 waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Matrix algebra; cf. Covariance matrices; Hessian matrices; Sparse matrices; Transmission line matrix methods Maximum likelihood estimation IR-UWB systs., different transceiver types, TOA estim. Guvenc, I., + , TMTT Jun 06 1876-1886 parametric UWB propag. channel estim. and perform. validation, anechoic chamber. Haneda, K., + , T-MTT Jun 06 1802-1811 UWB ad hoc nets., TOA, joint distrib. sync. and positioning. Denis, B., + , T-MTT Jun 06 1896-1911 Maxwell equations 3D precise integrat. time-domain method without restraints of courantfriedrich-levy stabil. condition for num. soln. of Maxwell's eqns. Xikui Ma, + , T-MTT Jul 06 3026-3037 extr. of dielec. props. from insulating substrs. utilizing evanescent perturb. method, data anal. Inoue, R., + , T-MTT Feb 06 522-532 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 simul. of HF act. devices, efficient num. methods. Movahhedi, M., + , TMTT Jun 06 2636-2645 time-domain Maxwell syst., cell-centered finite-vol.-based perfectly matched Layer. Sankaran, K., + , T-MTT Mar 06 1269-1276 + Check author entry for coauthors

uniaxial and radial anisotropy models for finite-volume Maxwellian absorber. Sankaran, K., + , T-MTT Dec 06 4297-4304 Measurement; cf. Distortion measurement; Dosimetry; Loss measurement; Noise measurement; Optical variables measurement; Reflectometry Measurement errors lin. eqns. of voltage and current variables, 16-term error model. Silvonen, K., + , T-MTT Jun 06 1464-1469 noise params. of scaled-CMOS devices, meas. and modeling errors. Banerjee, G., + , T-MTT Jun 06 2336-2345 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 Mechanical factors micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 Medical treatment specific microwave applicator for treatment of snoring, design and modeling. Cresson, P.-Y., + , T-MTT Jan 06 302-308 Medicine; cf. Telemedicine Meetings 2006 Asia-Pacific Microwave Conference (special section). T-MTT Jul 06 2901-2948 2006 International Microwave Symposium (special issue, part II). T-MTT Dec 06 4271-4579 35th European Microwave Conference (special issue). T-MTT Jun 06 2567-2898 35th European Microwave Conference (special issue intro.). Quere, R., + , T-MTT Jun 06 2567 Membranes; cf. Biomembranes MESFET circuits An SiC MESFET-Based MMIC Process. Sudow, M., + , T-MTT Dec 06 4072-4078 power amp., unilateralization and improved output return loss, feedback method. Zuo-Min Tsai, + , T-MTT Jun 06 1590-1597 MESFETs high-effic. class-F and inverse class-F power amps., anal. and expts. Young Yun Woo, + , T-MTT May 06 1969-1974 lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 Mesh generation H(curl)-conforming hierarchical basis fns. for tetrahedral meshes, set. Ingelstrom, P., T-MTT Jan 06 106-114 MIC geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 time-domain Maxwell syst., cell-centered finite-vol.-based perfectly matched Layer. Sankaran, K., + , T-MTT Mar 06 1269-1276 Metallization noise-free and jitterless cavity syst., distribute clocks, 10 GHz. Kato, H., + , T-MTT Nov 06 3960-3967 Metals; cf. Aluminum Metamaterials optimization of arbitrarily sized DNG metamaterial slabs with losses. Sounas, D. L., + , T-MTT Dec 06 4111-4121 Method of moments hybrid space-discretizing method, method of moments for the analysis of transient interference. Khlifi, R., + , T-MTT Dec 06 4440-4447 Microassembling; cf. Lead bonding Microelectromechanical devices 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 distrib. MEMS tunable matching net., minimal-contact RF-MEMS varactors. Qin Shen, + , T-MTT Jun 06 2646-2658 highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 intermodulation, RF MEMS variable capacitors. Girbau, D., + , T-MTT Mar 06 1120-1130 low-stress suspen. structs. and appls., RF MEMS parallel-plate variable capacitors, finite-element modeling. Elshurafa, A.M., + , T-MTT May 06 2211-2219 organic Wafer-Scale packaged miniature 4-bit RF MEMS phase shifter. Kingsley, N., + , T-MTT Mar 06 1229-1236

IEEE T-MTT 2006 INDEX — 46 package, LCP for RF/microwave MEMS switches, design and develop. Chen, M.J., + , T-MTT Nov 06 4009-4015 periodic distrib. MEMS-appl., design of variable true-time delay lines, modeling. Perruisseau-Carrier, J., + , T-MTT Jan 06 383-392 Micromachining atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 micromachined wide-band Li-niobate electrooptic Modulators. Yongqiang Shi, T-MTT Feb 06 810-815 Micromechanical devices 2-bit antenna-filter-antenna elements for reconfigurable millimeter-wave lens arrays. Chih-Chieh Cheng, + , T-MTT Dec 06 4498-4506 perfect-magnetic-coupling ultra-low-loss micromachined SMIS RF transformers for RFIC applications. Hsiao-Bin Liang, + , T-MTT Dec 06 4256-14267 Microresonators low-loss 5.15-5.70-GHz RF MEMS switchable filter for WLAN appls. Sang-June Park, + , T-MTT Nov 06 3931-3939 Microscopy; cf. Electron microscopy Microstrip 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 compact planar microstrip branch-line couplers, quasilumped elements approach, nonsymmetrical and symm. T-shaped struct. Shry-Sann Liao, + , T-MTT Sep 06 3508-3514 compact UWB bandpass filters, composite microstrip-CPW struct. TsungNan Kuo, + , T-MTT Oct 06 3772-3778 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 defected ground structs. (DGSs) incl. left-handed features, bandgap and slow/fast-wave characts. Hyung-Mi Kim, + , T-MTT Jul 06 3113-3120 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 ku-band MMIC phase shifter, parallel resonator, 0.18-ȝm CMOS technol. Dong-Woo Kang, + , T-MTT Jan 06 294-301 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 TWA vs. temp., SOI technol., behavior. Si Moussa, M., + , T-MTT Jun 06 2675-2683 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 Microstrip antennas 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603 broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 compact colinear coaxial-to-rect. waveguide transits., patch endLaunchers, family. Simeoni, M., + , T-MTT Jun 06 1503-1511 microwave dual-CP antenna, TW feed concept, design and meas. data. Kum Meng Lum, + , T-MTT Jun 06 2880-2886 satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 short-range commun. systs., reconfigurable circ. polarized antenna. Aissat, H., + , T-MTT Jun 06 2856-2863 small patch antennas providing tunable miniaturization factors, substr. Buell, K., + , T-MTT Jan 06 135-146 V-band front-end, 3D integr. cavity filters/duplexers and antenna, LTCC technols. Jong-Hoon Lee, + , T-MTT Jul 06 2925-2936 Microstrip arrays 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 5.8-GHz circ. polarized retrodirective rectenna arrays for wireless power transm. Yu-Jiun Ren, + , T-MTT Jul 06 2970-2976 + Check author entry for coauthors

broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 EM modeling of MEMS-controlled planar phase shifters, scale-changing tech. Perret, E., + , T-MTT Sep 06 3594-3601 half Maxwell fish-eye lens antennas, mm waves, design and charactn. Fuchs, B., + , T-MTT Jun 06 2292-2300 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 Microstrip circuits 3D IC, multiwafer vert. interconnects. Lahiji, R.R., + , T-MTT Jun 06 2699-2706 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 organic Wafer-Scale packaged miniature 4-bit RF MEMS phase shifter. Kingsley, N., + , T-MTT Mar 06 1229-1236 Microstrip components line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 multiband p-i-n diode switches, ladder ccts., design and fab. Shingo Tanaka, + , T-MTT Jun 06 1561-1568 toroidal inductor struct., through-hole vias, ground plane. Phillips, M.D., + , T-MTT Jun 06 1325-1330 wire-bonded interdigital capacitor, anal. model. Marquez-Segura, E., + , T-MTT Feb 06 748-754 Microstrip components; cf. Microstrip antennas; Microstrip circuits; Microstrip couplers; Microstrip filters; Microstrip resonators Microstrip couplers arbitrarily dual-band components, simplified structs. of conventional CRLH TLs. Xian Qi Lin, + , T-MTT Jul 06 2902-2909 broad-band microstrip vert. transits., cavity couplers, designs. Li, E.S., + , T-MTT Jan 06 464-472 compact planar microstrip branch-line couplers, quasilumped elements approach, nonsymmetrical and symm. T-shaped struct. Shry-Sann Liao, + , T-MTT Sep 06 3508-3514 compact wide-band branch-line hybrids. Young-Hoon Chun, + , T-MTT Feb 06 704-709 coupled-line bandpass filters, shortened coupled sects. for stopband extension. Chao-Huang Wu, + , T-MTT Feb 06 540-546 high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 PCB cct. design, 3-dB quadrature coupler suitable. Jui-Chieh Chiu, + , TMTT Sep 06 3521-3525 Microstrip filters 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 bandstop filter, improved Q factor, U-slot/V-slot DGSs. Duk-Jae Woo, + , T-MTT Jun 06 2840-2847 broadside-coupled bandpass filters, both microstrip and CPW resonators. Pu-Hua Deng, + , T-MTT Oct 06 3746-3750 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 compact net-type resonators and their appls., microstrip bandpass filters. Chi-Feng Chen, + , T-MTT Feb 06 755-762 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 compact size coupling controllable filter, separate elec. and mag. coupling paths. Kaixue Ma, + , T-MTT Mar 06 1113-1119

IEEE T-MTT 2006 INDEX — 47 compact UWB bandpass filters, composite microstrip-CPW struct. TsungNan Kuo, + , T-MTT Oct 06 3772-3778 complementary split-ring resonators, microstrip bandpass filters. Bonache, J., + , T-MTT Jan 06 265-271 coupled-line bandpass filters, shortened coupled sects. for stopband extension. Chao-Huang Wu, + , T-MTT Feb 06 540-546 coupled resonator filter CAD, quadratic prog. approach. Kozakowski, P., + , T-MTT Nov 06 3906-3913 defected ground struct., quasistatic modeling. Karmakar, N.C., + , T-MTT May 06 2160-2168 diplexers design, common resonator sects. for compact size, high isolation. Chi-Feng Chen, + , T-MTT May 06 1945-1952 dual- and triple-passband filters, alternately cascaded multiband resonators, design. Chi-Feng Chen, + , T-MTT Sep 06 3550-3558 dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 dual-mode bandpass filters, hexagonal loop resonators. Rui-Jie Mao, + , T-MTT Sep 06 3526-3533 ellipt.-fn. low-pass filters, distrib. elements, slotted ground struct. WenHua Tu, + , T-MTT Oct 06 3786-3792 engng. Optimization-theory and implement., space-mapping framework. Koziel, S., + , T-MTT Oct 06 3721-3730 high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 miniaturized microstrip and CPW filters, coupled metamaterial resonators. Garcia-Garcia, J., + , T-MTT Jun 06 2628-2635 multiple-stopband filters for interf. suppression, UWB appls., design. Rambabu, K., + , T-MTT Aug 06 3333-3338 periodic stepped-impedance ring resonator (PSIRR) bandpass filter, miniaturized area and desirable upper stopband characts. Kuo, J.-T., + , T-MTT Mar 06 1107-1112 quasidual-mode microstrip spiral filters, 1st. and second harmonic resons. Frederick Huang, T-MTT Feb 06 742-747 ripples, passbands of series/parallel loaded EBG filters, study and suppression. Chu Gao, + , T-MTT Jun 06 1519-1526 wide-band commun. systs., 10-35-GHz 6-channel microstrip MUX. Seungpyo Hong, + , T-MTT Jun 06 1370-1378 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Microstrip lines corrections to "Closed-form expressions for the current density on the ground plane of a microstrip line, with application to ground plane loss" (May 95 1204-1207). Holloway, C. L., + , T-MTT Nov 06 4018-4019 electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-of-band performance. Garcia-Garcia, J., + , T-MTT Dec 06 4136-4140 high-frequency circuit model for the gap excitation of a microstrip line. Rodriguez-Berral, R., + , T-MTT Dec 06 4100-4110 matching circuits for microstrip triplexers based on stepped-impedance resonators. Pu-Hua Deng, + , T-MTT Dec 06 4185-4192 nonuniform lossy/lossless transmission lines and tapered microstrips. Eghlidi, M. H., + , T-MTT Dec 06 4122-4129 Microstrip resonators 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 balanced/unbalanced composite right/left-handed transm. lines, design. Allen, C.A., + , T-MTT Jul 06 3104-3112 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 compact net-type resonators and their appls., microstrip bandpass filters. Chi-Feng Chen, + , T-MTT Feb 06 755-762 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553

+ Check author entry for coauthors

CPW bandpass filters, loaded air-bridge enhanced capacitors and broadside-coupled transit. structs. for wideband spurious suppression. Shih-Cheng Lin, + , T-MTT Aug 06 3359-3369 dielec. const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 diplexers design, common resonator sects. for compact size, high isolation. Chi-Feng Chen, + , T-MTT May 06 1945-1952 dual- and triple-passband filters, alternately cascaded multiband resonators, design. Chi-Feng Chen, + , T-MTT Sep 06 3550-3558 dual-mode bandpass filters, hexagonal loop resonators. Rui-Jie Mao, + , T-MTT Sep 06 3526-3533 high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 narrowband supercond. filter, spirals, reversal, winding direction. Huang, F., + , T-MTT Nov 06 3954-3959 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 planar components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 quasidual-mode microstrip spiral filters, 1st. and second harmonic resons. Frederick Huang, T-MTT Feb 06 742-747 synthesizing microwave bandpass filters constructed, symm., asymmetrical compact microstrip resonators, method. Yi-Chyun Chiang, + , T-MTT Nov 06 3947-3953 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Microwave amplifiers multisines, in-band distortion. Gharaibeh, K.M., + , T-MTT Aug 06 32273236 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 Microwave amplifiers; cf. Masers; Microwave power amplifiers; MMIC amplifiers Microwave antenna arrays 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 5.8-GHz circ. polarized retrodirective rectenna arrays for wireless power transm. Yu-Jiun Ren, + , T-MTT Jul 06 2970-2976 butler matrix, CPW multilayer technol. Nedil, M., + , T-MTT Jan 06 499507 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 UWB on-body radio channel modeling, ray theory and subband FDTD method. Yan Zhao, + , T-MTT Jun 06 1827-1835 Microwave antennas dual-CP antenna, TW feed concept, design and meas. data. Kum Meng Lum, + , T-MTT Jun 06 2880-2886 heating performs. of coaxial-slot antenna, endoscope for treatment of bile duct carcinoma, estim. Saito, K., + , T-MTT Aug 06 3443-3449 integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 LTCC technol., transceiver integrat. capability for UWB appls., planar antennas. Brzezina, G., + , T-MTT Jun 06 2830-2839 multiband operation, modified T-shaped planar monopole antennas. Sheng-Bing Chen, + , T-MTT Aug 06 3267-3270 near-range microwave Radar syst., UWB rugby-ball antenna. Ruengwaree, A., + , T-MTT Jun 06 2774-2779 Microwave antennas; cf. Lens antennas; Microwave antenna arrays; Waveguide antennas Microwave bipolar integrated circuits UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 Microwave bipolar transistors output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863

IEEE T-MTT 2006 INDEX — 48 Microwave circuits anal. of multilayered shielded microwave ccts., neural-net. method. Garcia, J.P., + , T-MTT Jan 06 309-320 broad-band pass. lumped equiv. ccts. of microwave discontinuities, extr. Araneo, R., T-MTT Jan 06 393-401 complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 design centering of microwave ccts. exploiting space-mapping interpolating surrogates, ellipsoidal tech. Abdel-Malek, H.L., + , T-MTT Oct 06 3731-3738 EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping. Rayas-Sanchez, J. E., + , T-MTT Dec 06 4528-4537 empirical bipolar device nonlinear noise modeling approach for large signal microwave circuit analysis. Traverso, P. A., + , T-MTT Dec 06 4341-4352 IM3 and IM5 phase charactn. and anal., simplified Newton approach. Crespo-Cadenas, C., + , T-MTT Jan 06 321-328 integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , TMTT Mar 06 1043-1047 leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 theoretical justification of space-mapping-based modeling utilizing a database and on-demand parameter extraction. Koziel, S., + , T-MTT Dec 06 4316-4322 UWB, Multi(Six)-port impulse radio. Yanyang Zhao, + , T-MTT Jun 06 1707-1712 Microwave circuits; cf. Microwave integrated circuits Microwave detectors microwave photonics (special issue). T-MTT Feb 06 777-989 microwave photonics (special issue intro.). Seeds, A., + , T-MTT Feb 06 777-779 planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 Microwave devices 2006 Asia-Pacific Microwave Conference (special section). T-MTT Jul 06 2901-2948 distrib. nonlinearities, ferroelectrics and superconds. for microwave appls., anal. and Simulation. Seron, D., + , T-MTT Mar 06 1154-1160 engng. optim., space-mapping-based interpolation. Koziel, S., + , T-MTT Jun 06 2410-2421 low-loss Si-on-Si DC-110-GHz reson.-free package. Byung-Wook Min, + , T-MTT Feb 06 710-716 package, LCP for RF/microwave MEMS switches, design and develop. Chen, M.J., + , T-MTT Nov 06 4009-4015 periodic distrib. MEMS-appl., design of variable true-time delay lines, modeling. Perruisseau-Carrier, J., + , T-MTT Jan 06 383-392 wide-band commun. systs., 10-35-GHz 6-channel microstrip MUX. Seungpyo Hong, + , T-MTT Jun 06 1370-1378 Microwave devices; cf. Microwave amplifiers; Microwave antennas; Microwave circuits; Microwave detectors; Microwave diodes; Microwave filters; Microwave mixers; Microwave oscillators; Microwave phase shifters; Microwave receivers; Microwave transistors; Superconducting microwave devices Microwave diodes planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 Microwave FET integrated circuits CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 low-power-consumption and high-gain CMOS distrib. amps., cascade of inductively coupled common-source gain cells for UWB systs. Xin Guan, + , T-MTT Aug 06 3278-3283 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 + Check author entry for coauthors

RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 Microwave FETs HV microwave AlGaN/GaN HFETs, nonlin. source resist. Trew, R.J., + , T-MTT May 06 2061-2067 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 Microwave filters asymmetrical dual-band bandpass filters, equiv. net. simplification, synthesis and design. Lenoir, P., + , T-MTT Jul 06 3090-3097 bandpass filters, resonators, nonuniform Q, design. Guyette, A.C., + , TMTT Nov 06 3914-3922 bandstop filters, extended upper passbands. Levy, R., + , T-MTT Jun 06 2503-2515 compact microstrip dual-band bandpass filters design, GA techs. Ming-Iu Lai, + , T-MTT Jan 06 160-168 complementary split-ring resonators, microstrip bandpass filters. Bonache, J., + , T-MTT Jan 06 265-271 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 coupled resonator filter CAD, quadratic prog. approach. Kozakowski, P., + , T-MTT Nov 06 3906-3913 dual-bandpass filters, serial config., LTCC technol. Ke-Chiang Lin, + , TMTT Jun 06 2321-2328 exact synthesis of UWB filtering responses, high-pass/low-pass sects., systematic method. Gomez-Garcia, R., + , T-MTT Oct 06 3751-3764 fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 look, practical design of compact diplexers. Morini, A., + , T-MTT Sep 06 3515-3520 miniature ridge-waveguide filter module employing moldable dielec. material. Rauscher, C., + , T-MTT Mar 06 1190-1195 miniaturized microstrip and CPW filters, coupled metamaterial resonators. Garcia-Garcia, J., + , T-MTT Jun 06 2628-2635 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 planar coupled-resonator microwave filters, space-mapping optim. Amari, S., + , T-MTT May 06 2153-2159 planar high-Q micromachined monolithic half-coaxial transmission-line filter. Llamas-Garro, I., + , T-MTT Dec 06 4161-4168 prog. photonic microwave filters, arbitrary UWB phase response. Shijun Xiao, + , T-MTT Nov 06 4002-4008 Si/glass technol. for filter, ka-band, low-cost inverted line. Martoglio, L., + , T-MTT Jul 06 3084-3089 sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832-846 synthesis of microwave diplexers. Macchiarella, G., + , T-MTT Dec 06 4281-4290 synthesizing microwave bandpass filters constructed, symm., asymmetrical compact microstrip resonators, method. Yi-Chyun Chiang, + , T-MTT Nov 06 3947-3953 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583 Microwave frequency conversion freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 Microwave frequency converters; cf. MMIC frequency converters Microwave generation corrected microwave multisine waveform generator. Carvalho, N.B., + , T-MTT Jun 06 2659-2664 sig., rational harmonic mode-locked fiber ring laser, photonic gener. Zhichao Deng, + , T-MTT Feb 06 763-767 Microwave imaging breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 breast cancer Detection-localization, 3 dimens., FDTD-based time reversal. Kosmas, P., + , T-MTT Jun 06 1921-1927 evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647

IEEE T-MTT 2006 INDEX — 49 subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450 UWB vs. narrowband microwave hyperthermia for breast cancer treatment, comput. study. Converse, M., + , T-MTT May 06 2169-2180 Microwave integrated circuits 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 domain decomp. FDTD algm. combined, num. TL calib. tech. and appl., param. extr. of substr. IC. Feng Xu, + , T-MTT Jan 06 329-338 dual-band planar quadrature hybrid, enhanced bandwidth response. Collado, C., + , T-MTT Jan 06 180-188 geometries via, dynamically adaptive mesh Refinement-FDTD tech., efficient modeling. Yaxun Liu, + , T-MTT Feb 06 689-703 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 Microwave integrated circuits; cf. MMIC Microwave isolators; cf. Ferrite isolators Microwave measurement; cf. Microwave reflectometry Microwave measurements complex permitt. meas., planar 4-port device, tech. Ocera, A., + , T-MTT Jun 06 2568-2575 deembedding/unterminating microwave fixtures, GA. Adalev, A.S., + , TMTT Jul 06 3131-3140 dielec. const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 extr. of dielec. props. from insulating substrs. utilizing evanescent perturb. method, data anal. Inoue, R., + , T-MTT Feb 06 522-532 freq.-depend. equiv. width of substr. integr. waveguide, meas. ChaoHsiung Tseng, + , T-MTT Jun 06 1431-1437 gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 large-sig. microwave meas., noise considerations, determining phase. Blockley, P.S., + , T-MTT Aug 06 3182-3190 meas. of dielec. anisotropy, multilayer samples, 2-resonator method. Dankov, P.I., T-MTT Jun 06 1534-1544 mixer, single-digit phase accuracy, sampling-oscilloscope meas. Williams, D.F., + , T-MTT Mar 06 1210-1217 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 nonlin. amps., load-pull AM-AM and AM-PM meas., large-sig. behavioral modeling. Jiang Liu, + , T-MTT Aug 06 3191-3196 on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 12961297 open-ended rect. waveguide probe, arbitrary-shape surface crack, lossy conductor, interact. Mazlumi, F., + , T-MTT Oct 06 3706-3711 Microwave mixers 5.25-GHz CMOS folded-cascode even-harmonic mixer for LV appls. Ming-Feng Huang, + , T-MTT Feb 06 660-669 high-order subharmonically pumped mixers, phased local oscillators. Zhiyang Liu, + , T-MTT Jul 06 2977-2982 mixer, single-digit phase accuracy, sampling-oscilloscope meas. Williams, D.F., + , T-MTT Mar 06 1210-1217 nonlin. mixing products, amplit. and phase charactn. Pedro, J.C., + , TMTT Aug 06 3237-3245 NRD guide ccts. incl. lumped elements, full-wave nonlin. anal. Pathak, N.P., + , T-MTT Jan 06 173-179 Microwave mixers; cf. MMIC mixers Microwave oscillators 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 anal. and design of coupled-oscillator systs., techs. Georgiadis, A., + , TMTT Nov 06 3864-3877 chaotic microwave radiation, gyro-BWO, source. Rozental, R.M., + , TMTT Jun 06 2741-2744 + Check author entry for coauthors

high-order subharmonically pumped mixers, phased local oscillators. Zhiyang Liu, + , T-MTT Jul 06 2977-2982 low phase-noise microwave oscillators, interferometric sig. proc. Ivanov, E.N., + , T-MTT Aug 06 3284-3294 low-power UWB wavelets generator, fast start-up cct. Barras, D., + , TMTT May 06 2138-2145 phase-noise meas., 2 inter-injection-locked microwave oscillators. Nick, M., + , T-MTT Jul 06 2993-3000 Microwave oscillators; cf. MMIC oscillators Microwave phase shifters 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 anal. and design of coupled-oscillator systs., techs. Georgiadis, A., + , TMTT Nov 06 3864-3877 improved wide-band Schiffman phase shifter. Yong-Xin Guo, + , T-MTT Mar 06 1196-1200 multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 organic Wafer-Scale packaged miniature 4-bit RF MEMS phase shifter. Kingsley, N., + , T-MTT Mar 06 1229-1236 tunable phase shifters by image-params. method, design. Ocera, A., + , TMTT Jun 06 2383-2390 Microwave phase shifters; cf. MMIC phase shifters Microwave photonics microwave photonics (special issue). T-MTT Feb 06 777-989 microwave photonics (special issue intro.). Seeds, A., + , T-MTT Feb 06 777-779 Microwave power amplifiers behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 C-band high-effic. second-harmonic-tuned hybrid power amp., GaN technol. Colantonio, P., + , T-MTT Jun 06 2713-2722 charactn. and behavioral modeling of nonlin. devices, memory, timedomain envelope meas. Macraigne, F., + , T-MTT Aug 06 3219-3226 envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 nonlin. amp., gain expansion phenom., Doherty amp., compensation method. Hyeong Tae Jeong, + , T-MTT Jun 06 1425-1430 Microwave power amplifiers; cf. MMIC power amplifiers Microwave power transmission 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 Microwave propagation UWB sig. propag., human head. Zasowski, T., + , T-MTT Jun 06 18361845 Microwave receivers 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 6-port software-defined radio receiver platform, anal. and implement. Xinyu Xu, + , T-MTT Jul 06 2937-2943 breast cancer Detection-localization, 3 dimens., FDTD-based time reversal. Kosmas, P., + , T-MTT Jun 06 1921-1927 microwave photonics (special issue). T-MTT Feb 06 777-989 microwave photonics (special issue intro.). Seeds, A., + , T-MTT Feb 06 777-779 turnstile jn. waveguide orthomode transducer. Navarrini, A., + , T-MTT Jan 06 272-277 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 UWB sig. propag., human head. Zasowski, T., + , T-MTT Jun 06 18361845 Microwave reflectometry quasiopt. refl. meas., scalar calib. Koers, G., + , T-MTT Jul 06 3121-3126 Microwave technology 35th European Microwave Conference (special issue). T-MTT Jun 06 2567-2898 35th European Microwave Conference (special issue intro.). Quere, R., + , T-MTT Jun 06 2567 Microwave technology; cf. Microwave generation; Microwave imaging; Microwave photonics; Microwave power transmission; Microwave propagation

IEEE T-MTT 2006 INDEX — 50 Microwave transistors coupled electrothermal, EM, phys. modeling of microwave power FETs. Denis, D., + , T-MTT Jun 06 2465-2470 Microwave transistors; cf. Microwave bipolar transistors Millimeter wave amplifiers 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amps., design and anal. Jeng-Han Tsai, + , T-MTT Jun 06 24872496 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 integr. planar spatial power combiner. Lin Li, + , T-MTT Jun 06 14701476 Millimeter wave amplifiers; cf. Millimeter wave power amplifiers Millimeter wave antenna arrays fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 Millimeter wave antennas 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603 half Maxwell fish-eye lens antennas, mm waves, design and charactn. Fuchs, B., + , T-MTT Jun 06 2292-2300 V-band front-end, 3D integr. cavity filters/duplexers and antenna, LTCC technols. Jong-Hoon Lee, + , T-MTT Jul 06 2925-2936 Millimeter wave antennas; cf. Millimeter wave antenna arrays Millimeter wave bipolar integrated circuits power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 Millimeter wave circuits 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 authors' reply [to comments on "W-Band multiport substrate-integrated waveguide circuits"]. Moldovan, E., + , T-MTT Nov 06 4017 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Millimeter wave circuits; cf. Millimeter wave integrated circuits Millimeter wave circulators mm-wave integrat., substr.-integr.-waveguide circulators suitable. D'Orazio, W., + , T-MTT Oct 06 3675-3680 Millimeter wave couplers w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Millimeter wave detectors planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842 Millimeter wave devices 2-bit antenna-filter-antenna elements for reconfigurable millimeter-wave lens arrays. Chih-Chieh Cheng, + , T-MTT Dec 06 4498-4506 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amps., design and anal. Jeng-Han Tsai, + , T-MTT Jun 06 24872496 low-loss Si-on-Si DC-110-GHz reson.-free package. Byung-Wook Min, + , T-MTT Feb 06 710-716 multilayer design techniques for extremely miniaturized CMOS microwave and millimeter-wave distributed passive circuits. Chirala, M. K., + , T-MTT Dec 06 4218-4224 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 wide-band commun. systs., 10-35-GHz 6-channel microstrip MUX. Seungpyo Hong, + , T-MTT Jun 06 1370-1378 Millimeter wave devices; cf. Millimeter wave amplifiers; Millimeter wave antennas; Millimeter wave circuits; Millimeter wave circulators; Millimeter wave couplers; Millimeter wave detectors; Millimeter wave diodes; Millimeter wave filters; Millimeter wave mixers; Millimeter wave oscillators; Millimeter wave receivers; Millimeter wave transistors Millimeter wave diodes planar isolated GaAs zero-biased PDB diodes for microwave/mm-wave power detectors/sens., optim. and realization. Van Tuyen Vo, + , T-MTT Nov 06 3836-3842

+ Check author entry for coauthors

Millimeter wave FET integrated circuits CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 Millimeter wave filters compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 design of very compact filters for Q-band appls., LTCC 3D resonators applied. Rigaudeau, L., + , T-MTT Jun 06 2620-2627 filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 liq.-cryst. polymer, 60-GHz direct-conversion gigabit modulator/demodulator. Sarkar, S., + , T-MTT Mar 06 1245-1252 Millimeter wave frequency conversion 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 heterostruct. barrier varactors, subharmonically pumped mm-wave upconverters. Haiyong Xu, + , T-MTT Oct 06 3648-3653 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 Millimeter wave generation 10-Gb/s data transm., 120-GHz-band mm-wave photonic wireless link. Hirata, A., + , T-MTT May 06 1937-1944 Brillouin amplif. and Er-doped fiber amplif. for gener. of mm waves, low phase noise props., comparative test. Junker, M., + , T-MTT Jun 06 1576-1581 Millimeter wave integrated circuits liq.-cryst. polymer, 60-GHz direct-conversion gigabit modulator/demodulator. Sarkar, S., + , T-MTT Mar 06 1245-1252 mm-wave integrat., substr.-integr.-waveguide circulators suitable. D'Orazio, W., + , T-MTT Oct 06 3675-3680 Millimeter wave measurements broadband space conservative on-wafer NWA calibs., complex load and thru models. Padmanabhan, S., + , T-MTT Sep 06 3583-3593 complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 deembedding/unterminating microwave fixtures, GA. Adalev, A.S., + , TMTT Jul 06 3131-3140 freq.-depend. equiv. width of substr. integr. waveguide, meas. ChaoHsiung Tseng, + , T-MTT Jun 06 1431-1437 Millimeter wave mixers broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 liq.-cryst. polymer, 60-GHz direct-conversion gigabit modulator/demodulator. Sarkar, S., + , T-MTT Mar 06 1245-1252 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 Millimeter wave oscillators 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 Millimeter wave power amplifiers power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 Millimeter wave receivers 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 mm-wave correl. receivers, orthomode transducer. Peverini, O.A., + , TMTT May 06 2042-2049 turnstile jn. waveguide orthomode transducer. Navarrini, A., + , T-MTT Jan 06 272-277 Millimeter waves low-loss integrated-waveguide passive circuits using liquid-crystal polymer system-on-package technology for millimeter-wave applications. Ki Seok Yang, + , T-MTT Dec 06 4572-4579 Millimeter wave technology 60-GHz mm waves and artificial biol. membranes, interacts. Zhadobov, M., + , T-MTT Jun 06 2534-2542 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248 phase retrieval of quasiopt. mm-wave beams, expt. verification. Idei, H., + , T-MTT Nov 06 3899-3905

IEEE T-MTT 2006 INDEX — 51 Millimeter wave transistors filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 MIM devices 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 MIMICs 60-GHz wireless chipsets, CSP technol. Pfeiffer, U.R., + , T-MTT Aug 06 3387-3397 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 neural-net.-based parasitic modeling and extr. verification for RF/mmwave IC design. Sen, P., + , T-MTT Jun 06 2604-2614 parylene-C, perform. of mm-wave ccts. Karnfelt, C., + , T-MTT Aug 06 3417-3425 power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 MIM structures; cf. MIM devices Minerals; cf. Quartz Minimization methods subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450 MIS devices active harmonic load-pull for on-wafer out-of-band device linearity optimization. Spirito, M., + , T-MTT Dec 06 4225-4236 MIS structures; cf. MIS devices Mixed analog-digital integrated circuits CMOS low-noise amps., on-chip low-Q inductors, noise optim. formulation. Kuo-Jung Sun, + , T-MTT Jun 06 1554-1560 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 Mixers ACPR, mixers, parametric harmonic-bal. approach. Crespo-Cadenas, C., + , T-MTT Jan 06 445-450 CMOS double-balanced mixer, multibias dual-gate transistors, IMD reduction. Chung-Fai Au-Yeung, + , T-MTT Jan 06 4-9 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 Mixers (circuits); cf. Microwave mixers; Millimeter wave mixers; Submillimeter wave mixers; UHF mixers MMIC 60-GHz-Band x 12 -multiplier MMIC with reduced power consumption. Ito, M., + , T-MTT Dec 06 4522-4527 An SiC MESFET-Based MMIC Process. Sudow, M., + , T-MTT Dec 06 4072-4078 MMIC; cf. MMIC amplifiers; MMIC frequency converters; MMIC mixers; MMIC oscillators; MMIC phase shifters MMIC amplifiers 45-dB variable-gain low-noise MMIC amp. Masud, M.A., + , T-MTT Jun 06 2848-2855 6.5-kV ESD-protected 3-5-GHz UWB BiCMOS LNA, interstage gain roll-off compensation. Mingxu Liu, + , T-MTT Jun 06 1698-1706 AlGaN/GaN Ka-band 5-W MMIC amplifier. Darwish, A. M., + , T-MTT Dec 06 4456-4463 CMOS low-noise amps., on-chip low-Q inductors, noise optim. formulation. Kuo-Jung Sun, + , T-MTT Jun 06 1554-1560 cryogenic amp. noise temps. below 5 K, precision meas. method. Randa, J., + , T-MTT Mar 06 1180-1189 integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 low-power-consumption and high-gain CMOS distrib. amps., cascade of inductively coupled common-source gain cells for UWB systs. Xin Guan, + , T-MTT Aug 06 3278-3283 parylene-C, perform. of mm-wave ccts. Karnfelt, C., + , T-MTT Aug 06 3417-3425

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RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 two-port vector network analyzer measurements in the 218-344- and 356 500-GHz frequency bands. Fung, A., + , T-MTT Dec 06 4507-4512 MMIC amplifiers; cf. MMIC power amplifiers MMIC frequency converters direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 MMIC mixers 0.18-ȝm CMOS technol., low-power oscillator mixer. To-Po Wang, + , TMTT Jan 06 88-95 22-29-GHz UWB appls., low-power up-conversion CMOS mixer. Verma, A., + , T-MTT Aug 06 3295-3300 MMIC oscillators 0.18-ȝm CMOS technol., low-power oscillator mixer. To-Po Wang, + , TMTT Jan 06 88-95 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 MMIC phase shifters composite right/left-handed transm. line metamaterial phase shifters (MPS), MMIC technol. Perruisseau-Carrier, J., + , T-MTT Jun 06 1582-1589 digitally controlled const. envelope phase-shift modulator for low-power broad-band wireless appls. Xiuge Yang, + , T-MTT Jan 06 96-105 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 ku-band MMIC phase shifter, parallel resonator, 0.18-ȝm CMOS technol. Dong-Woo Kang, + , T-MTT Jan 06 294-301 miniature 15-20-GHz continuous-phase/amplit. control MMICs, 0.18-ȝm CMOS technol. Pei-Si Wu, + , T-MTT Jan 06 10-19 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 MMIC power amplifiers class-E power amps., lumped-element load-net. design. Negra, R., + , TMTT Jun 06 2684-2690 MMICs 3D IC, multiwafer vert. interconnects. Lahiji, R.R., + , T-MTT Jun 06 2699-2706 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amps., design and anal. Jeng-Han Tsai, + , T-MTT Jun 06 24872496 broadband integr. mm-wave up- and down-converter GaAs MMICs. Mahon, J., + , T-MTT May 06 2050-2060 CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 compact and selective low-pass filter, reduced spurious responses, CPW tapered periodic structs. Kaddour, D., + , T-MTT Jun 06 2367-2375 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 electronically tunable act. duplexer for wireless transceiver appls. Sundaram, B., + , T-MTT Jun 06 2584-2592 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 low-power-consumption and high-gain CMOS distrib. amps., cascade of inductively coupled common-source gain cells for UWB systs. Xin Guan, + , T-MTT Aug 06 3278-3283 low-power UWB wavelets generator, fast start-up cct. Barras, D., + , TMTT May 06 2138-2145

IEEE T-MTT 2006 INDEX — 52 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 multilayer MMICs, 3D low-loss CPW transm. lines. Van Tuyen Vo, + , TMTT Jun 06 2864-2871 pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898 RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 substr. integr. image guide (SIIG), planar dielec. waveguide technol. for mm-wave appls. Patrovsky, A., + , T-MTT Jun 06 2872-2879 UWB communs. and Radar systs., power-efficient switching-based CMOS UWB transmitters. Rui Xu, + , T-MTT Aug 06 3271-3277 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583 Mobile communication 3-line balun and implement., multilayer config., design. Byoung Hwa Lee, + , T-MTT Jun 06 1405-1414 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 Modeling nonquasi-static empirical model of electron devices . Santarelli, A., + , TMTT Dec 06 4021-4031 transmission-line concept for integrated capacitors and inductors. Lee, K.Y., + , T-MTT Dec 06 4141-4148 Modeling; cf. Integrated circuit modeling Mode locked lasers microwave sig., rational harmonic mode-locked fiber ring laser, photonic gener. Zhichao Deng, + , T-MTT Feb 06 763-767 optically injection-locked VCSELs, microwave perform. Chrostowski, L., + , T-MTT Feb 06 788-796 Mode matching methods fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 miniature broadband bandpass filters, double-layer coupled stripline resonators. Yunchi Zhang, + , T-MTT Aug 06 3370-3377 periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 rect. hard waveguides, TE/TM modal soln. Epp, L.W., + , T-MTT Mar 06 1048-1054 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 Modems photonic freq.-conversion method, bandpass sampling, multicarrier operated radio-on-fiber link, proposal. Higashino, T., + , T-MTT Feb 06 973-979 MODFET circuits ACPR, mixers, parametric harmonic-bal. approach. Crespo-Cadenas, C., + , T-MTT Jan 06 445-450 g-band metamorphic HEMT-based freq. multipliers. Campos-Roca, Y., + , T-MTT Jul 06 2983-2992 MODFET integrated circuits 45-dB variable-gain low-noise MMIC amp. Masud, M.A., + , T-MTT Jun 06 2848-2855 filter synthesis design method, TW switch above 100 GHz, FET-integr. CPW and appl. Zuo-Min Tsai, + , T-MTT May 06 2090-2097 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898 wideband MMIC voltage controlled attenuator, bandpass filter topol. Daoud, S.M., + , T-MTT Jun 06 2576-2583 MODFETs 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amps., design and anal. Jeng-Han Tsai, + , T-MTT Jun 06 24872496 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603

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broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 broadband integr. mm-wave up- and down-converter GaAs MMICs. Mahon, J., + , T-MTT May 06 2050-2060 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 GaN HEMTs, accurate multibias equiv.-cct. extr. Crupi, G., + , T-MTT Oct 06 3616-3622 high-effic. envelope-tracking W-CDMA base-station amp., GaN HFETs. Kimball, D.F., + , T-MTT Nov 06 3848-3856 HV microwave AlGaN/GaN HFETs, nonlin. source resist. Trew, R.J., + , T-MTT May 06 2061-2067 low conversion loss and high LO-RF isolation 94-GHz act. down converter. Bok-Hyung Lee, + , T-MTT Jun 06 2422-2430 low gate bias model extr. tech. for AlGaN/GaN HEMTs. Guang Chen, + , T-MTT Jul 06 2949-2953 Modulation testing high-frequency electronic signals with reflection-mode electroabsorption modulators. Van Tuyl, R. L., + , T-MTT Dec 06 45564564 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 Modulation; cf. Amplitude modulation; OFDM modulation; Optical modulation; Pulse modulation Modulators; cf. Modems Modules; cf. Multichip modules Molecular electronics 60-GHz mm waves and artificial biol. membranes, interacts. Zhadobov, M., + , T-MTT Jun 06 2534-2542 Moment methods 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 accurate modeling, wave mechanisms, design considerations of substr. integr. waveguide. Deslandes, D., + , T-MTT Jun 06 2516-2526 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 comput. transm.-line params. of lossy lines, Quasi-TM MoL/MoM approach. Plaza, G., + , T-MTT Jan 06 198-209 direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 modal anal. of 1-D periodic microstrip structs., full-wave num. approach. Baccarelli, P., + , T-MTT Jun 06 1350-1362 multiple vert. conductors, PC, efficient full-wave simul. algm. Onal, T., + , T-MTT Oct 06 3739-3745 Monolithic integrated circuits layout scaling, Si integr. stacked transformers, anal. and modeling. Biondi, T., + , T-MTT May 06 2203-2210 Monolithic integrated circuits; cf. Bipolar integrated circuits; MMIC Monopole antennas antenna combinations for UWB ranging syst., exam. Takeuchi, Y., + , TMTT Jun 06 1858-1864 LTCC technol., transceiver integrat. capability for UWB appls., planar antennas. Brzezina, G., + , T-MTT Jun 06 2830-2839 multiband operation, modified T-shaped planar monopole antennas. Sheng-Bing Chen, + , T-MTT Aug 06 3267-3270 satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 wideband planar monopole antennas, dual band-notched characts. WangSang Lee, + , T-MTT Jun 06 2800-2806 Monte Carlo methods EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping. Rayas-Sanchez, J. E., + , T-MTT Dec 06 4528-4537

IEEE T-MTT 2006 INDEX — 53 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 MOS analog integrated circuits; cf. CMOS analog integrated circuits MOS digital integrated circuits; cf. CMOS digital integrated circuits MOSFET circuits accurate RF CMOS noise extr. and simul., freq. and bias depend., lossy substr. model. Jyh-Chyurn Guo, + , T-MTT Nov 06 3975-3985 MOSFETs behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 IM3 components, RF power amps., phase meas. tech. Seung-Yup Lee, + , T-MTT Jan 06 451-457 ku-band MMIC phase shifter, parallel resonator, 0.18-ȝm CMOS technol. Dong-Woo Kang, + , T-MTT Jan 06 294-301 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3-port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3-port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 1296-1297 MOSFETs under integr. inductors, RF operation. Nastos, N., + , T-MTT May 06 2106-2117 TWA vs. temp., SOI technol., behavior. Si Moussa, M., + , T-MTT Jun 06 2675-2683 MOS integrated circuits; cf. CMOS integrated circuits Multiaccess communication 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 Multi-access systems; cf. Code division multiple access Multibeam antennas WDM and dispers. fiber, receive mode, opt. multibeamforming net. Blanc, S., + , T-MTT Jan 06 402-411 Multichip modules BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 Multipath channels BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 high- and low-data-rate appls., UWB ranging accuracy. Cardinali, R., + , T-MTT Jun 06 1865-1875 IR-UWB systs., different transceiver types, TOA estim. Guvenc, I., + , TMTT Jun 06 1876-1886 self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 UWB ad hoc nets., TOA, joint distrib. sync. and positioning. Denis, B., + , T-MTT Jun 06 1896-1911 UWB ranging, multipath and multiuser environments, large error perform. Joon-Yong Lee, + , T-MTT Jun 06 1887-1895 Multiplexing; cf. Frequency division multiplexing; Subcarrier multiplexing; Wavelength division multiplexing Multiplying circuits pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898 variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 Multiport circuits gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 in-phase and split counter-rot. eigenvalues of 3-port circulator, refl. angles. Helszajn, J., T-MTT Mar 06 1076-1083 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3-port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3-port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 1296-1297 mixed-mode params. of cascaded balanced nets. and their appls., modeling of differential interconnects, props. Hao Shi, + , T-MTT Jan 06 360-372 power amp. charactn. Bensmida, S., + , T-MTT Jun 06 2707-2712 UWB, Multi(Six)-port impulse radio. Yanyang Zhao, + , T-MTT Jun 06 1707-1712 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632

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Multiport networks authors' reply [to comments on "W-Band multiport substrate-integrated waveguide circuits"]. Moldovan, E., + , T-MTT Nov 06 4017 Multiterminal networks; cf. Multiport networks N Network parameters; cf. S-parameters Networks (circuits); cf. Amplifiers; Analog circuits; Attenuators; Delay circuits; Differentiating circuits; Equalizers; Equivalent circuits; Filters; Magnetic circuits; Microwave circuits; Millimeter wave circuits; Multiplying circuits; Oscillators; Passive networks; Phase locked loops; Phase shifters; Printed circuits; RC circuits; Switching circuits Network synthesis; cf. Circuit optimization; Integrated circuit design Neural networks complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 neural-net.-based parasitic modeling and extr. verification for RF/mmwave IC design. Sen, P., + , T-MTT Jun 06 2604-2614 Newton method IM3 and IM5 phase charactn. and anal., simplified Newton approach. Crespo-Cadenas, C., + , T-MTT Jan 06 321-328 Niobium low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 Niobium compounds integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 Noise large-sig. microwave meas., noise considerations, determining phase. Blockley, P.S., + , T-MTT Aug 06 3182-3190 microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 Noise; cf. Circuit noise; Optical noise; Phase noise; Random noise Noise measurement cryogenic amp. noise temps. below 5 K, precision meas. method. Randa, J., + , T-MTT Mar 06 1180-1189 design to suppress wideband ground bounce noise in high-speed circuits by electromagnetic-bandgap-enhanced split powers. Chien-Lin Wang, + , T-MTT Dec 06 4209-4217 empirical bipolar device nonlinear noise modeling approach for large signal microwave circuit analysis. Traverso, P. A., + , T-MTT Dec 06 4341-4352 gen. eqns. for FET cold noise source design, expt. validation. Weatherspoon, M.H., + , T-MTT Feb 06 608-614 highly linear low-noise amplifier. Ganesan, S., + , T-MTT Dec 06 40794085 high-speed p-i-n photodiodes, flicker noise. Rubiola, E., + , T-MTT Feb 06 816-820 phase-noise meas., 2 inter-injection-locked microwave oscillators. Nick, M., + , T-MTT Jul 06 2993-3000 silicon-integrated differential bandpass filters based on recursive and channelized principles and methodology to compute their exact noise figure. Darfeuille, S., + , T-MTT Dec 06 4381-4396 Noncrystalline structure; cf. Polymer structure Nondestructive testing evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 Nonhomogeneous media 3D periodic bianisotropic metamaterials, homogenization. Ouchetto, O., + , T-MTT Nov 06 3893-3898 3D periodic multiphase composites by homogenization, modeling. Ouchetto, O., + , T-MTT Jun 06 2615-2619 measuring complex permitt. tensor of uniaxial composite materials, waveguide-based 2-step approach. Akhtar, M.J., + , T-MTT May 06 2011-2022 right/left-handed transm. line metamaterial phase shifters (MPS), MMIC technol. Perruisseau-Carrier, J., + , T-MTT Jun 06 1582-1589

IEEE T-MTT 2006 INDEX — 54 Nonlinear circuits behavior of RF amps., expt. charactn. Rolain, Y., + , T-MTT Aug 06 32093218 end-to-end performance of a microwave/RF link by means of nonlinear/electromagnetic co-simulation. Rizzoli, V., + , T-MTT Dec 06 4149-4160 high-power switching-mode oscillators, nonlin. design tech. Sanggeun Jeon, + , T-MTT Oct 06 3630-3640 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 IM3 and IM5 phase charactn. and anal., simplified Newton approach. Crespo-Cadenas, C., + , T-MTT Jan 06 321-328 NRD guide ccts. incl. lumped elements, full-wave nonlin. anal. Pathak, N.P., + , T-MTT Jan 06 173-179 RF ccts./systs. simul., driven by several modulated sigs. Carvalho, N.B., + , T-MTT Feb 06 572-579 Nonlinear distortion; cf. Harmonic distortion; Intermodulation distortion Nonlinear equations subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450 Nonlinear optics 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 Nonlinear programming; cf. Quadratic programming Nonlinear systems large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 metric for the quantification of memory effects in power amplifiers. Martins, J. P., + , T-MTT Dec 06 4432-4439 sparse macromodeling for parametric nonlinear networks. Min Ma, + , TMTT Dec 06 4305-4315 Nonradiative dielectric waveguides components via order-reduced vol.-integral-eqn. method combined, tracking of matrix eigenvalues. Bozzi, M., + , T-MTT Jan 06 339-347 guide ccts. incl. lumped elements, full-wave nonlin. anal. Pathak, N.P., + , T-MTT Jan 06 173-179 Notch filters microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 Numerical analysis; cf. Difference equations; Error analysis; Finite difference methods; Interpolation; Iterative methods; Method of moments; Monte Carlo methods Numerical stability 3D precise integrat. time-domain method without restraints of courantfriedrich-levy stabil. condition for num. soln. of Maxwell's eqns. Xikui Ma, + , T-MTT Jul 06 3026-3037 O OFDM modulation distortion analysis of ultra-wideband OFDM receiver front-ends. Ranjan, M., + , T-MTT Dec 06 4422-4431 Operational amplifiers gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 microwave integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , T-MTT Mar 06 1043-1047 Optical communication carrier-to-sideband ratio for improv. transm. perform., fiber-radio links. Lim, C., + , T-MTT May 06 2181-2187 Optical communication; cf. Optical communication equipment; Optical fiber communication Optical communication equipment analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 mm-wave-band radio-over-fiber syst., dense WDM bus archit. Xiupu Zhang, + , T-MTT Feb 06 929-937

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optically injection-locked VCSELs, microwave perform. Chrostowski, L., + , T-MTT Feb 06 788-796 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 photonic freq.-conversion method, bandpass sampling, multicarrier operated radio-on-fiber link, proposal. Higashino, T., + , T-MTT Feb 06 973-979 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 Optical communication equipment; cf. Optical receivers; Optical transmitters Optical constants; cf. Refractive index Optical data processing microwave channelizer and spectroscope, integr. opt. Bragg-grating Fabry-Perot and integr. hybrid Fresnel lens syst. Winnall, S.T., + , TMTT Feb 06 868-872 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 Optical delay lines microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 Optical dispersion; cf. Optical fiber dispersion Optical elements; cf. Optical delay lines; Optical fibers Optical fiber communication externally modulated long-haul analog fiber-optic links, wide-band predistortion linearization. Urick, V.J., + , T-MTT Jun 06 1458-1463 optically injection-locked VCSELs, microwave perform. Chrostowski, L., + , T-MTT Feb 06 788-796 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 Optical fiber dispersion WDM and dispers. fiber, receive mode, opt. multibeamforming net. Blanc, S., + , T-MTT Jan 06 402-411 Optical fiber filters phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 spectrum-sliced microwave-photonic filters, dispers. induced RF distortion. Yi, X., + , T-MTT Feb 06 880-886 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 Optical fiber lasers microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 microwave sig., rational harmonic mode-locked fiber ring laser, photonic gener. Zhichao Deng, + , T-MTT Feb 06 763-767 Optical fibers continuously variable true-time delay beamformer, multichannel chirped fiber grating, demons. Hunter, D.B., + , T-MTT Feb 06 861-867 Optical fibers; cf. Optical fiber dispersion; Optical fiber filters Optical interconnections freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73 Optical losses analog photonic links employing highly compress. Er-doped fiber amps., perform. Urick, V.J., + , T-MTT Jul 06 3141-3145 Optical modulation freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 multichannel WLAN syst., radio-over-fiber techs., transm. perform. Niiho, T., + , T-MTT Feb 06 980-989 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 spectrum-sliced microwave-photonic filters, dispers. induced RF distortion. Yi, X., + , T-MTT Feb 06 880-886

IEEE T-MTT 2006 INDEX — 55 wide-band electrooptic intens. modulator freq. response meas., opt. heterodyne down-conversion tech. Lam, A.K.M., + , T-MTT Jan 06 240246 Optical noise analog photonic links employing highly compress. Er-doped fiber amps., perform. Urick, V.J., + , T-MTT Jul 06 3141-3145 freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 Optical propagation in dispersive media spectrum-sliced microwave-photonic filters, dispers. induced RF distortion. Yi, X., + , T-MTT Feb 06 880-886 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 Optical properties; cf. Optical losses; Optical noise Optical receivers 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 Optical reflection Radar absorbing materials, 310 GHz, monostatic reflectivity meas. Lonnqvist, A., + , T-MTT Sep 06 3486-3491 Optical refraction split-ring resonator and wire loaded transm. line, fin-line technol., lefthanded EM props. Decoopman, T., + , T-MTT Jun 06 1451-1457 Optical switches fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 Optical transfer functions perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 Optical transmitters low-cost multimode fiber-fed indoor wireless nets., design. Das, A., + , TMTT Aug 06 3426-3432 Optical tuning; cf. Laser tuning Optical variables measurement quasiopt. refl. meas., scalar calib. Koers, G., + , T-MTT Jul 06 3121-3126 Optical waveguide filters; cf. Optical fiber filters Optical waveguides; cf. Optical fibers; Optical waveguide theory Optical waveguide theory algebraic invariants, full-wave simulators, rigorous anal. of opt. props. of nanowires. Rozzi, T., + , T-MTT Feb 06 797-803 Optics; cf. Geometrical optics; Integrated optics; Nonlinear optics Optimization; cf. Circuit optimization; Genetic algorithms Optimization methods engng. optim., space-mapping-based interpolation. Koziel, S., + , T-MTT Jun 06 2410-2421 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 Optoelectronic devices; cf. Integrated optoelectronics; Microwave photonics Oscillators elec. soliton oscillator. Ricketts, D.S., + , T-MTT Jan 06 373-382 freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 integrated subharmonic coupled-oscillator scheme for a 60-GHz phased array transmitter. Buckwalter, J. F., + , T-MTT Dec 06 4271-4280 mm-wave-band radio-over-fiber syst., dense WDM bus archit. Xiupu Zhang, + , T-MTT Feb 06 929-937 Oscillators; cf. Backward wave oscillators; Dielectric resonator oscillators; Injection locked oscillators; Phase locked oscillators Oscilloscopes microwave mixer, single-digit phase accuracy, sampling-oscilloscope meas. Williams, D.F., + , T-MTT Mar 06 1210-1217 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 P Packaging; cf. Integrated circuit packaging; Multichip modules; Plastic packaging Parameter estimation; cf. Maximum likelihood estimation; Phase estimation; Recursive estimation + Check author entry for coauthors

Parametric devices sparse macromodeling for parametric nonlinear networks. Min Ma, + , TMTT Dec 06 4305-4315 Particle accelerators; cf. Accelerator cavities; Accelerator RF systems; Linear accelerators Passive circuits broad-band pass. lumped equiv. ccts. of microwave discontinuities, extr. Araneo, R., T-MTT Jan 06 393-401 derived physically expressive cct. model for multilayer RF embedded passives. Jie Wang, + , T-MTT May 06 1961-1968 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Passive filters phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 Passive filters; cf. Surface acoustic wave filters Passive networks multilayer design techniques for extremely miniaturized CMOS microwave and millimeter-wave distributed passive circuits. Chirala, M. K., + , T-MTT Dec 06 4218-4224 Passive networks; cf. Passive filters Patient diagnosis; cf. Biomedical imaging Performance evaluation nonuniform lossy/lossless transmission lines and tapered microstrips. Eghlidi, M. H., + , T-MTT Dec 06 4122-4129 Permeability microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 Permeability measurement diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 Permittivity multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 optimization of arbitrarily sized DNG metamaterial slabs with losses. Sounas, D. L., + , T-MTT Dec 06 4111-4121 reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 small patch antennas providing tunable miniaturization factors, substr. Buell, K., + , T-MTT Jan 06 135-146 substr. integr. image guide (SIIG), planar dielec. waveguide technol. for mm-wave appls. Patrovsky, A., + , T-MTT Jun 06 2872-2879 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 Permittivity measurement complex permitt. meas., planar 4-port device, tech. Ocera, A., + , T-MTT Jun 06 2568-2575 complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 corrections to "Complex-permittivity measurement on high-Q materials via combined numerical approaches" (Oct 05 3130-3134). Fan, X.C., + , T-MTT Apr 06 1631 dielec. const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001 diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 extr. of dielec. props. from insulating substrs. utilizing evanescent perturb. method, data anal. Inoue, R., + , T-MTT Feb 06 522-532 freq.-depend. equiv. width of substr. integr. waveguide, meas. ChaoHsiung Tseng, + , T-MTT Jun 06 1431-1437 GA and gradient descent optmization methods for accurate inverse permitt. meas., combined. Requena-Perez, M.E., + , T-MTT Feb 06 615624 high loss liq., mm wavel., reson. spherical hole. Eremenko, Z.E., + , TMTT May 06 2243-2248

IEEE T-MTT 2006 INDEX — 56 meas. of dielec. anisotropy, multilayer samples, 2-resonator method. Dankov, P.I., T-MTT Jun 06 1534-1544 measuring complex permitt. tensor of uniaxial composite materials, waveguide-based 2-step approach. Akhtar, M.J., + , T-MTT May 06 2011-2022 microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 Perturbation methods extr. of dielec. props. from insulating substrs. utilizing evanescent perturb. method, data anal. Inoue, R., + , T-MTT Feb 06 522-532 planar components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 Phased arrays 2-bit X-band reflective waveguide phase shifter with BCB-based bias circuits. Martynyuk, A. E., + , T-MTT Dec 06 4056-4061 bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 compact colinear coaxial-to-rect. waveguide transits., patch endLaunchers, family. Simeoni, M., + , T-MTT Jun 06 1503-1511 continuously variable true-time delay beamformer, multichannel chirped fiber grating, demons. Hunter, D.B., + , T-MTT Feb 06 861-867 fixed and mobile broad-band wireless access nets., optically beamformed beam-switched adaptive antennas. Piqueras, M.A., + , T-MTT Feb 06 887-899 integrated subharmonic coupled-oscillator scheme for a 60-GHz phased array transmitter. Buckwalter, J. F., + , T-MTT Dec 06 4271-4280 ku-band antenna array feed distrib. net., ferroelec. phase shifters, Si. Taeksoo Ji, + , T-MTT Mar 06 1131-1138 UWB phased array, electron. beam-steering design. Chia, M.Y.-W., + , TMTT Jun 06 2431-2438 Phase estimation sources of phase error and design considerations for silicon-based monolithic high-pass/low-pass microwave phase shifters. Morton, M. A., + , T-MTT Dec 06 4032-4040 Phase locked loops 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 high-precision multitarget-level meas. syst., TDR, approach. Gerding, M., + , T-MTT Jun 06 2768-2773 Phase locked oscillators 12-GHz push-push phase-locked DRO, conception and anal. Gravel, J.-F., + , T-MTT Jan 06 153-159 low phase-noise microwave oscillators, interferometric sig. proc. Ivanov, E.N., + , T-MTT Aug 06 3284-3294 Phase measurement IM3 components, RF power amps., phase meas. tech. Seung-Yup Lee, + , T-MTT Jan 06 451-457 large-sig. microwave meas., noise considerations, determining phase. Blockley, P.S., + , T-MTT Aug 06 3182-3190 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 retrieval of quasiopt. mm-wave beams, expt. verification. Idei, H., + , TMTT Nov 06 3899-3905 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 Phase modulation modulated sigs., double-neg. slab, Gaussian pulse expansion. Monti, G., + , T-MTT Jun 06 2755-2761 Phase modulation; cf. Phase shift keying Phase noise anal. and design of coupled-oscillator systs., techs. Georgiadis, A., + , TMTT Nov 06 3864-3877 Brillouin amplif. and Er-doped fiber amplif. for gener. of mm waves, low phase noise props., comparative test. Junker, M., + , T-MTT Jun 06 1576-1581

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close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 high-speed p-i-n photodiodes, flicker noise. Rubiola, E., + , T-MTT Feb 06 816-820 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 low phase-noise CMOS VCO, harmonic tuned LC tank. Huijung Kim, + , T-MTT Jul 06 2917-2924 low phase-noise microwave oscillators, interferometric sig. proc. Ivanov, E.N., + , T-MTT Aug 06 3284-3294 meas., 2 inter-injection-locked microwave oscillators. Nick, M., + , T-MTT Jul 06 2993-3000 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 microwave sig., rational harmonic mode-locked fiber ring laser, photonic gener. Zhichao Deng, + , T-MTT Feb 06 763-767 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 phase-induced intens. noise, opt. delay-line sig. processors, differentialdetect. tech., suppression. Chan, E.H.W., + , T-MTT Feb 06 873-879 pHEMT/mHEMT technol., high-purity 60-GHz-band single-chip u8 multipliers. Karnfelt, C., + , T-MTT Jun 06 2887-2898 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 Phase shifters 2-bit antenna-filter-antenna elements for reconfigurable millimeter-wave lens arrays. Chih-Chieh Cheng, + , T-MTT Dec 06 4498-4506 2-bit X-band reflective waveguide phase shifter with BCB-based bias circuits. Martynyuk, A. E., + , T-MTT Dec 06 4056-4061 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part I, design. Gruszczynski, S., + , T-MTT Nov 06 3986-3994 compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 EM modeling of MEMS-controlled planar phase shifters, scale-changing tech. Perret, E., + , T-MTT Sep 06 3594-3601 full-duplex dual-freq. self-steering array, phase detect. and phase shifting. Shiroma, G.S., + , T-MTT Jan 06 128-134 high-order subharmonically pumped mixers, phased local oscillators. Zhiyang Liu, + , T-MTT Jul 06 2977-2982 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 sources of phase error and design considerations for silicon-based monolithic high-pass/low-pass microwave phase shifters. Morton, M. A., + , T-MTT Dec 06 4032-4040 Phase shifters; cf. Ferrite phase shifters; Microwave phase shifters; UHF phase shifters Phase shift keying 60-GHz wireless chipsets, CSP technol. Pfeiffer, U.R., + , T-MTT Aug 06 3387-3397 BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 low-power UWB radio transceivers, robust front-end archit. Barras, D., + , T-MTT Jun 06 1713-1723 subbanded UWB transmitters, Gaussian pulse Generators. Wentzloff, D.D., + , T-MTT Jun 06 1647-1655 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 wireless interconnect technol., impulse radio for interchip communs. Yuanjin Zheng, + , T-MTT Jun 06 1912-1920 Phase shift keying; cf. Quadrature phase shift keying Photoconducting devices; cf. Photodiodes

IEEE T-MTT 2006 INDEX — 57 Photoconductivity 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 Photodetectors 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 microwave sig., rational harmonic mode-locked fiber ring laser, photonic gener. Zhichao Deng, + , T-MTT Feb 06 763-767 mm-wave-band radio-over-fiber syst., dense WDM bus archit. Xiupu Zhang, + , T-MTT Feb 06 929-937 perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 Photodiodes sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 wide-band electrooptic intens. modulator freq. response meas., opt. heterodyne down-conversion tech. Lam, A.K.M., + , T-MTT Jan 06 240246 Photodiodes; cf. p-i-n photodiodes Photoelectric devices; cf. Photodetectors Photoelectricity; cf. Photoconductivity Photolithography quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 Piecewise linear approximation wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 Piezoelectric resonator filters dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 LTCC balanced-to-unbalanced extracted-pole bandpass filter, complex load. Lap Kun Yeung, + , T-MTT Jun 06 1512-1518 LTCC bandpass filters, diplexer, triplexer, transm. zeros, design methodologies. Ching-Wen Tang, + , T-MTT Feb 06 717-723 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 p-i-n diodes multiband p-i-n diode switches, ladder ccts., design and fab. Shingo Tanaka, + , T-MTT Jun 06 1561-1568 short-range commun. systs., reconfigurable circ. polarized antenna. Aissat, H., + , T-MTT Jun 06 2856-2863 p-i-n diodes; cf. p-i-n photodiodes p-i-n photodiodes high-speed p-i-n photodiodes, flicker noise. Rubiola, E., + , T-MTT Feb 06 816-820 Planar waveguides components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 integr. planar spatial power combiner. Lin Li, + , T-MTT Jun 06 14701476 Plastic films parylene-C, perform. of mm-wave ccts. Karnfelt, C., + , T-MTT Aug 06 3417-3425 Plastic packaging 60-GHz wireless chipsets, CSP technol. Pfeiffer, U.R., + , T-MTT Aug 06 3387-3397 p-n junctions transm. lines fabricated by CMOS proc., deep n-well implant. Nishikawa, K., + , T-MTT Feb 06 589-598 Polarization 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 5.8-GHz circ. polarized retrodirective rectenna arrays for wireless power transm. Yu-Jiun Ren, + , T-MTT Jul 06 2970-2976

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broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 microwave breast cancer Detection-localization, 3 dimens., FDTD-based time reversal. Kosmas, P., + , T-MTT Jun 06 1921-1927 microwave dual-CP antenna, TW feed concept, design and meas. data. Kum Meng Lum, + , T-MTT Jun 06 2880-2886 satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 short-range commun. systs., reconfigurable circ. polarized antenna. Aissat, H., + , T-MTT Jun 06 2856-2863 stability criterion for two-port network with input and output terminations varying in elliptic regions. Marietti, P., + , T-MTT Dec 06 4049-4055 Poles and zeros broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 design of very compact filters for Q-band appls., LTCC 3D resonators applied. Rigaudeau, L., + , T-MTT Jun 06 2620-2627 dual and triple passband filters, coupling-matrix design. Mokhtaari, M., + , T-MTT Nov 06 3940-3946 dual-band bandpass filter, LTCC technol., design. Ching-Wen Tang, + , TMTT Aug 06 3327-3332 efficient anal., design, filter appls. of EBG waveguide, periodic reson. loads. Goussetis, G., + , T-MTT Nov 06 3885-3892 high-power switching-mode oscillators, nonlin. design tech. Sanggeun Jeon, + , T-MTT Oct 06 3630-3640 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 microstrip diplexers design, common resonator sects. for compact size, high isolation. Chi-Feng Chen, + , T-MTT May 06 1945-1952 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 Polymer structure polymer-ceramic composites for microwave applications. Koulouridis, S., + , T-MTT Dec 06 4202-4208 Polynomials H(curl)-conforming hierarchical basis fns. for tetrahedral meshes, set. Ingelstrom, P., T-MTT Jan 06 106-114 Power amplifiers 44-GHz MMIC low-loss built-in linearizer for high-linearity medium power amps., design and anal. Jeng-Han Tsai, + , T-MTT Jun 06 24872496 amp. predistortion linearization, dynamically optimum lookup-table spacing. Chih-Hung Lin, + , T-MTT May 06 2118-2127 behavioral models for RF power amps., comparative anal. Isaksson, M., + , T-MTT Jan 06 348-359 broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 distortion-cancelled Doherty high-power amplifier using 28-V GaAs heterojunction FETs for W-CDMA base stations. Takenaka, I., + , TMTT Dec 06 4513-4521 dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers. Anding Zhu, + , T-MTT Dec 06 4323-4332 high-effic. envelope-tracking W-CDMA base-station amp., GaN HFETs. Kimball, D.F., + , T-MTT Nov 06 3848-3856 hysteresis and noisy precursors, power amps., anal. and elimination. Sanggeun Jeon, + , T-MTT Mar 06 1096-1106 IM3 components, RF power amps., phase meas. tech. Seung-Yup Lee, + , T-MTT Jan 06 451-457 metric for the quantification of memory effects in power amplifiers. Martins, J. P., + , T-MTT Dec 06 4432-4439 power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications. Feipeg Wang, + , T-MTT Dec 06 4086-4099 radial power combiners, simplified design approach. Fathy, A.E., + , TMTT Jan 06 247-255 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Power amplifiers; cf. Microwave power amplifiers; Millimeter wave power amplifiers; UHF power amplifiers

IEEE T-MTT 2006 INDEX — 58 Power combiners BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 dual-freq. wilkinson power divider. Lei Wu, + , T-MTT Jan 06 278-284 integr. planar spatial power combiner. Lin Li, + , T-MTT Jun 06 14701476 radial power combiners, simplified design approach. Fathy, A.E., + , TMTT Jan 06 247-255 turnstile jn. waveguide orthomode transducer. Navarrini, A., + , T-MTT Jan 06 272-277 Power dividers BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 broadband asymmetrical multisection wilkinson power divider, design and optim. Oraizi, H., + , T-MTT May 06 2220-2231 dual-freq. wilkinson power divider. Lei Wu, + , T-MTT Jan 06 278-284 high-order subharmonically pumped mixers, phased local oscillators. Zhiyang Liu, + , T-MTT Jul 06 2977-2982 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 MMIC direct up-converter, 44 GHz, multilayer CPW technol., thin-film microstrip stubs loading, size reduction. Hettak, K., + , T-MTT Sep 06 3453-3461 Power electronics; cf. Power integrated circuits Power FETs linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 Power integrated circuits amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 Power MESFETs amp. charactn. Bensmida, S., + , T-MTT Jun 06 2707-2712 Power MODFETs coupled electrothermal, EM, phys. modeling of microwave power FETs. Denis, D., + , T-MTT Jun 06 2465-2470 Power supplies to apparatus; cf. Accelerator RF systems Power transmission; cf. Microwave power transmission Prediction theory end-to-end performance of a microwave/RF link by means of nonlinear/electromagnetic co-simulation. Rizzoli, V., + , T-MTT Dec 06 4149-4160 Printed circuit design; cf. Printed circuit layout Printed circuit fabrication PCB cct. design, 3-dB quadrature coupler suitable. Jui-Chieh Chiu, + , TMTT Sep 06 3521-3525 Printed circuit layout leaky-wave directional coupler, hybrid dielec.-waveguide PC technol., simple anal. and design. Gomez-Tornero, J.L., + , T-MTT Sep 06 35343542 PCB cct. design, 3-dB quadrature coupler suitable. Jui-Chieh Chiu, + , TMTT Sep 06 3521-3525 serpentine and flat spiral delay lines, transient refl./transm. waveforms and eye diags., comparisons. Wei-Da Guo, + , T-MTT Jun 06 1379-1387 Printed circuits broadband high-effic. circ. polarized act. antenna and array for RF frontend appl. Yin Qin, + , T-MTT Jul 06 2910-2916 dielec. const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 eliminating simultaneously switching noise, high-speed cct., photonic cryst. power/ground layer. Tzong-Lin Wu, + , T-MTT Aug 06 3398-3406 multiple vert. conductors, PC, efficient full-wave simul. algm. Onal, T., + , T-MTT Oct 06 3739-3745 nonphysical leaky mode, field excited by source, significant contrib. Tsuji, M., + , T-MTT Jan 06 421-427 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 sig. vias, virtual islands, shorting vias, multilayer PCBs, perform. anal. Seungki Nam, + , T-MTT Jun 06 1315-1324 Printed circuit testing sig. vias, virtual islands, shorting vias, multilayer PCBs, perform. anal. Seungki Nam, + , T-MTT Jun 06 1315-1324 + Check author entry for coauthors

Programmable circuits; cf. Programmable filters Programmable filters photonic microwave filters, arbitrary UWB phase response. Shijun Xiao, + , T-MTT Nov 06 4002-4008 Programmable logic arrays; cf. Field programmable gate arrays Protocols operation, syst. archits., phys. Layer design considerations of distrib. MAC protocols for UWB. August, N.J., + , T-MTT Jul 06 3001-3012 Pulse circuits; cf. Counting circuits; Digital circuits; Driver circuits Pulse generation high-precision multitarget-level meas. syst., TDR, approach. Gerding, M., + , T-MTT Jun 06 2768-2773 impulse generator and miniaturized antennas for IR-UWB, codesign. Bagga, S., + , T-MTT Jun 06 1656-1666 integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 subbanded UWB transmitters, Gaussian pulse Generators. Wentzloff, D.D., + , T-MTT Jun 06 1647-1655 syst.-on-package UWB transmitter, CMOS impulse generator. Junwoo Lee, + , T-MTT Jun 06 1667-1674 UWB communs. and Radar systs., power-efficient switching-based CMOS UWB transmitters. Rui Xu, + , T-MTT Aug 06 3271-3277 Pulse modulation impulse generator and miniaturized antennas for IR-UWB, codesign. Bagga, S., + , T-MTT Jun 06 1656-1666 subbanded UWB transmitters, Gaussian pulse Generators. Wentzloff, D.D., + , T-MTT Jun 06 1647-1655 Pulse position modulation UWB sigs., nonGaussian noise, robust detect. Guney, N., + , T-MTT Jun 06 1724-1730 Pulse time modulation; cf. Pulse position modulation Q Q factor bandstop filter, improved Q factor, U-slot/V-slot DGSs. Duk-Jae Woo, + , T-MTT Jun 06 2840-2847 cellular commun. terminals, magnetically tunable filters. Krupka, J., + , TMTT Jun 06 2329-2335 compact fixed and tune-all bandpass filters, coupled slow-wave resonators. Pistono, E., + , T-MTT Jun 06 2790-2799 component Q distrib., microwave filters, effects. Chih-Ming Tsai, + , TMTT Jun 06 1545-1553 corrections to "Complex-permittivity measurement on high-Q materials via combined numerical approaches" (Oct 05 3130-3134). Fan, X.C., + , T-MTT Apr 06 1631 deembedding unloaded reson. freq. from meas. of microwave cavities, tech. Canos, A.J., + , T-MTT Aug 06 3407-3416 dual- and triple-passband filters, alternately cascaded multiband resonators, design. Chi-Feng Chen, + , T-MTT Sep 06 3550-3558 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 full-wave analysis of inhomogeneous deep-trench isolation patterning for substrate coupling reduction and Q-factor improvement. Wane, S., + , TMTT Dec 06 4397-4411 inductors, high amounts of dummy metal fill, phys.-based wideband predictive compact model. Tiemeijer, L.F., + , T-MTT Aug 06 33783386 microstrip resonators, balanced/unbalanced composite right/left-handed transm. lines, design. Allen, C.A., + , T-MTT Jul 06 3104-3112 microwave bandpass filters, resonators, nonuniform Q, design. Guyette, A.C., + , T-MTT Nov 06 3914-3922 narrowband supercond. filter, spirals, reversal, winding direction. Huang, F., + , T-MTT Nov 06 3954-3959 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 toroidal inductor struct., through-hole vias, ground plane. Phillips, M.D., + , T-MTT Jun 06 1325-1330 Quadratic programming coupled resonator filter CAD, quadratic prog. approach. Kozakowski, P., + , T-MTT Nov 06 3906-3913

IEEE T-MTT 2006 INDEX — 59 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 Quadrature amplitude modulation 6-port software-defined radio receiver platform, anal. and implement. Xinyu Xu, + , T-MTT Jul 06 2937-2943 CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 high power-amp. linearization, block-based predistortion. Safari, N., + , TMTT Jun 06 2813-2820 memoryless nonlinearities, M-QAM and DQPSK OFDM sigs., effects. Chorti, A., + , T-MTT Aug 06 3301-3315 self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 Quadrature phase shift keying 60-GHz bidirectional radio-on-fiber systs., SOA-EAM freq. up/downconverters. Jun-Hyuk Seo, + , T-MTT Feb 06 959-966 6-port software-defined radio receiver platform, anal. and implement. Xinyu Xu, + , T-MTT Jul 06 2937-2943 memoryless nonlinearities, M-QAM and DQPSK OFDM sigs., effects. Chorti, A., + , T-MTT Aug 06 3301-3315 opt. carrier-to-sideband ratio for improv. transm. perform., fiber-radio links. Lim, C., + , T-MTT May 06 2181-2187 self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 Quantization wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 Quartz 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 low-loss 5.15-5.70-GHz RF MEMS switchable filter for WLAN appls. Sang-June Park, + , T-MTT Nov 06 3931-3939 single-wire transm. lines, terahertz freqs. Akalin, T., + , T-MTT Jun 06 2762-2767 R Radar; cf. Adaptive radar; CW radar; FM radar; Radar applications; Radar detection; Radar signal processing; Radar tracking; Synthetic aperture radar Radar applications breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 Radar cross sections phase-hologram-based compact RCS test range, 310 GHz for scale models. Lonnqvist, A., + , T-MTT Jun 06 2391-2397 Radar absorbing materials, 310 GHz, monostatic reflectivity meas. Lonnqvist, A., + , T-MTT Sep 06 3486-3491 Radar detection near-range microwave Radar syst., UWB rugby-ball antenna. Ruengwaree, A., + , T-MTT Jun 06 2774-2779 Radar equipment; cf. Radar receivers; Radar transmitters Radar imaging breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 Radar receivers UWB monopulse receiver, design. Tan, A.E.-C., + , T-MTT Nov 06 38213827 Radar signal processing nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 Radar systs., opt. sig. proc. Tonda-Goldstein, S., + , T-MTT Feb 06 847853 Radar signal processing; cf. Radar imaging Radar tracking UWB monopulse receiver, design. Tan, A.E.-C., + , T-MTT Nov 06 38213827 Radar transmitters UWB communs. and Radar systs., power-efficient switching-based CMOS UWB transmitters. Rui Xu, + , T-MTT Aug 06 3271-3277

+ Check author entry for coauthors

Radial basis function networks uniaxial and radial anisotropy models for finite-volume Maxwellian absorber. Sankaran, K., + , T-MTT Dec 06 4297-4304 Radiation effects; cf. Biological effects of radiation Radio broadcasting; cf. Digital audio broadcasting Radio communication 10-Gb/s data transm., 120-GHz-band mm-wave photonic wireless link. Hirata, A., + , T-MTT May 06 1937-1944 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 opt. carrier-to-sideband ratio for improv. transm. perform., fiber-radio links. Lim, C., + , T-MTT May 06 2181-2187 Radiocommunication; cf. Frequency hop communication Radio communication equipment time-domain modeling of TWT amps. for high data-rate commun. appls., from freq.-domain phys.-based simul. Safier, P.N., + , T-MTT Oct 06 3605-3615 Radio equipment; cf. Radio receivers; Radio transmitters; Transceivers Radiofrequency amplifiers; cf. Microwave amplifiers; Millimeter wave amplifiers; Submillimeter wave amplifiers; UHF amplifiers Radiofrequency filters; cf. Microwave filters; Millimeter wave filters; UHF filters; VHF filters Radiofrequency integrated circuits perfect-magnetic-coupling ultra-low-loss micromachined SMIS RF transformers for RFIC applications. Hsiao-Bin Liang, + , T-MTT Dec 06 4256-14267 radio frequency integrated circuits (special section). T-MTT Jan 06 3-105 radio frequency integrated circuits (special section intro.). Steer, M.B., TMTT Jan 06 3 Radiofrequency integrated circuits; cf. Microwave integrated circuits; Millimeter wave integrated circuits; UHF integrated circuits Radiofrequency oscillators; cf. Microwave oscillators; Millimeter wave oscillators; UHF oscillators Radio interferometry low phase-noise microwave oscillators, interferometric sig. proc. Ivanov, E.N., + , T-MTT Aug 06 3284-3294 Radiometers; cf. Bolometers Radio receivers 14.6-GHz LiNbO3 microdisk photonic self-homodyne RF receiver. Hossein-Zadeh, M., + , T-MTT Feb 06 821-831 6-port software-defined radio receiver platform, anal. and implement. Xinyu Xu, + , T-MTT Jul 06 2937-2943 antenna combinations for UWB ranging syst., exam. Takeuchi, Y., + , TMTT Jun 06 1858-1864 compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 space-time selective RAKE receiver, finger selection strategies for UWB overlay communs. Tsung-Hui Chang, + , T-MTT Jun 06 1731-1744 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 turnstile jn. waveguide orthomode transducer. Navarrini, A., + , T-MTT Jan 06 272-277 UWB sigs., nonGaussian noise, robust detect. Guney, N., + , T-MTT Jun 06 1724-1730 UWB SIMO channel meas. and simul. Keignart, J., + , T-MTT Jun 06 1812-1819 wireless interconnect technol., impulse radio for interchip communs. Yuanjin Zheng, + , T-MTT Jun 06 1912-1920 Radio transmitters compact sub-nanosecond tunable monocycle pulse transmitter for UWB appls. Jeongwoo Han, + , T-MTT Jan 06 285-293 integr. CMOS-based UWB tunable-pulse transmit module. Meng Miao, + , T-MTT Oct 06 3681-3687 linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349

IEEE T-MTT 2006 INDEX — 60 subbanded UWB transmitters, Gaussian pulse Generators. Wentzloff, D.D., + , T-MTT Jun 06 1647-1655 syst.-on-package UWB transmitter, CMOS impulse generator. Junwoo Lee, + , T-MTT Jun 06 1667-1674 UWB communs. and Radar systs., power-efficient switching-based CMOS UWB transmitters. Rui Xu, + , T-MTT Aug 06 3271-3277 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Radiowave propagation; cf. Microwave propagation; Submillimeter wave propagation Radiowaves; cf. Millimeter waves Randomized algorithms; cf. Genetic algorithms Random noise close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 high-speed p-i-n photodiodes, flicker noise. Rubiola, E., + , T-MTT Feb 06 816-820 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 rem. detect. of heartbeat and respiration, low-power DSB transm., kaband, freq.-tuning tech. Yanming Xiao, + , T-MTT May 06 2023-2032 wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 Random noise; cf. Flicker noise; Gaussian noise Rare earth compounds; cf. Lanthanum compounds Rare earth metals; cf. Erbium Ray tracing BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 UWB on-body radio channel modeling, ray theory and subband FDTD method. Yan Zhao, + , T-MTT Jun 06 1827-1835 RC circuits compact sub-nanosecond tunable monocycle pulse transmitter for UWB appls. Jeongwoo Han, + , T-MTT Jan 06 285-293 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 Reactors (electric); cf. Capacitors; Inductors Receivers direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 distortion analysis of ultra-wideband OFDM receiver front-ends. Ranjan, M., + , T-MTT Dec 06 4422-4431 low-power RF direct-conversion receiver/transmitter for 2.4-GHz-band IEEE 802.15.4 standard in 0.18-ȝm CMOS technology. Trung-Kien Nguyen, + , T-MTT Dec 06 4062-4071 Receivers; cf. Microwave receivers; Millimeter wave receivers; Optical receivers; Radar receivers; Radio receivers; Submillimeter wave receivers; Transceivers Reconfigurable architectures 10-Gb/s reconfigurable CMOS equalizer employing a transition detector based output monitoring technique for band-limited serial links. Bien, F., + , T-MTT Dec 06 4538-4547 Rectangular waveguides 2D photonic-cryst. waveguides form. by rect. cylinders, improved Fourier series method, modal anal. Hongting Jia, + , T-MTT Feb 06 564-571 compact colinear coaxial-to-rect. waveguide transits., patch endLaunchers, family. Simeoni, M., + , T-MTT Jun 06 1503-1511 discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 freq.-depend. equiv. width of substr. integr. waveguide, meas. ChaoHsiung Tseng, + , T-MTT Jun 06 1431-1437 hard waveguides, TE/TM modal soln. Epp, L.W., + , T-MTT Mar 06 10481054 measuring complex permitt. tensor of uniaxial composite materials, waveguide-based 2-step approach. Akhtar, M.J., + , T-MTT May 06 2011-2022 open-ended rect. waveguide probe, arbitrary-shape surface crack, lossy conductor, interact. Mazlumi, F., + , T-MTT Oct 06 3706-3711 shielded rect. dielec. rod waveguide, atten. Wells, C.G., + , T-MTT Jul 06 3013-3018 + Check author entry for coauthors

solving thick irises, rect. waveguides, Integral-eqn. tech. Stevanovic, I., + , T-MTT Jan 06 189-197 TE10-TEq0-mode conversion, rect. waveguides, nonsymmetrical H-plane corners. Kirilenko, A.A., + , T-MTT Jun 06 2471-2477 turnstile jn. waveguide orthomode transducer. Navarrini, A., + , T-MTT Jan 06 272-277 Rectangular waveguides; cf. Ridge waveguides Rectifiers 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 5.8-GHz circ. polarized retrodirective rectenna arrays for wireless power transm. Yu-Jiun Ren, + , T-MTT Jul 06 2970-2976 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 Recursive estimation 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 Reduced order systems fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 TLM-MOR for high-Q structs., oblique-oblique projection. Lukashevich, D., + , T-MTT Oct 06 3712-3720 Reflectometry power amp. charactn. Bensmida, S., + , T-MTT Jun 06 2707-2712 testing high-frequency electronic signals with reflection-mode electroabsorption modulators. Van Tuyl, R. L., + , T-MTT Dec 06 45564564 waveguide flange misalignment, reflectometer calib. method resistant. Zhiyang Liu, + , T-MTT Jun 06 2447-2452 Reflectometry; cf. Microwave reflectometry Reflector antennas EM modeling of MEMS-controlled planar phase shifters, scale-changing tech. Perret, E., + , T-MTT Sep 06 3594-3601 Refractive index optimization of arbitrarily sized DNG metamaterial slabs with losses. Sounas, D. L., + , T-MTT Dec 06 4111-4121 Remotely operated vehicles Ka-band FMCW radar front-end with adaptive leakage cancellation. Kaihui Lin, + , T-MTT Dec 06 4041-4048 Resonance accurate modeling, wave mechanisms, design considerations of substr. integr. waveguide. Deslandes, D., + , T-MTT Jun 06 2516-2526 deembedding unloaded reson. freq. from meas. of microwave cavities, tech. Canos, A.J., + , T-MTT Aug 06 3407-3416 Resonator filters broadside-coupled bandpass filters, both microstrip and CPW resonators. Pu-Hua Deng, + , T-MTT Oct 06 3746-3750 capacitive-coupled dual-behavior resonator (CCDBR) filters, synthesis. Manchec, A., + , T-MTT Jun 06 2346-2355 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 compact net-type resonators and their appls., microstrip bandpass filters. Chi-Feng Chen, + , T-MTT Feb 06 755-762 compact partial H-plane filters. Dong-Won Kim, + , T-MTT Nov 06 39233930 compact size coupling controllable filter, separate elec. and mag. coupling paths. Kaixue Ma, + , T-MTT Mar 06 1113-1119 complementary split-ring resonators, microstrip bandpass filters. Bonache, J., + , T-MTT Jan 06 265-271 coupled resonator filter CAD, quadratic prog. approach. Kozakowski, P., + , T-MTT Nov 06 3906-3913 design of very compact filters for Q-band appls., LTCC 3D resonators applied. Rigaudeau, L., + , T-MTT Jun 06 2620-2627 dielec. const. of FR4 substr., parallel-coupled microstrip resonator, wideband meas. Holzman, E.L., T-MTT Jul 06 3127-3130 dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 engng. Optimization-theory and implement., space-mapping framework. Koziel, S., + , T-MTT Oct 06 3721-3730 LTCC balanced-to-unbalanced extracted-pole bandpass filter, complex load. Lap Kun Yeung, + , T-MTT Jun 06 1512-1518

IEEE T-MTT 2006 INDEX — 61 microstrip sq.-loop dual-mode bandpass filter, simultaneous size reduction and spurious response suppression. Si-Weng Fok, + , T-MTT May 06 2033-2041 microwave bandpass filters, resonators, nonuniform Q, design. Guyette, A.C., + , T-MTT Nov 06 3914-3922 miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095 miniaturized microstrip and CPW filters, coupled metamaterial resonators. Garcia-Garcia, J., + , T-MTT Jun 06 2628-2635 narrowband multicoupled resonator filters, anal. diagnosis and tuning. Wei Meng, + , T-MTT Oct 06 3765-3771 periodic stepped-impedance ring resonator (PSIRR) bandpass filter, miniaturized area and desirable upper stopband characts. Kuo, J.-T., + , T-MTT Mar 06 1107-1112 planar bandpass filter design, wide stopband, double split-end steppedimpedance resonators. Kongpop U-yen, + , T-MTT Mar 06 1237-1244 planar coupled-resonator microwave filters, space-mapping optim. Amari, S., + , T-MTT May 06 2153-2159 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 tunable bandstop defected ground struct. resonator, reconfigurable dumbbell-shaped CPW. Safwat, A.M.E., + , T-MTT Sep 06 3559-3564 wide-stopband microstrip bandpass filters, dissimilar qtr.-wavel. steppedimpedance resonators. Shih-Cheng Lin, + , T-MTT Mar 06 1011-1018 Resonators backward-wave propag., periodic waveguide structs., design and expt. verification. Carbonell, J., + , T-MTT Jun 06 1527-1533 compact fixed and tune-all bandpass filters, coupled slow-wave resonators. Pistono, E., + , T-MTT Jun 06 2790-2799 compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 dual- and triple-mode branch-line ring resonators and harmonic suppressed half-ring resonators. Choon Sik Cho, + , T-MTT Nov 06 3968-3974 dual-band lumped-element bandpass filter. Joshi, H., + , T-MTT Dec 06 4169-4177 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 electronically switchable bandpass filters using loaded stepped-impedance resonators. Shih-Fong Chao, + , T-MTT Dec 06 4193-4201 evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 ku-band MMIC phase shifter, parallel resonator, 0.18-ȝm CMOS technol. Dong-Woo Kang, + , T-MTT Jan 06 294-301 matching appls., tapped marchand baluns. Fathelbab, W.M., + , T-MTT Jun 06 2543-2551 matching circuits for microstrip triplexers based on stepped-impedance resonators. Pu-Hua Deng, + , T-MTT Dec 06 4185-4192 miniaturized open-sq.-loop resonator, inner split rings loading. Ooi, B.-L., + , T-MTT Jul 06 3098-3103 oversized Ka-band traveling-wave window for a high-power transmission. Bogdashov, A., + , T-MTT Dec 06 4130-4135 split-ring resonator and wire loaded transm. line, fin-line technol., lefthanded EM props. Decoopman, T., + , T-MTT Jun 06 1451-1457 spurious DC modes, edge element solns. for modeling 3D resonators, removal. Venkatarayalu, N.V., + , T-MTT Jul 06 3019-3025 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 Resonators; cf. Cavity resonators; Dielectric resonators Ridge waveguides efficient anal., design, filter appls. of EBG waveguide, periodic reson. loads. Goussetis, G., + , T-MTT Nov 06 3885-3892 Ring lasers microwave sig., dual-wavel. single-long.-mode fiber ring laser, photonic gener. Xiangfei Chen, + , T-MTT Feb 06 804-809 Routing serpentine and flat spiral delay lines, transient refl./transm. waveforms and eye diags., comparisons. Wei-Da Guo, + , T-MTT Jun 06 1379-1387

S Sampling methods; cf. Signal sampling + Check author entry for coauthors

Sapphire evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 Satellite antennas digital audio radio service (SDARS) appl., s-band dual-path dual-polarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 Satellite broadcasting satellite digital audio radio service (SDARS) appl., s-band dual-path dualpolarized antenna syst. Young-Pyo Hong, + , T-MTT Jun 06 1569-1575 Satellite communication multiport-amplifier-based architecture versus classical architecture for space telecommunication payloads. Mallet, A., + , T-MTT Dec 06 43534361 Satellite communication; cf. Satellite antennas Satellite navigation; cf. Global Positioning System Scattering hybrid space-discretizing method, method of moments for the analysis of transient interference. Khlifi, R., + , T-MTT Dec 06 4440-4447 Scattering matrices 2D photonic-cryst. waveguides form. by rect. cylinders, improved Fourier series method, modal anal. Hongting Jia, + , T-MTT Feb 06 564-571 broadband asymmetrical multisection wilkinson power divider, design and optim. Oraizi, H., + , T-MTT May 06 2220-2231 efficient anal., design, filter appls. of EBG waveguide, periodic reson. loads. Goussetis, G., + , T-MTT Nov 06 3885-3892 fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 mixed-mode params. of cascaded balanced nets. and their appls., modeling of differential interconnects, props. Hao Shi, + , T-MTT Jan 06 360-372 open-ended rect. waveguide probe, arbitrary-shape surface crack, lossy conductor, interact. Mazlumi, F., + , T-MTT Oct 06 3706-3711 periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 Scattering parameters 3D geometries, multilayer dielectrics, cct. model. Jayabalan, J., + , TMTT Jun 06 1331-1339 analog 60-GHz electroabsorption modulator module for RF/optic conversion, develop. and RF characts. Jeha Kim, + , T-MTT Feb 06 780787 broadband space conservative on-wafer NWA calibs., complex load and thru models. Padmanabhan, S., + , T-MTT Sep 06 3583-3593 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 complex microwave systs. represented by small FDTD modeling data sets, RBF net. optim. Murphy, E.K., + , T-MTT Jul 06 3069-3083 discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 electronically tunable act. duplexer for wireless transceiver appls. Sundaram, B., + , T-MTT Jun 06 2584-2592 GaN HEMTs, accurate multibias equiv.-cct. extr. Crupi, G., + , T-MTT Oct 06 3616-3622 gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 layout scaling, Si integr. stacked transformers, anal. and modeling. Biondi, T., + , T-MTT May 06 2203-2210 lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3-port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3-port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 1296-1297 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 nonlin. amps., load-pull AM-AM and AM-PM meas., large-sig. behavioral modeling. Jiang Liu, + , T-MTT Aug 06 3191-3196

IEEE T-MTT 2006 INDEX — 62 power amp., unilateralization and improved output return loss, feedback method. Zuo-Min Tsai, + , T-MTT Jun 06 1590-1597 scalable compact cct. model and synthesis for RF CMOS spiral inductors. Wei Gao, + , T-MTT Mar 06 1055-1064 scatt. params., EM time-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Jun 06 1598-1610 sig. vias, virtual islands, shorting vias, multilayer PCBs, perform. anal. Seungki Nam, + , T-MTT Jun 06 1315-1324 split-ring resonator and wire loaded transm. line, fin-line technol., lefthanded EM props. Decoopman, T., + , T-MTT Jun 06 1451-1457 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 waveguide scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Schottky diodes high-order subharmonically pumped mixers, phased local oscillators. Zhiyang Liu, + , T-MTT Jul 06 2977-2982 high-speed digital-to-analog converter using Schottky diode samplers. Kae-Oh Sun, + , T-MTT Dec 06 4291-14296 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 Semiconductor device modeling CAD-based design of internal matching nets. of high-power RF/microwave transistors, modeling techs. suitable. Aaen, P.H., + , TMTT Jul 06 3052-3059 complete small-sig. equiv.-cct. model of InGaP/GaAs HBT incl. base contact impedance and AC current crowding effect, extr. tech. Wen-Bin Tang, + , T-MTT Oct 06 3641-3647 coupled electrothermal, EM, phys. modeling of microwave power FETs. Denis, D., + , T-MTT Jun 06 2465-2470 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 GaN HEMTs, accurate multibias equiv.-cct. extr. Crupi, G., + , T-MTT Oct 06 3616-3622 HBT small-sig. model params., systematic and rigorous extr. method. Degachi, L., + , T-MTT Feb 06 682-688 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 low gate bias model extr. tech. for AlGaN/GaN HEMTs. Guang Chen, + , T-MTT Jul 06 2949-2953 self-consistent coupled carrier transport full-wave EM anal. of semicond. TW devices. Bertazzi, F., + , T-MTT Jun 06 1611-1618 Semiconductor device noise gen. eqns. for FET cold noise source design, expt. validation. Weatherspoon, M.H., + , T-MTT Feb 06 608-614 high-speed p-i-n photodiodes, flicker noise. Rubiola, E., + , T-MTT Feb 06 816-820 LF noise upconversion, InGaP/GaAs HBTs, simul. Rudolph, M., + , TMTT Jul 06 2954-2961 Semiconductor devices nonquasi-static empirical model of electron devices. Santarelli, A., + , TMTT Dec 06 4021-4031 Semiconductor devices; cf. Semiconductor lasers; Semiconductor switches Semiconductor device testing microwave on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3-port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3-port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 1296-1297 Semiconductor diodes; cf. Microwave diodes; Millimeter wave diodes; Photodiodes; p-i-n diodes; Schottky diodes; Varactors Semiconductor junctions; cf. p-n junctions Semiconductor lasers perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 radio-on-fiber syst., predistortion-type equi-path linearizer designed. Shingo Tanaka, + , T-MTT Feb 06 938-944 TW microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951958 Semiconductor materials SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 + Check author entry for coauthors

Semiconductor switches differential wireless communs. frontends, RF switch concepts. Erkens, H., + , T-MTT Jun 06 2376-2382 Sensitivity compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 net. params., EM freq.-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Feb 06 670-681 scatt. params., EM time-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Jun 06 1598-1610 Sensors; cf. Microwave detectors; Millimeter wave detectors; Photodetectors Series (mathematics); cf. Volterra series Shielding ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 Signal detection transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 UWB sigs., nonGaussian noise, robust detect. Guney, N., + , T-MTT Jun 06 1724-1730 Signal detection; cf. Radar detection Signal generators charactn. and behavioral modeling of nonlin. devices, memory, timedomain envelope meas. Macraigne, F., + , T-MTT Aug 06 3219-3226 corrected microwave multisine waveform generator. Carvalho, N.B., + , T-MTT Jun 06 2659-2664 low-power UWB wavelets generator, fast start-up cct. Barras, D., + , TMTT May 06 2138-2145 Signal generators; cf. Frequency synthesizers Signal processing compensation of nonlin. distortion, wideband multicarrier radio receivers, advanced DSP techs. Valkama, M., + , T-MTT Jun 06 2356-2366 microwave photonics. T-MTT Feb 06 777-989 microwave photonics. Seeds, A., + , T-MTT Feb 06 777-779 UWB, Multi(Six)-port impulse radio. Yanyang Zhao, + , T-MTT Jun 06 1707-1712 Signal processing; cf. Array signal processing; Deconvolution; Radar signal processing; Signal reconstruction; Signal resolution; Signal sampling Signal reconstruction reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 Signal reconstruction; cf. Image reconstruction Signal resolution reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 Signal sampling microwave sigs., photonic sig. proc. Minasian, R.A., T-MTT Feb 06 832846 nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 photonic freq.-conversion method, bandpass sampling, multicarrier operated radio-on-fiber link, proposal. Higashino, T., + , T-MTT Feb 06 973-979 sampling oscilloscopes, high-speed photodiodes, calib. Clement, T.S., + , T-MTT Aug 06 3173-3181 sampling oscilloscopes, min.-phase calib. Dienstfrey, A., + , T-MTT Aug 06 3197-3208 Silicon 0.18-ȝm CMOS technol., low-power oscillator mixer. To-Po Wang, + , TMTT Jan 06 88-95 ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 low-loss Si-on-Si DC-110-GHz reson.-free package. Byung-Wook Min, + , T-MTT Feb 06 710-716 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs, shield-based 3-port de-embedding method. Kaija, T., + , T-MTT Mar 06 1295-1296 microwave on-wafer charactn. of deep-submicrometer Si MOSFETs ), shield-based 3-port de-embedding method. Ming-Hsiang Cho, T-MTT Mar 06 1296-1297

IEEE T-MTT 2006 INDEX — 63 monolithic broadband Gilbert micromixer with an integrated marchand balun using standard silicon IC process. Sheng-Che Tseng, + , T-MTT Dec 06 4362-4371 permitt., dielec. loss tangent, resist. of float-zone Si, microwave freqs., meas. Krupka, J., + , T-MTT Nov 06 3995-4001 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 substr. integr. image guide (SIIG), planar dielec. waveguide technol. for mm-wave appls. Patrovsky, A., + , T-MTT Jun 06 2872-2879 transm. lines fabricated by CMOS proc., deep n-well implant. Nishikawa, K., + , T-MTT Feb 06 589-598 Silicon alloys behavioral modeling of nonlin. amps., memory, vector intermodulation analyzer applied. Walker, A., + , T-MTT May 06 1991-1999 broadband monolithic pass. differential coupler for K/ka-band appls. Hamed, K.W., + , T-MTT Jun 06 2527-2533 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 power amps., SiGe proc. technol., mm-wave design considerations. Pfeiffer, U.R., + , T-MTT Jan 06 57-64 SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 UWB LNA, resistive feedback, SiGe HBT technol., anal. and design. Jongsoo Lee, + , T-MTT Mar 06 1262-1268 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 Silicon compounds CMOS broad-band compact high-linearity modulators for gigabit microwave/mm-wave appls., design and anal. Hong-Yeh Chang, + , TMTT Jan 06 20-30 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 Silicon compounds; cf. Quartz Silicon on insulator technology ground-shielded CMOS test fixtures, improved model. Kaija, T., + , TMTT Jan 06 82-87 low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73 TWA vs. temp., SOI technol., behavior. Si Moussa, M., + , T-MTT Jun 06 2675-2683 Silver evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 Simulation; cf. Circuit simulation Skin breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 Skin effect atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 Slot antennas broadband high-effic. linearly and circ. polarized act. integr. antennas. Yi Qin, + , T-MTT Jun 06 2723-2732 heating performs. of coaxial-slot antenna, endoscope for treatment of bile duct carcinoma, estim. Saito, K., + , T-MTT Aug 06 3443-3449 wideband planar monopole antennas, dual band-notched characts. WangSang Lee, + , T-MTT Jun 06 2800-2806 Slotline wide-band microstrip-to-CPS/slotline transits. Wen-Hua Tu, + , T-MTT Mar 06 1084-1089 Slotline components microstrip ellipt.-fn. low-pass filters, distrib. elements, slotted ground struct. Wen-Hua Tu, + , T-MTT Oct 06 3786-3792 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 Slow wave structures 4-bit slow-wave MEMS phase shifters, design and modeling. Lakshminarayanan, B., + , T-MTT Jan 06 120-127 compact fixed and tune-all bandpass filters, coupled slow-wave resonators. Pistono, E., + , T-MTT Jun 06 2790-2799

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miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095 self-consistent coupled carrier transport full-wave EM anal. of semicond. TW devices. Bertazzi, F., + , T-MTT Jun 06 1611-1618 Solid lasers; cf. Semiconductor lasers Solitons elec. soliton oscillator. Ricketts, D.S., + , T-MTT Jan 06 373-382 S-parameters low-loss differential semicoaxial interconnects in CMOS process. Jun-De Jin, + , T-MTT Dec 06 4333-4340 Sparse matrices ICCAP, lin. time sparsification and reordering algm. for 3D BEM capacitance extr. Rong Jiang, + , T-MTT Jul 06 3060-3068 Spatial variables measurement; cf. Distance measurement; Level measurement Special issues and sections 2006 Asia-Pacific Microwave Conference (special section). T-MTT Jul 06 2901-2948 35th European Microwave Conference (special issue). T-MTT Jun 06 2567-2898 35th European Microwave Conference (special issue intro.). Quere, R., + , T-MTT Jun 06 2567 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section). T-MTT Aug 06 3161-3245 large-signal characterization and modeling of nonlinear analog devices, circuits, and systems (special section intro.). Borges Carvalho, N., + , TMTT Aug 06 3161-3162 microwave photonics (special issue). T-MTT Feb 06 777-989 microwave photonics (special issue intro.). Seeds, A., + , T-MTT Feb 06 777-779 radio frequency integrated circuits (special section). T-MTT Jan 06 3-105 radio frequency integrated circuits (special section intro.). Steer, M.B., TMTT Jan 06 3 ultra-wideband (special issue). T-MTT Apr 06 1633-1927 ultra-wideband (special issue intro.). Knochel, R.H., + , T-MTT Apr 06 1633-1636 Spectral analysis 3D spectral-element method, mixed-order curl conforming vector basis fns. for EM fields. Joon-Ho Lee, + , T-MTT Jan 06 437-444 multisines, in-band distortion. Gharaibeh, K.M., + , T-MTT Aug 06 32273236 nonlin. mixing products, amplit. and phase charactn. Pedro, J.C., + , TMTT Aug 06 3237-3245 power spectrum of ultra-wideband radio-frequency signals. McKinney, J. D., + , T-MTT Dec 06 4247-4255 spectral analysis of a low-power Ka-band heartbeat detector measuring from four sides of a human body. Changzhi Li, + , T-MTT Dec 06 44644471 subbanded UWB transmitters, Gaussian pulse Generators. Wentzloff, D.D., + , T-MTT Jun 06 1647-1655 Spectral domain analysis direct discrete complex image method from closed-form Green's fns., multilayered media. Mengtao Yuan, + , T-MTT Mar 06 1025-1032 SPICE (S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 Spread spectrum communication BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792 Sputter etching atten. and cross-coupling for edge-suspen. CPW, lossy Si substr., CAD equiv.-cct. modeling. Leung, L.L.W., + , T-MTT May 06 2249-2255 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 Sputtering; cf. Sputter etching Stability anal. and design of coupled-oscillator systs., techs. Georgiadis, A., + , TMTT Nov 06 3864-3877 matching appls., tapped marchand baluns. Fathelbab, W.M., + , T-MTT Jun 06 2543-2551 stability criterion for two-port network with input and output terminations varying in elliptic regions. Marietti, P., + , T-MTT Dec 06 4049-4055

IEEE T-MTT 2006 INDEX — 64 Stability; cf. Circuit stability; Numerical stability Standards; cf. IEEE standards Statistical analysis; cf. Higher order statistics; Maximum likelihood estimation Statistics; cf. Error statistics; Monte Carlo methods; Time series Stochastic processes gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 nonlin. behavior of RF amps., expt. charactn. Rolain, Y., + , T-MTT Aug 06 3209-3218 Stochastic processes; cf. Gaussian processes Stripline 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 Stripline circuits compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part I, design. Gruszczynski, S., + , T-MTT Nov 06 3986-3994 Strip line circuits; cf. Microstrip circuits Strip line components; cf. Microstrip components Stripline couplers compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 Strip line couplers; cf. Microstrip couplers Stripline discontinuities compensated coupled-stripline 3-dB directional couplers, phase shifters, magic-T's-part II, design. Gruszczynski, S., + , T-MTT Sep 06 3501-3507 Stripline filters 5.8-GHz circ. polarized dual-diode rectenna/rectenna array for microwave power transm. Yu-Jiun Ren, + , T-MTT Jun 06 1495-1502 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 miniature broadband bandpass filters, double-layer coupled stripline resonators. Yunchi Zhang, + , T-MTT Aug 06 3370-3377 syst.-on-package UWB transmitter, CMOS impulse generator. Junwoo Lee, + , T-MTT Jun 06 1667-1674 Strip line filters; cf. Microstrip filters Stripline resonators diffr. and multiple scatt., free-space microwave meas. of materials, error correction. Kai Meng Hock, T-MTT Feb 06 648-659 miniature broadband bandpass filters, double-layer coupled stripline resonators. Yunchi Zhang, + , T-MTT Aug 06 3370-3377 Strip line resonators; cf. Microstrip resonators Strip lines; cf. Microstrip lines Subcarrier multiplexing freq.-converted radio-on-fiber syst., relative-intens.-noise reduction tech. Taguchi, N., + , T-MTT Feb 06 945-950 mm-wave-band radio-over-fiber syst., dense WDM bus archit. Xiupu Zhang, + , T-MTT Feb 06 929-937 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972 Submillimeter wave amplifiers variable gain amp., gain-bandwidth product up, 354 GHz implemented, InP-InGaAs DHBT technol., design. Jie-Wei Lai, + , T-MTT Feb 06 599-607 Submillimeter wave devices; cf. Submillimeter wave amplifiers; Submillimeter wave mixers; Submillimeter wave receivers Submillimeter wave imaging integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 Submillimeter wave mixers integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 quasiopt. NbN supercond. HEB mixer, charactn. Ling Jiang, + , T-MTT Jul 06 2944-2948 terahertz hot electron bolometer mixers, quantum-noise theory. Kollberg, E.L., + , T-MTT May 06 2077-2089 Submillimeter wave propagation w-band multiport substr.-integr. waveguide Circuits. Ellis, T.J., T-MTT Nov 06 4016

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Submillimeter wave receivers integr. HEB/MMIC receivers for near-range terahertz imaging. RodriguezMorales, F., + , T-MTT Jun 06 2301-2311 quasiopt. NbN supercond. HEB mixer, charactn. Ling Jiang, + , T-MTT Jul 06 2944-2948 terahertz hot electron bolometer mixers, quantum-noise theory. Kollberg, E.L., + , T-MTT May 06 2077-2089 Submillimeter wave technology single-wire transm. lines, terahertz freqs. Akalin, T., + , T-MTT Jun 06 2762-2767 Substrates dual-band lumped-element bandpass filter. Joshi, H., + , T-MTT Dec 06 4169-4177 full-wave analysis of inhomogeneous deep-trench isolation patterning for substrate coupling reduction and Q-factor improvement. Wane, S., + , TMTT Dec 06 4397-4411 polymer-ceramic composites for microwave applications. Koulouridis, S., + , T-MTT Dec 06 4202-4208 Superconducting coils narrowband supercond. filter, spirals, reversal, winding direction. Huang, F., + , T-MTT Nov 06 3954-3959 Superconducting devices; cf. Superconducting coils; Superconducting microwave devices Superconducting films compact parallel coupled HTS microstrip bandpass filters for wireless communs. Pal, S., + , T-MTT Feb 06 768-775 Superconducting materials; cf. High-temperature superconductors Superconducting microwave devices distrib. nonlinearities, ferroelectrics and superconds. for microwave appls., anal. and Simulation. Seron, D., + , T-MTT Mar 06 1154-1160 high-temp. supercond. bandpass filter, microstrip qtr.-wavel. spiral resonators. Guoyong Zhang, + , T-MTT Feb 06 559-563 Superconducting mixers; cf. Superconductor-insulator-superconductor mixers Superconductivity; cf. High-temperature superconductors Superconductor-insulator-superconductor devices; cf. Superconductorinsulator-superconductor mixers Superconductor-insulator-superconductor mixers low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 Surface acoustic wave detectors nonlin. chirps, FMCW Radar SAW-ID tag request, sig. model and linearization. Scheiblhofer, S., + , T-MTT Jun 06 1477-1483 Surface acoustic wave devices; cf. Surface acoustic wave filters Surface acoustic wave filters SAW devices, chirp transform spectrometers, digital dispers. matching net. Villanueva, G.L., + , T-MTT Jun 06 1415-1424 Surface acoustic wave filters; cf. Surface acoustic wave resonator filters Surface acoustic wave resonator filters highly miniaturized RF bandpass filter, thin-film BAW resonator for 5GHz-band appl. Yong-Dae Kim, + , T-MTT Mar 06 1218-1228 Surface-emitting lasers low-cost multimode fiber-fed indoor wireless nets., design. Das, A., + , TMTT Aug 06 3426-3432 low-power fast VCSEL drivers for high-dens. links, 90-nm SOI CMOS, design. Sialm, G., + , T-MTT Jan 06 65-73 optically injection-locked VCSELs, microwave perform. Chrostowski, L., + , T-MTT Feb 06 788-796 perform. of RF-over-fiber links and their impact, device design, limits. Cox, C.H., III, + , T-MTT Feb 06 906-920 Switched filters low-loss 5.15-5.70-GHz RF MEMS switchable filter for WLAN appls. Sang-June Park, + , T-MTT Nov 06 3931-3939 Switched networks; cf. Switched filters Switches; cf. Optical switches; Semiconductor switches Switching circuits tunable phase shifters by image-params. method, design. Ocera, A., + , TMTT Jun 06 2383-2390 Synchronization antenna combinations for UWB ranging syst., exam. Takeuchi, Y., + , TMTT Jun 06 1858-1864 BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 high- and low-data-rate appls., UWB ranging accuracy. Cardinali, R., + , T-MTT Jun 06 1865-1875

IEEE T-MTT 2006 INDEX — 65 transm.-ref. UWB receiver, freq.-domain implement. Hoyos, S., + , TMTT Jun 06 1745-1753 transm.-ref. UWB systs., weighted autocorrelation receivers. Romme, J., + , T-MTT Jun 06 1754-1761 UWB ad hoc nets., TOA, joint distrib. sync. and positioning. Denis, B., + , T-MTT Jun 06 1896-1911 UWB nets., uncontrolled interf., robust sig.-detect. method. Fawal, A.E., + , T-MTT Jun 06 1769-1781 Synthetic aperture radar Ka-band FMCW radar front-end with adaptive leakage cancellation. Kaihui Lin, + , T-MTT Dec 06 4041-4048 T Table lookup linearization of broad-band wireless transmitters, augmented hammerstein predistorter. Taijun Liu, + , T-MTT Jun 06 1340-1349 power amp. predistortion linearization, dynamically optimum lookup-table spacing. Chih-Hung Lin, + , T-MTT May 06 2118-2127 wireless transmitter, Doherty amp., piecewise preequalized linearization. Wan-Jong Kim, + , T-MTT Sep 06 3469-3478 Telecommunication; cf. Data communication; Mobile communication; Optical communication; Satellite communication; Spread spectrum communication Telecommunication channels; cf. Gaussian channels; Multipath channels Telecommunication equipment; cf. Optical communication equipment Telecommunication networks; cf. Broadband networks Telemedicine spectral analysis of a low-power Ka-band heartbeat detector measuring from four sides of a human body. Changzhi Li, + , T-MTT Dec 06 44644471 Test facilities radial extr. output cavity for freq.-doubling gyroklystron, design and cold testing. Bharathan, K., + , T-MTT Jun 06 1301-1307 Testing; cf. Materials testing Thin film capacitors 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 Thin film devices; cf. Thin film capacitors Thin films; cf. Epitaxial layers Three-dimensional displays 3-D finite-difference time-domain scheme based on a transversely extended-curl operator. Panaretos, A. H., + , T-MTT Dec 06 4237-4246 Time division multiaccess operation, syst. archits., phys. Layer design considerations of distrib. MAC protocols for UWB. August, N.J., + , T-MTT Jul 06 3001-3012 Time domain analysis 2D freq. converter utilizing cpd. nonlin. photonic-cryst. struct. by condensed node spatial net. method. Satoh, H., + , T-MTT Jan 06 210215 3-D finite-difference time-domain scheme based on a transversely extended-curl operator. Panaretos, A. H., + , T-MTT Dec 06 4237-4246 BPSK direct-seq. indoor UWB commun. syst., discone antenna. Yongwei Zhang, + , T-MTT Jun 06 1675-1680 charactn. and behavioral modeling of nonlin. devices, memory, timedomain envelope meas. Macraigne, F., + , T-MTT Aug 06 3219-3226 comput. electromagnetics, high-order Runge-Kutta multiresolution timedomain methods. Qunsheng Cao, + , T-MTT Aug 06 3316-3326 dispers. dynamics, hetero FET, multiple time const. modeling. Kallfass, I., + , T-MTT Jun 06 2312-2320 effects of antenna dispers., UWB waveforms via opt. pulse-shaping techs., compensation. McKinney, J.D., + , T-MTT Jun 06 1681-1686 envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 gener. of stable and accurate hybrid TD-FD MoM solns., conds. Mengtao Yuan, + , T-MTT Jun 06 2552-2563 microwave integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , T-MTT Mar 06 1043-1047 reconstructing stratified permitt. profiles, super-resoln. techs. Aly, O.A.M., + , T-MTT Jan 06 492-498 scatt. params., EM time-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Jun 06 1598-1610 serpentine and flat spiral delay lines, transient refl./transm. waveforms and eye diags., comparisons. Wei-Da Guo, + , T-MTT Jun 06 1379-1387

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(S)PEEC, Time- and freq.-domain surface formulation for modeling conductors and dielectrics, combined cct. EM simul. Gope, D., + , TMTT Jun 06 2453-2464 testing high-frequency electronic signals with reflection-mode electroabsorption modulators. Van Tuyl, R. L., + , T-MTT Dec 06 45564564 UWB SIMO channel meas. and simul. Keignart, J., + , T-MTT Jun 06 1812-1819 Time domain reflectometry high-precision multitarget-level meas. syst., TDR, approach. Gerding, M., + , T-MTT Jun 06 2768-2773 Time series envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 Titanium compounds low-noise 0.8-0.96- and 0.96-1.12-THz SIS mixers for herschel space observatory. Jackson, B.D., + , T-MTT Feb 06 547-558 Tolerance analysis fast full-wave optim. of microwave filters, adjoint higher order sensitivities. Sabbagh, M.A.E., + , T-MTT Aug 06 3339-3351 Tomography subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450 Tracking; cf. Radar tracking Transceivers 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 electronically tunable act. duplexer for wireless transceiver appls. Sundaram, B., + , T-MTT Jun 06 2584-2592 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 IR-UWB systs., different transceiver types, TOA estim. Guvenc, I., + , TMTT Jun 06 1876-1886 low-complexity noncoherent IR-UWB transceiver archit., TOA estim. Stoica, L., + , T-MTT Jun 06 1637-1646 low-power UWB radio transceivers, robust front-end archit. Barras, D., + , T-MTT Jun 06 1713-1723 LTCC technol., transceiver integrat. capability for UWB appls., planar antennas. Brzezina, G., + , T-MTT Jun 06 2830-2839 memoryless nonlinearities, M-QAM and DQPSK OFDM sigs., effects. Chorti, A., + , T-MTT Aug 06 3301-3315 optimized mm-wave fiber radio links, perform. anal. Kurniawan, T., + , TMTT Feb 06 921-928 rem. detect. of heartbeat and respiration, low-power DSB transm., kaband, freq.-tuning tech. Yanming Xiao, + , T-MTT May 06 2023-2032 self-heterodyne scheme for mm-wave wireless pers. area net., 70-GHzband OFDM transceivers. Shoji, Y., + , T-MTT Oct 06 3664-3674 V-band front-end, 3D integr. cavity filters/duplexers and antenna, LTCC technols. Jong-Hoon Lee, + , T-MTT Jul 06 2925-2936 wide-band commun. systs., 10-35-GHz 6-channel microstrip MUX. Seungpyo Hong, + , T-MTT Jun 06 1370-1378 Transducers multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 Transfer functions envelope-domain time series (ET) behavioral model of Doherty RF power amp. for syst. design. Wood, J., + , T-MTT Aug 06 3163-3172 microwave mixer, single-digit phase accuracy, sampling-oscilloscope meas. Williams, D.F., + , T-MTT Mar 06 1210-1217 parametric UWB propag. channel estim. and perform. validation, anechoic chamber. Haneda, K., + , T-MTT Jun 06 1802-1811 Transformers gen. mixed-mode S-params. Ferrero, A., + , T-MTT Jan 06 458-463 layout scaling, Si integr. stacked transformers, anal. and modeling. Biondi, T., + , T-MTT May 06 2203-2210 microstrip line employing periodically perforated ground metal and appl., highly miniaturized on-chip pass. components, GaAs MMIC, basic RF characts. Yun, Y., + , T-MTT Oct 06 3805-3817 Transforms 3D metallic objs. arranged, 2D lattices, Ewald transform., integral-eqn. anal. Stevanovic, I., + , T-MTT Oct 06 3688-3697

IEEE T-MTT 2006 INDEX — 66 Transforms; cf. Hilbert transforms; Laplace transforms; Wavelet transforms; Z transforms Transient analysis fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 high-speed IC appls., state-space dyn. neural net. tech. Yi Cao, + , T-MTT Jun 06 2398-2409 hybrid space-discretizing method, method of moments for the analysis of transient interference. Khlifi, R., + , T-MTT Dec 06 4440-4447 Transient response breast cancer detect.-investigs. of improved skin-sens. method, tissue sens. adaptive Radar. Williams, T.C., + , T-MTT Jun 06 1308-1314 effects of antenna dispers., UWB waveforms via opt. pulse-shaping techs., compensation. McKinney, J.D., + , T-MTT Jun 06 1681-1686 Transistor circuits; cf. Bipolar transistor circuits Transistors; cf. Field effect transistors; Microwave transistors; Millimeter wave transistors Transition metal compounds; cf. Niobium compounds; Titanium compounds Transition metals; cf. Copper; Gold; Niobium; Silver; Tungsten Transmission line matrix methods EM wave propag., biisotropic media, TLM method, time-domain modeling. Cabeceira, A.C.L., + , T-MTT Jun 06 2780-2789 scatt. params., EM time-domain simulators, sensitivity anal. Nikolova, N.K., + , T-MTT Jun 06 1598-1610 TLM-MOR for high-Q structs., oblique-oblique projection. Lukashevich, D., + , T-MTT Oct 06 3712-3720 Transmission lines 3-line balun and implement., multilayer config., design. Byoung Hwa Lee, + , T-MTT Jun 06 1405-1414 arbitrarily dual-band components, simplified structs. of conventional CRLH TLs. Xian Qi Lin, + , T-MTT Jul 06 2902-2909 combined left- and right-handed tunable transmission lines. Hongjoon Kim, + , T-MTT Dec 06 4178-4184 compact microstrip bandpass filters, good selectivity and stopband rejection. Pu-Hua Deng, + , T-MTT Feb 06 533-539 compact second harmonic-suppressed bandstop and bandpass filters, open stubs. Wen-Hua Tu, + , T-MTT Jun 06 2497-2502 composite right/left-handed transm. line metamaterial phase shifters (MPS), MMIC technol. Perruisseau-Carrier, J., + , T-MTT Jun 06 1582-1589 comput. transm.-line params. of lossy lines, Quasi-TM MoL/MoM approach. Plaza, G., + , T-MTT Jan 06 198-209 deembedding unloaded reson. freq. from meas. of microwave cavities, tech. Canos, A.J., + , T-MTT Aug 06 3407-3416 defected ground structs. (DGSs) incl. left-handed features, bandgap and slow/fast-wave characts. Hyung-Mi Kim, + , T-MTT Jul 06 3113-3120 distrib. MEMS tunable matching net., minimal-contact RF-MEMS varactors. Qin Shen, + , T-MTT Jun 06 2646-2658 elec. soliton oscillator. Ricketts, D.S., + , T-MTT Jan 06 373-382 evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 fabricated by CMOS proc., deep n-well implant. Nishikawa, K., + , TMTT Feb 06 589-598 fast and direct coupled-micro strip interconnect reduced-order modeling, FEM. Se-Ho You, + , T-MTT May 06 2232-2242 GA and gradient descent optmization methods for accurate inverse permitt. meas., combined. Requena-Perez, M.E., + , T-MTT Feb 06 615624 LTCC bandpass filters, diplexer, triplexer, transm. zeros, design methodologies. Ching-Wen Tang, + , T-MTT Feb 06 717-723 micromachined rect.-coaxial transm. lines. Reid, J.R., + , T-MTT Aug 06 3433-3442 microstrip transm.-line method for broad-band meas. of permeab. tensor, extension and error anal. Mallegol, S., + , T-MTT Mar 06 1065-1075 microwave integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , T-MTT Mar 06 1043-1047 nonphysical leaky mode, field excited by source, significant contrib. Tsuji, M., + , T-MTT Jan 06 421-427 nonuniform lossy/lossless transmission lines and tapered microstrips. Eghlidi, M. H., + , T-MTT Dec 06 4122-4129 periodic distrib. MEMS-appl., design of variable true-time delay lines, modeling. Perruisseau-Carrier, J., + , T-MTT Jan 06 383-392 quasiplanar high-Q mm-wave resonators. Vanhille, K.J., + , T-MTT Jun 06 2439-2446 + Check author entry for coauthors

split-ring resonator and wire loaded transm. line, fin-line technol., lefthanded EM props. Decoopman, T., + , T-MTT Jun 06 1451-1457 transmission-line concept for integrated capacitors and inductors. Lee, K.Y., + , T-MTT Dec 06 4141-4148 tunable phase shifters by image-params. method, design. Ocera, A., + , TMTT Jun 06 2383-2390 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 Transmission lines; cf. Coplanar transmission lines Transmission line theory 3 simple scalable MIM capacitor models. Mellberg, A., + , T-MTT Jan 06 169-172 bandpass filters, normally fed microstrip resonators loaded by highpermitt. dielec., design optim. and implement. Hennings, A., + , T-MTT Mar 06 1253-1261 broadband quasiChebyshev bandpass filters, multimode steppedimpedance resonators (SIRs). Yi-Chyun Chiou, + , T-MTT Aug 06 33523358 leaky-wave structs. and appls., anal. of neg.-refr.-index leaky-wave antennas, periodic FDTD anal. Kokkinos, T., + , T-MTT Jun 06 16191630 Transmission line theory; cf. Transmission line matrix methods Transmitters SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 Transmitters; cf. Optical transmitters; Radar transmitters; Radio transmitters; Transceivers Traveling wave amplifiers microwave fiber-optic links. Hashim, H.H., + , T-MTT Feb 06 951-958 time-domain modeling of TWT amps. for high data-rate commun. appls., from freq.-domain phys.-based simul. Safier, P.N., + , T-MTT Oct 06 3605-3615 TWA vs. temp., SOI technol., behavior. Si Moussa, M., + , T-MTT Jun 06 2675-2683 Traveling wave tubes microwave dual-CP antenna, TW feed concept, design and meas. data. Kum Meng Lum, + , T-MTT Jun 06 2880-2886 multiport-amplifier-based architecture versus classical architecture for space telecommunication payloads. Mallet, A., + , T-MTT Dec 06 43534361 oversized Ka-band traveling-wave window for a high-power transmission. Bogdashov, A., + , T-MTT Dec 06 4130-4135 time-domain modeling of TWT amps. for high data-rate commun. appls., from freq.-domain phys.-based simul. Safier, P.N., + , T-MTT Oct 06 3605-3615 Traveling wave tubes; cf. Slow wave structures Trees (graphs) spurious DC modes, edge element solns. for modeling 3D resonators, removal. Venkatarayalu, N.V., + , T-MTT Jul 06 3019-3025 Tungsten evanescent microwave microscope, sensitivity and resoln. Kleismit, R.A., + , T-MTT Feb 06 639-647 Tuning cellular commun. terminals, magnetically tunable filters. Krupka, J., + , TMTT Jun 06 2329-2335 distrib. MEMS tunable matching net., minimal-contact RF-MEMS varactors. Qin Shen, + , T-MTT Jun 06 2646-2658 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 Tuning; cf. Circuit tuning Two-port circuits lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 stabil. of lin. microwave ccts., tutorial, rollett proviso. Jackson, R.W., TMTT Mar 06 993-1000 U UHF amplifiers 45-dB variable-gain low-noise MMIC amp. Masud, M.A., + , T-MTT Jun 06 2848-2855 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105

IEEE T-MTT 2006 INDEX — 67 high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 mismatched Doherty amps., accurate load-pull-based model, design and perform. anal. Hammi, O., + , T-MTT Aug 06 3246-3254 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 UHF amplifiers; cf. UHF power amplifiers UHF circuits; cf. UHF integrated circuits UHF couplers compact planar microstrip branch-line couplers, quasilumped elements approach, nonsymmetrical and symm. T-shaped struct. Shry-Sann Liao, + , T-MTT Sep 06 3508-3514 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 PCB cct. design, 3-dB quadrature coupler suitable. Jui-Chieh Chiu, + , TMTT Sep 06 3521-3525 UHF devices differential wireless communs. frontends, RF switch concepts. Erkens, H., + , T-MTT Jun 06 2376-2382 UHF devices; cf. UHF amplifiers; UHF couplers; UHF filters; UHF mixers; UHF oscillators; UHF phase shifters UHF filters broadside-coupled bandpass filters, both microstrip and CPW resonators. Pu-Hua Deng, + , T-MTT Oct 06 3746-3750 cellular commun. terminals, magnetically tunable filters. Krupka, J., + , TMTT Jun 06 2329-2335 compact microstrip 2-layer bandpass filter, aperture-coupled SIR-hairpin resonators, transm. zeros. Djaiz, A., + , T-MTT May 06 1929-1936 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 dual-band microstrip bandpass filter, stepped-impedance resonators, coupling schemes. Yue Ping Zhang, + , T-MTT Oct 06 3779-3785 dual-bandpass filters, serial config., LTCC technol. Ke-Chiang Lin, + , TMTT Jun 06 2321-2328 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 inductively compensated parallel coupled microstrip lines and their appls. Phromloungsri, R., + , T-MTT Sep 06 3571-3582 quasidual-mode microstrip spiral filters, 1st. and second harmonic resons. Frederick Huang, T-MTT Feb 06 742-747 self-coupled dual-mode ring resonator and appls., bandpass filters. YngHuey Jeng, + , T-MTT May 06 2146-2152 UHF frequency conversion BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 UHF integrated circuits 45-dB variable-gain low-noise MMIC amp. Masud, M.A., + , T-MTT Jun 06 2848-2855 digitally controlled const. envelope phase-shift modulator for low-power broad-band wireless appls. Xiuge Yang, + , T-MTT Jan 06 96-105 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 hybrid rectenna and monolithic integr. zero-bias microwave rectifier. Zbitou, J., + , T-MTT Jan 06 147-152 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 SiGe BiCMOS for UWB communs., sub-nanosecond pulse-forming net. Adrian Eng-Choon Tan, + , T-MTT Mar 06 1019-1024 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 UHF measurements subwavelength-resoln. microwave tomography, wire grid models and enhanced regularization techs. Omrane, B., + , T-MTT Jun 06 14381450

+ Check author entry for coauthors

UHF mixers direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 low-power CMOS direct conversion receiver, 3-dB NF and 30-kHz flicker-noise corner for 915-MHz band IEEE 802.15.4 ZigBee std. Trung-Kien Nguyen, + , T-MTT Feb 06 735-741 UHF oscillators BPSK, ASK sig. conversion, injection-locked oscillators-part II. LopezVillegas, J.M., + , T-MTT Jan 06 226-234 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 high-power switching-mode oscillators, nonlin. design tech. Sanggeun Jeon, + , T-MTT Oct 06 3630-3640 low phase-noise CMOS VCO, harmonic tuned LC tank. Huijung Kim, + , T-MTT Jul 06 2917-2924 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 UHF phase shifters bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 digitally controlled const. envelope phase-shift modulator for low-power broad-band wireless appls. Xiuge Yang, + , T-MTT Jan 06 96-105 direct-conversion quadrature modulator MMIC design, 90° phase shifter incl. package and PCB effects for W-CDMA appls. Jian-Ming Wu, + , T-MTT Jun 06 2691-2698 improved wide-band Schiffman phase shifter. Yong-Xin Guo, + , T-MTT Mar 06 1196-1200 multiband phase shifters, 180-nm RF CMOS technol., act. loss compensation. Chao Lu, + , T-MTT Jan 06 40-45 UHF power amplifiers 3G multicarrier amps., DSP, expt. validation, power and effic. enhanc. Helaoui, M., + , T-MTT Jun 06 1396-1404 high-effic. class-F and inverse class-F power amps., anal. and expts. Young Yun Woo, + , T-MTT May 06 1969-1974 high power-amp. linearization, block-based predistortion. Safari, N., + , TMTT Jun 06 2813-2820 power amp. charactn. Bensmida, S., + , T-MTT Jun 06 2707-2712 power amp., unilateralization and improved output return loss, feedback method. Zuo-Min Tsai, + , T-MTT Jun 06 1590-1597 Ultra-large-scale integration noise-free and jitterless cavity syst., distribute clocks, 10 GHz. Kato, H., + , T-MTT Nov 06 3960-3967 Ultra wideband communication power spectrum of ultra-wideband radio-frequency signals. McKinney, J. D., + , T-MTT Dec 06 4247-4255 Ultra wideband radar RF chipset for impulse UWB radar using 0.13-ȝm InP-HEMT technology. Kawano, Y., + , T-MTT Dec 06 4489-4497 Ultra wideband technology distortion analysis of ultra-wideband OFDM receiver front-ends. Ranjan, M., + , T-MTT Dec 06 4422-4431 electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-of-band performance. Garcia-Garcia, J., + , T-MTT Dec 06 4136-4140 ultra-wideband (special issue). T-MTT Apr 06 1633-1927 ultra-wideband (special issue intro.). Knochel, R.H., + , T-MTT Apr 06 1633-1636

V

Varactors bidirectionally fed phased-array antenna downsized, variable impedance phase shifter for ISM band. Tsuji, M., + , T-MTT Jul 06 2962-2969 combined left- and right-handed tunable transmission lines. Hongjoon Kim, + , T-MTT Dec 06 4178-4184 compact fixed and tune-all bandpass filters, coupled slow-wave resonators. Pistono, E., + , T-MTT Jun 06 2790-2799

IEEE T-MTT 2006 INDEX — 68 distrib. MEMS tunable matching net., minimal-contact RF-MEMS varactors. Qin Shen, + , T-MTT Jun 06 2646-2658 electronically tunable act. duplexer for wireless transceiver appls. Sundaram, B., + , T-MTT Jun 06 2584-2592 eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 heterostruct. barrier varactors, subharmonically pumped mm-wave upconverters. Haiyong Xu, + , T-MTT Oct 06 3648-3653 intermodulation, RF MEMS variable capacitors. Girbau, D., + , T-MTT Mar 06 1120-1130 low-stress suspen. structs. and appls., RF MEMS parallel-plate variable capacitors, finite-element modeling. Elshurafa, A.M., + , T-MTT May 06 2211-2219 varactor-based freq. multipliers and dividers, simul.-assisted design and anal. Suarez, A., + , T-MTT Mar 06 1166-1179 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500 varactor-loaded split-ring resonators, tunable metamaterial transm. lines. Gil, I., + , T-MTT Jun 06 2665-2674 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 Vehicles; cf. Remotely operated vehicles Very-large-scale integration capture HF partial inductance accurately by gauss quadrature integrat., skin-effect model. Yu Du, + , T-MTT Mar 06 1287-1294 VHF devices; cf. VHF filters VHF filters narrowband supercond. filter, spirals, reversal, winding direction. Huang, F., + , T-MTT Nov 06 3954-3959 Voltage comput. transm.-line params. of lossy lines, Quasi-TM MoL/MoM approach. Plaza, G., + , T-MTT Jan 06 198-209 Voltage controlled oscillators 0.18-ȝm CMOS technol., low-power oscillator mixer. To-Po Wang, + , TMTT Jan 06 88-95 close-in phase-noise enhanced VCO employing parasitic V-NPN transistor, CMOS proc. Yeonwoo Ku, + , T-MTT Jun 06 1363-1369 direct conversion receiver for wireless CDMA cellular phones, GPS capability, dual-b and RF front-end. Woonyun Kim, + , T-MTT May 06 2098-2105 dual-band monolithic CMOS LC-tuned VCO, switched resonators and their appls. Seong-Mo Yim, + , T-MTT Jan 06 74-81 eliminating range ambiguity for low-cost FMCW radar, VCO tuning characts., efficient method. Jung Dong Park, + , T-MTT Oct 06 36233629 low phase-noise CMOS VCO, harmonic tuned LC tank. Huijung Kim, + , T-MTT Jul 06 2917-2924 micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technol. Tao Wang, + , T-MTT Feb 06 580-588 neural-net.-based parasitic modeling and extr. verification for RF/mmwave IC design. Sen, P., + , T-MTT Jun 06 2604-2614 output extr. from capacitive common node, GaInP/GaAs HBT technol., 17-GHz push-push VCO. Hyunchol Shin, + , T-MTT Nov 06 3857-3863 wideband Ȉǻ fractional-N freq. synthesizers, closed-loop nonlin. modeling. Hedayati, H., + , T-MTT Oct 06 3654-3663 wide tuning-range CMOS VCO, differential tunable act. inductor. LiangHung Lu, + , T-MTT Sep 06 3462-3468 Volterra series dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers. Anding Zhu, + , T-MTT Dec 06 4323-4332 high-effic. lin. RF Amplifier, unified cct. approach, achieving compactness and low distortion. Yum, T.Y., + , T-MTT Aug 06 32553266 highly linear low-noise amplifier. Ganesan, S., + , T-MTT Dec 06 40794085 package and PCB effects, W-CDMA upconverter RFICs, rigorous study. Fu-Yi Han, + , T-MTT Oct 06 3793-3804 RF CMOS short-channel low-noise amps., distortion. Baki, R.A., + , TMTT Jan 06 46-56 UWB SiGe HBT LNA for noise, linearity, min. group delay var. Yunseo Park, + , T-MTT Jun 06 1687-1697 varactor diode-tuned microwave filters, distortion mechanisms. CareySmith, B.E., + , T-MTT Sep 06 3492-3500

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W Wave analyzers full-wave analysis of inhomogeneous deep-trench isolation patterning for substrate coupling reduction and Q-factor improvement. Wane, S., + , TMTT Dec 06 4397-4411 Waveform analysis; cf. Spectral analysis Waveguide antennas advanced launcher for 2-MW 170-GHz TE34,19 coaxial cavity gyrotron, theor. investig. Jianbo Jin, + , T-MTT Mar 06 1139-1145 Waveguide antennas; cf. Horn antennas; Microstrip antennas; Slot antennas Waveguide components backward-wave propag., periodic waveguide structs., design and expt. verification. Carbonell, J., + , T-MTT Jun 06 1527-1533 mm-wave correl. receivers, orthomode transducer. Peverini, O.A., + , TMTT May 06 2042-2049 multilayer arbitrarily biased anisotropic structs.-appl., phase shifters, transducers, magnetis. angle effect, green's fn. Elshafiey, T.F., + , TMTT Feb 06 513-521 TE10-TEq0-mode conversion, rect. waveguides, nonsymmetrical H-plane corners. Kirilenko, A.A., + , T-MTT Jun 06 2471-2477 Waveguide components; cf. Circulators; Directional couplers; Power combiners; Power dividers; Waveguide couplers; Waveguide filters Waveguide couplers authors' reply [to comments on "W-Band multiport substrate-integrated waveguide circuits"]. Moldovan, E., + , T-MTT Nov 06 4017 w-band multiport substr.-integr. waveguide ccts. Moldovan, E., + , T-MTT Feb 06 625-632 wideband multisection 180° hybrid rings, vertically installed planar couplers, class. Chun-Hsiang Chi, + , T-MTT Jun 06 2478-2486 Waveguide couplers; cf. Directional couplers Waveguide discontinuities discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 solving thick irises, rect. waveguides, Integral-eqn. tech. Stevanovic, I., + , T-MTT Jan 06 189-197 ultrahigh-speed digital interconnects, substr. integr. waveguides optimized. Simpson, J.J., + , T-MTT May 06 1983-1990 Waveguide filters cellular commun. terminals, magnetically tunable filters. Krupka, J., + , TMTT Jun 06 2329-2335 compact and selective low-pass filter, reduced spurious responses, CPW tapered periodic structs. Kaddour, D., + , T-MTT Jun 06 2367-2375 compact Millimeter-wave filters, distrib. capacitively loaded CPW resonators. Aryanfar, F., + , T-MTT Mar 06 1161-1165 compact partial H-plane filters. Dong-Won Kim, + , T-MTT Nov 06 39233930 composite right/left-handed CPW bandpass and dual-passband filters, design. Shau-Gang Mao, + , T-MTT Sep 06 3543-3549 CPW bandpass filters, loaded air-bridge enhanced capacitors and broadside-coupled transit. structs. for wideband spurious suppression. Shih-Cheng Lin, + , T-MTT Aug 06 3359-3369 design of side-coupled coaxial filters, close correspondence, phys. struct., adaptive prototype. Morini, A., + , T-MTT Mar 06 1146-1153 dual and triple passband filters, coupling-matrix design. Mokhtaari, M., + , T-MTT Nov 06 3940-3946 in-line pseudoelliptic band-reject filters, nonresonating nodes and/or phase shifts. Amari, S., + , T-MTT Jan 06 428-436 miniature ridge-waveguide filter module employing moldable dielec. material. Rauscher, C., + , T-MTT Mar 06 1190-1195 miniaturized CPW bandpass filters, multisection stepped-impedance resonators. Hualiang Zhang, + , T-MTT Mar 06 1090-1095 Si/glass technol. for filter, ka-band, low-cost inverted line. Martoglio, L., + , T-MTT Jul 06 3084-3089 Waveguides 2D freq. converter utilizing cpd. nonlin. photonic-cryst. struct. by condensed node spatial net. method. Satoh, H., + , T-MTT Jan 06 210215 accurate modeling, wave mechanisms, design considerations of substr. integr. waveguide. Deslandes, D., + , T-MTT Jun 06 2516-2526

IEEE T-MTT 2006 INDEX — 69 complex permitt. of packaging materials, mm-wave freqs., determ. Zwick, T., + , T-MTT Mar 06 1001-1010 in vitro exposure of mammalian cells, 1.95 GHz, high-effic. waveguide applicator. Calabrese, M.L., + , T-MTT May 06 2256-2264 multilayered samples, S-param. waveguide meas., complex permitt. and permeab. extr. Faircloth, D.L., + , T-MTT Mar 06 1201-1209 phase retrieval of quasiopt. mm-wave beams, expt. verification. Idei, H., + , T-MTT Nov 06 3899-3905 Waveguides; cf. Chirowaveguides; Circular waveguides; Coaxial waveguides; Coplanar waveguides; Dielectric waveguides; Planar waveguides; Rectangular waveguides; Waveguide discontinuities; Waveguide transitions Waveguide theory backward-wave propag., periodic waveguide structs., design and expt. verification. Carbonell, J., + , T-MTT Jun 06 1527-1533 discontinuities, chirowaveguides, comprehensive study. Solano, M.A., + , T-MTT Mar 06 1297-1298 discontinuities, chirowaveguides ), comprehensive study. Wu, T.X., + , TMTT Mar 06 1298 engng. Optimization-theory and implement., space-mapping framework. Koziel, S., + , T-MTT Oct 06 3721-3730 envelope ADI-FDTD method, num. perform. and appls. Choi, C.T.M., + , T-MTT Jan 06 256-264 in-phase and split counter-rot. eigenvalues of 3-port circulator, refl. angles. Helszajn, J., T-MTT Mar 06 1076-1083 periodic waveguide, gen. conservation of complex power tech., propag. characts. Hui Kan Liu, + , T-MTT Sep 06 3479-3485 planar components grounded by via-holes and their expt. verification, cavity models. Kouzaev, G.A., + , T-MTT Mar 06 1033-1042 radial power combiners, simplified design approach. Fathy, A.E., + , TMTT Jan 06 247-255 scatt. problems by appl. of extended Huygens formulation, soln. Geschke, R.H., + , T-MTT Oct 06 3698-3705 Waveguide theory; cf. Optical waveguide theory Waveguide transitions authors' reply [to comments on "W-Band multiport substrate-integrated waveguide circuits"]. Moldovan, E., + , T-MTT Nov 06 4017 Wavelength division multiplexing 60-GHz point-to-multipoint mm-wave fiber-radio commun. syst. Sung Tae Choi, + , T-MTT May 06 1953-1960 mm-wave-band radio-over-fiber syst., dense WDM bus archit. Xiupu Zhang, + , T-MTT Feb 06 929-937 SCM/WDMA radio-on-fiber bus link, opt. FM method, presence of opt. beat interf., high-perform. RF sigs. transm. Murakoshi, A., + , T-MTT Feb 06 967-972

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WDM and dispers. fiber, receive mode, opt. multibeamforming net. Blanc, S., + , T-MTT Jan 06 402-411 widely tunable RF photonic filter, WDM and multichannel chirped fiber grating. Hunter, D.B., + , T-MTT Feb 06 900-905 Wavelet transforms simul. of HF act. devices, efficient num. methods. Movahhedi, M., + , TMTT Jun 06 2636-2645 Welding; cf. Lead bonding Wideband amplifiers active harmonic load-pull for on-wafer out-of-band device linearity optimization. Spirito, M., + , T-MTT Dec 06 4225-4236 Wire single-wire transm. lines, terahertz freqs. Akalin, T., + , T-MTT Jun 06 2762-2767 Wireless LAN 60-GHz WLAN/WPAN appls., high gain act. microstrip antenna. Karnfelt, C., + , T-MTT Jun 06 2593-2603 broadband single-stage equivalent circuit for modeling LTCC bandpass filters. Yu-Shun Tsai, + , T-MTT Dec 06 4412-4421 dual-band planar quadrature hybrid, enhanced bandwidth response. Collado, C., + , T-MTT Jan 06 180-188 extended true single-phase clock-based prescaler, design and optim. Xiao Peng Yu, + , T-MTT Nov 06 3828-3835 high stopband-rejection LTCC filter, multiple transm. zeros. Yng-Huey Jeng, + , T-MTT Feb 06 633-638 low-cost multimode fiber-fed indoor wireless nets., design. Das, A., + , TMTT Aug 06 3426-3432 miniature CMOS SPDT switch, body-floating tech., improve power perform., design and anal. Mei-Chao Yeh, + , T-MTT Jan 06 31-39 multichannel WLAN syst., radio-over-fiber techs., transm. perform. Niiho, T., + , T-MTT Feb 06 980-989 power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications. Feipeg Wang, + , T-MTT Dec 06 4086-4099 UWB radio, template waveform proc., interf. mitigation study. Ohno, K., + , T-MTT Jun 06 1782-1792

Z Z transforms lumped-net. FDTD method, lin. 2-port lumped ccts., extension. Gonzalez, O., + , T-MTT Jul 06 3045-3051 microwave integrators, transm. lines, time-const. control. Ching-Wen Hsue, + , T-MTT Mar 06 1043-1047