FEBRUARY 2010 IEEE MTT-V058-I02 (2010-02) [58, 2 ed.]

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FEBRUARY 2010

VOLUME 58

NUMBER 2

IETMAB

(ISSN 0018-9480)

PAPERS

Smart Antennas, Phased Arrays, and Radars A Single-Channel Microstrip Electronic Tracking Antenna Array With Time Sequence Phase Weighting on Sub-Array . .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ........ H. Wang, D.-G. Fang, and M. Li Planar -Band 4 4 Nolen Matrix in SIW Technology ........ ......... ........ . T. Djerafi, N. J. G. Fonseca, and K. Wu Integrated Active Pulsed Reflector for an Indoor Local Positioning System ..... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ........ S. Wehrli, R. Gierlich, J. Hüttner, D. Barras, F. Ellinger, and H. Jäckel Active Circuits, Semiconductor Devices, and ICs Analysis and Design of Two Low-Power Ultra-Wideband CMOS Low-Noise Amplifiers With Out-Band Rejection ... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ... C.-P. Liang, P.-Z. Rao, T.-J. Huang, and S.-J. Chung Analysis and Design of a CMOS UWB LNA With Dual-Branch Wideband Input Matching Network ... ......... .. .. ........ ......... ......... ........ .. Y.-S. Lin, C.-Z. Chen, H.-Y. Yang, C.-C. Chen, J.-H. Lee, G.-H. Huang, and S.-S. Lu A New Six-Port Transformer Modeling Methodology Applied to 10-dBm 60-GHz CMOS ASK Modulator Designs .. .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... . J. Brinkhoff, D.-D. Pham, K. Kang, and F. Lin A CMOS Class-E Power Amplifier With Voltage Stress Relief and Enhanced Efficiency ........ ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... .... Y. Song, S. Lee, E. Cho, J. Lee, and S. Nam Signal Generation, Frequency Conversion, and Control A Dual-Band Self-Oscillating Mixer for -Band and -Band Applications .... ....... B. R. Jackson and C. E. Saavedra A Novel Alternating and Outphasing Modulator for Wireless Transmitter ...... ......... ...... Y. Zhou and M. Y.-W. Chia Millimeter-Wave and Terahertz Technologies Enhanced Plasma Wave Detection of Terahertz Radiation Using Multiple High Electron-Mobility Transistors Connected in Series ........ ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .. .. ........ .. T. A. Elkhatib, V. Y. Kachorovskii, W. J. Stillman, D. B. Veksler, K. N. Salama, X.-C. Zhang, and M. S. Shur 60-GHz Repeater Link for an ISDB-T Gap-Filler System Based on Self-Heterodyne Technique Applying an Adaptive Distortion Suppression Technique ..... ......... ........ ......... ......... ........ ........ Y. Shoji, C.-S. Choi, and H. Ohta

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(Contents Continued on Back Cover)

(Contents Continued from Front Cover) Wireless Communication Systems A 60-GHz 38-pJ/bit 3.5-Gb/s 90-nm CMOS OOK Digital Radio ........ ........ ......... ... E. Juntunen, M. C.-H. Leung, F. Barale, A. Rachamadugu, D. A. Yeh, B. G. Perumana, P. Sen, D. Dawn, S. Sarkar, S. Pinel, and J. Laskar

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Field Analysis and Guided Waves Effects of Geometrical Discontinuities on Distributed Passive Intermodulation in Printed Lines ........ ......... ......... .. .. ........ ......... ......... ........ ......... A. P. Shitvov, T. Olsson, B. El Banna, D. E. Zelenchuk, and A. G. Schuchinsky

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CAD Algorithms and Numerical Techniques Unconditional Stability Boundaries of a Three-Port Network .... ......... ........ . ......... ........ R.-F. Kuo and T.-H. Chu Analysis and Synthesis of Double-Sided Parallel-Strip Transitions ...... ......... ......... .... P. L. Carro and J. de Mingo

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Filters and Multiplexers High- RF-MEMS 4–6-GHz Tunable Evanescent-Mode Cavity Filter .. ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ........ S.-J. Park, I. Reines, C. Patel, and G. M. Rebeiz Compact Hybrid Resonator With Series and Shunt Resonances Used in Miniaturized Filters and Balun Filters ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... T. Yang, M. Tamura, and T. Itoh Packaging, Interconnects, MCMs, Hybrids, and Passive Circuit Elements Radio-Optical Dual-Mode Communication Modules Integrated With Planar Antennas . ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ... A. O. Boryssenko, J. Liao, J. Zeng, S. Deng, V. M. Joyner, and Z. R. Huang Instrumentation and Measurement Techniques A Generalized Formulation for Permittivity Extraction of Low-to-High-Loss Materials From Transmission Measurement ... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... U. C. Hasar A New 12-Term Open–Short–Load De-Embedding Method for Accurate On-Wafer Characterization of RF MOSFET Structures ...... ......... ........ ......... ... L. F. Tiemeijer, R. M. T. Pijper, J. A. van Steenwijk, and E. van der Heijden On a Method to Reduce Uncertainties in Bulk Property Measurements of Two-Component Composites .... C. Engström Extended Through-Short-Delay Technique for the Calibration of Vector Network Analyzers With Nonmating Waveguide Ports ... ......... ......... ........ ......... ......... ........ O. A. Peverini, G. Addamo, R. Tascone, G. Virone, and R. Orta Accurate Complex Permittivity Inversion From Measurements of a Sample Partially Filling a Waveguide Aperture ... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... U. C. Hasar Measurement Bandwidth Extension Using Multisine Signals: Propagation of Error ..... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ... K. A. Remley, D. F. Williams, D. Schreurs, and M. Myslinski Phase-Noise Measurement of Microwave Oscillators Using Phase-Shifterless Delay-Line Discriminator ...... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... H. Gheidi and A. Banai

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MEMS and Acoustic Wave Components Capacitive RF MEMS Switches Fabricated in Standard 0.35- m CMOS Technology .. .. S. Fouladi and R. R. Mansour

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Information for Authors .. ........ ......... ......... ........ ......... .......... ........ ......... ......... ........ ......... ......... .

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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 $17.00, plus an annual subscription fee of $23.00 per year for electronic media only or $46.00 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. 2009 ADMINISTRATIVE COMMITTEE B. PERLMAN, President L. BOGLIONE M. GUPTA J. HACKER

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2009 MTT-S Chapter Chairs Albuquerque: H. J. WAGNON Atlanta: D. LEATHERWOOD Austria: A. SPRINGER Baltimore: N. BUSHYAGER Bangalore: T. SRINIVAS Beijing: Z. FENG Belarus: A. GUSINSKY Benelux: D. VANHOENACKER-JANVIER Boston: J. MULDAVIN Brasilia: J. DA COSTA/ A. KLAUTAU Buenaventura: M. QUDDUS Buffalo: J. WHALEN Bulgaria: K. ASPARUHOVA Cedar Rapids/Central Iowa: M. ROY Central & South Italy: G. D’INZEO Central No. Carolina: N. S. DOGAN Chengdu: Z. NEI Chicago: H. LIU Cleveland: M. SCARDELLETTI Columbus: F. TEXEIRA Connecticut: C. BLAIR Croatia: Z. SIPUS

Czech/Slovakia: P. HAZDRA Dallas: Q. ZHANG Dayton: A. TERZUOLI Delhi/India: S. KOUL Denver: M. JANEZIC Eastern No. Carolina: T. NICHOLS Egypt: E. HASHISH Finland: A. LUUKANEN Florida West Coast: K. A. O’CONNOR Foothills: F. FREYNE France: P. EUDELINE Germany: K. SOLBACH Greece: R. MAKRI Harbin: Q. WU Hawaii: R. MIYAMOTO Hong Kong: W. S. CHAN Houston: J. T. WILLIAMS Houston, College Station: G. H. HUFF Hungary: T. BERCELI Huntsville: H. G. SCHANTZ Hyderabad: M. CHAKRAVARTI India/Calcutta: B. GUPTA India: D. BHATNAGER Indonesia: E. T. RAHARDO Israel: S. AUSTER Japan: K. ARAKI Kansai: T. OHIRA

Kitchener-Waterloo: R. R. MANSOUR Lithuania: V. URBANAVICIUS Long Island/New York: J. COLOTTI Los Angeles, Coastal: W. DEAL Los Angeles, Metro/San Fernando: F. MAIWALD Malaysia: M. ESA Malaysia, Penang: Y. CHOW Melbourne: K. LAMP Mexico: R. M. RODRIGUES-DAGNINO Milwaukee: S. G. JOSHI Mohawk Valley: E. P. RATAZZI Montreal: K. WU Nanjing: W. X. ZHANG New Hampshire: D. SHERWOOD New Jersey Coast: D. REYNOLDS New South Wales: A. M. SANAGAVARAPU New Zealand: A. WILLIAMSON North Italy: G. VECCHI North Jersey: H. DAYAL/K. DIXIT Northern Australia: M. JACOB Northern Nevada: B. S. RAWAT Norway: Y. THODESEN Orange County: H. J. DE LOS SANTOS Oregon: T. RUTTAN Orlando: X. GONG Ottawa: Q. YE

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Digital Object Identifier 10.1109/TMTT.2010.2042674

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 2, FEBRUARY 2010

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A Single-Channel Microstrip Electronic Tracking Antenna Array With Time Sequence Phase Weighting on Sub-Array H. Wang, Member, IEEE, D.-G. Fang, Fellow, IEEE, and M. Li

Abstract—We have designed and tested a novel electronic tracking antenna array that is formed by 2 2 microstrip sub-arrays. Through time sequence phase weighting on each sub-array, the amplitude and phase on each sub-array can be recovered from the output of the resultant single channel. The amplitude and phase on each array can be used to produce the sum and difference radiation pattern by digital signal processing. In comparison with the monopulse system, the RF comparator is eliminated and the number of the receiver channels is reduced from 3 to 1. A proof-of-concept prototype was fabricated and tested. The measured results confirmed the validity and advantages of the proposed scheme. The procedure of channel correction is given. Index Terms—Electronic tracking, microstrip monopulse antenna, single channel, time sequence phase weighting (TSPW), Walsh–Hadamard transform.

I. INTRODUCTION

A

UTOMATIC tracking of targets has found wide application in radar, mobile satellite communication, automotive industry, and remote sensing [1]–[4]. The monopulse system, also called a simultaneous lobe comparison, has been developed to overcome disadvantages in the early conical scan technique used in automatic tracking [1]. The monopulse system needs an RF comparator and three receiver channels in its usual implementation that result in undesirable complexity and extra cost. Much effort has been made to alleviate these problems. In -band [5], a highly compact waveguide comparator for the monopulse radar was proposed. Due to the lightweight, low profile, and low cost of the microstrip structure, several microstripbased monopulse antennas have been proposed [6]–[11]. The number of receiver channels of these monopulse antennas is two for one-plane tracking and three for two-plane tracking. To reduce the cost and complexity, many techniques have been developed by using single or two channels. However, all the techniques have reduced performance compared with the original monopulse technique. There is a tradeoff between

Manuscript received October 13, 2008; revised November 01, 2009. First published January 22, 2010; current version published February 12, 2010. This work was supported by the Nature Science Foundation under Grant 60671038 and by the Key Laboratory of Target Detection, Nanjing University of Science and Technology (NJUST). The authors are with the Millimeter Wave Technique Laboratory, Nanjing University of Science and Technology (NJUST), Nanjing 210094, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037854

the performance of an antenna and the complexity and cost. Comprehensive studies have been done by many researchers [12]–[16]. In addition to the channel reduction techniques, the sequential lobing techniques have been developed and applied in radar [4], [17]. In these techniques, not only the number of the channels is reduced, but also the RF monopulse comparator is eliminated. The comparison between simultaneous lobing and sequential lobing was given in [18]. The theoretical analysis of the sequential lobing technique was performed in [19]. The authors pointed out in [19] that “for fluctuation targets, the angle estimate is biased unless the target is located at the reference direction. However, the bias will be negligible if the SNR at each beam position is sufficiently large. The fluctuation can have a more adverse effect on the angular root-mean-square error as compared with noise.” In [4], the authors proposed an improved electronic scan tracking antenna (ESCAN) and claimed that the ESCAN can compete against the monopulse system in complexity and cost at the same target tracking capability. The ESCAN system includes a parabolic antenna fed by a multielement planar array with a beamforming network. A p-i-n diode switching network, integrated within the beamforming network, sequentially chooses four discrete subsets of array elements such that offset beams are produced both in azimuth and in elevation to obtain the error signals. In ESCAN, the monopulse comparator network is eliminated and the requirement for a three-channel receiver is also removed. Most importantly, all the drawbacks in the mechanical conical scanning [18] are removed as well. Inspired by the recent successful application of ESCAN, here we propose a single-channel microstrip planar electronic tracking antenna array with time sequence phase weighting (TSPW). The TSPW technique has been successfully applied in angular superresolution of a phased array [20]. Its basic principle is to recover the amplitude and phase distribution of each channel from the resultant output of the single channel through TSPW. Here, we used a microstrip planar antenna array that includes four 2 2 sub-arrays. Three equal power dividers were used to combine four sub-arrays into one channel. Each sub-array is connected to a 0 180 phase shifter. After doing orthogonal phase weighting four times, we can obtain the information on amplitude and phase of each sub-array. Compared with the work done in [20], the common technique is to use the TSPW to recover the field distribution on the aperture. This technique will be introduced in Section II. After having this distribution, in [20] the nonlinear spectrum estimation algorithm, such as

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In general, if the signal on the aperture is , where is the number of the elements (in Fig. 1, it is 4). The output to the receiver is (1) is the weighting matrix. Define have

, and then we (2)

The weighting matrix is chosen to be the Hadamard matrix , i.e., . According to the property of Hadamard matrix,

Fig. 1. Block diagram of a TSWP system with four subarrays. The outputs of the four subarrays are fed to separately controlled variable phase shifters.

where

denotes the Kronecker product. If

, (3)

RELAX, is used to equivalently enlarge the size of the aperture and to obtain the angle super-resolution. In this paper, this distribution is used to produce the sum and difference patterns by digital beamforming. Compared with the work done in [4], the common technique is to use the time sequence weighting to obtain the error signal. In [4], the time sequence amplitude weighting (TSAW) is used on the primary feed of a reflector antenna. Consider a two-element feed, if the two feed elements are equally amplitude weighted, then the resultant feed phase center would be half the distance between the two elements. This phase center would be shifted when the element amplitude weighting changes resulting in the scan secondary beam. It is seen that this technique is quite similar to the amplitude-comparison monopulse technique. In this paper, we used the array antenna and the TSPW. From the principle described above, it is seen that our technique is quite similar to the phase-comparison monopulse technique. A comprehensive study on different monopulse techniques has been done in [12] and [21]. In some applications, the phase-comparison monopulse technique is superior to the other techniques. In addition, the proposed antenna array is a planar printed structure that is easy to fabricate with low cost and the calibration of the channels is easy to carry out by digital signal processing. Since many issues related to TSPW, such as motion compensation and error analysis, have been discussed in [20], we will not repeat them in this paper. This paper is organized as follows. In Section II, the principle of the TSPW technique is briefly summarized. In Section III, the design of the antenna array and the equal loss 0 180 phase shifter is presented. The experimental results are given in Section IV. Section V presents the conclusion. II. PRINCIPLE OF TSPW The principle of TSPW may be illustrated through four subarrays. In Fig. 1, denotes the th sub-array, denotes the th 0 180 phase shifter, PD denotes a 3-dB Wilkinson power divider or a conventional power divider, and denotes the coherent receiver from which both the amplitude and phase of the signal could be obtained.

From (3), one can see that the weighting matrix relates to a 0 180 phase modulation. This is easy both for real-time calculation and for hardware realization. Actually, and are the Walsh–Hadamatd transform pair (4) times phase Therefore, for an -element array, through weighting, the amplitude and phase distribution may be recovered. This technique may also be considered as using pattern diversity to obtain the space information. After the aperture distribution is recovered, a nonlinear spectrum estimation algorithm, such as RELAX, could be used to obtain the super-resolution, as was done in [20], and the digital signal processing could be used to obtain the sum and difference radiation patterns, as is done in this paper. According to Parseval’s theorem, the following identities hold: (5a)

(5b) Formulas (5a) and (5b) show that the energy in the domain (space or element domain) is equal to that in the domain (time domain). In other words, the Walsh–Hadamard transfomation is subjected to the energy conservation law. The total power received by one receiver for times is equal to that received by receivers once. However, the total power by an array times should be . The power is absorbed by the matched loads if a Wilkinson power divider is used and the power is scattered if the conventional power divider is used. III. DESIGN OF THE PROTOTYPE As a proof-of-concept, a prototype antenna was designed. This prototype includes four sub-arrays and four phase shifters.

WANG et al.: SINGLE-CHANNEL MICROSTRIP ELECTRONIC TRACKING ANTENNA ARRAY

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Fig. 3. 3-D perspective of the aperture-coupled patch element.

Fig. 4. 0 =180 reflected-type phase shifter. It is composed of one 3-dB hybrid, two p-i-n diodes, and an impedance transformer.

Fig. 2. Schematic of our prototype antenna array. This prototype was formed by four sub-arrays and four phase shifters. (a) Top view of the upper substrate layer. (b) Bottom view of the lower substrate layer. (c) Side view of the array.

Each sub-array was formed by a 2 2 aperture-coupled microstrip patch antennas. The phase shifters are connected to the ports of the sub-arrays. The structure of an aperture-coupled microstrip antenna array is shown in Fig. 2. The radiating patches are on the top of the upper substrate layer. There is a 2.5-mmthick air spacer between the substrate layer and ground plane. The coupling apertures are etched on the ground plane. The microstrip feed network is located on the bottom of the lower substrate layer. The two layers are fixed together by plastic screws. This structure has the advantage that the spurious radiation from the feed network is isolated by the ground plane. It also provides the flexibility to use different substrates for the antenna and feed network. Especially in the present case, the bottom layer provides enough space for the feed network and phase

shifters. The detailed dimensions of the patch obtained from the usual design procedure [22] are shown in Fig. 3. The dielectric substrate used is Arlon AD 270 with a relative dielectric constant of 2.7 and a thickness of 0.5 mm. Four reflected-type phase shifters are adopted in the design. Fig. 4 shows the design of the 0 180 reflected-type phase shifter, which is composed of one 3-dB hybrid, two p-i-n diodes, and an impedance transformer. The goal of the phase shifter design is to achieve the 0 180 two states with equal insertion losses. The detailed dimensions of the two-section branch-line coupler hybrid are shown in Fig. 5. The p-i-n diodes are MP5084 type. The equivalent circuits of the two states are shown in Fig. 6. The key parameters are as follows: pF, , pF, and nH at 5 GHz. To achieve equal insertion loss, we added an impedance transformer between the hybrid and p-i-n diode. The layout of the impedance transformer is shown in Fig. 7. The input impedances of the two states at the input port of the p-i-n are and . The corresponding reflection coefficients are and . To satisfy the equal insertion loss for both states, the condition should be satisfied that results in the design formulas given in [23]. Based on the transmission line theory, the reflection coefficient can be obtained from (6) (6)

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Fig. 5. 3-dB branch-line coupler.

Fig. 6. Equivalent circuits of p-i-n diode. C C : pF, and L nH at 5 GHz.

=01

=1

= 0:1 pF, R = R = 2 , Fig. 8. Simulated results of the phase shifter. (a) Phase shift versus the frequency. (b) Insertion loss versus the frequency.

commercial software IE3D. It is observed that within the 8% bandwidth centered at 5 GHz, the amplitude unbalance of the two-state is less than 0.36 dB, the maximum phase deviation is 20 . The online measurement of the phase shifter was carried out in the correction procedure and will be given in Section IV. IV. EXPERIMENTAL RESULTS Fig. 7. Layout of the impedance transformer.

where (7) (8) (9) is the phase delay related to different lines. If is given, and can be obtained through solving the equations. The value of was chosen to reduce the size of the phase shifter. However it should not be too small in order to avoid the strong mutual coupling between two stubs. According to these values, the layout of phase shifter has been designed. All the dimensions of the phase shifter at the central frequency of 5 GHz are given in Fig. 7. The simulated phase shift and insertion loss of this phase shifter are shown in Fig. 8. The simulation tool is the

To verify the theoretical results, we manufactured and tested the antenna array. The far-field radiation patterns from nearfield measurement are shown in Figs. 9 and 10. It is observed that the sum pattern in -plane are shifted to 1.6 and the location of the difference pattern is at 0.6 with a null depth of 16.51 dB. The data in the -plane are 2.3 , 4.0 , and 18.33 dB, respectively. The deterioration in the performances is due to the errors of the phase shifters in amplitude and phase. These errors could be corrected for the - and -plane separately. For each plane, they could be corrected for the sum pattern and for the difference pattern separately as well. Below, we take the -plane as an example to illustrate the correction procedure. We take the right sub-arrays as a reference with the amplitude to be unity and the phase to be 0 . According to the near-field measurement, in the 0 state, the amplitude of left arrays is 1.08 and the phase is 4.83 , in the 180 state, they are 0.82 and 5.85 , respectively. This measurement corresponds to the online test of the phase shifters. From them, the deviations of the amplitude and phase of the

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Fig. 9. Amplitude distributions of the far field. (a) Sum port. (b) ference port. (c) -plane difference port.

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phase shifters are known. The correction to de-embedding the phase-shifter errors may be simply implemented by multi-

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Fig. 10. Measured radiation patterns. (a) -plane sum pattern. (b) -plane difference pattern. (c) -plane sum pattern. (d) -plane difference pattern.

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plying a correction factor on the amplitude and compensating the phase.

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The same correction procedure can be carried out for the -plane. The 2-D radiation patterns can be obtained from the Fourier transform of the resulting aperture distribution. V. CONCLUSION AND DISCUSSIONS A single-channel microstrip electronic tracking planar antenna array with TSPW on sub-arrays has been developed. The proof-of-concept prototype was designed and tested. Good measured results were obtained, which validate the proposed scheme. This electronic tracking antenna array possesses several features, which are: 1) the complicated monopulse comparator network is eliminated; 2) only a single channel is required; 3) the planar microstrip structure is easy to fabricate by printed circuit technology and provides an opportunity to integrate RF devices and digital circuits into the package; and 4) the sum and difference patterns are obtained through digital beamforming, and the calibration of the channels is easy to carry out. Although,the prototype shown in this paper is a 4 4 array with uniform amplitude distribution, the underlying principle applied can also be applied to larger arrays with nonuniform amplitude distributions in order to realize lower sidelobe levels. In some cases, this antenna can replace the monopulse antenna when there is enough time for the weightings in a single pulse and there is enough frequency bandwidth for the RF channel. The amplitude balance in two states of the phase shifter in 8% frequency bandwidth is acceptable. However, the phase deviation in the bandwidth needs to be further improved in the future. REFERENCES [1] S. M. Sherman, Monopulse Principle and Techniques. Norwood, MA: Artech House, 1984. [2] H. Miyashita and T. Katagi, “Radial line planar monopulse antenna,” IEEE Trans. Antennas Propag., vol. 44, no. 8, pp. 1158–1165, Aug. 1996. [3] K. V. Cackenberghe and K. Sarabandi, “Monopulse-Doppler radar front-end concept for automotive applications based on RF MEMS technology,” in IEEE Int. Electro/Inform. Technol Conf., May 2006, pp. 1–5. [4] J. H. Cook and R. Munoz, “An improved electronic scan tracking antenna for S -band telemetry and remote sensing applications,” in Proc. Telesyst. Conf., Mar. 1991, vol. 1, pp. 291–296, National. [5] Y. K. Singh and A. Chakrabarty, “Design and sensitivity analysis of highly compact comparator for Ku-band monopulse radar,” in Int. Radar Symp., May 20–26, 2006, pp. 1–4. [6] C. M. Jackson, “Low cost K -band microstrip patch monopulse antenna,” Microw. J., vol. 30, no. 7, pp. 125–126, Jul. 1987. [7] B. J. Andrews, T. S. Moore, and A. Y. Niazi, “Millimeter wave microstrip antenna for dual polar and monopulse applications,” presented at the 3rd Int. Antennas Propag. Conf., Apr. 12–15, 1983. [8] S. G. Kim and K. Chang, “Low-cost monopulse antenna using bi-directionally-fed microstrip patch array,” Electron. Lett., vol. 39, no. 20, pp. 1428–1429, 2003. [9] H. Wang, D. G. Fang, and X. G. Chen, “A compact single layer monopulse microstrip antenna array,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 503–509, Feb. 2006. [10] Y. J. Cheng, W. Hong, and K. Wu, “Millimetre-wave monopulse antennna incorporating substrate integrated waveguide phase shifter,” IET Microw. Antennas Propag., vol. 2, no. 1, pp. 48–52, Jan. 2008. [11] Y. J. Cheng, W. Hong, and K. Wu, “Multimode substrate integrated waveguide H -plane monopulse feed,” Electron. Lett., vol. 44, no. 2, pp. 78–79, Feb. 2008. [12] M. I. Skolnik, Radar Handbook, 2nd ed. New York: McGraw-Hill, 1990, ch. 20. [13] W. L. Rubin and S. K. Kamen, “SCAMP—A single-channel monopulse radar signal processing technique,” IEEE Trans. Military Electron., vol. ME-6, pp. 146–152, Apr. 1962.

[14] J. E. Abel, S. F. George, and O. D. Sledge, “The possibility of cross modulation in the SCAMP signal processing,” Proc. IEEE, vol. 53, no. 3, pp. 317–318, Mar. 1965. [15] R. S. Noblit, “Reliability without redundancy from a radar monopulse receiver,” Microwaves, pp. 56–60, Dec. 1967. [16] A. J. Massanova, “A comparison of full and single channel spread spectrum monopulse trackers in the presence of jamming,” in Military Commun. Conf., 1983, pp. 760–764. [17] M. I. Skolnik, Radar Handbook, 2nd ed. New York: McGraw-Hill, 1990, ch. 20. [18] D. R. Rhodes, Introduction to Monopulse. New York: McGraw-Hill, 1959. [19] K. W. Lo, “Theoretical analysis of the sequential lobing technique,” IEEE Trans. Aerosp. Electron. Syst., vol. 35, no. 1, pp. 282–292, Jun. 1999. [20] W. X. Sheng, D. G. Fang, D. J. Li, and P. K. Liang, “Angular superresolution for phased antenna array by phase weighting,” IEEE Trans. Aerosp. Electron. Syst., vol. 37, no. 4, pp. 1450–1458, Oct. 2001. [21] M. I. Skolinik, Radar Handbook, 3rd ed. New York: McGraw-Hill, 2008, ch. 9. [22] I. J. Bahl and P. Bhartia, Microstrip Antennas. Dedham, MA: Artech House, 1980. [23] D. G. Fang, “Design of X band equal insertion loss 0 =180 phase shifter,” J. East China Inst. Technol., pp. 16–20, 1979.

H. Wang (M’08) received the B.E. and Ph.D. degrees from the Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2002 and 2009. He is currently a Lecturer with NJUST. His research is focused on microstrip antennas and related electromagnetic simulation.

D.-G. Fang (SM’90–F’03) was born in Shanghai, China. He graduated from the Graduate School of the Beijing Institute of Posts and Telecommunications, Beijing, China, in 1966. From 1980 to 1982, he was a Visiting Scholar with Laval University, Quebec, QC, Canada, and the University of Waterloo, Waterloo, ON, Canada). Since 1986, he has been a Professor with the Nanjing University of Science and Technology (NJUST), Nanjing, China. Since 1987, he had been a Visiting Professor with six universities in Canada and Hong Kong. He has authored or coauthored three books, two book chapters, and over 380 papers. He is an Associate Editor of two Chinese journals and is on the editorial or reviewer boards of several international and Chinese journals. He holds three patents. His research interests include computational electromagnetics, microwave integrated circuits and antennas, and electromagnetic (EM) scattering. He is listed in Marquis’ Who’s Who in the World (1995) and the International Biographical Association Directory (1995). Prof. Fang is a Fellow of the Chinese Institute of Electronics (CIE). He was the Technical Program Committee (TPC) chair of ICMC 1992 and vice general chair of PIERS 2004. He was a member of the International Advisory Committee of six international conferences. He was TPC co-chair of APMC 2005 and general co-chair of ICMMT 2008. He was the recipient of the National Outstanding Teacher Award, People’s Teacher Medal, and Provincial Outstanding Teacher Award.

M. Li was born in Chongqing, China, in 1984. He received the B.S. degree from Nankai University, Tianjin, China, in 2007, and the M.A. degree from the Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2009, both in communication engineering. His research interests include microstrip antennas and microwave circuits.

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Tarek Djerafi, Nelson J. G. Fonseca, Senior Member, IEEE, and Ke Wu, Fellow, IEEE

Abstract—In this paper, a 4 4 Nolen matrix beam-forming network for multibeam antenna applications is designed and demonstrated at 12.5-GHz center frequency. The structure is implemented using substrate integrated waveguide (SIW) technology for its attractive advantages including compact size, low loss, light weight, and planar form well suitable for high-density integration with other microwave and millimeter-wave planar integrated circuits. SIW cruciform couplers are used as fundamental building blocks for their wide range of coupling factors and their specific topology well adapted to the serial feeding topology of a Nolen matrix. The network performances are investigated over a 500-MHz frequency bandwidth ranging from 12.25 to 12.75 GHz. The matrix definition based on SIW cruciform couplers is similar to its microstrip counterpart in terms of coupling factors and phase delays. The whole network is fabricated. Measured results are in good agreement with the theoretical predictions, thus validating the proposed design concept. Using this matrix with a four radiating elements array antenna enables us to investigate the impact of the proposed matrix on the beam pointing angles versus frequency. Index Terms—Beam-forming network, beam scanning, Blass matrix, Butler matrix, Nolen matrix, smart antenna system, space division multiple access (SDMA), substrate integrated waveguide (SIW).

I. INTRODUCTION

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OBILE communication systems make use of three main types of multiple access schemes: frequency division multiple access (FDMA), time division multiple access (TDMA), and code division multiple access (CDMA). Significant improvement in system capacity, data rate, and wireless coverage is required to satisfy future wireless applications. Another scheme that could increase further the channel capacity and be combined with the previously mentioned multiple access techniques is the space division multiple access (SDMA). This technique assigns channels depending on the position of a user. Using SDMA, two users with sufficiently different locations can transmit or receive simultaneously at the same carrier frequency, over the same time slot or the same code as long as the distance between the users ensures a sufficient isolation to minimize interferences [1]. Such a technique is Manuscript received March 25, 2009; revised August 17, 2009. First published January 15, 2010; current version published February 12, 2010. T. Djerafi and K. Wu are with the Department of Electrical Engineering, Poly-Grames Research Center, Center for Radiofrequency Electronics Research of Quebec, École Polytechnique de Montréal, Montréal, QC, Canada H3T 1J4 (e-mail: [email protected]; [email protected]). N. J. G. Fonseca was with the Antenna Department, Centre National d’Etudes Spatiales (CNES), 31401 Toulouse, France. He is now with the Antenna and Sub-Millimeter Wave Section, European Space Agency (ESA), 2201 AG Noordwijk, The Netherlands (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2037866

commonly used in terrestrial communications, and particularly in high user-density areas. Typical simple implementation uses several sufficiently directive antennas with different pointing directions. More recently, this technique has been successfully applied to the design of satellite multimedia communications systems requiring high capacity, with notable realizations such as Anik-F2 and Spaceway [2], [3]. The accommodation of antennas being limited on spacecrafts, multibeam antennas are preferred to produce cellular coverage with a reduced number of radiating apertures. It has been known that the multiple fixed beams can be formed using lens antennas such as Luneberg [4] or Rotman lenses [5] with multiple feeds. Lenses focus energy radiated by feed antennas with lower directivity [6] and can be made from dielectric materials or implemented as space-fed arrays. Multiple input/multiple output (MIMO) matrices such as Butler [7] and Blass [8] matrices use transmission lines connected by power splitters and couplers to form multiple beam networks. When used as a beam-forming network (BFN), the outputs of such matrices are linked to the radiating elements and each input produces one beam. The phase delays required to produce the beam deviation for a given input are provided, adding extra transmission line lengths or phase shifters. Aperture amplitude distributions are controlled by the power-splitter ratios [6], [9]. The Butler matrix is built by interconnecting couplers, phase shifters, and crossovers. The crossovers increase the design complexity and path loss. Crossovers also impose multilayer design or extra components (two back-to-back 3-dB couplers) for planar realizations [10]. The Blass matrix is far more flexible in terms of amplitude and phase laws than the Butler one, but has lower efficiency due to the presence of loads at line terminations to produce a traveling wave serial feeding. Despite this flexibility, the Blass matrix had limited application compared to the Butler matrix mainly because of its inherent loss. The Nolen matrix is a special case of the Blass matrix, where the termination loads are suppressed [11]. This lossless characteristic of the Nolen matrix imposes the excitation laws to be orthogonal, just like in the Butler matrix. As shown in Fig. 1, the Nolen matrix is composed of directional couplers and phase shifters. The number of output ports can be greater to provide more flexibility in the design. than input ports The main advantage of the Nolen matrix is that it does not require any line crossings, thus making it particularly attractive for planar realizations [12]–[14]. The waveguide is the recommended technology for the BFN because of its field shielding nature that avoids radiation loss and the interference on other circuit’s elements such as the antennas, but the waveguide structures have usually high cost, low

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TABLE I DIRECTIONAL COUPLER PARAMETERS [12]

Fig. 1. Nolen matrix beam-forming network [12].

integration profile, and significant weight, which present application problems for space aircrafts or satellites. The recently emerging substrate integrated waveguide (SIW) concept then appears as an attractive manner to keep waveguide advantages while avoiding its main drawbacks. The SIW, which is part of the substrate integrated circuit (SIC) family [15], is synthesized by placing two rows of metallic vias in a dielectric substrate. It provides a cost-effective solution to embed high quality factor components in the same substrate used for planar circuits [15]. A different type of SIW antenna can be integrated with the BFN [16]–[19]. Associated with many passive components such as filters, multiplexers, circulator, and power dividers [15], [16], a high antenna efficiency and low fabrication-cost RF front end can be built [19], [20]. Combining the two above-mentioned fields of interest as suggested by one of the authors in [12], a novel planar Nolen matrix -band, configuration using a SIW is designed to operate over namely, from 12.25 to 12.75 GHz. SIW technology was already associated to other multiple BFNs [21], but this paper is the first to the best of our knowledge to apply the SIW to Nolen matrices. The structure is constructed using a number of cross couplers with different coupling factors and phase shifters. The selected cross-coupler topology is particularly well adapted to the Nolen matrix topology. Simulation and measurement results of the proposed 4 4 Nolen matrix and its constituting components are reported in this paper. II. ARCHITECTURE DESCRIPTION In the design of Blass matrices, the two sets of line structures, usually referred to as lines and columns of the matrix, are interconnected at each crossover point or node by a directional coupler. A signal applied at the input port travels along the feed line to its end, where the line is terminated by a matched load to suppress signal reflections and produce the desired traveling-wave behavior. At each node, a portion of the signal is coupled towards each column, thereby exciting the corresponding radiating element. The beam direction is then controlled by the path difference between the input and each radiating element, whereas the power distribution throughout the array is controlled by the coupling coefficients. The Nolen matrix is a special case of the Blass matrix in which the diagonal couplers are replaced by bends connecting directly to port1 and port2 (according to notations of the detailed node in Fig. 1),

then all the couplers beyond the diagonal can be suppressed since they are no longer linked to the inputs or outputs. In [12], Fonseca introduced a design technique for Nolen matrices as an asymptotic singular case of the Blass matrix design algorithm proposed by Mosca et al. in [22]. This algorithm offers a simple recursive design method to find an optimum serial feeding network for orthogonal excitations. Each node of the matrix is made up of a directional coupler fully defined with and phase shifter . The proposed design with parameter four inputs and four outputs correspond to a 4 4 Butler matrix using 3-dB/90 hybrid couplers. These parameters are used as entry into the Mosca et al. algorithm and the results were given in [12]. The theoretical parameters of directional couplers and phase shifters obtained for the matrix described above are reported in Table I. The Nolen matrix consists of 3.01-, 4.77-, and 6.02-dB couplers and phase shifters ranging from 45 to 180 compared to a reference line (0 ). The SIW cross-coupler acts as the input and power delivery component instead of the conventional 90 or hybrid coupler. The Nolen matrix is designed at the center frequency of 12.5 GHz with a 500-MHz bandwidth. The topologies chosen for the design of various constituting elements of the matrix are presented in Section II-A. A. SIW Cross Coupler A standard -plane coupler with a continuous coupling aperture over the entire width of the common broadside wall of two adjacent SIW waveguides may lead to coupling values varying between 3–5 dB [23]. For a lower coupling factor, multiple apertures must be used or two couplers must be cascaded at the expenses of the size and signal loss. The cruciform -plane SIW coupler, proposed for the first time in SIW technology in [24], has the capability to achieve a wide range of coupling ratios while maintaining a very compact size since the coupling occurs in the crossing area of two simple SIW transmission lines, as shown in Fig. 2. Furthermore, this perpendicular configuration is particularly adapted to Blass or Nolen matrices design according to the topology presented in Fig. 1. From notations in Fig. 2, port 1 is the input port, port 2 is the coupling port, port 3 is the direct port, and port 4 is the isolated is the equivalent rectangular waveguide model width, port. set for proper behavior over a targeted frequency range. Two posts are added in the crossing area to achieve the desired coupling; these posts have the same diameter and are diagonally separated by . Two inductive posts are added in each port close

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Fig. 2. Top view of the SIW cross coupler. TABLE II GEOMETRIC PARAMETERS OF DIRECTIONAL COUPLERS

Fig. 4. Simulation and measurement results for the H -plane SIW 3-dB coupler. (a) S11 and S41. (b) S21 and S31.

Fig. 3.

S -parameters simulated result of the 3-dB cross coupler.

to the crossing area in order to achieve a low return loss. The inductive matching posts have diameter and position relative to a corner of the crossing area. These parameters are adjusted to accomplish the desired coupling factor while minimizing S11 and S41. The parameters are tuned using a 3-D electromagnetic (EM) simulation software, High-Frequency Structure Simulator (HFSS) by the Ansoft Corporation, to achieve wideband performances. A substrate with a relative permittivity of and a thickness of 0.787 mm (RT/Duroid 5870) is used. Accordmm, ingly, the SIW characteristic dimensions are mm, and mm, where is the distance between two successive posts and is the diameter of the posts. The final dimensions of the needed SIW couplers are reported in Table II. As an example of performance demonstration, a 3-dB coupler is fabricated and measured (Fig. 3). Microstrip to SIW transitions are placed at each ports of the device for measurement purposes [25].

Fig. 5. Measured and simulated phase shifts between the outputs of coupler.

Simulation and measured results agree well in all the waveguide bandwidth. The measured isolation and return loss are below 17 dB in a bandwidth larger than 12–13 GHz with a worst case value at 12 GHz, as shown in Fig. 4. In this bandwidth, 0.5-dB power equality is achieved in measurements (versus 0.2 dB in simulations). This slight degradation may be due in part to the feeding transitions for the measurement purpose. Fig. 5 compares the simulated and measured relative phase differences between direct and coupled ports. As shown in this figure, the relative phase difference is close to the theoretical

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Fig. 7. Manufactured 4

Fig. 6. Topology of SIW Nolen matrix in equivalent waveguide configuration.

90 and has a worst case variation under 7 over the operating bandwidth in measurements. The two other couplers were only simulated as the manufactured 3-dB coupler proved good agreement with simulations and a coupling range compatible with the present need was already validated in [24]. For the 4.77-dB coupler, the magnitude of S21 is 4.77 dB with a ripple of 0.2 dB from 12 to 13 GHz and isolation below 17 dB over the same bandwidth. For the 6.02-dB coupler, the isolation is better than 18 dB in the 12–13-GHz frequency range with reflection below 15 dB. The coupling factor offers good amplitude stability around the center frequency with a center value of 6.02- and 0.2-dB balance over the 12–13-GHz frequency range. B. SIW Nolen Matrix In standard couplers, as described in [23], the phase difference between the direct port and coupled port is 90 . The recursive relation in the Mosca algorithm is derived using an ideal directional coupler, as shown in Fig. 1. The scattering matrix of the ideal directional couplers considered is

(1)

This leads to a phase difference between the direct port and the coupling port of 90 . This phase characteristic was verified by the microstrip branch line coupler, as used in [12]. Interestingly, the proposed SIW cross coupler has the same phase char-

2 4 Nolen matrix (13.7cm 2 10.5cm).

acteristic. For this SIW design, one can then use the same phase delays as used in microstrip technology. A broadside wall aperture coupler would have required adapting the phase delays to realize the proposed 4 4 matrix. Thus, it is noteworthy that the selected SIW cross coupler is well adapted to the Nolen matrix design process described by Fonseca in [12] and does not require to adapt the algorithm. Its geometry is also particularly adapted to the Nolen or Blass matrix topologies, making this cross coupler the best choice for our design. Combining the SIW couplers dimensioned in Section II-A, a complete experimental SIW Nolen matrix has been constructed. To reduce the simulation time, the structure was initially designed using an equivalent rectangular waveguide model shown in Fig. 6. Additional SIW phase shifters are introduced to realize 45 , 90 , 135 , and 180 phase delays optimized at the specified center frequency. As illustrated in Fig. 6, phase shifts are done using either meander lines or waveguide cross-section broad-wall modification. In the first phase-shifter technique, the lines are arranged in meanders in order to introduce a different phase shift in each output port due to different electrical path lengths that allows one to produce a proper phase distribution in the array profile, while compensating the additional delay given by the routing. This meander is realized by connecting 90 bends. For reflection cancellation, a via-hole element is added in each corner. The line must be properly routed in order to connect the coupler output to the next stage of the matrix. The second phase-shifter type used in this study is made by chaining sections of SIW lines of different widths with different corresponding phase propagation constants. Thus, an additional fixed delay at the output ports is used to recover the proper phase excitation of the radiating elements and between the different couplers. As for the directional couplers, the SIW phase shifters are synthesized in a planar substrate with arrays of a metallic via by the easy and low-cost standard PCB fabrication process in order to manufacture the whole matrix in a unique board.

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Fig. 10. Simulated means of the transmissions coefficients amplitude for each input port. Fig. 8. Measured return loss of the four input ports.

Fig. 11. Measured means of the transmissions coefficients amplitude for each input port.

Fig. 12. Simulated and measured relative phase differences between adjacent output ports for port1. Fig. 9. Measured isolation between the four input ports. (a) S21, S31, and S41. (b) S32, S42, and S43

III. EXPERIMENTAL RESULTS

According to notations in Fig. 6, ports 1–4 are the input ports of the matrix. Ports 5–8 are the output ports used to feed the antenna array with the adequate phase and amplitude profile. Finally, the SIW structure formed by the metallized holes is optimized. SIW-to-microstrip transitions are placed at each port of the circuit for measurement purposes [25].

The photograph of the proposed eight-port matrix is shown in Fig. 7. It was fabricated on a printed circuit board (PCB) with a dielectric constant of 2.33 and loss tangent 0.002. The board size is 13.7 cm 10.5 cm without the transitions. The via-holes were manufactured first by a mechanical process and then metallized. The Nolen matrix is designed for a 500-MHz frequency range operation around 12.5 GHz. Fig. 8 shows the experimental return losses. The measured results include the influences of the

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TABLE III PHASE DIFFERENCE ON TRANSMISSION COEFFICIENTS (SIMULATED/MEASURED)

SIW-microstrip transitions and SMA connectors at all ports. A thru-reflect-line (TRL) calibration set was used to minimize these effects. It can be noted that the return loss of the input ports is lower than 10 dB over the entire frequency band (12–13 GHz). Measured results agree well with the simulated ones, except for input port 4 where some performance degradation is observed. An essential criterion of a BFN performance for SDMA applications is the isolation between input ports, as it contributes to the level of interferences. Fig. 9 plots the results of the measured isolations, representing the isolations between each couple of input ports (S21, S31, S41, S32, S42, and S43) of the proposed Nolen matrix. Over the entire operating frequency band, the isolation level is lower than 12 dB. The isolation between port1 and port2 is below 19 dB over the working frequency range and below 15 dB over an extended 12–13-GHz band. In simulations, these results are about 5 dB lower. The worst case both in measurement and simulation is related to the isolation between ports 2 and 3. Depending on the application (electronically controlled beam, SDMA in both transmit and receive systems), system analyses are needed to evaluate the impact of isolation on the global system performances. Fig. 10 presents the simulated mean transmission coefficient for each input port and Fig. 11 the measured means values. Good agreement is found between simulations and measurements over the nominal 500-MHz operating frequency range. Transmission coefficients are well equalized and are close to the theoretical predicted value of 6 dB with an average value of 6.5 dB. The maximum error is less than 0.5 dB in simulations and around 1 dB in measurements. Line losses in the dielectric are estimated to be around 0.75 dB, but this value varies with the electrical path length: the shorter one (1 toward 5) presents lower losses while the longer one (4 toward 8) has line losses around 1.2 dB. The performances of the first path also have wider bandwidth behavior than the longer one. Furthermore, measured results degrade faster outside the operating band than predicted in simulations. The possible sources of loss in an SIW structure are: 1) conductor losses due to the finite conductivity of the metal walls; 2) dielectric losses due to the loss tangent of the dielectric material; and 3) radiation losses due to the presence of the slots in the sidewalls. The dielectric loss may cause the major part of the attenuation. The radiations are very small, and in fact, completely negligible when the metal via dimension and space are adequately selected.

The observed shift between simulations and measurements may be related to the SIW-microstrip transitions and fabrication errors. It must especially be mentioned that the mechanical and chemical processes developed at the Poly-Grames Research Center, Montréal, QC, Canada, and used, respectively, to make the holes and metallize them are at the limit with the required dimensions of this circuit. Fig. 12 compares simulation and measurement transmission phases for port 1 of the proposed matrix. It is found that the simulated and measured results are in good agreement and the transmission phase coefficients are close to the theoretical values over the operating frequency band. Similar performances were found for the other input ports. The values of the phase difference of all the input port are reported in Table III at 12.25, 12.5, and 12.75 GHz. At the center frequency (12.5 GHz), the measured means phase differences are, respectively ( 41.85 136.93 48.13 134.08) compared to the optimized ones ( 42.3 131.09 44.12 135.82), and the theoretical ones ( 45 135 45 135) ranging from ports 1 to 4, respectively. Compared with the simulated results, the measurement results have some phase shift, which may be mainly due to the connectors. The achieved results are all in good agreement with a worst case error of 7 over the operating bandwidth. The frequency-dependent phase behavior of this matrix was expected and is due to the serial feeding characterizing a Blass or Nolen matrix. In fact, the incremental phase shift between adjacent outputs varies with frequency. For instance, as shown in Table III, when the first input is used over the bandwidth GHz, the phase difference between adjacent outputs changes by 20 . This gradient for each output can be used to control the beam squint effect, as investigated in [14]. To evaluate the impact of the proposed matrix on beam squint and compare it with its microstrip counterpart in -band [14], the measured Nolen matrix is used to feed a four-element linear array with a spacing defined at center frequency of 0.63 . A square patch is used as array element; the radiation pattern is given as , with . Fig. 13 shows the array patterns in polar coordinates produced by the four inputs, each pointing in direction depending on the phase difference between adjacent ports. These parameters are linked by the following formula: (2) is the angular wavenumber in free space and where distance between two radiating elements.

is the

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H -plane radiation patterns versus frequency of a four-patch array fed by the designed Nolen matrix for: (a) port1, (b) port2, (c) port3, and

Let us first evaluate the beam squint of the four beams over the operational bandwidth, i.e., 12.25–12.75 GHz. For port1, at the center frequency, and the beam pointing is over the targeted bandwidth, the main beam scans from 5.3 to 15.3 . In comparison to the gain at center frequency, the beam squint effect induces a gain drop around 0.2 dB, which remains acceptable for most applications. For port 2, the beam squint is 9.6 varying from 28.7 to 38.3 . For port 3, it scans from 6.9 to 16.2 with center frequency beam pointing at 11.5 . For port 4, it scans from 27.7 to 40.7 . One may then note that the beam squint is quite similar for all beams. In fact, the bandwidth analyzed being relatively small (4%), the beam squint due to the linear array is negligible compared to the beam squint introduced by the matrix. To compare this matrix with the microstrip one realized in -band, we investigate the beam squint over similar -band leading to an 8% relative bandwidths: 12–13 GHz in bandwidth to be compared with 9% (2.1–2.3 GHz) in -band. -band with 1-GHz bandwidth, the beam squint is around In 20 and is very similar for all ports (from 0 to 20 for port 1, from 44 to 25.2 for port 2, from 21.8 to 2.3 for port 3, and from 22 to 43.1 for port 4, the first values for each port being at 12 GHz and the second at 13 GHz). In -band over a similar relative bandwidth, the beam squint is much smaller and depends more on the input port. From 2.1 to 2.3 GHz, the beams scan from 7 to 15 , from 39 to 27 , from 14 to 7 , and from 31 to 35 for ports 1–4, respectively. This is understood by the fact that electrical paths are smaller in the microstrip realization, which reduces the phase dispersion induced by the matrix. Further investigations are needed on the proposed SIW concept to evaluate the possibility to reduce electrical paths and reach improved performances in terms of beam squint. For narrowband applications, the presented performances may be acceptable. If higher constraints are defined on the beam-pointing accuracy, this may require selecting another technology. Still this has to be put in balance with the advantages brought by the SIW technology such as lower coupling, lower line losses, etc.

IV. CONCLUSION A Nolen matrix based on SIW technology has been proposed and validated experimentally for the first time. The matrix is optimized using the commercial software HFSS and fabricated to operate from 12.25 to 12.75 GHz. 3.01-, 4.77-, and 6.02-dB SIW cross couplers are designed, as well as different phase shifters to build a complete 4 4 Nolen matrix. The measured power-split unbalance stays within 0.5 dB over the design bandwidth. The relative phase-difference distribution is used to estimate the variation of the beam-pointing angle over the bandwidth. The proposed SIW design has the advantage of low cost, low profile, light weight, high integration density, and ease of fabrication. We also expect this design to reduce line losses when compared to its microstrip counterpart. Further investigations are in process to fully compare SIW and microstrip technologies for multiple input/multiple output (MIMO) matrices. In this comparison, the power handling is also planned to be addressed, as it is a real concern in RF communication systems. It will be of interest to evaluate how SIW compares to other technologies and mainly standard waveguide technology in this regard. REFERENCES [1] C. Godara, “Application of antenna arrays to mobile communications—Part I: Performance improvement, feasibility and system considerations,” Proc. IEEE, vol. 85, no. 7, pp. 1029–1070, Jul. 1997. -band [2] D. Le Doan, E. Amyotte, C. Mok, and J. Uher, “Anik-F2 transmit multibeam antenna,” in Proc. ANTEM2004, Ottawa, ON, Canada, 2004, pp. 159–162. [3] “SPACEWAY 1, 2 North America,” Boeing, 2008. [Online]. Available: http://www.boeing.com/defense-space/space/bss/factsheets/702/ spaceway/spaceway.html [4] R. K. Luneberg, Mathematic Theory of Optics. Providence, RI: Brown Univ. Press, 1944, pp. 189–212. [5] W. Rotman and R. Turner, “Wide-angle microwave lens for line source applications,” IEEE Trans. Antennas Propag., vol. AP-11, no. 6, pp. 623–632, Nov. 1963. [6] Y. T. Lo and S. W. Lee, Antenna Handbook: Theory, Applications, and Design. New York: Van Nostrand, 1988.

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[7] J. Butler and R. Lowe, “Beam-forming matrix simplifies design of electronically scanned antennas,” Electron. Design, pp. 170–173, Apr. 1961. [8] J. Blass, “Multidirectionnal antenna, a new approach to stacked beams—Part I,” in IRE Int. Conf. Rec., 1960, vol. 8, pp. 48–50. [9] P. S. Hall and S. J. Vetterlein, “Review of radio frequency beamforming techniques for scanned and multiple beam antennas,” Proc. Inst. Elect. Eng.—Microw., Antennas, Propag., vol. 137, no. 5, pt. H, pp. 293–303, Oct. 1990. [10] S. Yamamoto, J. Hirokawa, and M. Ando, “A beam switching slot array with a 4-way Butler matrix installed in single layer post-wall waveguides,” IEICE Trans. Commun, vol. E86-B, no. 5, pp. 1653–1659, May 2003. [11] J. Nolen, “Synthesis of multiple beam networks for arbitrary illuminations,” Radio Div., Bendix Corpration, Baltimore, MD, 1965, Ph.D. dissertation. [12] N. J. G. Fonseca, “Study and design of a S -band 4 4 Nolen matrix for satellite digital multimedia broadcasting applications,” in 12th Int. ANTEM URSI Symp., Montreal, QC, Canada, Jul. 16–19, 2006, pp. 481–484. [13] N. J. G. Fonseca, “Etude des matrices de Blass et Nolen,” CNES, Toulouse, France, Tech. Note 152, Nov. 2007 [Online]. Available: http://cct/cct13/infos/notestech.htm, 98 pp [14] N. J. G. Fonseca, “Printed s-band 4 4 Nolen matrix for multiple beam antenna applications,” IEEE Trans. Antennas Propag., vol. 57, no. 6, pp. 1673–1678, Jun. 2009. [15] K. Wu, “Integration and interconnect techniques of planar and nonplanar structures for microwave and millimeter-wave circuits—Current status and future trend,” in Asia–Pacific Microw. Conf., Taipei, Taiwan, Dec. 3–6, 2001, pp. 411–416. [16] W. Hong, “Development of microwave antennas, components and subsystems based on SIW technology,” in IEEE Int. Microw., Antenna, Propag., EMC Technol. Wireless Commun. Symp., 2005, vol. 1, pp. 14–17. [17] J. Z. Peng, S. Q. Xiao, X. J. Tang, and J. C. Lu, “A novel Ka-band wideband slot antenna for system-on-package application,” J. Electromagn. Waves Appl., vol. 22, pp. 1705–1712, Dec. 2008. [18] Z. C. Hao, W. Hong, J. X. Chen, X. P. Chen, and K. Wu, “A novel feeding technique for antipodal linearly tapered slot antenna array,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 1641–1643. [19] D. Stephens, P. R. Yong, and I. D. Robertson, “W -band substrate integrated waveguide slot antenna,” Electron. Lett., vol. 41, pp. 165–167, Feb. 2005. [20] R. V. Gatti, L. Marcaccioli, E. Sbarra, and R. Sorrentino, “Flat array antennas for Ku-band mobile satellite terminals,” Int. J. Antennas Propag., vol. 2009, Feb. 2009, Art. ID 836074. [21] Y. J. Cheng, W. Hong, K. Wu, Z. Q. Kuai, Y. Chen, J. X. Chen, J. Y. Zhou, and H. J. Tang, “Substrate integrated waveguide (SIW) rotman lens and its Ka-band multibeam array antenna applications,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2504–2513, Aug. 2008. [22] S. Mosca, F. Bilotti, A. Toscano, and L. Vegni, “A novel design method for Blass matrix beam-forming networks,” IEEE Trans. Antennas Propag., vol. 50, no. 2, pp. 225–232, Feb. 2002. [23] Y. Cassivi, D. Deslandes, and K. Wu, “Substrate integrated waveguide directional couplers,” in Proc. Asia–Pacific Microw. Conf., Kyoto, Japan, 2002, vol. 3, pp. 1409–1412. [24] T. Djerafi and K. Wu, “Super-compact substrate integrated waveguide cruciform directional coupler,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 11, pp. 757–759, Nov. 2007. [25] D. Deslandes and K. Wu, “Integrated microstrip and rectangular waveguide in planar form,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 2, pp. 68–70, Feb. 2001.

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Tarek Djerafi was born in Constantine, Algeria, in 1975. He received the Dipl.Ing. degree from the Institut d’Aeronautique de Blida (IAB), Blida, Algeria, in 1998, the M.A.Sc. degree in electrical engineering from the École Polytechnique de Montréal, Montréal, QC, Canada, in 2005, and is currently working toward the Ph.D. degree at the École Polytechnique de Montréal. His research deals with design of millimeter-wave antennas and smart antenna systems, microwaves, and RF components design.

Nelson J. G. Fonseca (M’06–SM’09) was born in Ovar, Portugal, in 1979. He received the Engineering degree from the École Nationale Supérieure d’Electrotechnique, Electronique, Informatique, Hydraulique et Telecommunications (ENSEEIHT), Toulouse, France, in 2003, the Master degree from the École Polytechnique de Montréal, Montréal, QC, Canada, in 2003, and is currently working toward the Ph.D. degree at the Institut National Polytechnique de Toulouse, Université de Toulouse, Toulouse, France. He has been an Antenna Engineer with the Antenna Study Department, Alcatel Alénia Space (now Thalès Alénia Space–France), and with the Antenna Department, French Space Agency (CNES), Toulouse, France, prior to joining the Antenna and Sub-Millimeter Wave Section, European Space Agency (ESA), Noordwijk, The Netherlands, in 2009. He has authored or coauthored over 50 papers in journals and conferences including two CNES technical notes. He has ten patents pending. He is currently a Technical Reviewer for the Journal of Electromagnetic Waves and Applications—Progress in Electromagnetic Research (PIER), Massachusetts Institute of Technology (MIT). His research interests cover telecommunication antennas, beam-forming network designs, and new enabling technologies such as metamaterials and membranes applied to antenna applications. Mr. Fonseca is a member of the Electromagnetic and Microwave Circuit CNES Technical Competence Center Board. He was the recipient of the Special Prize of Toulouse City for abroad studies in 2003 and the Best Young Engineer Paper Award presented at the 29th ESA Workshop on Antennas in 2007. He was corecipient of the Best Application Paper Award presented at the 30th ESA Workshop on Antennas in 2008.

Ke Wu (M’87–SM’92–F’01) is Professor of electrical engineering, and Tier-I Canada Research Chair in RF and millimeter-wave engineering with the École Polytechnique de Montréal, Montéal, QC, Canada. He also holds the first Cheung Kong endowed chair professorship (visiting) with Southeast University, the first Sir Yue-Kong Pao chair professorship (visiting) with Ningbo University, and an honorary professorship with the Nanjing University of Science and Technology and the City University of Hong Kong. He has been the Director of the Poly-Grames Research Center and the founding Director of the Center for Radiofrequency Electronics Research of Quebec (Regroupement stratégique of FRQNT). He has authored or coauthored over 700 referred papers and a number of books/book chapters. He holds numerous patents. His current research interests involve SICs, antenna arrays, advanced computer-aided design (CAD) and modeling techniques, and development of low-cost RF and millimeter-wave transceivers and sensors for wireless systems and biomedical applications. He is also interested in the modeling and design of microwave photonic circuits and systems. Dr. Wu is a member of the Electromagnetics Academy, Sigma Xi Honorary Society, and URSI. He is a Fellow of the Canadian Academy of Engineering (CAE) and the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He is an IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Distinguished Microwave Lecturer from 2009 to 2011. He has held key positions in and has served on various panels and international committees including the chair of Technical Program Committees, International Steering Committees, and international conferences/symposia. In particular, he will be the general chair of the 2012 IEEE MTT-S International Microwave Symposium (IMS). He has served on the Editorial/Review Boards of many technical journals, transactions, and letters, as well as scientific encyclopedia as an editor and guest editor. He is currently the chair of the joint IEEE chapters of MTT-S/AP-S/LEOS, Montréal, QC, Canada. He is an elected IEEE MTT-S Administrative Committee (AdCom) member for 2006–2012 and is the chair of the IEEE MTT-S Member and Geographic Activities (MGA) Committee. He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of IEEE Canada, and the 2009 Thomas W. Eadie Medal of the Royal Society of Canada.

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Integrated Active Pulsed Reflector for an Indoor Local Positioning System Silvan Wehrli, Student Member, IEEE, Roland Gierlich, Student Member, IEEE, Jörg Hüttner, Student Member, IEEE, David Barras, Student Member, IEEE, Frank Ellinger, Senior Member, IEEE, and Heinz Jäckel, Member, IEEE

Abstract—This paper presents an indoor localization system based on a frequency modulated continuous wave radar in the industrial–scientific–medical band at 5.8 GHz. An integrated active pulsed reflector behaves as a backscatter by regenerating the incoming phase with phase coherent startup at a constant frequency. The base station (BS) determines the distance to this reflector with a round-trip time-of-flight measurement. The active pulsed reflector is built around a switchable and tunable oscillator. The circuit has been fully integrated in a 0.18- m CMOS technology. Outdoor measurements revealed a positioning accuracy of 15 cm, while in a harsh multipath environment with omnidirectional antennas a positioning accuracy of 32.88 cm was measured. The localization system is capable of detecting multiple reflectors at the same time, and no synchronization between BSs is needed. Index Terms—Chirp radar, distance measurement, frequency modulated (FM) radar, FM continuous wave (FMCW) secondary radar approach, indoor multipath propagation environment, radar scattering, tunable oscillators.

I. INTRODUCTION OR WAREHOUSE management, automated forklifts, robotic control, and for interactive guiding, a highly accurate indoor local positioning system is needed [1]. Different approaches exist for local positioning. A comparison between different local positioning systems including Bluetooth, wireless fidelity (WiFi), RF identification (RFID), ultrasound, ultra-wideband (UWB), and worldwide interoperability for microwave access (WiMAX) is given in [2]. While systems based on existing wireless standards are cheap and broadly applicable [3], only ultrasound and UWB systems can deliver so far an accuracy below 15 cm. However, frequency modulated

F

Manuscript received April 15, 2009; revised September 27, 2009. First published January 19, 2010; current version published February 12, 2010. This work was supported by the European Communities Six Framework Programme (FP6/2002-2006) under Grant 026851 (RESOLUTION). S. Wehrli, D. Barras, and H. Jäckel are with the Electronics Laboratory, Swiss Federal Institute of Technology (ETHZ), CH-8092 Zürich, Switzerland (e-mail: [email protected]; [email protected]; [email protected]). R. Gierlich and J. Hüttner are with Corporate Technology, Wireless Sensors and RF Technology, Siemens AG, D-81730 Munich, Germany (e-mail: Roland. [email protected]; [email protected]). F. Ellinger is with the Chair for Circuit Design and Network Theory, Dresden University of Technology, 01062 Dresden, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037870

Fig. 1. FMCW radar system consisting of a BS and an active pulsed reflector.

continuous wave (FMCW)-based radar systems were not included in the comparison. The positioning system based on ultrasound techniques can achieve accuracies below 9 mm with a 90% confidence level in an area of 4 m [4]. Unfortunately, ultrasonic system exhibit poor performance in the presence of ultrasonic noise [5], and thus cannot be used in an industrial environment. Today, most indoor positioning systems are either based on FMCW [6]–[8], pulse-based UWB radar systems [9], or FMCW-based UWB systems [10], [11]. In a basic FMCW radar system, the base station (BS) transmits a frequency ramp, which is reflected by a backscatter. The round-trip time-of-flight (RTOF) causes a frequency offset between the transmitted and received frequency ramp at the BS, which is proportional to the distance between the BS and backscatter. The delayed frequency ramp is then down-converted with the transmitted ramp. This paper describes a local positioning system based on an active pulsed phase coherent reflector (APR) as backscatter for an FMCW radar system designed in the framework of the RESOLUTION European Union (EU) project [12], [13]. The main difference to conventional FMCW systems is that the reflector regenerates the phase of the incoming signal every time it is switched on, but oscillates at a constant frequency. Fig. 1 illustrates this radar system consisting of a BS and an active pulsed reflector. The concept of the active pulsed reflector was originally proposed by [8]. The novel compact integrated active reflector application specific integrated circuit (ASIC) was presented in [14]. This paper describes the active pulsed reflector in greater detail and additionally presents the BS and 1-D measurements with directional and omnidirectional antennas in indoor and outdoor scenarios.

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. The angular frequency is the center with the amplitude is the phase at . The time-dependent frequency and linear ramp is defined as (2) where is the sweep bandwidth and is the frequency ramp duration. This signal is received at the reflector after the and has been attenuated by . The time-of-flight incoming signal at the reflector can be written ideally as (3) Fig. 2. (a) Phase  of the transmitted linear frequency ramp increases quadratically. This phase is received at the active reflector. Every time the T 1 n, the reflector synchronizes its phase reflector is switched on at t to the phase of the incoming signal. The sweep time T is much larger than . (b) Phase difference between the transmitted and the on-time T and T  0  increases linearly. The first derivative reflected signal  t = t depends on the time-of-flight  .

=

d1 d

1 () =

II. THEORY The theory of an active pulsed reflector, also called “switched injection locked oscillator,” is covered originally in [8] and is summarized in this section. The principle of the active pulsed reflector can be qualitatively understood by investigating the phase of the transmitted and received signal at the BS. The BS transmits signal a linear frequency ramp like a conventional FMCW radar, thus increases quadratically with time. the phase of the signal Fig. 2(a) illustrates the phase of the transmitted signal versus the sweep time . The active pulsed reflector receives this signal . Every time the reflector is switched on, with a delay is generated with the initial phase an oscillation of duration imposed by the received signal. The condition reflector starts oscillating with a determined phase , ideally , and a frequency , which is not necessarily the same frequency as the received signal. Thus, the phase of the reflector is synchronized to the incoming signal and the phase information is transmitted back to the BS. The difference of the at the BS, transmitted and reflected phase plotted in Fig. 2(b), increases linearly over time and the gradient is directly dependent on the time-of-flight . Every time the reflector is switched on, the phase of the reflector is synchronized owing to the phase coherent startup. to the incident phase Furthermore, the switching also modulates the reflected signal and allows the distinction with the switching frequency and between reflectors between reflectors with different and passive reflections. The following calculation summarizes the resulting baseband signal for this FMCW radar system with an active pulsed reflector. The BS transmits a linear frequency ramp given as

(1)

Assuming the reflector is switched on at time instantaneous phase of the received signal

, the at

is

(4)

In case of an ideal startup behavior of the oscillator, the reflector starts to oscillate with the same phase as the received signal, but with the constant and different oscillation frequency of the oscillator. The reflector output signal is transmitted back to the BS and delayed by and attenuated by factor . Therefore, the received signal at the BS is given by (5) with , defined in (4), which represents the deterministic phase . is the amplitude of the oscillation of of the signal the reflector. We are interested in the resulting baseband signal, during the emiswhen the reflector is switched on once at . The frequency ramp duration of the radar sion duration during which the reflector is is much longer than the time , thus can be approximated on with the constant value during . The calculation can be further simplified by setting , which can be achieved by tuning the oscillation frequency with the tuning voltage . The low-pass filter after the BS mixer represents an integration in the time domain, thus the filtered down-converted signal for one pulse of the APR can be written as

(6) The variable is the amplitude of the signal, depending on , , the attenuation factor , as well as the antenna, lownoise amplifier (LNA), and mixer gain.

WEHRLI et al.: INTEGRATED ACTIVE PULSED REFLECTOR FOR INDOOR LOCAL POSITIONING SYSTEM

Fig. 3. Ideal spectrum of the down-mixed signal s = 0:5 s, and d = 2:5 m. T = 33 ns, T

269

(t) for T = 0:5 ms,

The integrator value is a constant value that depends on the time at which the reflector has been switched on. By repeating this process periodically with the frequency , we obtain an up-converted baseband time-domain signal

Fig. 4. Ideal time signal and spectrum of the output signal of the reflector s for f = 1 MHz and T = 13:3 ns. The first zeros of the sinc envelope lie at the edge of the ISM band at 5.725 and 5.875 GHz, respectively.

A. Influence of Pulsewidth

(7) where (8)

Pulsing a sinusoidal signal with a rectangular signal leads to a sinc-shaped envelope in the frequency domain, as depicted in . Thus, the optimal Fig. 4. The width of the main lobe is is determined by the available bandwidth of the on-time industrial–scientific–medical (ISM) band. For an optimal usage of the available 150-MHz bandwidth, the first zeros of the sinc function should lie at 5.725 and 5.875 GHz, respectively. The optimal on-time is

and

ns

(11)

(9) The spectrum of of this signal around the fundais depicted in Fig. 3. The sinc envemental frequency signal leads to rectangular peaks in the speclope of the of the inner edges at the trum. The frequency difference 3-dB points of these peaks is proportional to the time-of-flight . Hence, the distance between the BS and reflector can be calculated from

The spectrum of the perfect rectangular signal leads to strong sidelobes, which violates the ISM band requirements of 74.8-dBm/Hz spectral power density outside the band [15]. However, the startup and the switching off of the reflector is not instantaneous. The envelope rise time can be approximated by one half of a Gaussian curve. With this realistic approximation, one can see that the sidelobes are reduced and the regulations can be fulfilled. The sidelobes are further reduced due to the bandpass characteristics of the balun and antenna.

(10) B. Link Budget with as the propagation velocity. It is possible to detect multiple reflectors at the same time by using different modulafor every reflector. The square function tion frequencies modulates the baseband signal. Thus, the two peaks in the spectrum can be seen around the , but also around the higher harfundamental frequency . Therefore, to identify multiple reflectors at monics and the same time, the lowest modulation frequency limits the available frequency twice this frequency is determined by the sampling space. The highest usable frequency of the ADC in the BS.

The power received at the reflector can be calculated by the Friis transmission equation

(12)

with as the wavelength, as the distance, and and as and the received and transmitted power, respectively. are the antenna gains of the receiver and transmitter. The Friis transmission equation can be used because the wanted signal

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Fig. 5. Fully differential analog tunable reflector ASIC consists of two tunable amplifiers and a switching network. The modulation signal is generated off-chip on the PCB.

Fig. 6. Tunable fully differential output amplifier OutAmp.

for radar localization is the line of sight (LOS) signal. The freespace loss at 5.8 GHz over the operation range of 30 m is dB

(13)

The output power of the BS after the antenna is 10 dBm. The reflector uses a directional antenna with an antenna gain between 3–14 dBi, thus the received power of the reflector is more than 64 dBm. The needed output swing of the reflector is calculated using the same assumptions. The BS has a receiver sensitivity of 70 dBm and an antenna with at least 6-dBi gain. Therefore, in order to compensate the transmission loss, the signal at the reflector antenna has to be above 1 dBm. With an antenna gain of larger than 3 dBi, the reflector has to be able to transmit . more than 2 dBm equaling to

Fig. 7. Simulated behavior of the matching S 11 and oscillation frequency depending on v .

III. ACTIVE PULSED REFLECTOR The active pulsed reflector consists of the active pulsed reflector ASIC described in [14], a pulse generator for the on-off switching of the reflector, and a linear voltage regulator. A. Active Pulsed Reflector ASIC Based on the localization principle described above, an active pulsed reflector was designed in 0.18- m CMOS technology. The schematic of the implemented analog tunable reflector is illustrated in Fig. 5. The reflector is a fully differential oscillator and consists of an input amplifier, an output amplifier driving the antenna, and a differential on–off-switching circuit. An external controls low-frequency quartz stabilized pulse generator the switching and modulates the reflected signal. The singleended antenna is connected through an external balun, thus the reflector has to be matched to 50 . The reflector is tunable in order to compensate process variations and has to be impedance matched to the antenna over the complete tuning range. Both input and output amplifiers use the same differential structure shown in Fig. 6. This circuit consists of a differential pair with a tunable LC load. The output and input amplifiers behave as bandpass filters. The pass frequency determines and can be tuned the oscillation frequency with two hyper-abrupt junction varactors. The simulated extracted tuning range is 1.1 GHz, and the measured tuning range to the 50- antenna folis 1.24 GHz. The output matching lows the oscillation frequency, as shown in Fig. 7. Simulation

results show that the output matching is better than 9 dB over the complete tuning range. The output amplifier is capable of directly driving the equivalent load of the antenna. The simulated output power is between 3.5–7 dBm, the measured output power varies from 2.17 to 6.11 dBm depending on the oscillation fre. The phase noise at 1-MHz offset is 116 dBc/Hz. quency System simulations predict no measurement error due to the phase noise. The measurement accuracy starts to decrease for a phase noise above 100 dBc/Hz @ 1-MHz offset. The active reflector is not sensitive to close to carrier phase noise due to and the synchronization process at every the short on-time startup. The die micrograph of the reflector circuit is shown in Fig. 8. The die area is 0.85 mm . All inputs and outputs are electrostatic discharge (ESD) protected, except the differential connection to input. the antenna and the tuning voltage B. Pulse Generation The optimal on-time of the reflector is 13.3 ns, as discussed in Section II-A. If multiple reflectors are detected at the same time, then every reflector needs a different modula, but the pulsewidth is the same for tion frequency every reflector. Therefore, duty-cycle control is necessary. For the pulse generation, a quartz oscillator generates the modula. This signal is applied to a flip-flop with tion frequency asynchronous reset. The delay in the reset path determines the

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TABLE I SIMULATION RESULTS VERSUS MEASUREMENT RESULTS FOR THE ANALOG TUNABLE REFLECTOR

Fig. 8. Chip micrograph: chip size 0.85 mm

Fig. 9. Reflector PCB: dimension: 4.15 cm

2 1 mm.

2 4.8 cm.

and is responsible for the linear frequency ramp generation. The frequency ramp uses the available 150-MHz bandwidth and the ramp duration is 0.65 ms. The chosen ramp duration is a compromise between high update rate and achievable positioning range. The low-pass filtered IF signal is sampled by a 14-bit analog–digital converter. Inside a Virtex 4 field-programmable gate array (FPGA), the time signal is additionally filtered and decimated. In order to obtain an interpolated spectrum, the windowed signal is zero padded by a factor of 16 before the calculation of the power spectrum by a fast Fourier transform. In a high multipath environment, detecting the peak location in the spectrum may lead to a large positioning error because the first multipath component (MPC) can be stronger than the line-of-sight (LOS) component. A better method is to detect the inner edges of the peaks. The best results are achieved by detecting the peaks and search then for the edge, which is 3 dB below the peak. The measured distance is then calculated by (10). Data communication with a host computer is done over an Ethernet connection. V. MEASUREMENT RESULTS

Fig. 10. BS architecture.

A. Active Reflector Performance Analysis pulsewidth. With this methodology, it is possible to generate the desired pulse length. The requirements on frequency stability are not critical because the absolute drift does not play a role in (10), but only the drift during one measurement sweep time ms. Assuming a worst case scenario with a long-term , the frequency drifts frequency stability of 25 ppm on by 50 Hz. This leads to a broadening of the peaks in Fig. 3 by 50 Hz, which corresponds to a positioning error of 1.25 cm. In Fig. 9, the complete reflector printed circuit board (PCB) is depicted.

The performance of the active pulsed reflector in a laboratory setup without any multipath was presented in [14] and only a short summary is presented here. The basic characteristics for the active reflector ASIC are summarized in Table I. The active reflector has an oscillation rise time below 4 ns and a fall time below 3 ns. This allows to use fast pulses with an on-time of 13 ns. The reflector PCB with pulse generation, active pulsed reflector ASIC, quartz oscillator, and linear voltage regulator consumes 78 mA, the ASIC alone draws 30 mA from a 1.8-V supply. However, the 78 mA are only needed during the short . emission duration

IV. BSs The active pulse reflector (APR) has been tested using the BS hardware depicted in Fig. 10. A pseudomonostatic front-end is employed in order to achieve a good receiver noise figure of 3.5 dB. RF shielding on the front-end board and sufficient spacing of the TX and RX antennas have been provided to avoid receiver saturation by the transmitter. According to [16], the positioning accuracy depends on the linearity of the frequency ramp. Thus, a 1-GS direct digital synthesizer (DDS) generates a reference frequency for a 5.8-GHz phase-locked loop (PLL)

B. Sensitivity of the APR to CW Signal The sensitivity of the active pulsed reflector to CW signals is a good measure for the coherent startup of the reflector. Assuming a perfect startup of the reflector, the resulting output spectrum of the APR looks like Fig. 4 with the center frequency , and the distance between the peaks is equal to . at When the external signal strength reduces, the signal-to-noise ratio (SNR) decreases and the starting phase of the oscillator is influenced by the noise. This widens each peak and leads to a

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Fig. 11. Measured spectrum of the active reflector output with an applied CW signal. The distance between the peaks and the noise floor increases directly with the signal power of the CW signal.

noisy output spectrum. When no input signal is applied, the oscillator starts each time with a random phase, the peaks in the spectrum vanish, and only a noisy sinc envelope is visible. In simulations, the behavior of the ratio between the peaks and the noise in the spectrum was analyzed. The noise was modeled as a sinusoidal wave at the same frequency as the CW signal, but with a random phase at every startup of the reflector. The ratio between the peaks in the spectrum and the noise increases linearly with higher input SNR. The measurement results in Fig. 11 show that the noise floor decreases by 25 dB if the applied continuous wave (CW) signal power increases by 25 dBm. For an input power of 78 dBm, the peak to noise distance is 6 dB, which is equivalent to an SNR of 0 dB. Thus, the reflector starts phase coherent even with an input power of 78 dBm. For the operation range of 30 m, the received signal at the reflector is 64 dBm, thus the equivalent SNR is 14 dB. The resulting positioning error is less than 1 cm. The influence of the on-switching pulse could be kept very low, and thus, has only a minor influence on the positioning accuracy.

Fig. 12. Indoor measurement conducted in a high multipath environment.

Fig. 13. Plot of the measured distance d for outdoor measurement. Each dot represents one position measurement. The solid line represents the averaged position.

C. Distance Measurement The positioning system was tested in different multipath environments and with a directional and omnidirectional antenna. Fig. 12 displays the measurement setup for a strong multipath scenario. The TX and RX antennas of the BS are mounted on a tripod. The active reflector connected to an antenna is mounted on a movable sledge. 1) Outdoor Measurement: By measuring outdoors, the number of existing multipaths is kept very low and the excess delays are larger. In this favorable environment, good positioning accuracy could be achieved. Fig. 13 depicts the measured distances. The overall standard deviation is 15 cm and the values are well reproducible. By measuring at the same position 50 times, the average standard deviation is only 1.6 cm, the highest measured standard deviation is 5.2 cm, the smallest is 1 cm. Additional measurements verified the functionality up to 24 m. The local standard devia-

tion increases with larger distance. The overall standard is below 31 cm from deviation of the measurement error 4 m up to 14 m. 2) Indoor Measurement: Indoor measurements were conducted in a strong multipath environment. The room is small and has partially metallic walls and measurement equipment inside. For a 14-dBi directional antenna, only the MPCs close to the LOS affects the positioning accuracy. For this indoor scenario, 260 positions were measured, and for each position, ten measurements were carried out. The overall standard deviincreases to 26.6 cm. Fig. 14 compares the measured ation distance error against the real distance. The measurements at a single position have a small standard deviation (minimum: 0 cm, average: 5.96 cm, maximum: 122.5 cm); therefore, the measurement error is due to MPCs. The biggest discrepancy occurs at 3.53 m. There, the error is due to a MPC,

WEHRLI et al.: INTEGRATED ACTIVE PULSED REFLECTOR FOR INDOOR LOCAL POSITIONING SYSTEM

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Fig. 14. Plot of the measured distance error d for 2600 indoor measurements with a 14-dBi antenna. The standard deviation for consecutive measurements at the same position is only 5.96 cm. The distance error is dominated by multipath propagation. The solid line is the weighted average of the measurement. With the weighted average, the standard deviation over the whole range decreases from 26.6 to 7.17 cm.

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Fig. 16. Plot of the measured distance error d for 830 indoor measurements with a whip antenna. The standard deviation of all measurements is 74.21 cm. The solid line represents the weighted average of all measurements and results in a standard deviation of 32.88 cm. The dashed red line (in online version) was calculated by randomly selecting only one measurement per distance and then calculating the weighted average. The standard deviation in this case is 33.38 cm.

measurement with directional antenna, and with an omnidirectional 6-dBi antenna are depicted. The outdoor measurement shows clearly distinct peaks unaffected MPCs. For the indoor measurement with a directional antenna, the disturbance due to multipath is already visible. In Fig. 16, the measured distances with the whip antenna are plotted. The standard deviation increases from 26.6 to 74.21 cm, and the repeatability of the measurement at a single position decreases (minimum: 4 cm, mean: 26 cm, maximum: 139 cm). For a few positions of the reflector, the peaks are almost not visible in the baseband spectrum. This indicates that, at this point, the LOS component and the first MPC interfere destructively. This problem can be reduced by improving the edge detection algorithm and filtering, as described below. Fig. 15. Measured spectrum for a distance of 3.83 m for outdoor, indoor with a directional 14-dBi antenna, and indoor with a whip antenna with 6-dBi gain. The measured spectrums agree with the theory. The peaks are well visible and detectable when only a few multipaths exist. In a high multipath environment, the inner edges of the peak can be better identified as the peaks.

which is stronger than the LOS component. Through the additional delay, additional peaks are formed. In Fig. 15, this effect exists for the 6-dBi antenna. Hence, the detection algorithm is sometimes mislead and detects the wrong edge. The overall without the two areas with the worst mulstandard deviation tipath condition is 9.1 cm. This value can be compared to the measurements presented in [17], a similar radar system with a more complex and larger reflector, directional antennas, and additional signal processing in the BS is measured in an industrial environment. The achieved accuracy is 8 cm. In a 2-D localization system, highly directional antennas cannot be used for the reflector. If the mobile reflector uses a whip antenna with 6-dBi antenna gain, more multipaths components are received and the positioning accuracy decreases. In Fig. 15, the spectra of an outdoor measurement, an indoor

D. Edge Detection Algorithm Two different edge detection algorithms were studied. The first studied detects the peak of the spectrum and then searches the edge, which is 3 dB below this peak. This algorithm works well for outdoor measurements with almost no multipath propagation. However, with strong multipaths, it is possible, that the MPC leads to a higher peak than the LOS component, and thus, the wrong 3-dB point is detected. The second detection algorithm searches for the steepest edge in the spectrum by searching the peak in the derivative of the spectrum. This method detects the right edge even for overlapping peaks. The overall standard , as well as the local standard deviation imdeviation proved with the steepest edge detection as depicted in Fig. 17. However, if the peaks are split into two peaks, sometimes the second edge was detected, leading to a large positive measurement error. Hence, the positioning accuracy can improve with further optimization of the peak detection algorithm. Possible improvements include a weighting of the edges so that only the steepest

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Fig. 17. Plot of the measurement error distribution for 2600 indoor measurements for a distance between 1.75–4.3. The dashed curve is the distribution if the point which is 3 dB below the peak is searched. The solid curve illustrates the measurement error distribution for steepest edge detection algorithm.

0

and highest edge is detected or by helping the detection algorithm by giving an estimation of the position before the position is detected. E. Distance Measurement Filtering In indoor environments with strong multipaths, there are places with very bad multipath conditions and this leads to a large measurement error. In a nonstatic environment, the multipath conditions always change. In such an environment, the overall accuracy can be improved by using a filter. The best solution is to use a Kalman filter, which is fitted to the specific application [18]. In this paper, a sliding window averaging is applied for simplicity. The average is weighted by the variance of the data to reduce the influence of the points with large multipath conditions. With this filter, the standard deviation for our indoor measurements with a 14-dBi antenna improved from 26.6 to 7.17 cm. For the 6-dBi antenna, the standard deviation improved from 74.21 to 32.88 cm. Randomly selecting one measurement at each position and filtering leads to a standard deviation of 33.38 cm. Thus, multiple measurements at the same position does not significantly improve the accuracy. F. Comparison Between Simulation and Measurement Results The influence of multipaths on the positioning accuracy is investigated with Simulink simulations. The active reflector is simplified to a loop gain A and a bandpass filter with center freand a factor. The startup of the reflector is corquency rectly modeled, but the phase noise and distortion of the initial phase due to the switching process is neglected. First simulations are conducted using a simple multipath model with only one multipath. With a path delay close to and the same amplitude as the LOS component, the detection error increases to 1 m. The measurement results showed a worst case standard deviation of 1.39 m, which is close to the simulated result. Thus, the large standard deviation in the measurements can already be qualitatively explained by this simple model.

For further simulations, more realistic channel models are used, as proposed by [19]. Channel models for residential LOS, office LOS, industrial LOS, and outdoor LOS exist. The office LOS scenario models small rooms with many reflections, residential LOS has less reflections. The industrial LOS scenario models large rooms, with a few (but strong) multipaths, as is to be expected in a factory hall. The measurement laboratory in Fig. 12 is a rather small room with strong and many multipaths, thus the office LOS scenario is the best suited model. The multipath propagation is added to both directions, from the BS to the reflector and also to the way back. The distance between the reflector and BS is assumed to be 3 m. By simulating 30 different realizations of the same channel model, the resulting standard deviation is 18.27 cm. The measurement results for an indoor environment with a 14-dBi antenna showed a standard deviation of 26.6 cm, which is 8 cm larger than simulated. The simulation does not take the phase noise of both the reflector and BS into account and also does not model nonlinearity in the frequency ramp generation, and thus it is expected that the simulation results are more optimistic than the measurement results. VI. IMPROVEMENTS For 2-D localization, at least three BSs are needed. The more BSs employed, the better the positioning accuracy. A higher space diversity is better than averaging multiple measurements from the same BS because the MPCs at one point do not change significantly between subsequent measurements, but they are different for different BSs. With multiple BSs, an algorithm such as the mass spring model [3] outperforms on geometry-based multilateration. For nonstatic environments, the positioning accuracy can be further improved by applying Kalman filtering [18] instead of a sliding window weighted average. The active pulsed reflector generates a phase coherent output signal to the interrogating signal, and thus a secondary radar synthetic aperture technique could, in principle, also be applied [20], [21]. VII. COMPARISON WITH STATE-OF-THE-ART The comparison of the achieved detection accuracy with the state-of-the art is difficult because most papers present measurement results in an idealized environment and with directional antennas. Reference [17] presents comparable measurments. They achieve the same accuracy, but with a larger and more complex reflector. An UWB system based on an FMCW radar was presented in [10]. This UWB system uses the same principle as [17], except that the output signal is chopped in order to make it UWB compliant. Both systems use a reflector, where the received frequency ramp is downmixed with an internal frequency ramp generated with direct digital synthesizing and a PLL. A digital signal processor (DSP) then calculates the time shift between the incoming frequency ramp and the internal ramp and synchronizes the internal ramp to the incoming. At the next receiving ramp, the reflector transmits the generated ramp. The BS then calculates the time difference between the ramp it has transmitted and the delayed ramp from the mobile station.

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TABLE II COMPARISON OF DIFFERENT REFLECTOR TYPES BASED ON FMCW RADAR

Only outdoor measurements available. With sliding window averaging. Possibility to measure multiple reflectors simultaneously during one measurement.

Table II compares the state-of-the art with this study. The simple and elegant active reflector approach delivers comparable measurement accuracies as the more complex reflectors. Our active reflector is the smallest and the only integrated reflector solution. VIII. CONCLUSION A novel compact active pulsed reflector for a low-complexity FMCW indoor positioning system is integrated in a 0.18- m CMOS technology. The advantages of the novel active reflector approach are manifold. First, no clock synchronization between the BSs is needed. Moreover, the reflectors are power efficient and multiple reflectors can be identified at the same time. The presented localization system was tested indoors and outdoors with directional, and more importantly, with omnidirectional antennas. The measurements proved that the APR even works under harsh multipath conditions with an omnidirectional antenna. The system offers a compact reflector with a positioning accuracy good enough for many applications such as interactive guiding and automatic guided vehicles. The position accuracy can be increased with an improved peak detection algorithm and with further signal processing such as Kalman filtering on a system level. The positioning accuracy will increase and the susceptibility to multipath propagation is reduced by applying adaptive beam steering in the BSs. ACKNOWLEDGMENT The authors would like to thank all project partners in RESOLUTION for their valuable contributions. A special thank to M. Lanz, Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland, for PCB fabrication and excellent bonding. REFERENCES [1] M. Vossiek, L. Wiebking, P. Gulden, J. Wieghardt, C. Hoffmann, and P. Heide, “Wireless local positioning,” IEEE Microw. Mag., vol. 4, no. 4, pp. 77–86, Dec. 2003. [2] C. Benavente-Peces, V. Moracho-Oliva, A. Dominguez-Garcia, and M. Lugilde-Rodriguez, “Global system for location and guidance of disabled people: Indoor and outdoor technologies integration,” in 5th Int. Network. Services Conf., Apr. 2009, pp. 370–375.

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[3] T. Magedanz, F. Schreiner, and H. Ziemek, “Grips generic radio based indoor positioning system,” presented at the Joint 2nd Positioning, Navigat., Commun. Workshop/1st Ultra-Wideband Expert Talk, Hannover, Germany, Mar. 2005. [4] J. Prieto, A. Jimenez, and J. Guevara, “Subcentimeter-accuracy localization through broadband acoustic transducers,” in IEEE Int. Intell. Signal Process. Symp., Oct. 2007, pp. 1–6. [5] M. Hazas and A. Hopper, “Broadband ultrasonic location systems for improved indoor positioning,” IEEE Trans. Mobile Comput., vol. 5, no. 5, pp. 536–547, May 2006. [6] A. Stelzer, K. Pourvoyeur, and A. Fischer, “Concept and application of LPM—A novel 3-D local position measurement system,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 12, pp. 2664–2669, Dec. 2004. [7] L. Wiebking, M. Glanzer, D. Mastela, M. Christmann, and M. Vossiek, “Remote local positioning radar,” in IEEE Radio Wireless Conf., Sep. 2004, pp. 191–194. [8] M. Vossiek and P. Gulden, “The switched injection-locked oscillator: A novel versatile concept for wireless transponder and localization systems,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 4, pp. 859–866, Apr. 2008. [9] A. Fujii, H. Sekiguchi, M. Asai, S. Kurashima, H. Ochiai, and R. Kohno, “Impulse radio UWB positioning system,” in IEEE Radio Wireless Symp. Dig., Jan. 2007, pp. 55–58. [10] B. Waldmann, P. Gulden, M. Vossiek, and R. Weigel, “A pulsed frequency modulated ultra wideband technique for indoor positioning systems,” Freq. J. RF Eng. Telecommun., vol. 62, no. 7, pp. 195–198, 2008. [11] B. Waldmann, R. Weigel, P. Gulden, and M. Vossiek, “Pulsed frequency modulation techniques for high-precision ultra wideband ranging and positioning,” in IEEE Int. Ultra-Wideband Conf., Sep. 2008, vol. 2, pp. 133–136. [12] F. Ellinger, R. Eickhoff, A. Ziroff, J. Hüttner, R. Gierlich, J. Carls, and G. Böck, “European project RESOLUTION—Local positioning systems based on novel FMCW radar,” in Proc. Int. Microw. Optoelectron. Conf., Oct. 2007, pp. 499–502. [13] F. Ellinger, R. Eickhoff, R. Gierlich, J. Hüttner, A. Ziroff, S. Wehrli, T. Ußmüller, J. Carls, V. Subramanian, M. Krcmar, R. Mosshammer, S. Spiegel, D. Doumenis, A. Kounoudes, K. Kurek, Y. Yashchyshyn, C. B. Papadias, P. Tragas, A. Kalis, and E. Avatagelou, “Local positioning for wireless sensor networks,” in Proc. IEEE GLOBECOM, Nov. 2007, pp. 1–6. [14] S. Wehrli, D. Barras, F. Ellinger, and H. Jäckel, “Integrated active pulsed reflector for FMCW radar localization,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2009, pp. 81–84. [15] ETSI, “Electromagnetic compatibility and radio spectrum matters (ERM); short range devices; radio equipment to be used in the 1 GHz to 40 GHz frequency range; part 1: Technical characteristics and test methods,” ETSI, Sophia-Antipolis, France, ETSI Tech. Rep. 300 440-1 v1.3.1, 2001. [16] M. Pichler, A. Stelzer, P. Gulden, and M. Vossiek, “Influence of systematic frequency-sweep non-linearity on object distance estimation in fmcw/fscw radar systems,” in IEEE 33rd Eur. Microw. Conf., Oct. 2003, vol. 3, pp. 1203–1206. [17] S. Roehr, P. Gulden, and M. Vossiek, “Precise distance and velocity measurement for real time locating in multipath environments using a frequency-modulated continuous-wave secondary radar approach,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 10, pp. 2329–2339, Oct. 2008. [18] M. Navarro and M. Najar, “Toa and doa estimation for positioning and tracking in IR-UWB,” in IEEE Int. Ultra-Wideband Conf., Sep. 2007, pp. 574–579. [19] A. Molisch, D. Cassioli, C.-C. Chong, S. Emami, A. Fort, B. Kannan, J. Karedal, J. Kunisch, H. Schantz, K. Siwiak, and M. Win, “A comprehensive standardized model for ultrawideband propagation channels,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3151–3166, Nov. 2006. [20] M. Vossiek, A. Urban, S. Max, and P. Gulden, “Inverse synthetic aperture secondary radar concept for precise wireless positioning,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 2447–2453, Nov. 2007. [21] S. Max, P. Gulden, and M. Vossiek, “Localization of backscatter transponders based on a synthetic aperture secondary radar imaging approach,” in 5th IEEE Sens. Array Multichannel Signal Process. Workshop, Jul. 2008, pp. 437–440.

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Silvan Wehrli (S’07) was born in Zürich, Switzerland, in 1980. He received the M.S. degree in electrical engineering and information technology from the Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland, in 2005, and is currently working toward the Ph.D. degree at ETH Zürich, Zürich, Switzerland. In 2006, he joined the Electronics Laboratory, ETH Zürich,. His research interests are in the field of analog and mixed-signal circuit design with a current focus on RF circuits for local positioning systems.

Roland Gierlich (S’07) was born in Bonn, Germany, in 1982. He received the Diploma degree in electrical engineering from the Aachen University of Technology, Aachen, Germany, in 2006, and is currently working toward the Ph.D. degree with the Wireless Sensors and RF Technology Group, Siemens Corporate Technology, Munich, Germany.. His research is focused on system development and signal processing for industrial local positioning systems.

Jörg Hüttner (S’07) was born in Hof, Germany, in 1980. He received the Diploma degree in electrical engineering from the University of Erlangen, Erlangen, Germany, in 2005, and is currently working toward the Ph.D. degree with the Wireless Sensors and RF Technology Group, Siemens Corporate Technology, Munich, Germany.. His research is focused on the field of UWB—radar and local positioning systems.

David Barras (S’02) was born in Sierre, Switzerland, in 1972. He received the Master degree in electrical engineering (EE) from the Swiss Federal Institute of Technology of Lausanne (EPFL), Lausanne, Switzerland, in 1997, and is currently working toward the Ph.D. degree at the Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland. From 1997 to 2001, he was an RF/Antenna Engineer with a subsidiary of the Swatch Group, Biel, Switzerland. In 2001, he joined ETHZ. His main interests are wireless personal area networks, RF transceivers and the design of silicon-based RF circuits for low-power wireless applications.

Frank Ellinger (S’97–M’01–SM’06) was born in Friedrichshafen, Germany, in 1972. He received the Diploma degree in electrical engineering (EE) from the University of Ulm, Ulm, Germany, and the MBA, Ph.D., and Habilitation degrees from the Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland. Since August 2006, he has been a Full Professor and Head of the Chair for Circuit Design and Network Theory, Dresden University of Technology, Dresden, Germany. From 2001 to 2006, he was Head of the RFIC Design Group, Electronics Laboratory, ETHZ, and Project Leader of the IBM/ETHZ Competence Center for Advanced Silicon Electronics,IBM Research, Rüschlikon, Switzerland.

Heinz Jäckel (M’82) received the Ph.D. degree from ETH Zürich, Zürich, Switzerland, in 1979 Since 1993, he has been a Full Professor with the Electronics Laboratory, Swiss Federal Institute of Technology (ETH Zürich), Zürich, Switzerland, where he heads the High Speed Electronics and Photonics Group. From 1979 to 1993, he was with the IBM Research Division holding scientific and management positions with IBM Rüschlikon, Rüschlikon, Switzerland, and IBM, Yorktown Heights, NY. He has authored or coauthored over 200 publications. He holds 20 patents. His research has included superconducting Josephson computers, GaAs MESFET integrated circuits (ICs) and optoelectronics. His research in electronics with ETH Zürich concerns III/V technology, design of ultrafast InP-HBT transistors for 100-Gb/s ICs and multi-10-GHz RF and digital 40-Gb/s CMOS IC design. In the area of ultra-dense optical ICs (OICs) and Terabit/s (Tb/s) lightwave communication research topics are integrated InP-based mode-locked diode lasers, all-optical switches for Tb/s optical signal processing, and planar InP-based photonic crystals.

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Analysis and Design of Two Low-Power Ultra-Wideband CMOS Low-Noise Amplifiers With Out-Band Rejection Ching-Piao Liang, Pei-Zong Rao, Tian-Jian Huang, and Shyh-Jong Chung, Senior Member, IEEE

Abstract—Two 3–5-GHz low-power ultra-wideband (UWB) low-noise amplifiers (LNAs) with out-band rejection function using 0.18- m CMOS technology are presented. Due to the Federal Communications Commission’s stringent power-emission limitation at the transmitter, the received signal power in the UWB system is smaller than those of the close narrowband interferers such as the IEEE 802.11 a/b/g wireless local area network, and the 1.8-GHz digital cellular service/global system for mobile communications. Therefore, we proposed a wideband input network with out-band rejection capability to suppress the out-band properties for our first UWB LNA. Moreover, a feedback structure and dual-band notch filter with low-power active inductors will further attenuate the out-band interferers without deteriorating the input matching bandwidth in the second UWB LNA. The 55/48/45 dB maximum rejections at 1.8/2.4/5.2 GHz, a power gain of 15 dB, and 3.5-dB minimum noise figure can be measured while consuming a dc power of only 5 mW.

Fig. 1. Spectrum of the UWB system with large interferers. TABLE I NOTCH FILTER SPECIFICATIONS

Index Terms—Complementary metal–oxide semiconductor (CMOS), low-noise amplifier (LNA), out-band rejection, ultrawideband (UWB).

I. INTRODUCTION LTRA-WIDEBAND (UWB) systems realize high data rate in the short-range wireless transmission, which are suitable for integration in various consumer electronics such as PCs, cellular phones, digital cameras, and PDAs. The minimum received power in the UWB channel is 47 and 67 dB, in the worst case, lower than those of the wireless local area network (WLAN) interferer powers at 5.2 and 2.4 GHz, respectively [1]. In addition, a tone is measured at 1.87 GHz in a smart phone currently on the market, and the power level is 35 dB higher than the UWB signal [2]. All of these interferers, as shown in Fig. 1, have a harmful effect on the received UWB signal; they can especially lead to the receiver gain compression and their possible intermodulation products can fall in-band. Although the interferers may further be attenuated by the baseband filter in the receiver, this does not address the problems of the intermodulation distortion and the receiver gain desensitization. In order to achieve reasonable performance for the above considerations, as summarized in Table I, more than 10-dB attenuation over the bandwidth of each interferer with 20-dB peak attenuation

U

Manuscript received January 13, 2009; revised August 30, 2009. First published January 15, 2010; current version published February 12, 2010. This work was supported by the National Science Council of Taiwan under Contract NSC96-2752-E009-003-PAE. The authors are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu 30050, Taiwan (e-mail: sjchung@cm. nctu.edu.tw). Digital Object Identifier 10.1109/TMTT.2009.2037855

is appropriate in the front-end [3]–[7]. On the other hand, a larger attenuation in the front-end can also relax the baseband filter achieving an implementation with the smaller group-delay variations and lower dc power consumption [5]. Recently, a design of multiple-stopband filters is presented for the suppression of interfering signals such as global system for mobile communicatins (GSM), WLAN, and worldwide interoperability for microwave access (WIMAX) in UWB applications [3]. The coupled resonator stopband filter sections with bent resonators were adopted in order to more effectively suppress harmonics and the maximum rejection is about 25 dB at 1.8 GHz. However, this prototype of the filter, which was fabricated on the basis of the standard printed circuit board (PCB) process, will increase the entire UWB system area. Moreover, the multiple receivers with equal-gain combining were employed to eliminate the narrowband interferers received in the two paths and combined out-of-phase to cancel each other by selecting the optimal local oscillator (LO) phase [4]. A maximum 28-dB attenuation of the interferers was measured, but it is unavoidable to increase the system’s complexity. On the other hand, the topologies utilized for wideband amplifiers generally include the distributed configuration [8], [9], resistive shunt-feedback structure [10]–[12], common-gate termination [13]–[15], and LC input network [16], [17]. The distributed amplifiers are attractive for their ultra-wide bandwidth; however, the major drawbacks are the large area and high dc power consumption, which make them unsuitable for many applications. The resistive shunt-feedback and common-gate

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amplifiers can provide good impedance matching and moderate gain while dissipating small amounts of dc power, but without the out-band rejection capability. Recently, a new topology of the broadband amplifier for out-band rejection, which adopted a notch filter circuit with negative-resistance cell embedded, has been reported in [18] and [19]. Inevitably, the extra notch filter circuit made of inductors and cross-coupled transistors will occupy additional chip area and dc power simultaneously. In this paper, we propose two topologies of the 3–5-GHz UWB low-noise amplifier (LNA) with out-of-band suppression by using the CMOS technology. In the first UWB LNA, a new wideband input impedance-matching network, which is based on the LC structure with focus on the improvement of out-of-band rejection capability, is presented. By suitably introducing two additional capacitors in the traditional LC input network, two transmission zeros at 1.8 and 8.5 GHz are generated to achieve the out-band rejection property without suffering from deterioration of the in-band performance. As an improvement of the first approach, the second proposed UWB LNA introduces a capacitive feedback path to the input LC network for further enhancing the rejection capability at the lower band transmission zero (1.8 GHz). A maximum 32-dB improvement is attained due to the usage of a feedback capacitor. A dual-band notch filter made of active inductors, which occupies only a small chip area, is also employed after the LNA core so as to attenuate the WLAN interferers at 2.4 and 5.2 GHz without influencing the noise figure (NF) of the LNA. The proposed active inductors are designed based on the cascode gain-boosting stage with a feedback resistor, which are with low consumption power while maintaining a sufficient value. The introducing of both the feedback capacitor and the dual-band notch filter achieves maximum rejections of about 50 dB on the out-band interferers, which is superior to those presented in the literature [3], [4], [18], [19]. This paper is organized as follows. Sections II and III present the analyses of the first and second UWB LNAs, respectively. The circuit implementation and experimental results are illustrated in Section IV, followed by a conclusion in Section V. In this study, the circuit simulation is performed via Agilent’s Advanced Design System (ADS) software with a TSMC design kit. II. FIRST UWB LNA The first 3–5-GHz CMOS UWB LNA proposed here adopts a source-degenerated cascode configuration, as shown in Fig. 2. An LC input network for wideband operation is utilized with and for increasing the higher and two new capacitors lower out-band rejections, respectively. The load inductor in series with the resistor helps to enhance the gain flatness. with a purely resistive load is emThe buffer transistor ployed for testing purposes.

Fig. 2. Complete schematics of the first UWB LNA with out-band rejection.

where

(2) with

(3) is the 50- source resistance, , and is and the total capacitance between the drain of the transistor is the reflection coefficient at the input port. From ground. (1), it is seen that extra transmission zeros (i.e., ) can be created when the following conditions are satisfied: or

(4)

means that the input impedance of the LNA in which , i.e., the is short circuit, and it occurs as the impedance tank in series with the capacitor impedance of the (see Fig. 2) is equal to zero, where (5) By using (2), (4), and (5), the locations of transmission zeros can be predicted as (6)

A. Power Gain

B. Optimum Out-Band Rejection

The overall gain of the proposed LNA can be easily obtained as follows after a straightforward derivation:

The above ratiocination reveals that the additional capaciand will bring about two transmission zeros to tors ameliorate the out-band performance. However, the out-band rejection characteristics are restricted by the series resistance of the on-chip inductor. As seen from(6), the higher and lower out-band transmission zeros are associated with the inductors and , respectively. These component values influence not

(1)

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Fig. 4. Impedance Z versus frequency with different values of L . The transmission zero ! is kept constant.

Fig. 3. (a) Simulated power gain (S ) and (b) input return loss (1=S ) for different values of L with L = 2:0 nH, C = 0:82 pF, and C = 2:95 pF. is kept constant. The transmission zero !

only the zeros’ frequencies, but also the out-band suppression levels, as shown below. versus frequency with Fig. 3(a) shows the power gain different values of . To begin with, it can be anticipated that the higher frequency out-band elimination efficiency is mainly detertank at the resonant fremined by the impedance of the quency (i.e., the larger impedance, the superior out-band suppresto arrive at sion). Therefore, the first step is to assign a larger larger resonant impedance [20, Ch. 14]. In addition, a preferable power gain in the target frequency range can be procured contemporaneously by using a larger , as shown in Fig. 3(a). However, an overlarge will lead to over abounded input impedance, as shown in Fig. 3(b), thus decreasing the input matching bandwidth of the LNA, which is not desirable for this design. in Fig. 2 produces As is clear from (5), the impedance one series and one parallel resonance from which the lower transmission zero can be created. It is expectable that a smaller at the series resonant frequency will accomplish impedance the superior out-band elimination efficiency. Fig. 4 shows the reand frequency for different lation between the impedance values. As is seen, a smaller results in a smaller . This, in (1.8 GHz), as turn, does cause a deeper suppression level at can be observed from the power gain versus frequency diagram shown in Fig. 5(a). Nevertheless, a drawback that may make the design unsatisfactory is that a diminishing , and thus, a , may reduce the input impedance, and thus, detedeceasing riorate the matching condition, as demonstrated in Fig. 5(b).

Fig. 5. (a) Simulated power gain (S ) and (b) input return loss (1=S ) for different values of L with L = 2:0 nH, L = 0:5 nH, C = 0:17 pF, and C = 0:23 pF. The transmission zero ! is kept constant.

From the above discussion, it should be taken into account and to punctiliously by choosing appropriate values of achieve the tradeoff between the input match and out-band rejection performances. It is interesting to see the influence of the input network on the LNA’s NF. After a straightforward derivation following the procedure in [21], the NF of the circuit shown in Fig. 2 can be obtained as (7)

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Fig. 6. Simulated NF of the first UWB LNA due to the active gain stages and the losses of the input network.

Obviously, the proposed UWB LNA will produce double-peak maxima in noise factor at the two transmission zeros. Consequently, it must be cautious to prevent from worsening the noise property in the desired frequency range when designing the locations of the zeros. Fig. 6 shows the simulation results of the only, NFs due to the active gain stage with the input network, and the total circuit. It can be observed that the dominant noise contributor is the active gain stage. The out-band rejection input network has a minor influence on the total NF as long as the designed transmission zeros are not too close to the in-band. To reduce the noise contribution from the will be chosen active gain stage, the width of the transistor for optimum noise property [22].

Fig. 7. Principle of the interferer-canceling technique with a feedback capacitor C and active dual-band notch filter.

III. SECOND UWB LNA The first UWB LNA improves the higher and lower out-band and . performances by introducing the capacitors However, a tradeoff between the input matching and out-band rejection should be carefully considered so as to make an optimum design. In the second approach, we utilize a feedback and active dual-band notch filter, as shown in capacitor Fig. 7, to attenuate the out-band interferers without deteriorating the input matching bandwidth. A. Effect of the Feedback Capacitor The capacitor will engender the lower band transmission zero such as 1.8 GHz, but the rejection characteristic is restricted by the series resistance of on-chip inductor. For further suppression of the unwanted signal at 1.8 GHz, we introduce a feedback capacitor to the input LC network. As shown is equal to if approin Fig. 7, the voltage gain at node and are selected so that the ratio priate device sizes of equals unity. This makes the signal at node 180 out-of-phase with the input signal . On the other hand, the tank, which provides a parallel resonance at the in-band operation, behaves as an equivalent inductor at 1.8 GHz. Conin series sequently, a suitably designed feedback capacitor with the equivalent inductor can produce a series resonance at 1.8 GHz so that the out-of-phase signal at can be brought back to further cancel the input 1.8-GHz unwanted signal. In short,

Fig. 8. Simulated power gain (S ) of the second UWB LNA with and without the additional capacitor C .

the tank behaves like an open circuit in the in-band, and thus, has little influence on the input impedance, while it may introduce an out-of-phase feedback signal to eliminate the unwanted 1.8-GHz signal. Fig. 8 shows the simulation results of . the power gain with and without the additional capacitor It can be observed and demonstrated that a maximum 32-dB decrease in power gain is attained at 1.8 GHz while maintaining an identical in-band characteristic. B. Dual-Band Notch Filter An on-chip dual-band notch filter is to be placed before the output of the second LNA, as shown in Fig. 7. Here, to avoid the deterioration in NF due to the loss of this notch filter, the filter stage is chosen to place after the gain stage. Fig. 9 illustrates the schematic of the proposed dual-band notch filter. The shown in the figure can be derived as impedance (8)

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Fig. 9. Dual-band notch filter circuit.

Fig. 11. Simulated transmission coefficient S nH. values of Q with L

=5

Fig. 10. Simulated transmission coefficient S values of L .

of the notch filter for different

of the notch filter for different

The notch frequencies of the filter can be obtained by letting the numerator equal null or (9) which results in two transmission zeros

and

satisfying (10) (11)

Also, from (8), the impedance

Fig. 12. (a) Schematic and (b) equivalent circuit of the active inductor with a resistor in the feedback path.

contains a pole at (12)

, , and correspond In this study, we contrive that to 2.4, 5.2, and 3.9 GHz, respectively. We will determine the apfor the dual-band notch propriate values of , , , and filter circuit in order to attenuate the WLAN interferers. It is noted that, after the decision of the positions of zeros and pole, we get three equations, i.e., (10)–(12), for the four filter components, which means that there is still one degree of freedom, let us say , left for the circuit design. Fig. 10 shows the transmission coefficients of the notch filter with different values. increases, the in-band performance from 3.1 As the value of to 4.8 GHz will be improved; this means that we may use a larger inductance to maintain a better property in the target frequency

range. To achieve a 10-dB attenuation in both 2.4- and 5.2-GHz bands without suffering from deterioration of the in-band pernH in the proposed notch filter formance, the value of will be chosen. On the other hand, the quality factor of the inductor also influences the performance of the filter, as can be observed from Fig. 11, where the transmission coefficients of the filter for different inductor values are shown. It is seen that a low quality factor will deteriorate the maximum attenuation of the notch filter. To obtain a 20-dB attenuation of the notch filter for the required specifications, the value of the quality factor must be higher than 100. In general, the negative-resistance cell by using cross-coupled transistors can be employed to ameliorate the value of the on-chip inductor. However, the larger inductors with cross-coupled transistors will concurrently occupy an overlarge chip area and dc power. Therefore, we are inclined to utilize active circuitry to substitute for the integrated passive inductors. C. Low-Power Active Inductors The realization of inductances and is based on the active inductor with a feedback resistor proposed in [23].

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Fig. 13. Complete schematics of the proposed second UWB LNA.

Fig. 12(a) and (b) illustrates the circuit schematic and corresponding equivalent circuit. Through a simple derivation, the components of the equivalent circuit can be obtained as (13) (14) (15) (16) , , and being the gate–source capacitance, with output conductance, and transconductance of the corresponding transistors, respectively. In general, the quality factor of the active inductor can be promoted by decreasing the values of and . From (14), the use of the feedback resistor does by introducing reduce the value of the parallel conductance . In addition, a larger is rethe factor . However, quired, as shown in (15), to get lower value of this will increase the whole dc power consumption in the active is proportional to the current of transistors. inductor since To overcome this drawback, here we modify the active inductor circuit by using the gain-boosting technique [24] to achieve a small amount of dc current while maintaining a sufficient value. This is accomplished by using a cascode stage and to replace the only common-source transistor , resulting in a new active inductor configuration, as shown in the complete schematic of the second UWB LNA in Fig. 13. The voltage gain in (15) can thus be substantially augmented and the value of will be obtained as (17)

Fig. 14. Simulated quality factor of the proposed active inductors L and L .

Therefore, a low-power active inductor is easily accomplished due to the use of the cascode gain-boosting stage with a feedback resistor. Fig. 14 illustrates the simulated factor of the proposed active inductor, which shows that the active inductor factor larger than 1000 at both 2.4- and 5-GHz exhibits a bands. These high- inductors undoubtedly provide a larger attenuation at the interferer frequencies, as can be observed from Fig. 11. Only 0.55-mA (for ) and 0.8-mA (for ) dc currents are required in the second UWB LNA circuit shown in Fig. 13, which are smaller than those in the previous literature [23]–[25]. Moreover, it is obvious in (13) that the inductance of an active inductor is related to the transconductances, and thus, the bias currents, of the transistors. Consequently, the notch frequencies will be effectively tuned by adjusting the bias currents of the and active inductor. The externally controlled bias voltages in Fig. 13 are designed here for adjusting the bias currents to compensate the frequency shift due to the process variation.

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2

Fig. 15. Microphotograph of: (a) the first UWB LNA with 0.78 0.8 mm die area and (b) the second UWB LNA with 0.9 0.85 mm die area.

2

Fig. 18. Measured and simulated power gain (S ) and input return loss (1=S ) of the second UWB LNA.

Fig. 16. Measured and simulated power gain (S ) and input return loss (1=S ) of the first UWB LNA.

Fig. 19. Measured and simulated NF of the second UWB LNA.

Fig. 17. Measured and simulated NF of the first UWB LNA. Fig. 20. Measured IP

For further design, these control voltages and can be utilized together with a feedback mechanism demonstrated in [6] and [7] and [26] and [27] for automatically calibrating the frequency drift of the notch filters. IV. IMPLEMENTATION AND MEASUREMENTS The proposed out-band rejection UWB LNAs are designed and fabricated using the TSMC 0.18- m CMOS process. Moreover, on-wafer probing is performed to measure the characteristics of the LNA circuits.

of the proposed UWB LNAs.

A. First UWB LNA With Capacitors

and

For the first UWB LNA shown in Fig. 2, the width of the m is optimized with 2.5-mW power dissitransistor pation to achieve good noise property. The size of the cascode m is selected to be as large as possible to transistor reduce its voltage headroom requirement, which is conducive to low-voltage operations. In addition, the design of the input network will engender the tradeoff between the input match and out-band rejection characteristics, which can be observed

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TABLE II UWB LNA PERFORMANCE SUMMARY

in Figs. 3 and 5. Hence, it should be chosen cautiously to obtain a reasonably out-band rejection performances in the target input matching bandwidth. In this study, the components values of the nH, nH, nH, input network are pF, pF, pF, and pF . The load consists of the on-chip inductor in series to achieve flat gain over the whole bandwith the resistor width. The components values of the load are nH and . Moreover, the value of in this and the following LNAs is set as 50 to achieve output match for testing purposes. A die microphotograph of the first UWB LNA is shown in Fig. 15(a) and the die area including pads is 0.78 0.8 mm . The first UWB LNA drew a 2.8-mA dc core current from the 0.9-V supply voltage. The -parameters of the designed LNAs were measured using the Agilent 8510C vector network analyzer. The simulated and measured results of power gain and input return loss are depicted in Fig. 16. The measured peak gain is 11.5 dB with a 3-dB bandwidth of 3.4 GHz from 2.8 to 6.2 GHz and the input return loss is better than 8.7 dB in the operation bandwidth. Moreover, due to the addition of the capacand , extra transmission zeros are created and itors measured at 1.7 and 10 GHz. The NF was measured using the Agilent N8975A NF analyzer with Agilent 346C noise source. The simulated and measured NFs at the same bias condition are depicted in Fig. 17. It is seen that the minimum value of the measured NF is equal to 3.8 dB at 3.6 GHz. B. Second UWB LNA With a Feedback Capacitor Active Dual-Band Notch Network

and

For the second UWB LNA shown in Fig. 13, the components values of the active inductors are as follows: m, m, m, m, m, m, m,

m, m, , and k .A die microphotograph of the second LNA is shown in Fig. 15(b) and the die area including pads is 0.9 0.85 mm . The total dc power of the second UWB LNA without an output buffer is 5 mW, drawn from 0.9- and 1.8-V power supply. The simulated and measured results of power gain and input return loss are depicted in Fig. 18. The measured peak gain is 15 dB from 3 to 4.8 GHz and the input return loss is better than 10 dB in the operation frequencies while the maximum rejections at 1.8, 2.4, and 5.2 GHz are 55, 48, and 45 dB, respectively. The simulated and measured NFs are depicted in Fig. 19 and the measured minimum NF is 3.5 dB at 3.9 GHz. The input-referred ) of the proposed LNAs per1-dB compression point ( formed with an Agilent 83640B signal generator and 8564EC spectrum analyzer are depicted in Fig. 20. Minimum values of in the first and second UWB LNAs are the measured 16 and 18 dBm, respectively. The presented LNAs are compared with a recently published CMOS LNA and summarized in Table II. V. CONCLUSION In this paper, we proposed two UWB LNA configurations with out-band rejection ability and demonstrated them by using the TSMC 0.18- m CMOS process. Extra transmission zeros are created in the first UWB LNA due to the use of an LC and for iminput network with additional capacitors proving the higher and lower out-band performances, respectively. Furthermore, using a feedback capacitor and dual-band notch filter made of the low-power active inductors can achieve the maximum rejections of about 50 dB at the out-band interferers, which was demonstrated in the proposed second UWB LNA. The measured results, including the power gain, return loss, and NF, agree quite well with the simulated results.

LIANG et al.: ANALYSIS AND DESIGN OF TWO LOW-POWER UWB CMOS LNAs

ACKNOWLEDGMENT The authors would like to thank the National Chip Implementation Center (CIC), Taiwan, for the help of chip fabrication. REFERENCES [1] S. Lo, I. Sever, S.-P. Ma, P. Jang, A. Zou, C. Arnott, K. Ghatak, A. Schwartz, L. Huynh, V. T. Phan, and T. Nguyen, “A dual-antenna phased-array UWB transceiver in 0.18-m CMOS,” IEEE J. SolidState Circuits, vol. 41, no. 12, pp. 2776–2786, Dec. 2006. [2] T. W. Fischer, B. Kelleci, K. Shi, A. I. Karsilayan, and E. Serpedin, “An analog approach to suppressing in-band narrow-band interference in UWB receivers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 5, pp. 941–950, May 2007. [3] K. Rambabu, M. Y.-W. Chia, K. M. Chan, and J. Bornemann, “Design of multiple-stopband filters for interference suppression in UWB applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 8, pp. 3333–3338, Aug. 2006. [4] I. Sever, S. Lo, S.-P. Ma, P. Jang, A. Zou, C. Arnott, K. Ghatak, A. Schwartz, L. Huynh, and T. Nguyen, “A dual-antenna phase-array ultra-wideband CMOS transceiver,” IEEE Commun. Mag., vol. 44, no. 8, pp. 102–110, Aug. 2006. [5] A. Valdes-Garcia, C. Mishra, F. Bahmani, J. Silva-Martinez, and E. Sánchez-Sinencio, “An 11-band 3–10 GHz receiver in SiGe BiCMOS for multiband OFDM UWB communication,” IEEE J. Solid-State Circuits, vol. 42, no. 4, pp. 935–948, Apr. 2007. [6] A. Bevilacqua, A. Maniero, A. Gerosa, and A. Neviani, “An integrated solution for suppressing WLAN signals in UWB receivers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 8, pp. 1617–1625, Aug. 2007. [7] A. Vallese, A. Bevilacqua, C. Sandner, M. Tiebout, A. Gerosa, and A. Neviani, “Analysis and design of an integrated notch filter for the rejection of interference in UWB systems,” IEEE J. Solid-State Circuits, vol. 44, no. 2, pp. 331–343, Feb. 2009. [8] X. Guan and C. Nguyen, “Low-power-consumption and high-gain CMOS distributed amplifiers using cascade of inductively coupled common-source gain cells for UWB systems,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 8, pp. 3278–3283, Aug. 2006. [9] P. Heydari, “Design and analysis of a performance-optimized CMOS UWB distributed LNA,” IEEE J. Solid-State Circuits, vol. 42, no. 9, pp. 1892–1905, Sep. 2007. [10] Y. Park, C.-H. Lee, J. D. Cressler, and J. Laskar, “The analysis of UWB SiGe HBT LNA for its noise, linearity, and minimum group delay variation,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1687–1697, Apr. 2006. [11] P. Z. Rao, Y. C. Cheng, C. P. Liang, and S. J. Chung, “Cascode feedback amplifier combined with resonant matching for UWB system,” in Proc. Progr. Electromagn. Res. Symp., Mar. 2007, pp. 1040–1043. [12] J. Lee and J. D. Cressler, “Analysis and design of an ultra-wideband low-noise amplifier using resistive feedback in SiGe HBT technology,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp. 1262–1268, Mar. 2006. [13] G. Cusmai, M. Brandolini, P. Rossi, and F. Svelto, “A 0.18-m CMOS selective receiver front-end for UWB applications,” IEEE J. Solid-State Circuits, vol. 41, no. 8, pp. 1764–1771, Aug. 2006. [14] Y. Lu, K. S. Yeo, A. Cabuk, J. Ma, M. A. Do, and Z. Lu, “A novel CMOS low-noise amplifier design for 3.1- to 10.6-GHz ultra-wideband wireless receivers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 8, pp. 1683–1692, Aug. 2006. [15] X. Li, S. Shekhar, and D. J. Allstot, “Gm-boosted common-gate LNA and differential Colpitts VCO/QVCO in 0.18-m CMOS,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2609–2619, Dec. 2005. [16] A. Bevilacqua and A. M. Niknejad, “An ultrawideband CMOS lownoise amplifier for 3.1–10.6-GHz wireless receivers,” IEEE J. SolidState Circuits, vol. 39, no. 12, pp. 2259–2268, Dec. 2004. [17] A. Ismail and A. A. Abidi, “A 3–10-GHz low-noise amplifier with wideband LC-ladder matching network,” IEEE J. Solid-State Circuits, vol. 39, no. 12, pp. 2269–2277, Dec. 2004. [18] A. Bevilacqua, A. Vallese, C. Sandner, M. Tiebout, A. Gerosa, and A. Neviani, “A 0.13-m CMOS LNA with integrated balun and notch filter for 3 to 5 GHz UWB receivers,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2007, pp. 420–421.

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[19] Y. Gao, Y. J. Zheng, and B. L. Ooi, “0.18-m CMOS dual-band UWB LNA with interference rejection,” Electron. Lett., vol. 43, no. 20, pp. 1096–1098, Sep. 2007. [20] B. Razavi, Design of Analog CMOS Integrated Circuits. New York: McGraw-Hill, 2000. [21] D. K. Shaeffer and T. H. Lee, “A 1.5-V, 1.5-GHz CMOS low noise amplifier,” IEEE J. Solid-State Circuits, vol. 32, no. 5, pp. 745–759, May 1997. [22] K.-J. Sun, Z.-M. Tsai, K.-Y. Lin, and H. Wang, “A noise optimization formulation for CMOS low-noise amplifiers with on-chip low-Q inductors,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1554–1560, Apr. 2006. [23] M.-J. Wu, J.-N. Yang, and C.-Y. Lee, “A constant power consumption CMOS LC oscillator using improved high-Q active inductor with wide tuning-range,” in Proc. IEEE 47th Midwest Circuits Syst. Symp., Jul. 2004, vol. 3, pp. 347–350. [24] U. Yodprasit and J. Ngarmnil, “Q-enhancing technique for RF CMOS active inductor,” in Proc. IEEE Int. Symp. Circuits Syst., May 2000, pp. 589–592. [25] H.-H. Hsieh, Y.-T. Liao, and L.-H. Lu, “A compact quadrature hybrid MMIC using CMOS active inductors,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1098–1104, Jun. 2007. [26] T. Das, A. G. C. Washburn, and P. R. Mukund, “Self-calibration of input-match in R.F. front-end circuitry,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 12, pp. 821–825, Dec. 2005. [27] A. Vallese, A. Bevilacqua, C. Sandner, M. Tiebout, A. Gerosa, and A. Neviani, “An analog front-end with integrated notch filter for 3–5 GHz UWB receivers in 0.13 m CMOS,” in Proc. IEEE Eur. Solid-State Circuits Conf., Munich, Germany, Sep. 2007, pp. 139–142. [28] C.-P. Chang and H.-R. Chuang, “0.18-m 3–6 GHz CMOS broad-band LNA for UWB radio,” Electron. Lett., vol. 41, no. 12, pp. 696–698, Jun. 2005. [29] J. Lerdworatawee and W. Namgoong, “Wide-band CMOS cascode low noise amplifier design based on source degeneration topology,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 11, pp. 2327–2334, Nov. 2005. [30] R. Gharpurey, “A broad-band low noise front-end amplifier for ultrawideband in 0.13 m,” IEEE J. Solid-State Circuits, vol. 40, no. 9, pp. 1983–1986, Sep. 2005. [31] M. 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,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1698–1706, Apr. 2006. [32] A. Bevilacqua, C. Sandner, A. Gerosa, and A. Neviani, “A fully integrated differential CMOS LNA for 3–5 GHz ultra-wideband wireless receivers,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 3, pp. 134–136, Mar. 2006. [33] F. Zhang and P. R. Kinget, “Low-power programmable gain CMOS distributed LNA,” IEEE J. Solid-State Circuits, vol. 41, no. 6, pp. 1333–1343, Jun. 2006. [34] Y.-J. E. Chen and Y.-I. Huan, “Development of integrated broad-band CMOS low noise amplifiers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 10, pp. 2120–2127, Oct. 2007. [35] M. l. Jeong, J. N. Lee, and C. S. Lee, “Design of UWB switched gain controlled LNA using 0.18-m CMOS,” Electron. Lett., vol. 44, no. 7, pp. 477–478, Mar. 2008. [36] S.-K. Tang, K.-P. Pun, C.-S. Choy, C.-F. Chan, and K. N. Leung, “A fully differential band-selective low-noise amplifier for MB-OFDM UWB receivers,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 7, pp. 653–657, Jul. 2008.

Ching-Piao Liang was born in Changhwa, Taiwan, in 1980. He received the B.S. and M.S. degrees in communication engineering from Yuan Ze University, Taoyuan, Taiwan, in 2003 and 2005, respectively, and is currently working toward the Ph.D. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan. His primary research interests include RF integrated circuits and monolithic microwave integrated circuits.

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Pei-Zong Rao was born in Kaohsiung, Taiwan, in 1980. He received the B.S. degree in physics from National Kaohsiung Normal University, Kaohsiung, Taiwan, in 2002, and is currently working toward the Ph.D. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan. His research interests include RF integrated circuits, multiband wireless systems, and frequency synthesizer designs.

Tian-Jian Huang was born in Taichung, Taiwan, in 1983. He received the B.S. and M.S. degrees in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, in 2006 and 2008, respectively. His research focuses on RF integrated circuit design.

Shyh-Jong Chung (M’92–SM’06) was born in Taipei, Taiwan. He received the B.S.E.E. and Ph.D. degrees from National Taiwan University, Taipei, Taiwan, in 1984 and 1988, respectively. Since 1988, he has been with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, where he is currently a Professor and serves as the Director of the Institute of Communication Engineering. From September 1995 to August 1996, he was a Visiting Scholar with the Department of Electrical Engineering, Texas, A&M University, College Station. His areas of interest include the design and applications of active and passive planar antennas, low-temperature co-fired ceramic (LTCC)-based RF components and modules, packaging effects of microwave circuits, vehicle collision warning radars, and communications in intelligent transportation systems (ITSs). Dr. Chung was the treasurer of the IEEE Taipei Section (2001–2003) and the chairman of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Taipei Chapter (2005–2007). He was the recipient of the 2005 Outstanding Electrical Engineering Professor Award of the Chinese Institute of Electrical Engineering and the 2005 Teaching Excellence Award of National Chiao Tung University.

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Analysis and Design of a CMOS UWB LNA With Dual-RLC -Branch Wideband Input Matching Network Yo-Sheng Lin, Senior Member, IEEE, Chang-Zhi Chen, Hong-Yu Yang, Chi-Chen Chen, Jen-How Lee, Guo-Wei Huang, Member, IEEE, and Shey-Shi Lu, Senior Member, IEEE

Abstract—A wideband low-noise amplifier (LNA) based on the current-reused cascade configuration is proposed. The wideband input-impedance matching was achieved by taking advantage of the resistive shunt–shunt feedback in conjunction with a parallel LC load to make the input network equivalent to two parallel -branches, i.e., a second-order wideband bandpass filter. Besides, both the inductive series- and shunt-peaking techniques are used for bandwidth extension. Theoretical analysis shows that both the frequency response of input matching and noise figure (NF) can be described by second-order functions with quality factors as parameters. The CMOS ultra-wideband LNA dissipates 10.34-mW power and achieves 11 below 8.6 dB, 22 below 10 dB, 12 below 26 dB, flat 21 of 12.26 0.63 dB, and flat 0.5 dB over the 3.1–10.6-GHz band of interest. BeNF of 4.24 sides, good phase linearity property (group-delay variation is only 22 ps across the whole band) is also achieved. The analytical, simulated, and measured results agree well with one another. Index Terms—CMOS, inductive peaking, LC load, low-noise amplifier (LNA), quality factor ( factor), resistive feedback, ultrawideband (UWB).

I. INTRODUCTION

R

ECENTLY, RF-CMOS processes have become more and more popular for RF integrated circuit (RFIC) design because it is cost effective and compatible with the silicon-based system-on-a-chip (SOC) technology [1]–[11]. In ultra-wideband (UWB) receiver front-end design, the UWB low-noise amplifier (LNA) is a critical block that receives small signals from the whole UWB band (3.1–10.6 GHz) and amplifies them with a good signal-to-noise ratio property. In , good input and output addition, high and flat power gain Manuscript received October 03, 2008; revised July 22, 2009. First published January 22, 2010; current version published February 12, 2010. This work was supported by the National Science Council, R.O.C. under Contracts NSC97-2221-E-260-009-MY3, NSC97-2221-E-260-010-MY3, and NSC98-2221-E-002-155-MY2. Y.-S. Lin, C.-Z. Chen, C.-C. Chen, and J.-H. Lee are with the Department of Electrical Engineering, National Chi Nan University, 545 Puli, Taiwan (e-mail: [email protected]). H.-Y. Yang was with the Department of Electrical Engineering, National Chi Nan University, 545 Puli, Taiwan. He is now with VIA Technologies Inc., Sindian 231, Taiwan. G.-W. Huang is with National Nano Device Laboratories, Hsinchu 300, Taiwan. S.-S. Lu is with the Graduate Institute of Electronics Engineering and Department of Electrical Engineering, National Taiwan University, 106 Taipei, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037863

and ), and low and flat impedance matching (i.e., low noise figure (NF) performances across the whole UWB band are required. Recently, several CMOS UWB LNAs have been reported [1]–[9]. For a UWB LNA designed for orthogonal frequency-division multiplexing (OFDM) systems [1], power linearity is a tight requirement for suppressing adjacent channel interferences, while it is relaxed in the UWB pulse-radio system [10], [11]. In order to keep the shape of the pulse while receiving radio signals from an antenna, good phase linearity (i.e., small group-delay variation) is required instead. Many wideband input-matching networks for UWB LNAs have been proposed lately. For instance, a wideband input matching with small power dissipation and die size can be realized by the common-gate input topology [4]. Nevertheless, it was found that single-stage common-gate amplifier cannot provide sufficient power gain, and hence, extra stages are required to boost the gain, resulting in ripples in the passband due to the nonbroadband inter-stage matching. Besides, in [1], a cascode CMOS LNA with a bandpass response at the input for wideband impedance matching was reported. The three-order Chebyshev-filter-based topology incorporated the input impedance of the conventional narrowband cascode amplifier as a part (i.e., one order) of the filter. However, the adoption of the filter at the input required a number of addiin [1]), tional reactive elements (four, i.e., , , , and which inevitably resulted in larger die size and higher NF (due to the finite quality factor ( factor) of the reactive elements) when implemented on-chip. To avoid the drawbacks of the filter-based input matching network, in this study, based on the current-reused cascade configuration, we propose a UWB -branch input-matching LNA with an “internal” dualnetwork, which is suitable for UWB pulse-radio system applications. The wideband input matching was achieved by taking advantage of the resistive shunt–shunt feedback and the parallel LC load to make the input network equivalent to -branches in parallel, i.e., a second-order wideband two bandpass filter. In this way, below 17.5 dB and small group-delay variation of 16.7 ps over the 3.1–10.6-GHz band of interest, and state-of-the-art NF of 2.5 dB at 10.5 GHz were achieved for a test 0.13- m CMOS UWB LNA [12]. Besides, both the inductive series- and parallel-peaking techniques were used for bandwidth extension. It is noteworthy that though low NF of 2.5 dB (at 10.5 GHz) was obtained for the test 0.13- m CMOS UWB LNA in [12], over the 3.1–10.6-GHz band of interest, the NF variation of

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TABLE I SUMMARY OF THE IMPLEMENTED CMOS WIDEBAND LNAs IN THIS STUDY, AND THE RECENTLY REPORTED STATE-OF-THE-ART CMOS WIDEBAND LNAs

1.03 dB (see Table I) is not good enough. In contrast to [12], is added to in this study, a source-degeneration inductor the input transistor to achieve wideband flat NF performance. For example, over the 3.1–10.6-GHz band, the NF variation is only 0.5 dB for LNA-2 (see Table I). In a word, the LNA topology in this study is not the same as that in [12]. Besides, the idea proposed in this study is a method of the preliminary design of an LNA with simultaneous low and flat NF, high , and good characteristics over the band of inand flat terest using hand analysis. This idea is based on our theoretical analysis that both the frequency responses of input matching and NF can be described by second-order functions with factors as parameters. This paper is organized as follows. The input impedance matching and power gain along with the frequency responses of NF are derived in Section II. The proposed UWB LNA is described in Section III. In Section IV, we discuss the measurement results of the proposed UWB LNAs and make comparisons with previous studies. Section V then presents the conclusion. II. PRINCIPLE OF CIRCUIT DESIGN A. UWB Input Impedance Matching Fig. 1(a) and (b) shows the schematic and corresponding small-signal equivalent circuit of an amplifier with the proposed resistive shunt–shunt feedback in conjunction with a parallel of the amplifier can be expressed as follows: LC load. (1)

Fig. 1. (a) Schematic and (b) small-signal equivalent circuit of an amplifier with the proposed resistive shunt–shunt feedback in conjunction with a parallel LC load.

in which the input impedance

can be represented as follows:

(2)

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is the input impedance of the LNA if the effect of the is negligible, and resistive feedback is the current-gain cutoff frequency of transistor . is the impedance looking into the shunt–shunt feedback, and is given by

(3)

Suppose

and hold over the low-frequency part of the frequency band of interest, which is usually the case. Equation (3) can then be simplified as follows: (4) From (2) and (4), we can define

and

as follows: (5) (6)

and Clearly, if at frequencies around

are not too close, we can show that

(7) while at frequencies around (8) Therefore, at frequencies around be expressed as follows:

,

Fig. 2. Calculated S versus frequency characteristics of the amplifier in Fig. 1(a): (a) based on (2), (7), and (8) and (b) based on (2) and under various values of R .

That is, a decrease of [see Fig. 2(b)] or an increase of results in an increase of . Besides, at frequencies , of the amplifier can be expressed as follows: around

of the amplifier can (12) in which (9)

in which (10) Note that good input impedance matching at frequencies is assumed for simplicity, i.e., . around and represent the pole frequency and pole factor, respectively, of the input network of the amplifier at frequencies . Now it is clear that at frequencies around , around is a standard notch function with lower frequency-band 10-dB bandwidth as follows [13], [14]: (11)

(13) Note that good input impedance matching at frequencies around is also assumed for simplicity, i.e., . and represent the pole frequency and pole factor, respectively, of the input network of the amplifier at frequencies . Now it is clear that at frequencies around , around is a standard notch function with upper frequency-band 10-dB bandwidth as follows: (14) That is, a decrease of or results in an increase of . The overall 10-dB bandwidth of the amplifier can be roughly regarded as the union of and if they overlap.

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, nH, nH, fF, mS, nH, and fF. The results is 25.54 dB at 3.7 GHz, and decreases show the peak monotonously with the increase of frequency over the frequency range of 3.7–13 GHz. Over the 3.1–10.6-GHz band of of 21.54 2.51 dB is not flat interest, the corresponding and to avoid the loading effect, a enough. To flatten the common-source (CS) stage with inductive load can be added as the buffer stage of the amplifier, , which will be discussed in more detail later. To take into account the effect of the buffer expression in (15) should be modified as follows: stage, the (16) Fig. 3. Calculated S versus frequency characteristics of the amplifiers in Fig. 1(a) both with and without a buffer stage.

Fig. 2(a) shows the calculated versus frequency characteristics of the amplifier in Fig. 1(a) based on (2), (7), and (8). , nH, The parameters used are as follows: nH, fF, mS, , nH, and fF. As can be seen, the calcuby (2) is below 10 dB over the frequency range of lated 1.7–20.4 GHz. Besides, the combination of the calculated by (7) (for frequencies around ) and (8) (for frequencies ) is close to the calculated one by (2). This justifies around analysis. the above-mentioned versus frequency Fig. 2(b) shows the calculated characteristics of the amplifier under various values of . The frequency range corresponding to smaller than 10 dB is 1.1–25.1, 1.7–20.4, and 2.1–19.2 GHz for and , respectively. That is, the input , matching bandwidth decreases with the increases of value is preferred to consistent with (11). Since a higher achieve a lower NF, there is a tradeoff between input matching bandwidth and NF. B.

Frequency Response

For the amplifier shown in Fig. 1(a), its , which is equal in a 50- system to two times the voltage gain (i.e., ) [14] can be represented as follows:

where

(17) What is also shown in Fig. 3 are the calculated versus frequency characteristics of the buffer stage and the amplifier in Fig. 1(a) with the buffer stage (i.e., the one with legend “1stStage Buffer-Stage”). The parameters of the buffer stage are fF ( pF since fF), as follows: mS, pH, and . As can be seen, a flatter of 22.05 1.53 dB over the 3.1–10.6-GHz band of interest is achieved after the buffer stage is added. C. NF Frequency Response In wideband applications, a flat and low-NF frequency response is also required in addition to wideband input impedance matching and a flat and high-gain frequency response. Traditional low-noise design based on an optimum NF at each frequency is not suitable for wideband design because the resultant NF frequency response is not flat. In order to achieve a flat NF response, the factors that control the shape of the NF frequency response must be derived first. In this section, the NF response of the circuit shown in Fig. 1(a) is analyzed. Fig. 4 shows the equivalent circuit of the LNA in Fig. 1(a) for its NF calculation. can be exThe noise factor of the LNA pressed as follows [15]:

(15) where and [see (5) and (10)] represent the pole frequency and factor, respectively, of the input . network of the amplifier at frequencies around is the equivalent transconductance of the amplifier. Note that and over the 3.1–10.6-GHz band of interest is assumed, which is usually the case. Fig. 3 shows the calculated versus frequency characteristics (i.e., the one with legend “1st-Stage”) of an amplifier with the following parameters:

(18)

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Fig. 4. Equivalent circuit of Fig. 1(a) for noise calculation.

where (19) (20) (21) (22) , , and represent the corresponding noise factor and drain noise to the LNA, recontributions of gate noise spectively. Note that over the 3.1–10.6-GHz band of interest is assumed for simto zero-bias drain conductance ) plicity. (the ratio of of 0.85, of 4.1, and of 2.21 are adopted for the following NF calculation [15], [16]. Since the NF [see (18)] has been put in the form of a second-order function of , its frequency response and . is well known and controlled by factors , , Fig. 5(a) shows the characteristics of calculated and versus frequency of the wideband amplifier with mS, fF, the following parameters: , nH, and nH. over the The result shows that the NF was dominated by 3.1–10.6-GHz band of interest. The is equal to 1.094 according to (22), which means the corresponding NF frequency response is slightly under-damped [see Fig. 5(b)]. Fig. 5(b) shows the characteristics of calculated NF versus . Note frequency of the amplifier under various values of is changed by varying the value of , that the value of , and while keeping the same of 11.9 GHz of 51.1 GHz. Some wideband LNAs [7], [9], [17] in and the literature exhibited flat gain. However, the corresponding NF was response was not flat enough because an over-damped chosen. That is, their NF responses were similar to the two overand ) in Fig. 5(b). damped curves ( In the case of , the flattest NF response of the LNA

Fig. 5. (a) Calculated f , f , and f versus frequency characteristics. (b) Calculated NF versus frequency characteristics under various values of Q of the proposed UWB LNA.

was achieved. In this study, of 1.094 was adopted, which corresponded to a slight under-damped, but nearly maximally flat NF response. We must stress that this is the main strength of our proposed circuit, as shown in Fig. 1(a) [or Fig. 6(a)]: both the gain and NF response can be tuned to approximate the maximally flat condition simultaneously. III. PROPOSED UWB LNA Recently, the current-reused cascade amplifier has become one of the most popular LNA topologies due to its merits such as low power consumption, high gain, and high reverse isolation [18]. Therefore, in this study, based on the traditional narrowband current-reused cascade amplifier, we propose a wideband CMOS LNA architecture, as shown in Fig. 6(a). Since the dc current of the output stage of the LNA was reused in the input stage, no additional driving current was needed for the and of the input stage. Moreover, the inductive load input and the output stage have made a low of 1.8 V (or even 1.0 V) possible since the voltage drop across them was negligible. This is the way to achieve low power consumption. The output of each stage was equivalently loaded with a lowparallel resonant circuit to maximize the 3-dB bandwidth of the gain. Based on the methodology in [15] and the theory in Section II, simultaneous input impedance and NF matching over the 3.1–10.6-GHz band of interest was achieved by appro, , , and , and priately selecting the values of

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Fig. 7. Simulated S versus frequency characteristics under various values of: (a) L and (b) L of the proposed UWB LNA. Fig. 6. (a) Schematic, (b) complete small-signal equivalent circuit, and (c) simplified small-signal equivalent circuit (for analyzing S ) of the proposed UWB LNA.

the size and bias of the transistors and , i.e., , , , and . As a result, the LNA exhibited wideband input , small group-delay variation, and matching, flat and high low and flat NF at the same time. The standard 1P6M 0.18- m CMOS process (with substrate cm) provided by the commercial foundry resistivity of 8–12 Taiwan Semiconductor Manufacturing Company (TSMC) was adopted to design the 3.1–10.6-GHz CMOS UWB LNAs. To and on the study the effect of the peaking inductors performance of the LNA, one LNA (LNA-1) with smaller of 0.813 nH and of 0.796 nH, and the other (LNA-2) with larger of 1.03 nH and of 0.816 nH were designed. The other component parameters of the two LNAs are the same nH, pH, and are listed as follows: nH, , k , k , , fF, pF, and pF. All transistors ( and ) had the same gate length of 0.18 m. The gatewidth per finger/finger numbers of and were 3 m/40 and 5.9 m/22, respectively. The interconnection lines as well as the inductors were placed on the 2.34- m-thick topmost metal to minimize the resistive loss. At and , the bias conditions of of and are 47 and 48 GHz, respectively, and

of and were 60 and 62 GHz, respectively. The good and performances of the transistors indicate that it is possible to apply this CMOS process on the implementation of a high-performance 3.1–10.6-GHz CMOS UWB LNA. Fig. 7(a) versus frequency characteristics under shows the simulated various values of . As can be seen, the high-frequency valley increased with the decrease of , which is consistent versus frequency with (6). Fig. 7(b) shows the simulated . As can be seen, the characteristics under various values of increased with the decrease of low-frequency valley [i.e., in Fig. 1(a) or Fig. 6(c)], which is consistent with (5). IV. RESULTS AND DISCUSSIONS Fig. 8(a) and (b) shows the chip micrographs of LNA-1 and LNA-2, respectively. The chip areas of LNA-1 and LNA-2 were only 0.75 0.753 mm and 0.715 0.75 mm , respectively, excluding the test pads. On-wafer measurement was performed by an Agilent Technologies’ vector network analyzer. The LNAs were biased at 5.74 mA and 1.8 V. That is to say, the LNA only consumed 10.34-mW power. Fig. 9(a) shows the versus frequency characteristics of measured and simulated was lower than 10 the LNAs. For LNA-1, the measured dB for frequencies of 2.6–11.9 GHz, close to the simulated result of 2.7–11.4 GHz. Besides, for LNA-2, the measured was lower than 10 dB for frequencies of 2.6–10.4 GHz, close to the simulated result of 2.6–10.9 GHz. Fig. 9(b) shows the versus frequency characteristics measured and simulated

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Fig. 8. Chip micrographs of: (a) LNA-1 and (b) LNA-2.

of the LNAs. For LNA-1, the measured was lower than 10 dB for frequencies of 1–11.3 GHz, close to the simulated result of 1–11.6 GHz. Besides, for LNA-2, the measured was lower than 10 dB for frequencies of 1–10.6 GHz, close to the simulated result of 1–10.8 GHz. and versus freFig. 9(c) shows the measured quency characteristics of the LNAs. As can be seen, flat of 12.24 0.62 dB was achieved for LNA-2 over the 3.1–10.6-GHz band of interest, which was flatter than that 2.3 dB) of LNA-1. This is mainly because a larger (11.2 was adopted for LNA-2. Beseries-peaking inductor sides, good reverse isolation of 27.7 41.9 and 26 44.4 dB were achieved for LNA-1 and LNA-2, respectively, over the 3.1–10.6-GHz band of interest. Fig. 10 shows the measured group delay versus frequency characteristics of LNA-2. Good phase linearity property was achieved, i.e., group-delay variation was only 22 ps across the whole band. By definition, group delay is the derivation of the . Thus, any resonance in the signal path (or pole phase of ) will contribute distortion to the group delay [11]. As a in result, the small group-delay variation characteristic of the proposed UWB LNA architecture is attributed to the pushing of the high-frequency poles outside of the 3.1–10.6-GHz band of inand . terest by the peaking inductor (or ) It has been shown that stability factor alone is necessary and sufficient for a circuit to be unconditionversus ally stable [19]. Fig. 11 shows the measured and

Fig. 9. Measured and simulated: (a) S and (b) (c) Measured S and S of LNA-1 and LNA-2.

S

of LNA-1 and LNA-2.

Fig. 10. Measured and simulated group delay versus frequency characteristics of LNA-2.

frequency characteristics of the LNAs. Clearly, the LNAs were unconditionally stable over the 3.1–10.6-GHz band of interest.

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Fig. 11. Measured and simulated stability factors versus frequency characteristics of LNA-1 and LNA-2.

Fig. 12. Measured, simulated, and calculated NF versus frequency characteristics of LNA-1 and LNA-2.

Fig. 13. Measured P

and IIP3 of LNA-2.

The NF characteristics of the LNAs were measured with an ATN NP-5 system. Fig. 12 shows the measured, simulated, and calculated NF versus frequency characteristics of LNA-1 and LNA-2. As can be seen, over the 3.1–10.6-GHz band of interest, the measured results (3.61–4.68 dB for LNA-1 and 3.74–4.74 dB for LNA-2) were consistent with the simulated (3.44–4.31 dB) and calculated (3.75–4.54 dB) results. Fig. 13 and shows the measured 1-dB compression point input third-order inter-modulation point (IIP3) at 6 GHz of of 22 dBm and IIP3 of 11 dBm were the LNA-2. achieved.

Table I is a summary of the implemented 3.1–10.6-GHz CMOS UWB LNAs in this study, and the recently reported state-of-the-art CMOS UWB LNAs. Note that the standard 1P8M 0.13- m CMOS process provided by the commercial foundry TSMC has also been adopted to design and implement a 3.1–10.6-GHz UWB LNA with similar architecture [12], i.e., LNA-3 in Table I. As can be seen, compared with other , reasonable , studies, LNA-2 exhibits high and flat good phase linearity, low and flat NF, and has small chip areas and power consumption. This result shows that our proposed LNA architecture is suitable for UWB pulse-radio system applications. Besides, in contrast to LNA-2, which exhibits a maximum flat response, LNA-1 is intentionally designed with and , i.e., a slightly over-damped relatively smaller of LNA-1 is inferior response. Thus, the 3-dB bandwidth of to those of most of the other studies. In comparison, LNA-2 and , is intentionally designed with relatively larger i.e., a maximum flat response. Thus, the 3-dB bandwidth of of LNA-2 is comparable or superior to the other studies. of LNA-2 is not superior Furthermore, the reason why to those of most of the other studies is follows: the measured of LNA-2 conforms well to the simulated result over the , i.e., 3.1–10.6-GHz band, except for frequencies around the high-frequency dip. Since the simulated of LNA-2 is better than 12 dB over the 3.1–10.6-GHz band, i.e., superior to those of most of the other studies, this suggests the measured should be as good as the simulated one after the accuracy of the ADS model (provided by the foundry) is improved. A comparison between the -parameters generated from the ADS model and the measured -parameters from the inductors testkey found that the practical equivalent inductance of of LNA-2 is higher than that obtained from the ADS model. should be lower than that of the That is, the measured simulated one [see (5) and Fig. 6(c)], and the measured should be larger than that of the simulated one [see (10)]. This, in turn, results in a smaller measured than the simulated one. This is consistent with the measured and simulated can be easily results in Fig. 9(a). Moreover, a large achieved based on the methodology introduced in Section II. of 18.8 GHz (from 1.67 to 20.47 GHz) For example, is achieved for the case in Fig. 2(a). This means, in a real case, instead of improving the accuracy of the ADS model, a larger can be designed to increase the margin of . V. CONCLUSION In this study, we have proposed a wideband LNA architecture, in which the wideband input-impedance matching was achieved by taking advantage of the resistive shunt–shunt feedback in conjunction with a parallel LC load to make the input network -branches. Due to the unique feature equivalent to two of the proposed circuit topology, simultaneous wideband input impedance matching, and low and flat NF can be achieved by factors ( , , and ) of the input controlling the stage of the wideband LNA. Besides, high and flat gain response can be obtained by a series- and a shunt-peaking inductor. The measured results conform to the analytical and simulated results well. Furthermore, compared with other CMOS-based wideband LNAs in the literature, our LNA-2 exhibits high and flat

LIN et al.: ANALYSIS AND DESIGN OF CMOS UWB LNA

, good phase linearity and NF, and has a small chip area and power consumption. The results indicate that the proposed LNA topology is very suitable for UWB pulse-radio system applications. ACKNOWLEDGMENT The authors are very grateful for the support from the National Chip Implementation Center (CIC), Taiwan, for chip fabrication. REFERENCES [1] A. Bevilacqua and A. M. Niknejad, “An ultrawideband CMOS lownoise amplifier for 3.1–10.6-GHz wireless receivers,” IEEE J. SolidState Circuits, vol. 39, no. 12, pp. 2259–2268, Dec. 2004. [2] C. F. Liao and S. I. Liu, “A broadband noise-canceling CMOS LNA for 3.1–10.6-GHz UWB receiver,” IEEE J. Solid-State Circuits, vol. 42, no. 2, pp. 329–339, Feb. 2007. [3] C. C. Chen, Z. Y. Huang, C. C. Huang, and N. K. Lu, “Time-constant compensated LNA for ultra-wideband receiver,” in Proc. Int. Intell. Signal Process. Commun. Syst. Symp., 2005, pp. 13–16. [4] Y. Lu, K. S. Yeo, A. Cabuk, J. Ma, M. A. Do, and Z. Lu, “A novel CMOS low noise amplifier design for 3.1-to-10.6-GHz ultra-wide-band wireless receiver,” IEEE Trans. Circuits Syst., I: Reg. Papers, vol. 53, no. 8, pp. 1683–1692, Aug. 2006. [5] Y. J. Lin, S. S. H. Hsu, J. D. Jin, and C. Y. Chan, “A 3.1–10.6 GHz ultrawideband CMOS low noise amplifier with current-reused technique,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 3, pp. 232–234, Mar. 2007. [6] H. Xie, X. Wang, A. Wang, Z. Wang, C. Zhang, and B. Zhao, “A fullyintegrated low-power 3.1–10.6 GHz UWB LNA in 0.18 m CMOS,” in IEEE Radio Wireless Symp., 2007, pp. 197–200. [7] K. H. Chen, J. H. Lu, B. J. Chen, and S. I. Liu, “An ultra-wide-band 0.4–10-GHz LNA in 0.18- m CMOS,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 3, pp. 217–221, Mar. 2007. [8] C. C. Chen, J. H. Lee, Y. S. Lin, C. Z. Chen, G. W. Huang, and S. AA-mesh inductors for CMOS UWB S. Lu, “Low noise-figure P RFIC applications,” IEEE Trans. Electron Devices, vol. 55, no. 12, pp. 3542–3548, Dec. 2007. [9] Q. Li and Y. P. Zhang, “A 1.5 V 2–9.6 GHz inductorless low-noise amplifier in 0.13 m CMOS,” IEEE Trans. Mircrow. Theory Tech., vol. 55, no. 10, pp. 2015–2023, Oct. 2007. [10] Y. Park, C. H. Lee, J. D. Cressler, and J. Laskar, “Theoretical analysis of a low dispersion SiGe LNA for ultra-wideband applications,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 9, pp. 517–519, Sep. 2006. [11] Y. Park, C. H. Lee, J. D. Cressler, and J. Laskar, “The analysis of UWB SiGe HBT LNA for its noise, linearity, and minimum group delay variation,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1687–1697, Apr. 2006. [12] H. Y. Yang, Y. S. Lin, and C. C. Chen, “2.5 dB NF 3.1–10.6 GHz CMOS UWB LNA with small group-delay variation,” IET Electron. Lett., vol. 44, no. 8, pp. 528–529, 2008. [13] A. S. Sedra and K. C. Smith, Microelectronic Circuits, 5th ed. New York: Oxford Univ. Press, 2004, pp. 840, 1103–1105. [14] T. Wang, H. C. Chen, H. W. Chiu, Y. S. Lin, G. W. Huang, and S. S. Lu, “Micromachined CMOS LNA and VCO by CMOS-compatible ICP deep trench technology,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 580–588, Feb. 2006. [15] H. W. Chiu, S. S. Lu, and Y. S. Lin, “A 2.17 dB NF, 5 GHz band monolithic CMOS LNA with 10 mW DC power consumption,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 813–824, Mar. 2005. [16] P. Heydari, “Design and analysis of performance-optimized CMOS UWB distributed LNA,” IEEE J. Solid-State Circuits, vol. 42, no. 9, pp. 1892–1905, Sep. 2007. [17] C. W. Kim, M. S. Jung, and S. G. Lee, “Ultra-wideband CMOS low noise amplifier,” Electron. Lett., vol. 41, no. 7, pp. 384–385, Mar. 2005. [18] C. Y. Cha and S. G. Lee, “A low power, high gain LNA topology,” in IEEE Int. Microw. Millimeter Wave Technol. Conf., 2005, pp. 420–423. [19] M. L. Edwards and J. H. Sinsky, “A new criterion for linear 2-port stability using geometrically derived parameters,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 12, pp. 2303–2311, Dec. 1992.

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Yo-Sheng Lin (M’02–SM’06) was born in Puli, Taiwan, on Oct. 10, 1969. He received the Ph.D. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1997. His doctoral thesis concerned the fabrication and study of GaInP–InGaAs–GaAs doped-channel field-effect-transistors and their applications to monolithic microwave integrated circuits (MMICs). In 1997, he joined the Taiwan Semiconductor Manufacturing Company (TSMC), as a Principle Engineer for 0.35/0.32-m DRAM and 0.25-m embedded DRAM technology development in the Integration Department, Fab-IV. Since 2000, he has been responsible for 0.18/0.15/0.13-m CMOS low-power device technology development in the Department of Device Technology and Modeling, Research and Development, and in 2001 became a Technical Manager. In August 2001, he joined the Department of Electrical Engineering, National Chi Nan University (NCNU), Puli, Taiwan, where he is currently a Professor. From June to September, 2004, he was a Visiting Researcher with the High-Speed Electronics Research Department, Bell Laboratories, Lucent Technologies, Murray Hill, NJ. From February 2007 to January 2008, he was a Visiting Professor with the Department of Electrical Engineering, Stanford University, Stanford, CA. His current research interests are in the areas of characterization and modeling of RF active and passive devices (especially 30–100-GHz interconnections, inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits), and RFICs/monolithic microwave integrated circuits (MMICs). Dr. Lin was a recipient of the Excellent Research Award from NCNU in 2006, and was a recipient of the Outstanding Young EE Engineer Award from Chinese Institute of Electrical Engineering in 2007.

Chang-Zhi Chen was born in Beigang, Yunlin, Taiwan, on August 27, 1973. He received the B.S. degree in electronic engineering from Southern Taiwan University, Tainan County, Taiwan, in 2001, the Master degree in electrical engineering from National Chi Nan University, Puli, Taiwan, in 2003, and is currently working toward the Ph.D. degree at National Chi Nan University. His Master’s thesis concerned the study of phase-locked loops and frequency synthesizers. His current research is focused on the design of RF inductors, varactors, and related RFICs topics for wireless communication. Mr. Chen is a member of Phi Tau Phi.

Hung-Yu Yang was born in Taipei, Taiwan, on March 22, 1984. He received B.S. degree in communications engineering from Feng Chia University, Taichung, Taiwan, in 2006, and the M.S. degree in electrical engineering from National Chi Nan University, Puli, Taiwan, in 2008. His Master’s thesis concerned RF and millimeter-wave LNAs. Since 2008, he has been with VIA Technologies Inc., Sindian, Taiwan, where he is currently an Engineer. His research interests include RFIC design and high-speed digital signal integrity.

Chi-Chen Chen was born in Tainan, Taiwan, on February 10, 1975. He received the M.S. degree in electrical engineering from National Chi Nan University, Puli, Taiwan, in 2003, and is currently working toward the Ph.D. degree at National Chi Nan University. His Master’s thesis concerned RF monolithic LNAs and mixers. From 2003 to 2004, he was an Analog Integrated Circuit (IC) Design Engineer with the Anachip Corporation, Taipei, Taiwan. His current research is the design of RF transformers and RF front-ends for cellular applications.

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Jen-How Lee was born in I-Lan, Taiwan, on February 28, 1979. He received the M.S. degree in electronic engineering from National Chi Nan University, Puli, Taiwan, in 2007, and is currently working toward the Ph.D. degree at National Chi Nan University. His Master’s thesis concerned UWB LNAs. His current research interests include the design of RF inductors by various layout skills for UWB applications.

Guo-Wei Huang (S’94–M’97) was born in Taipei, Taiwan, in 1969. He received the B.S. degree in electronics engineering and Ph.D. degree from National Chiao Tung University, Hsinchu, Taiwan, in 1991 and 1997, respectively. In 1997, he joined National Nano Device Laboratories, Hsinchu, Taiwan, where he is currently a Researcher. His current research interests focus on microwave device design, characterization, and modeling.

Shey-Shi Lu (S’89–M’91–SM’99) was born in Taipei, Taiwan, on October 12, 1962. He received the B.S. degree from National Taiwan University, Taipei, Taiwan, in 1985, the M.S. degree from Cornell University, Ithaca, NY, in 1988, and the Ph.D. degree from the University of Minnesota at Minneapolis–St. Paul, in 1991, all in electrical engineering. His M.S. thesis concerned the planar doped barrier hot electron transistor. His doctoral dissertation concerned the uniaxial stress effect on the AlGaAs/GaAs quantum well/barrier structures. In August 1991, he joined the Department of Electrical Engineering, National Taiwan University, where he is currently a Professor. Since August 2007, he has also been the Director of the Graduate Institute of Electronics Engineering, National Taiwan University. His current research interests are in the areas of RFIC/monolithic microwave integrated circuits (MMICs), and micromachined RF components.

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A New Six-Port Transformer Modeling Methodology Applied to 10-dBm 60-GHz CMOS ASK Modulator Designs James Brinkhoff, Member, IEEE, Duy-Dong Pham, Kai Kang, Member, IEEE, and Fujiang Lin, Senior Member, IEEE

Abstract—This paper presents a new broadband equivalent-circuit model for millimeter-wave transformers on silicon. The model includes a center tap on the primary and secondary, and considers coupling between all segments of the windings. A corresponding methodology to analytically extract the model from electromagnetic (EM) simulations is developed. The broadband model is verified by EM simulations and measurements. Two amplitude modulatable power oscillators with high power efficiency are demonstrated using low-loss transformers. One achieves an output power of 10.4 dBm near 57 GHz with a total efficiency of 23.6%. Applying amplitude-shift keying modulation, their maximum data rate exceeds 2 Gb/s. Simulations of these circuits showed the transformer model performs well in time-domain simulations. Index Terms—Amplitude-shift keying (ASK), CMOS millimeter-wave integrated circuits, integrated circuit modeling, transformers.

I. INTRODUCTION

T

RANSFORMERS have proven to be useful components for CMOS millimeter-wave circuits. For example, they have been used as interstage matching and balun elements in the 60-GHz power amplifier in [1], as feedback elements in the low-noise amplifier of [2], and as peaking elements in the broadband amplifier of [3]. Transformers serve multiple functions in a single compact component. They can be used for inter-stage coupling, impedance matching and transformation, power combining, bias supply, common-mode rejection, and single-ended to differential conversion (balun) [4]. Since the wavelength in the millimeter-wave range is small, the transformer size can also be small, leading to very compact circuits. Millimeter-wave inductor modeling has been discussed in [5] and [6]. A new model that includes scalability and easy extraction was reported in [7]. Modeling transformers presents more challenges. To begin with, they are not simple two-port devices Manuscript received April 23, 2009; revised September 04, 2009. First published January 12, 2010; current version published February 12, 2010. This work was supported by the Agency for Science, Technology and Research (A*STAR), Singapore, under SERC Grant 062 115 0051. J. Brinkhoff was with the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore 117685. He is now with Sapphicon Semiconductor, Sydney 2127, N.S.W., Australia (e-mail: [email protected]). D.-D. Pham, K. Kang, and F. Lin are with the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore 117685. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037868

so their equivalent circuits are much more complex. The model must take account of all the possible interactions between all the terminals. They include inductive, as well as capacitive coupling, and it can be challenging to isolate these two effects. There is a wide range of possible millimeter-wave transformer layouts, raising difficulties in developing a model that can easily be extracted and that can accurately fit a range of devices. Most of the transformer modeling efforts have not considered transformers with center taps [8]–[11] so they are simplified to four-terminal devices. However, when the transformer is used to supply bias to a circuit, or operated as a balanced-to-unbalanced interface, the center tap becomes important. Although numerous millimeter-wave circuits using transformers have been published, very few studies have been done on transformer modeling at millimeter-wave frequencies. Some of the circuits that have been reported may have used simulated -parameters, but this is not a feasible solution for oscillators or other large-signal circuits that require good performance in time-domain simulations. Generalized equivalent-circuit fitting methods such as [12] are very useful for fitting a wide variety of devices, but may produce unphysical or noncausal behavior for some structures [13]. For robust time-domain simulations, an efficient equivalent-circuit model is needed. Achieving reasonable output power while maintaining efficiency at 60 GHz using CMOS is a challenge. Around 10-dBm output power is required from a transmitter. An amplitude-shift keying (ASK) transmitter is simple, and can achieve high data rates with good power efficiency. A transmitter, working at 46 GHz, was presented in [14], with 1% power efficiency in the “on” state. It integrated an oscillator and buffer, with modulation applied by switching the supply current. A 60-GHz modulator implemented in SiGe was described in [15] that achieved 9-dBm output power and 5.5% efficiency. A 60-GHz CMOS modulator achieved 5.4% efficiency, with 2.7-dBm differential output power in [16]. A complete ASK transceiver with antennas was shown in [17]. The saturated output power was 7.6 dBm with an efficiency of 3.1%. This paper will describe new modulators, using transformers in the oscillator and buffer, one of which achieves more than 10-dBm output power with an efficiency of more than 20%. Section II discusses the new six-port modeling methodology. The core model includes comprehensive mutual inductances and accurately captures the frequency-dependent behavior to 100 GHz. An analytic extraction procedure for all the components of the model is developed. Section III gives two ex-

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Fig. 1. Transformer equivalent-circuit model.

amples of model extraction using electromagnetic (EM) simulations of transformers that have been fabricated in a 90-nm CMOS process. The model’s performance is verified with twoport 100-GHz measurements. Section IV describes two 60-GHz ASK modulators that have been designed using the transformer models. The modulators perform very closely to simulations, and feature high output power and efficiency. Their performance with multigigabit/second modulation is demonstrated. Conclusions are drawn in Section V. II. TRANSFORMER MODELING Transformers are often modeled as four-terminal devices with two terminals for the primary and two for the secondary. In RF integrated circuits (RFICs), however, transformers are frequently used differentially or in balun applications with a center tap on the primary and/or the secondary. Therefore, a more useful model needs to include six terminals, including the center taps on the primary and secondary. Symmetry is a desirable property of such transformers to preserve differential operation. Extracting a model for such a six-terminal symmetric transformer is complicated by the many interactions between the primary and secondary inductors. The model used in this paper is shown in Fig. 1. Each winding is separated into two impedance segments, the primary ones indicated by symbols and and the secondary ones by and . There is magnetic coupling between all the inductive segments, which can be modeled by mutual inductances. There are six mutual inductances between the four segments to extract and ). There is also electrical ( coupling, modeled by coupling capacitances. There are nine possible coupling capacitances between primary and secondary ( and ). There is

also a shunt admittance to ground attached to each terminal. These components are shown in Fig. 1. The complexity of transformer behavior is contributed to by their multiple ports and multiple complex electrical and magnetic interactions between segments of the windings. This paper aims to provide a simple and accurate analytic extraction procedure for a comprehensive transformer model, usable over a broad range from dc into the millimeter-wave range, and compatible with both frequency- and time-domain simulators. The model generation begins with running EM simulations of the six-port transformers to obtain the device -parameters. The Sonnet EM simulator has been used extensively in this study.1 Extracting models from EM simulations has multiple advantages over extraction from physical structures on test chips. Fabricating a wide variety of test structures is expensive. Accurate measurements at millimeter-wave frequencies of the small impedances and admittances in passive devices is extremely error prone due to calibration, de-embedding, and dynamic range limitations. This is especially the case for devices with more than two-ports. Using EM simulations, a wide variety of device structures can be analyzed and optimized, and the -parameters returned have very good dynamic range. The models developed from the simulations can then be compared with measurements of a small number of representative fabricated test structures and circuits to verify the accuracy of the simulations. Sections II-A and B detail the new six-terminal transformer model and the method to extract all the components in the model. A. Core Model Format The new model is shown in Fig. 1. Terminals 1 and 2 are for the primary, with corresponding center tap terminal 5. Sim1[Online].

Available: http://www.sonnetsoftware.com/

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ilarly, the secondary has terminals 3 and 4 with the center tap connected to terminal 6. The model is extracted by processing the six-port -parameters obtained from an EM simulator. Each of the terminals has a shunt admittance, denoted , where is the terminal number. The admittance is modeled by and substrate capacitance and an oxide capacitance . Extraction of these elements will be deconductance tailed in Section II-B.2. The primary and secondary windings are divided into two series impedances each with corresponding mutual inductances. or to inThe impedances are denoted by , where is dicate which pair of terminals the impedance is bridging. Each of the impedances is modeled with a series impedance, as shown in the inset in Fig. 1. This network was described in [7]. With three parallel – branches, the model can be fit to dc and three other frequencies with a simple extraction procedure. The three frequencies are chosen to span the frequency range of interest (up to the millimeter-wave range in this case). This allows easy modeling of the skin and current crowding effects that cause broadband frequency-dependent behavior of the inductance and resistance. For the transformers in this study, the coupling capacitances were the dominant cause of self-resonance so winding self-capacitance was not needed. The procedure to extract the series branch model is discussed in Section II-B.4. Each of the four series branches have mutual inductances coupling to the other three series branches. The mutual inductances for the coupling between will be denoted by, for example, series branches and . Extraction of the mutual inductances is described in Section II-B.1. Extraction of the nine coupling capacitances shown in Fig. 1 is challenging because nine independent equations are needed. In this study, the network is simplified by using the inherent symmetry of the devices and by neglecting coupling capacitances that are much smaller than others in the network. The considerations in simplifying this network, and extraction method are discussed in Section II-B.3.

Fig. 2. 1:1 transformer. The light colored trace is metal 9, the dark is metal 8. The port numbers corresponding to the model equivalent circuit in Fig. 1 are shown.

The mutual inductances can be easily extracted from (1) at a low frequency where they are flat. The positive signs for all the terms in (1) are a consequence of the position of the dots in Fig. 1. Some of the mutual inductances are likely to be negative depending on the structure of the device that is being modeled. Often, transformers with center taps are designed to be and symmetric so that (1) can be simplified with . An example of a symmetric transformer is shown in Fig. 2. 2) Shunt Admittance Extraction: After finding the mutual inductances, the remaining elements are extracted using the six-port -parameters. The -parameters are derived from Fig. 1. Expanding the equations is very complex due to the mutual inductances. Therefore, the currents through the series and are left as variables in the -parambranches eter equations. For example, the -parameters when all the terminal voltages are zero (grounded), except terminal 1, are given as follows: (2) (3) (4) (5)

B. Model Extraction 1) Mutual Inductance Extraction: To extract the mutual inductances, the center taps, terminals 5 and 6, are grounded. One way to do this is to take the six-port -parameters and form a (ground) at termisubmatrix from ports 1 to 4. This places nals 5 and 6 from the definition of -parameters. This four-port -matrix is then transformed to a -matrix. Capacitances are ignored for this part of the model extraction, as they will only start having an effect near the resonance frequencies. The mutual inductances are, therefore, extracted at low frequencies. The real parts of the mutual impedances [18] are neglected. The real part is due to the lossy coupling through the substrate, which is often not significant in small millimeter-wave transformers, particularly when the coils are stacked on top of each other. Further research may quantify the effects of the real parts and include them in the model. The -matrix is then

(1)

(6) (7) The shunt admittance at terminal 1 can easily be found by summing all the -parameters with the voltage applied at terminal 1 (8) Similarly, the shunt admittances at the other terminals are found to be (9)

For each of the six shunt admittances, a model consisting of an oxide dielectric capacitance in series with a substrate conductance/capacitance, as shown in Fig. 1, is used. The capacitances

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and conductance are found using a procedure similar to [19] as follows: (10) (11) (12) (13) (14) Two characteristic frequencies are used in these equations. The lowest frequency point available from EM simulations or measurements is denoted by . The high-frequency point, where the capacitance has settled to a constant value, is denoted by [19]. As seen in Fig. 3(c), a suitable choice is and . The choice of these frequencies are discussed further in Section II-B.4. 3) Coupling Capacitance Extraction: There are nine possible coupling capacitances between the six nodes. However, a number of them are usually negligible, allowing some assumptions to be made to simplify the extraction. To find the coupling capacitances, we derive the total capacitance from the primary to each node on the secondary and vice versa. By examining (2)–(7), the total coupling capacitance from terminal 1 to the secondary is

There are four unknowns in (21)–(24), but it can be shown that there are only three independent equations. Therefore, one additional assumption is needed, and this can be obtained from knowledge from the device structure or by observing that some of the coupling capacitances in (21)–(24) are much smaller than is very small, the others. For example, if so can be found from (22) and from (24). Extracting the coupling capacitances of two example transformers will be examined in Section III. 4) Series Impedance Extraction: The series impedances are also extracted using the six-port -parameters. The mutual inductances have to be removed from the series impedances, which complicates the extraction. In addition, we have to remove the influence of all the capacitances so that self-resonant effects do not corrupt the extracted series impedance characteristics. To illustrate the method, the case for extracting the series in Fig. 1 is discussed. The -parameters with impedance the voltage applied to terminal 1 are used, as given in (2)–(7). By examining Fig. 1, the voltage across the impedance can be derived as follows: (29) Since the mutual inductances and capacitances are known, (29) can be divided by , and the variables substituted with the -parameters from (2)–(7). This yields

(15) The total coupling capacitances from the other terminals to their opposite winding can be similarly found as follows: (16) (17) (18) (19) (20) Examining (15)–(20), there are nine unknowns, but only six equations. Therefore, some additional information is needed. The additional information can usually be obtained by to . On-chip center-tap calculating and inspecting transformers are usually symmetric, which can be confirmed by checking that and . If symmetry is observed, (15)–(20) can be simplified to (21) (22) (23) (24) where (25) (26) (27) (28)

(30) The denominator of (30) is the total impedance, while the numerator removes the impedance contributed by mutual inductance. Thus, in (30), only the branch self-impedance remains. Similarly, by examining the -parameters when the voltage is applied to terminals 2–4, and using the equations for and , respectively, the remaining series impedances can be found as follows:

(31) (32) (33) The advantage of using this six-port method of extracting the individual branch impedances, as opposed to finding the impedance between each pair of terminals independently, is that all the capacitances are taken care of. Thus, even though the transformers used in this study have self-resonant frequencies below 100 GHz [as seen in Fig. 3(a)], no resonance is evident in the inductance and resistance curves from (30)–(33), as seen in Fig. 3(e) and (f). This allows the series impedance model to be correctly extracted and the full model is able to predict self-resonant effect accurately. This method can also be simplified to extract a differential inductor model, leading to a simple and

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Fig. 3. EM simulated (points) and modeled (lines) characteristics of the 1:1 55-m-diameter transformer. (a) Mutual inductances. (b) Coupling capacitance sums. C and C C ). (d) Shunt conductances (G G and G G ). (e) Series branch inductances (L L and L L ). (c) Shunt capacitances (C (f) Series branch resistances (R R and R R ).

=

=

=

=

=

accurate extraction procedure that takes account the mutual inductance between the two segments. The series impedance model shown in Fig. 1 is fit to each of the series impedances found by (30)–(33). This model uses three parallel – branches to fit the frequency-dependent behavior of the resistance and inductance. As discussed in [7], this model is much simpler to extract, and more flexible and accurate than the usual – model used for on-silicon interconnects and inductors [19]. A full description of the model and extraction procedure is given in [7]. Here, we simply note that there are three characteristic frequencies as follows:

=

=

=

or is denoted by in (34)–(36). The The series branch and is exchoice of the characteristic frequencies plained in [7]. In order for the extraction equations (39)–(43) to be valid, the frequencies are chosen so that . In this study, and , which covers the frequency range over which the impedance characteristics are varying rapidly, as seen in Fig. 3(e) and (f). The corner frequencies were the same in all four series branches. The frequency-dependent resistance and inductance of each of the series branches is found using

(34) (35)

(37)

(36)

(38)

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Each of the components in the series branch model for each of the branches can then be found using [7] (39) (40) (41) (42) (43) and can be found from the corresponding resistances using (34)–(36). III. MODEL EXTRACTION EXAMPLES AND VERIFICATION To illustrate and verify the transformer model and its extraction method, two different transformers are processed. They were both designed to be used in 60-GHz circuits, and were fabricated in a nine-metal 90-nm CMOS process. The transformers were designed and their models were extracted from EM simulations. The extracted models were used in the designs in Section IV even before test structures were fabricated and physical measurements were obtained. The first transformer is a 1:1 transformer, with the one-turn primary on the top metal, and the secondary on the layer below. The second example is a 1:2 transformer, with the primary on metal 8, and the two-turn secondary on metal 9. A. 1:1 Transformer Example The 1:1 transformer has its primary on metal 9, and secondary on metal 8, as shown in Fig. 2. Each winding has one turn, with a design similar to that used in the power amplifier design of [1]. The metal width is 10 m. This leads to a high coupling , but to a lower self-resonant frequency because of factor the large coupling capacitances compared with transformers that have their primary and secondary on the same metal layer. The mutual inductances are extracted first by grounding the center taps and processing the resulting four-port -parameters, as detailed in Section II-B.1. The results are shown in Fig. 3(a). The negative mututal inductances are simply a consequence of the dot convention used in the model (Fig. 1) rather than nonphysical behavior. The dot placement was chosen to simplify the derivations. The low resonant frequency is caused by the significant capacitances, which are taken care of in later extraction steps. The mutual inductance graphs are flat at low frequencies so the mutual inductances can be extracted at a suitably low freand , and quency. There is 0.1% difference between and , which confirms the symmetry of the also between transformer. The six-shunt admittances are then extracted, and the threeelement model shown in Fig. 1 are fitted to each of them. The shunt admittances are very small for this transistor, with capacitances less than 10 fF. This is a consequence of the small size of the transformer and of using only the two top metals, far away from the substrate. Due to their relative insignificance compared with other components of the transformer, the results from the EM simulation may include some uncertainty. The capacitances and conductances calculated from the EM simulations, and the modeled ones, are shown in Fig. 3(c) and (d).

To determine the coupling capacitances between the primary and secondary, one assumption is needed, as discussed in Section II-B.3. Fig. 3(b) shows the computed capacitances from every node to the opposite winding, as defined in Section II-B.3. As expected, due to the symmetry of the device, and . None of the capacitance sums shown in Fig. 3(b) are negligible, therefore, we require an assumption from the physical device structure. This device has the two center taps on opposite sides. The capacitance between these nodes is, therefore, extremely small in comparison to all the . other capacitances. Therefore, we may assume that and can then easily be found from (23) and (24). After can be computed from finding these capacitances, (21) or (22). It is found that these are less than 5.5% of the other capacitances, and thus can be neglected (along with their and ). Thus, four significant symmetric counterparts and . coupling capacitances remain, i.e., and are significant The fact that only is reasonable from the physical structure of the transformer in Fig. 2 because those respective branches are in close proximity. Finally, the inductance and resistance of the series branches are shown in Fig. 3(e) and (f). One out of the two branches from the primary and one from the secondary are shown because they are symmetric. The model has been able to correctly capture the frequency dependence of the resistance and inductance over a wide frequency range. We also note that even though the transformer has self-resonant frequencies lower than 100 GHz [as is evident from Fig. 3(a)], the extraction procedure takes care of the coupling capacitances so the series impedances calculated from (30)–(33) do not exhibit any self-resonant behavior and the series model can be correctly extracted. If we had not applied the formulas in (30)–(33), the significant self-resonance would corrupt the analytic model extraction procedure. The model was directly extracted from the EM simulations. No optimization or tuning was performed, the parameter values came straight from the equations in Section II. EM data at only and ) are three frequency points (corresponding to needed, making the extraction very efficient. Fig. 3(a)–(f) shows that the analytic extraction gives accurate behavior for all the characteristics of the device. The model closely reproduces the frequency-dependent impedances, admittances, and couplings obtained from the EM simulation. All of the parameters of the model are given in Table I. This transformer was fabricated in a nine-metal 90-nm CMOS process, and connected in a test structure in inverting configuration. In this configuration, terminals 2 and 3 grounded, the center taps (5) and (6) are not connected, and the two test ports are connected to terminals 1 and 4. A corresponding open-short test structure for de-embedding was also fabricated [20]. The test structure was measured with a vector network analyzer (VNA) that was calibrated using the line–reflect–reflect–match (LRRM) procedure. The measured -parameters and the -parameters predicted by the model are shown in Fig. 4(a). It can be seen that the model is able to predict the inverting transformer performance to well beyond the self-resonance frequency. Note that the transformer in this configuration has a lower self-resonant frequency than in other configurations [11]. It will be used in a differential con-

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TABLE I TRANSFORMER MODEL PARAMETERS

figuration in the circuits in Section IV, which makes it useful above 60 GHz. We also note from Fig. 4(a) that the minimum insertion loss at the center frequency is less than 1.7 dB, making this wide metal, 1:1 transformer topology useful for power designs [1]. The inductances and factors of the primary and secondary windings are shown in Fig. 4(b) and (c). It can be seen that the inductance is predicted accurately, as well as the self-resonant frequency. The measured above resonance is lower than simulated, probably because the resistance is very small for these compact millimeter-wave transformers. The resistance of the primary winding is less than 0.2 at dc, making it difficult for a 50- VNA to measure accurately. The of the secondary is lower than the primary as expected because the primary is fabricated on the thick top metal. The measured and simulated real and imaginary coupling factors are shown in Fig. 4(d). They are defined as [18] (44) (45) The test structure included 20- m-long interconnects between the grounded terminals (3 and 4) and ground, which has a significant impact on the transformer coupling factors. Therefore, the simulations including (dotted line) and excluding (solid line) a model of these interconnects is shown. The interconnect model was extracted using the procedure reported in [7]. The interconnects cause the coupling factor to drop at lower frequencies, and lowers the resonant frequency of the coupling factor. After the addition of the interconnect model, the model predicts the coupling factor accurately. More research is needed to assess the coupling between these interconnects and the transformer itself. Fig. 4(d) shows the significance that small parasitics ( 20 pH in this case) can have on millimeter-wave devices. It is also interesting to note that even though the model did not include the

Fig. 4. Measured (points) and modeled (lines) performance of the 1:1 55-m-diameter transformer in inverting configuration. (a) S -parameters. (b) Inductance and Q factor of the primary. (c) Inductance and Q factor of the secondary. (d) Real and imaginary coupling factors (the dashed line simulation includes 20-m interconnects from the grounded terminals to ground, corresponding to the layout).

real part of the mutual coupling impedances (Section II-B.1), the real coupling factor is accurately predicted up to moderate

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. This also applies to their symmetric counterparts from and ) terminal 2. The remaining capacitances ( can then be very simply found from (22)–(24). Since there are three equations and only two unknowns, a consistency check, from (23) can be carried out. such as This residual on the right-hand side of the equation was 2 fF (practically negligible in comparison to the other capacitances), showing that the simplifications are reasonable. IV. TRANSFORMER OSCILLATORS/MODULATORS

Fig. 5. 1:2 transformer. The light colored trace is metal 9, the dark is metal 8.

Fig. 6. Coupling capacitances between each terminal and the opposite winding of the 1:2 transformer.

frequencies. At higher frequencies, the real part of these transimpedances may need to be included, as the substrate effects become more significant. This section has shown that the reported transformer model is able to very closely fit the EM simulated parameters of a millimeter-wave transformer using the new analytic extraction algorithm. After fabricating the transformer, the measured and modeled transformer performance match well with no model tuning necessary. B. 1:2 Transformer Example Another example is given of a transformer with a different structure. The diameter is 30 m. The primary is one turn on metal 8 with 8- m width. The secondary is on metal 9, with two symmetric turns, using an underpass to metal 8 to form the crossover. The metal width of the secondary is 3 m. Thus, it is a 1:2 transformer. The transformer layout is shown in Fig. 5. The same procedure was followed for the model parameter extraction. However, the coupling capacitor assumptions had to be modified. A graph of the capacitance sums from each node to the opposite windings is shown in Fig. 6. The transformer and holds to symmetry very well, as evidenced by . For this transformer, it can be seen that . This is expected from the physical structure again because most of the overlap between the primary and secondary is from the center tap of the primary (terminal 5) rather than terminals 1 and 2. From (21), this implies that

Having developed a new transformer model and corresponding extraction methodology, and having extracted and verified the models with test structure measurements, it is useful to test the models in a real design situation. Often, problems may come up, especially in time-domain simulations if a model has some nonphysical characteristics that are not evidenced in -parameters [13]. Large-signal simulations of autonomous circuits such as oscillators are particularly sensitive to a model having physical characteristics over a wide range of frequencies. Any inconsistencies can lead to nonconvergence. This was observed in the current circuits when -parameters and a generic broadband model extracted by the EM simulator was used [12] instead of the models extracted in this paper. This motivates the development of a consistent and reliable equivalent-circuit model compatible with time-domain simulations such as the one described in this paper. The test circuits were 60-GHz ASK modulators. They include a free-running oscillator and a buffer that can be switched at multigigabit/second to impose the modulation. These circuits have found application in a short-range high-speed communications link with one of the modulators being integrated with an on-chip antenna. ASK modulation allows very low energy usage architectures in terms of joules/bit. In [16], we described a low-power modulator that uses only 13.2 pJ/bit at 2 Gb/s. The power output was less than 3 dBm and the power efficiency (defined as the output power divided by the total dc power consumption) was 5.4%. The modulators in this study increase the power output to around 10 dBm, and the efficiency to greater than 20%. A. Design Description Fig. 7 shows a simplified circuit schematic of the modulators. The goal throughout was to increase the power output and power efficiency. The transformers described in Section III are suitable devices to use for resonators and inter-stage couplers because of their low loss. The field-effect transistors (FETs) and form a cross-coupled pair for the oscillator core. . Their bias is supplied through the center-tap of transformer The frequency of oscillation is set by the resonance between the transformer inductance; and the capacitances contributed by: 1) the FETs; 2) the second stage; and 3) the transformer itself. The transformers were sized in order to give the oscillation frequency close to 60 GHz. No current source is used so that the largest swing and highest efficiency can be achieved. Frequency stability is not a major concern in our simple one-user ASK link. and . They The buffering is accomplished by FETs are common-source FETs with no current source to maximize power and efficiency. Their drain bias is supplied through the

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Fig. 7. Circuit schematic of the modulators.

center tap of the second transformer . The amplitude modulation is applied by varying the gate voltage, and hence, the gain, of the buffer FETs. This gate voltage is applied through . This baseband input uses the center tap of transformer and to provide some low-pass filtering and a 50- input impedance at the baseband terminal. For ASK systems, the ratio between the output power when the baseband input is “1” to when it is “0” should be as high as possible. There is not a large difference in the gain of a common-source FET at 60 GHz as the gate voltage is varied because the low-impedance gate–drain capacitance passes power to the output even when the FET is off. In this design, the caand are used to partially cancel the gate–drain pacitors and in the off state. This allows on/off capacitances of ratios of more than 10 dB to be achieved. , together with capacitor , constitutes The transformer the output matching network to match the impedance to 50 . It also functions as a differential to single-ended converter or balun. It can be seen that the use of transformers in this circuit has enabled a very simple and compact design with good functionality. In addition, high output power can be obtained because of the low loss of the transformers, their power-combining effect when converting from differential to single-ended outputs, and the minimization of the number of lossy passive matching and coupling elements that need to be used. Two modulators were designed. The first one used the 1:1 , here55- m transformer described in Section III-A for after called the 1:1 modulator. A die photograph is shown in Fig. 8(a). The second used the 1:2 30- m transformer described , called the 1:2 modulator. A die phoin Section III-B for tograph is shown in Fig. 8(b). The output buffer stage of both modulators was identical, they both used the 1:1 55- m trans. former for

Fig. 8. Die photograph of the two modulators. (a) 1:1 modulator. (b) 1:2 modulator.

parallel tank near the resonant frequency, and an approximation of the resonant frequency and load resistance will be given. The complete equivalent circuit of a six-port transformer shown in Fig. 1 is very complex and not useful for hand analysis. To obtain a more useful model to begin a derivation, assume that the desired resonant frequency of the tank is well below the self-resonant frequency of the transformer. This allows the coupling capacitances to be neglected, as the magnetic coupling is dominant below self-resonance. The shunt admittances are also neglected, as their effect only becomes significant at very high frequencies. The load is assumed to be a capacitor, which is a reasonable approximation of the input impedance of the and in Fig. 7. This load capacitance together gates of with the transformer creates the resonant tank. The inputs and outputs are differential, with the input voltage denoted by , the input current by , the output voltage by , and the output current by , as shown in Fig. 9. It is assumed and . Noting the transformer is symmetrical so and solving for the input voltage in terms of that the input and output currents, we obtain

B. Resonator Analysis It is interesting to consider how the transformer connected to the cross-coupled pair in Fig. 7 functions as part of the resonant tank, setting the oscillator frequency. It will be shown that the impedance presented to the cross-coupled pair is similar to a

(46) Similarly, the output voltage can be found to be (47)

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of 205.1 . The approximations in (51) and (53) give 70.2 GHz and 192.0 . These results show that this approximation of the transformer tank is a useful tool for understanding and load by an what contributes to the tank behavior at resonance. Equations (51) and (53) can be used for preliminary hand design of a transformer-based oscillator before schematic entry, simulation, extraction, retuning and final layout. tuning, C. Simulations and Measurements

Fig. 9. Schematic of the differential transformer with load.

The output current can be eliminated using (48) To find the impedance as seen by the cross-coupled pair, (46)–(48) are solved to obtain (49) The approximate resonant frequency can be found by assuming the transformer is lossless (i.e., and ). Assume the load impedance is . In that case, the input impedance a capacitor becomes (50) The resonant frequency of the tank is then (51) Including the loss of the transformer windings, finding the tank impedance at resonance gives (52) (53) Thus, from (51) and (53), we can approximate the resonant tank, consisting of the transformer and capacitive load, by a parallel network with and . To verify the approximations made in the above analysis, we compare the results from a numerical evaluation of (49) to the resonant frequency and impedance approximations in (51) and (53). The parameters for the 1:1 transformer from Table I are used, together with a load capacitance of 160 fF. This capacitance is an approximation of the capacitances presented by the gates of the 64- m-wide amplifier transistor, the capacitance contributed by the 32- m-wide oscillator FET and the sum of and from Table I. The numerical evaluation of (49) gives a resonant frequency of 70.2 GHz and a load resistance

In contrast to [6], which used a full EM simulation to extract capacitance parasitics of the device layouts, we have used the foundry supplied – parasitic extraction. This is quick and integrates well with the layout environment, and no additional manual entering of parasitic elements is needed. A full model for the transformers has already been defined, and we do not want the capacitances and resistances of the transformers to be double counted. Therefore, the transformers were removed from the layout for the – extraction, and then the transformer models were re-added after the parasitic extraction so the entire circuit could be simulated. This methodology of extracting custom models for the inductive elements, and doing – extraction everywhere else in the layout, has produced very good correspondence between measurements and simulations for numerous 60-GHz circuits. The modulators were measured using an on-chip wafer probing system. The dc supply was set to 1 V. The baseband input was supplied by a pseudorandom bit sequence (PRBS) generator. The output was measured using a power meter and a 67-GHz spectrum analyzer. The losses of the output cable, adapters, and probes were de-embedded. The modulators were measured in a continuous wave (CW) mode with a constant voltage applied to the baseband input port. The output frequency, power level, and dc current consumption was measured. Fig. 10 shows the measured and simulated performance of the 1:1 modulator. The maximum output power is more than 10.4 dBm. This could be increased with a supply voltage of more than 1 V (the rated supply voltage of this process is 1.2 V), but for reliability considering the large-signal swings, the supply voltage is fixed at 1 V [21]. The dc current is 47 mA, which gives a total dc–RF efficiency of more than 23.5%. The on/off ratio was 13.6 dB. The frequency varied from 56.6 to 58.2 GHz between the on and off states, caused by the modulation of the gate capacitance of the buffer stage by the baseband input, which varies the resonant frequency of the oscillator tank. Fig. 10 shows the correspondence between the measured power output, efficiency, and frequency is very good. Before parasitic extraction, the difference between measured and simulated oscillation frequency was greater than 4%. After parasitic extraction, the difference was less than 2%. The difference between the measured and simulated power was less than 1 dB for control voltages above 0.2 V. This validates the modeling methodology using the custom transform model, and – extraction everywhere else in the circuit. Phase noise is not a critical issue in an ASK system. However, in order to provide some further insight into the performance of the modulators, the phase noise of the 1:1 modulator is shown in Fig. 11. The phase noise at 1-MHz offset is 96 dBc/Hz and

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Fig. 12. Measured (lines) and simulated (points) performance of the 1:2 modulator in CW mode.

Fig. 10. Measured (lines) and simulated (points) performance of the 1:1 modulator in CW mode.

Fig. 11. Measured phase noise of the 1:1 modulator in CW mode.

is 116 dBc/Hz at 10-MHz offset. Compared to the simulated phase noise, these are 5 dB better and 1 dB worse, respectively. The 1:2 modulator performance is shown in Fig. 12. The maximum output power is 8.5 dBm with 15.2% efficiency. The output power reduction is due to the higher loss of the 1:2 transformer. The frequency variation between on and off states is much smaller—from 58.5 to 57.5 GHz. This is due to the inherent impedance transformation of the 1:2 transformer so the

input capacitance of the buffer does not load the tank of the oscillator as much. This modulator achieves a much better on/off ratio of almost 30 dB. The performance of recently published ASK modulators is shown in Table II. Due to the design techniques, which optimize the power concerns, the on/off ratio is not as good as other reported modulators. The on/off ratio of the 1:1 modulator can be improved by optimizing the capacitance degeneration ( and in Fig. 7) after extraction. The modulators reported in this study achieve the highest output power and power efficiency. To test the operation of the 1:1 modulator, a PRBS signal was applied to the baseband input. The output of the modulator was fed through cables and attenuators with a total loss of more than 40 dB. This was input to a commercial off-the-shelf 60-GHz ASK receiver. The specified maximum data rate of the receiver was 1.5 Gb/s. The dc consumption of the 1:1 modulator with the baseband signal applied went down to 31 mW because the buffer is only drawing current half the time. The measurements are shown in Fig. 13. Fig. 13(a) shows the eye diagram with a 1-Gb/s signal applied. The eye opening is very wide, indicating that the modulator is capable of much higher data rates than that. The eye diagram at 2 Gb/s is shown in Fig. 13(b). The eye is still open with a rare closure. This is due to a squelch function not being implemented in the commercial receiver so that the output oscillates if the detected power level is low. In addition, the rating of the receiver is only 1.5 Gb/s. It is expected the modulator is able to achieve much higher data rates, as indicated

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TABLE II ASK MODULATOR COMPARISON

Fig. 13. Measured modulator performance with PRBS modulation. (a) Eye pattern at 1 Gb/s. (b) Eye pattern at 2 Gb/s. (c) Transmitted and recovered waveform at 2 Gb/s. (d) RF spectrum at 2 Gb/s from 0 to 67 GHz. A commercial ASK receiver is used to recover the data.

by simulation. Fig. 13(c) shows a measurement of the baseband data input to the modulator and the corresponding received data at 2 Gb/s. The bits are being transmitted correctly. Finally, Fig. 13(d) shows the spectrum at the output of the modulator with the 2-Gb/s random baseband signal. The spectrum is asymmetric due to the frequency shift between the “1” and “0” states (that is control voltages of 1 and 0 V, respectively), as shown in Fig. 10. V. CONCLUSION A new six-terminal transformer model and corresponding comprehensive analytical extraction methodology has been described. The model has proven suitable for time-domain simulations of CMOS circuits and provides accuracy well into the millimeter-wave range. The model takes account of the magnetic and electrical coupling between all branches of the windings, and is thus able to correctly predict the transformer characteristics beyond the self-resonant frequency. The transformer model has been applied to the design of two 60-GHz ASK modulators. The modulators achieve the highest reported output power and efficiency, and have been demonstrated to work to at least 2 Gb/s.

ACKNOWLEDGMENT The authors would like to thank the United Microelectronics Corporation (UMC), Hsinchu, Taiwan, for fabrication and Sonnet Software, North Syracuse, NY, for provision of the EM simulation tool. REFERENCES [1] D. Chowdhury, P. Reynaert, and A. M. Niknejad, “A 60 GHz 1 V 12.3 dBm transformer-coupled wideband PA in 90 nm CMOS,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., 2008, pp. 560–561. [2] M. Khanpour, K. W. Tang, P. Garcia, and S. P. Voinigescu, “A wideband -band receiver front-end in 65-nm CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1717–1730, Aug. 2008. [3] J. D. Jin and S. S. H. Hsu, “A miniaturized 70-GHz broadband amplifier in 0.13- m CMOS technology,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 3086–3092, Dec. 2008. [4] T. LaRocca and M.-C. F. Chang, “60 GHz CMOS differential and transformer-coupled power amplifier for compact design,” in IEEE RFIC Symp. Dig., 2008, pp. 65–68. [5] T. O. Dickson, M.-A. LaCroix, S. Boret, D. Gloria, R. Beerkens, and S. P. Voinigescu, “30–100-GHz inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 123–133, Jan. 2005. [6] C. Liang and B. Razavi, “Systematic transistor and inductor modeling for millimeter-wave design,” IEEE J. Solid-State Circuits, vol. 44, no. 2, pp. 450–457, Feb. 2009.

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[7] J. Brinkhoff, K. S. S. Koh, K. Kang, and F. Lin, “Scalable transmission line and inductor models for CMOS millimeter-wave design,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 2954–2962, Dec. 2008. [8] A. Zolfaghari, A. Chan, and B. Razavi, “Stacked inductors and transformers in CMOS technology,” IEEE J. Solid-State Circuits, vol. 36, no. 4, pp. 620–628, Apr. 2001. [9] O. El-Gharniti, E. Kerherve, and J.-B. Begueret, “Modeling and characterization of on-chip transformers for silicon RFIC,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 4, pp. 607–615, Apr. 2007. [10] W. Jin, X. Li, C. Shi, Y. Xu, and Z. Lai, “A novel approach to parameter extraction for on-chip transformers,” Analog Integr. Circuits Signal Process., vol. 50, no. 3, pp. 279–281, 2007. [11] J. R. Long, “Monolithic transformers for silicon RF IC design,” IEEE J. Solid-State Circuits, vol. 35, no. 9, pp. 1368–1382, Sep. 2000. [12] J. C. Rautio, “Synthesis of compact lumped models from electromagnetic analysis results,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2548–2554, Dec. 2007. [13] P. Triverio, S. Grivet-Talocia, M. S. Nakhla, F. G. Canavero, and R. Achar, “Stability, causality, and passivity in electrical interconnect models,” IEEE Trans. Adv. Packag., vol. 30, no. 4, pp. 795–808, Apr. 2007. [14] H.-Y. Chang, M.-F. Lei, C.-S. Lin, Y.-H. Cho, Z.-M. Tsai, and H. Wang, “A 46-GHz direct wide modulation bandwidth ASK modulator in 0.13-m CMOS technology,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 9, pp. 691–693, Sep. 2007. [15] M. Devulder, N. Deparis, I. Telliez, S. Pruvost, N. Rolland, F. Danneville, and P. A. Rolland, “60 GHz UWB transmitter for use in WLAN communication,” in Int. Signals, Syst., Electron. Symp., 2007, pp. 371–374. [16] F. Lin, J. Brinkhoff, K. Kang, D.-D. Pham, W.-G. Yeoh, and X.-J. Yuan, “A low power 60 GHz OOK transceiver system in 90 nm CMOS with innovative on-chip AMC antenna,” in IEEE Asian Solid-State Circuits Conf., Nov. 2009, pp. 349–352. [17] J. Lee, Y. Huang, Y. Chen, H. Lu, and C. Chang, “A low-power fully integrated 60 GHz transceiver system with OOK modulation and on-board antenna assembly,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2009, pp. 316–317. [18] K. T. Ng, B. Rejaei, and J. N. Burghartz, “Substrate effects in monolithic RF transformers on silicon,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 1, pp. 377–383, Jan. 2002. [19] S. Sun, R. Kumar, S. C. Rustagi, K. Mouthaan, and T. K. S. Wong, “Wideband lumped element model for on-chip interconnects on lossy silicon substrate,” in IEEE RFIC Symp. Dig., Jun. 2006. [20] M. C. A. M. Koolen, J. A. M. Geelen, and M. P. J. G. Versleijen, “An improved de-embedding technique for on-wafer high-frequency characterization,” in Proc. IEEE Bipolar Circuits Technol. Meeting, Minneapolis, MN, 1991, pp. 188–191. [21] M. Tanomura, Y. Hamada, S. Kishimoto, M. Ito, N. Orihashi, K. Maruhashi, and H. Shimawaki, “TX and RX front-ends for 60 GHz band in 90 nm standard bulk CMOS,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., 2008, pp. 558–559.

James Brinkhoff (S’02–M’05) received the B.E. degree from the University of Tasmania, Tasmania, Australia, in 2001, and the Ph.D. degree from Macquarie University, Sydney, N.S.W., Australia, in 2005. From 2005 to 2006, he was a Research Fellow involved with modeling the nonlinear behavior of GaAs HEMTs in microwave circuits. In 2006, he joined the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore, where he was involved in modeling and design for millimeter-wave systems in CMOS. In 2009, he joined Sapphicon Semiconductor, Syndey, N.S.W., Australia. His research interests include nonlinear device characterization and analysis, modeling active and passive devices, and analog/RF/millimeter-wave circuit design.

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Duy-Dong Pham was born in 1981. He received the B.S. degree in telecommunications and electrical engineering from the Post and Telecommunication Institute of Technology, Hanoi, Vietnam, in 2003, and the M.S. degree in electrical engineering from Kyung Hee University, Suwon, Korea, in 2008. From 2004 to 2006, he was with the Research Institute of Post and Telecommunication, Hanoi, Vietnam. Since March 2008, he has been a Research Engineer with the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore. His research interest includes RFICs and mixed signal and millimeter-wave circuit design in CMOS technology.

Kai Kang (M’08) was born in 1979. He received the B.Eng. degree in electrical engineering from the Northwestern Polytechnical University, X’ian, Shaanxi, China, in 2002, and the joint Ph.D. degree from the National University of Singapore, Singapore, and the Ecole Suprieure Dlectricit, Gif-sur-Yvette, France, in 2008. From 2003 to 2006, he was a Research Scholar with the National University of Singapore. From 2005 to 2006, he was with the Laboratoire de Gnie Electrique de Paris, Paris, France. Since October 2006, he has been a Senior Research Engineer with the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore. His research interest is the modeling of on-chip passive devices and millimeter-wave circuits design in CMOS technology.

Fujiang Lin (M’93–SM’99) received the B.S. and M.S. degrees from the University of Science and Technology of China (USTC), Hefei, China, in 1982 and 1984, respectively, and the Dr.-Ing. degree from the Universitt Kassel, Kassel, Germany, in 1993, all in electrical engineering. In 1995, he joined the Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), Singapore, as a Member of Technical Staff, where he pioneered practical RF modeling for RFIC development. In 1999, he joined HP EEsof, as the Technical Director, where he established the Singapore Microelectronics Modeling Center, providing accurate state-of-the-art device and package characterization and modeling solution service worldwide. From 2001 to 2002, he started up and headed Transilica Singapore Pte. Ltd., a research and development design center of Transilica Inc., a Bluetooth and IEEE 802.11 a/b wireless system-on-chip (SoC) company. The company was acquired by Microtune Inc. After the close of Transilica Singapore in 2002, he joined Chartered Semiconductor Manufacturing Ltd. (third largest foundry), as Director, where he led the SPICE modeling team in support of company business. In 2003, he rejoined IME as a Senior Member of Technical Staff, where he is currently focused on upstream research and development initiatives and leadership toward next waves. As an Adjunct Associate Professor with the National University of Singapore, Singapore, he is actively involved in educating and training postgraduate students. He has authored or coauthored over 70 scientific papers. He holds two patents. His current research interest is in the development of CMOS as a cost-effective technology platform for 60-GHz band millimeter-wave SoCs. Dr. Lin has served IEEE activities in different functions since 1995 including chair of the Singapore IEEE Microwave Theory and Techniques (MTT)/Antennas and Propagation (AP) Chapter, Board of Reviewers member for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), and Technical Program Committee (TPC) member of ESSCIRC. He has been the initiator and co-organizer of international workshops and short courses at APMC99, SPIE00, ISAP06, and IMS07. Recently, he and his team initiated and organized the conference-style IEEE International Workshop on Radio-Frequency Integration Technology (RFIT), Singapore. He was the recipient of the 1998 Innovator Award presented by EDN Asia Magazine.

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A CMOS Class-E Power Amplifier With Voltage Stress Relief and Enhanced Efficiency Yonghoon Song, Student Member, IEEE, Sungho Lee, Student Member, IEEE, Eunil Cho, Jaejun Lee, Student Member, IEEE, and Sangwook Nam, Member, IEEE

Abstract—This paper proposes a class-E power amplifier (PA) with double-resonance circuit to reduce voltage stress on CMOS transistors. The voltage waveform applied to the CMOS transistor is shaped by harmonic control and the transistors are relieved from breakdowns. A negative capacitance is also implemented for efficiency enhancement, compensating for surplus capacitance from parasitic components on the drain node. Thus, nominal class-E operation is restored and high efficiency is achieved. We present a cascode differential class-E RF PA that is fabricated using a 0.13- m CMOS technology that delivers 31.5-dBm output power with 54% drain efficiency and 51% power-added efficiency at 1.8 GHz. Index Terms—Class-E, CMOS power amplifiers (PAs), switching amplifiers, zero voltage switching (ZVS).

Fig. 1. Basic class-E amplifier schematic with CMOS switch.

I. INTRODUCTION OBILE equipment demands highly efficient RF transmitters to conserve battery life. The power amplifier (PA) is the most critical component used to determine overall RF transmitter efficiency because it consumes the largest portion of dc power in the transmitter. Thus, highly efficient PAs are necessary to improve overall efficiency. A class-E PA is adaptable for a high-efficiency transmitter due to its high efficiency and simplicity. A class-E amplifier with a shunt capacitor was introduced by Sokal and Sokal in 1975 and was examined by Raab in an analysis of idealized operation [1], [2]. As a kind of switching amplifier, it can achieve the ideal 100% drain (or collector) efficiency by shaping the voltage waveform and current waveform so that they do not overlap, making it a strong candidate for a highly efficient RF PA [3]–[10]. Many designs have been presented on new devices, such as GaAs HBTs, GaN HEMTs, and InP double HBTs (DHBTs), used to operate on microwave and higher frequencies with better RF performances [11]–[13]. Recently, many researchers have been conducted about watt-level output power PAs using CMOS technology on microwave due its low cost [14]–[22]. In spite of its cost effectiveness, the CMOS PA has a serious weakness: a low breakdown voltage. As the process scale becomes smaller, the breakdown voltage is also reduced. As a re-

sult, supply voltage is limited to avoid breakdowns. In delivering large output power under a low-supply voltage, low load impedance is inevitable, which causes efficiency degradation and a narrowband load matching network [15], [18]. This study presents a double-resonance circuit for harmonic control, which gives relief to CMOS transistors from breaking downs. This circuit shapes a voltage waveform applied to the transistor gate and reduces voltage stress across the CMOS transistors. When voltage stress is reduced, the voltage margin from the breakdown increases, enabling the application of a higher supply voltage. With higher supply voltage, higher load impedance can be implemented to deliver the same output power with greater efficiency. Additionally, CMOS PAs require wide gatewidths to reduce on-resistance for high efficiency and to drive sufficient currents for watt-level output power. The maximum operation frequency is also proportional to peak drain current of class-E . For these reasons, the applicable gatewidths are some millimeters wide [14]–[17], [21]. However, widening the gatewidth introduces undesired parasitic components, such as parasitic capacitance. Parasitic capacitance increases the value , depicted in Fig. 1, which of shunt drain capacitance determines the nominal operation condition and maximum is deteroperation frequency of a class-E amplifier since ratio [23]. When deviates from its mined by an optimum value determined by the condition of nominal class-E operation, the efficiency degradation occurs. To maintain high efficiency, the surplus capacitance from parasitic capacitance should be tuned out. We set a negative capacitance using a simple capacitor to tune out surplus capacitance without adding external circuits. In this paper, differential architecture is used to deliver higher output power than a single-ended PA. Differential architecture can provides 3-dB more output power with the same supply voltage and load impedance than single-ended architecture.

M

Manuscript received July 15, 2009; revised October 25, 2009. First published January 12, 2010; current version published February 12, 2010. This work was supported by the Korea Science and Engineering Foundation (KOSEF) under the National Research Laboratory Program funded by the Ministry of Education, Science and Technology [ROA-2007-000-20118-0(2007)]. The authors are with the Institute of New Media Communication, School of Electrical Engineering and Computer Science, Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037877

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Differential architecture also disturbs other circuits less than a single-ended architecture in the same chip during the operation. Furthermore, it restrains the second harmonic at the output. balun is used to transform the output An off-chip passive structure from differential to single-ended. This paper is organized as follows. Section II introduces the fundamental theory of a class-E PA. In Section III, a double-resonance circuit for voltage stress relief is addressed. In Section IV, we present a cascode class-E PA with negative . After that, we capacitance to compensate for the surplus explain our CMOS PA design in Section V, and our measurement results are shown in Section VI. Conclusions are given in Section VII. II. FUNDAMENTAL THEORY OF CLASS E The class-E amplifier is composed of a switch (usually a transistor) and a shunt capacitor. Its basic schematic is shown in is determined as Fig. 1 and (1) In addition, based on previous study, the voltage across the and the current through the switch are switch stated as follows [24]:

(2) (3) The operation of class E is the charging/discharging of following an operating signal. For a nominal class-E opershould satisfy two conditions, which are: 1) ation, zero voltage switching (ZVS) and 2) zero voltage derivative switching (ZVDS). ZVS prevents the dissipation of the energy when it turns on, and ZVDS makes the circuit stored by the robust in the face of variations in the components, frequency, and switching instants [25], [26]. When a class-E amplifier operates in a nominal condition with a 50% duty cycle (the and off for ), the transistor is on for value of is determined as 32.482 . Consequently, (2) and (3) can be written in normalized form as (4) (5) where . A class-E amplifier operation with waveforms of (4) and (5) achieves 100% drain (or collector) efficiency because, in theory, and in they do not create dc losses by overlapping the operation. The relationship between the operation frequency and the load impedance is calculated as in a nominal class-E operation [27]. However, in the real world, variation exists in the desired value based on parasitic capacitance or process variation in value cannot maintain the CMOS process. Thus, the 0.1836 with fixed at a given frequency. When the values deviate from 0.1836, there is a loss in the class-E amplifier operation, degrading the drain (or collector) efficiency.

Fig. 2. Schematic of: (a) double-resonance circuit implementation and (b) its ac equivalent circuit.

Another characteristic of a class-E amplifier is a high-peak voltage swing. Maximum voltage on the drain (or collector) of the transistor in the operation conditions given above is depicted [28]: in the following equation under a supply voltage (6) and the value of threatens the transistor’s reliability, especially in CMOS technology, due to its low breakdown voltage. To ensure circuit reliability, several research studies have been conducted to analyze voltage stress on CMOS transistors [15], [21]. In order to reduce voltage stress on transistors, we present a double-resonance scheme in Section III. III. DOUBLE-RESONANCE CIRCUIT The double-resonance circuit shapes the voltage waveform at the transistor gate of the PA at node A in Fig. 2 using harmonic control. The voltage waveform at node B in Fig. 2 is usually induced by the switching-mode driver stage because the switching-mode driver amplifier’s output is adaptable to drive the class-E PA [16], [20]–[22]. Thus, the switching-mode driver amplifier operates in the nonlinear region, containing many harmonics in the output waveform. When the output signal from the driver stage is applied to the main stage, there is only a dc-bias difference between the driver stage output node and the main stage input node, which are indicated as “B” and “A,” respectively, in Fig. 2. Thus, the waveform on node A in Fig. 2 can be written in general form as

(7) where

represents the coefficient of th harmonics.

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Fig. 3. Waveforms of input voltage (v ) and output voltage (v ) of CMOS class-E amplifier (Fig. 1), and voltage stress reduction (1V ) by double-resonance circuit with maintaining duty cycle (transistor threshold voltage = 0:5 V = 1:0 V). and V

The resonance frequencies of the double-resonance circuit are fundamental frequency and second harmonic. The control of these harmonics shapes the voltage waveform , as described in Fig. 3, by reducing even harmonics. The double-resonance circuit trespasses fundamental frequency and third harmonic from driver stage to the main stage and removes the second harmonic. Since the voltage of the drain (or collector) hits its peak value in a 50% duty cycle) when the switch (theoretically is in the off state, the highest voltage stress is applied across the gate–oxide during this period (see Fig. 3). Applying the doubleresonance circuit increases the dc offset of and does not to stay too far below the transistor’s threshold voltage allow during the off state, without deteriorating the duty cycle. Therein the off state decreases maximum voltage fore, a higher stress across the transistor. This voltage shaping by the double-resonance circuit using harmonic control differs from dc-bias increasing. DC-bias increasing changes the duty cycle of the amplifier and different duty cycles have different drain (or collector) peak voltages [10]. As the duty cycle increases, the peak voltage also increases, and it worsens the voltage stress on the transistor. However, voltage shaping via harmonic control exhibits the same duty cycle in 0.5-V threshold voltage transistors in Fig. 3 and allows the PA to maintain its performance. Above all, our double-resonance circuit using harmonic control relieves transistors from breakdowns through voltage stress reduction. In a CMOS class-E amplifier with 1.0-V supply voltage, voltage stress is reduced about 0.3 V from 4.3 to 4.0 V in simulation. Furthermore, eliminating the second harmonic and trespassing odd harmonics (fundamental freto have faster rising quency and third harmonic) moves and falling times, which aids in switching the amplifier’s operation. To implement the double-resonance circuit, we used two resonators. One is the parallel resonator consisting of gate

Fig. 4. Normalized voltage v (on transistor drain) and current i (flowing transistor) waveforms of class E for different values of !C R with 50% duty cycle.

inductor and main stage input capacitance , as described in Fig. 2. It is designed to resonate at the fundamental frequency to drive the main amplifier efficiently, overcoming reslarge input capacitance. The other resonator is a series attached to the output node of driver stage, reonator jecting the second harmonic and trespassing the fundamental frequency and third harmonic at node B in Fig. 2. With the proposed double-resonance circuit, transistors are relieved from breakdowns and obtain margins to increase supply voltage in the main stage of operation. Higher supply voltage brings enhanced PA performance. Obviously, a PA with a higher supply voltage delivers a greater output power with the same load impedance. In addition, in watt-level output power CMOS PAs, load impedance is usually a few ohms, and thus, a higher ratio of impedance transformer is required to obtain higher output power. However, when a higher supply voltage can be applied using this double-resonance scheme, a higher load impedance can be implemented for the same output power with efficiency enhancement. IV. NEGATIVE CAPACITANCE A. Shunt Capacitance Analysis As we stated in Section II, efficiency declines when the value deviates from its optimum value and we derived as the relationship between and (8)

which has an inverse proportion between and . When increases from 0.1836, decreases and the transistor . On the other side, drain voltage is a positive value at decreases from 0.1836, increases, resulting in when a negative drain voltage at . The waveforms of and in a single period are shown in Fig. 4 for different values when 50% duty cycle is applied. The transistor and off for . When is on for

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the ZVS condition is not satisfied is not 0.1836), the voltage and current waveforms will overlap at the beginning of the next period because transient time is required to have zero voltage across the transistor drain and source. This transition time results in a loss during the finite transient time [29]. Therevalue should fore, with the given frequency and fixed be maintained with optimum value to achieve high efficiency in the class-E amplifier. B. Negative Capacitance In the field of a CMOS PA, a large gatewidth is inevitable in delivering watt-level output power. The gatewidths are some millimeters wide and these wide transistors contain picofarad capacitance on the drain node. This adds parasitic capacitance , increasing from its desired optimum value and on resulting in drain efficiency (DE) degradation. In addition, in the class-E CMOS amplifier, cascode topology is preferred for its reliability due to the characteristic of high-peak voltage. The additional common-gate (CG) amplifier usually has a large gatewidth to reduce on-resistence and it also contributes to the . Thus, as increases, compensation for surincrease of plus capacitance is more significant for efficiency restoration. value, surplus capacitance To maintain the optimum should be tuned out. One of the techniques used to tune out surplus capacitance is to place an inductor on the same node with a dc block [21]. However, the inductor requires a large area to be implemented into an integrated circuit. Moreover, it contains parasitic components, such as parasitic capacitance and resistance in itself, and has a low quality factor ( factor). Therefore, we use negative capacitance to tune out surplus in cascode topology. Basically, negative capacitance works in the same manner as polarity-inversed Miller capacitance. Miller capacitance is stated as (9) where tional

indicates the voltage gain of the ’s nodes. Convenis applied with negative , increasing capacitance to times . On the contrary, we applied positive to obtain negative capacitance. The realization of negative capac. Since is conitance is shown in Fig. 5(a), as noted by nected between the input and output CG amplifier, which has positive gain , it generates negative capacitance on node A, as described in Fig. 5(b). This negative capacitance compensates for surplus capacitance on node A in Fig. 5, adjusting to optimum value and restoring nominal class-E PA operation. Negative capacitance using a capacitor benefits the integrated CMOS PA. A capacitor demands a much smaller area than an inductor and has a higher factor with less parasitic components than an inductor. Moreover, it can be tuned by arraying parallel capacitors with switches and requires a very small value thanks to CG amplifier gain . Parasitic capacitance on node B is not as much of a concern as that of node A because the value of parasitic capacitance on

Fig. 5. Schematic of: (a) negative capacitance realization and (b) its equivalent circuit.

node B is smaller than that on node A in Fig. 5. In addition, the CG amplifier is always turned on to reduce on-resistence so most of the capacitor charging/discharging occurs at node A in Fig. 5 based on the switching operation.

V. CIRCUIT DESIGN A. Main Stage A class-E amplifier has high peak voltage across the transistor so the voltage stress on CMOS transistors should be considered carefully. For this reason, we adopt cascode topology to ensure freedom from breakdowns because the cascode structure divides large output voltage swing into two series transistors [15]. For the given standard 0.13- m CMOS process, the foundry provided two different types of transistors, which are: 1) a thin gate–oxide transistor, which has a 0.13- m gate length for 1.2-V supply voltage and 2) a thick gate–oxide transistor, which has a 0.34- m gate length for 3.3-V supply voltage. We used a thin gate–oxide transistor as the common source (CS) amplifier and a thick gate–oxide transistor as the CG amplifier to ensure the best performance. This combination works better than two thick gate–oxide transistors because the thin gate–oxide transistor demonstrates a better RF performance and has smaller on-resistence than the thick gate–oxide transistor. Better RF performance alleviates the complexity of the driver amplifier and leads to higher operation efficiency. Furthermore, it contains fewer parasitic components such as drain capacitance, which affects increase of the value. In this study, we used 4000- m gatewidth transistors for the CS amplifier. For the CG amplifier, we used a thick gate–oxide transistor for its sustainability. In class-E cascode topology, large voltage swing is applied on the CG amplifier [21]. Thick gate–oxide transistors prevent breakdowns and they are biased to be on-state all the time, lowering on-resistence to maintain high efficiency.

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Fig. 7. Chip photograph of proposed CMOS class-E PA.

Fig. 6. Schematic of proposed differential PA with cascode topology, including driver amplifiers and input balun, realized in a 0.13-m CMOS technology.

For the CG amplifier, total gatewidths of 7000- m transistors were implemented. The entire schematic is described in Fig. 6. B. Driver Stage For the driver stage, a class-E amplifier is implemented. Since a class-E amplifier has a large voltage swing on its output, it can drive the main amplifier sufficiently with low supply voltage. Low supply voltage on the driver amplifier consumes low dc power so it reduces efficiency degradation from DE to poweradded efficiency (PAE). Double-resonance circuit is also considered for designing load impedance of the driver stage. In this study, the difference in efficiency between DE and PAE is only 3–4 %-points. We also chose cascode topology to prevent breakdowns of the thin gate–oxide transistors, which have 200- m gatewidths. In addition, a transformer was implemented on a chip as an input balun. This transformed the single-ended structure to a differential structure in order to drive differential amplifiers. C. Double-Resonance Circuit Shaping the voltage waveform at the input of the main amplifier was accomplished by using a double-resonance circuit. As described in Section III, an inductor on the main amplifier gate was used as part of the resonance circuit and it resonated with the main amplifier input capacitance at the operation frequency.

The other resonator is attached on the output of driver amplifier resonator. This series resonator deprives the using the series second harmonic from the signal flowing to the main amplifier input and allows the third harmonic to trespass into the main amplifier. The proposed double-resonance circuit reduces voltage stress on the CS amplifier implemented with a thin gate–oxide transistor on the main stage cascode structure, and shapes the voltage waveform without deteriorating the PA performance and duty cycle. We simulated its effectiveness using the Advanced Design System (ADS) and 0.2-V voltage stress was relieved from the CMOS transistor. D. Negative Capacitance The negative capacitance is connected to the input and output of the CG amplifier in the main stage. It compensates for , restoring it to its optimum value. surplus capacitance on This scheme provides negative capacitance simply with a capacitor, without an additional circuit, to generate negative capacitance. There is tradeoff between the value of and stability beprovides a feedback path on the CG amplifier. Howcause ever, thanks to the CG amplifier gain , the required capaciis small and a 1.0-pF capacitor was inserted tance value of in our design. On simulation assisted by ADS, stability degradation was not observed. In addition, this negative capacitance and PAE was enhanced by compensated about 10.0 pF of about 6 %-points in simulation. VI. MEASUREMENT AND RESULTS The proposed PA, including the driver stage and input balun, is fabricated using the 0.13- m standard CMOS process. The chip photograph is shown in Fig. 7. The die area, including the bonding pads, is 1.0 mm . We used multiple bonding pads to minimize the effects from bonding inductance variation. Twelve pads were implemented to reduce ground resistance and provide PA heat sink. Off-chip passive components were implemented on an FR4 printed circuit board (PCB).

SONG et al.: CMOS CLASS-E PA WITH VOLTAGE STRESS RELIEF AND ENHANCED EFFICIENCY

Fig. 8. Measured (solid line) and simulated (dashed line) output power (P . DE, and PAE versus supply voltage V

),

Fig. 9. Measured output spectrum and emission mask of GSM.

The measured and the simulated DE and PAE versus main are plotted in Fig. 8, along with output supply voltage varies from 0.3 to 3.5 V with mainpower, at 1.8 GHz. tained 2.5-V CG amplifier gate bias during the sweep. 31.5-dBm output power, and DE and PAE were measured as 54% and 51%, V. increasing from 3.3 to 3.5 respectively, with V resulted in 0.4-dB output power increment on measurement. For the test, input signal was set as 6.5 dBm and a 25-dB power gain was achieved. The class-E PA is a switching amplifier, thus, constant envelope modulation signals are suitable. To test this PA, the GMSK modulated signal with 0.3 bandwidth time (BT) product is applied, and the measured spectrum is shown in Fig. 9. With average output power of 31.5 dBm, this PA satisfies the given spectrum mask with 0.6% error vector magnitude (EVM). The second and third harmonic suppressions were obtained as 52 and 29 dBc, respectively. Due to the differential architecture, the second harmonic is clearly suppressed. Fig. 10 shows DE, PAE, and output power according to operating frequency. Maximum output power was measured as 31.5 dBm at 1.8 GHz. The maximum DE and PAE were measured as 58% and 54%, respectively, at 1.9 GHz with 31-dBm

Fig. 10. Measured output power (P frequency.

Fig. 11. Measured output power (P

315

), DE, and PAE versus operating

), DE, and PAE versus time.

output power. Over the range from 1.6 to 2.0 GHz, more than 29-dBm output powers were measured. Fig. 11 demonstrates the reliability of our cascode class-E PA. We operated the PA at maximum output power for 4 h. Over the course of 4 h, we checked output power, DE, and PAE, mainV. We could not observe obvious output taining power and efficiency degradation during the test. Output power dropped only 0.05 dB, and DE and PAE were dropped 0.7% and 0.8%, respectively, after 4-h operation. Finally, to compare the performance of this study against state-of-the-art CMOS PAs, we used the figure of merit (FoM) introduced by the International Technology Roadmap for Semiconductor (ITRS), which normalizes major performances such ), PAE, power gain ( ), and the square of as output power ( [30] operating frequency (10) with relative works, differential structure CMOS PAs around watt-level output power, are plotted in Fig. 12 according to maximum output power. This proposed PA shows high performance compared to other studies.

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[11] J. Jeon, J. Kim, and Y. Kwon, “Temperature compensating bias circuit for GaAs HBT RF power amplifiers with a stage bypass architecture,” Electron. Lett., vol. 44, no. 19, pp. 1141–1143, Sep. 2008. [12] S. Gao, H. Xu, S. Heikman, U. K. Mishra, and R. A. York, “Two-stage quasi-class-E power amplifier in GaN HEMT technology,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 1, pp. 28–30, Jan. 2006. [13] P. Watson et al., “An indium phosphide -band class-E power MMIC with 40% bandwidth,” in IEEE Compound Semiconduct. Integr. Crcuits. Symp., Palm Springs, CA, Nov. 2005, pp. 220–223. [14] K.-C. Tsai and P. R. Gray, “A 1.9-GHz, 1-W CMOS class-E power amplifier for wireless communications,” IEEE J. Solid-State Circuit, vol. 34, no. 7, pp. 962–970, Jul. 1999. [15] C. Yoo and Q. Huang, “A common-gate switched 0.9-W class-E power amplifier with 41% PAE in 0.25- m CMOS,” IEEE J. Solid-State Circuits, vol. 36, no. 5, pp. 823–830, May 2001. [16] J. Jang, C. Park, H. Kim, and S. Hong, “A CMOS RF power amplifier using an off-chip transmision line transformer with 62% PAE,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 5, pp. 385–387, May 2007. [17] R. Brama, L. Larcher, A. Mazzanti, and F. Svelto, “A 30.5 dBm 48% PAE CMOS class-E PA with integrated balun for RF applications,” IEEE J. Solid-State Circuits., vol. 43, no. 8, pp. 1755–1762, Aug. 2008. [18] K. L. R. Mertens and M. S. J. Steyaert, “A 700-MHz, 1-W fully differential CMOS class-E power amplifier,” IEEE J. Solid-State Circuits, vol. 37, no. 1, pp. 137–141, Jan. 2006. [19] R. Negra and W. Bächtold, “Lumped-element load-network design for class-E power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2684–2690, Jun. 2006. [20] M. Apostolidou et al., “A 65 nm CMOS 30 dBm class-E RF power amplifier with 60% power added efficiency,” in IEEE Radio Freq. Integr. Circuits Symp. Dig., Jun. 2008, pp. 141–144. [21] A. Mazzanti, L. Larcher, R. Brama, and F. Svelto, “Analysis of reliability and power efficiency in cascode class-E PAs,” IEEE J. Solid-State Circuits., vol. 41, no. 5, pp. 1222–1229, May 2006. [22] C.-C. Ho, C.-W. Kuo, C.-C. Hsiao, and Y.-J. Chan, “A fully integrated class-E CMOS amplifier with a class-F driver stage,” in IEEE Radio Freq. Integr. Circuits Symp. Dig., Jun. 2003, pp. 211–214. [23] E. Cipriani, P. Colantonio, F. Giannini, and R. Giofrè, “Optimization of class-E power amplifier design above theoretical maximum frequency,” in Proc. 38th Eur. Microw. Conf., Oct. 2008, pp. 1541–1544. [24] A. Grebennikov and N. O. Sokal, Switchmode RF Power Amplifiers. Burlington, MA: Newnes, 2007, pp. 186–190. [25] F. H. Raab, “Effects of circuit variations on the class E tuned power amplifier,” IEEE J. Solid-State Circuits, vol. SSC-13, no. 4, pp. 239–247, Apr. 1978. [26] N. O. Sokal, “Class E high efficiency switching-mode power amplifiers, from HF to microwave,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1998, pp. 1109–1112. [27] N. O. Sokal, “Class-E power amplifiers,” QEX/Commun. Quart., pp. 9–20, Jan./Feb. 2001. [28] M. Kazimierczuk, “Collector amplitude modulation of the class E tuned power amplifier,” IEEE Trans. Circuits Syst., vol. CAS-31, no. 6, pp. 543–549, Jun. 1984. [29] F. H. Raab and N. O. Sokal, “Transistor power losses in the class E tuned power amplifier,” IEEE J. Solid-State Circuits, vol. SSC-13, no. 6, pp. 912–914, Dec. 1978. [30] International Technology Roadmap for Semiconductors, System Drivers, 2005.

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Fig. 12. Comparison of watt-level CMOS PAs (differential structure) through ITRS FoM . * indicates integrated output balun.

VII. CONCLUSION In this paper, we presented a differential class-E PA, including a double-resonance circuit using harmonic control, and it reduced voltage stress on the transistors. We also used a negative capacitance to compensate for surplus capacitance on the drain of a class-E amplifier in order to achieve high efficiency with cascode topology. This amplifier delivers 31.5-dBm output power with 54% DE and 51% PAE at 1.8 GHz using the 0.13- m standard CMOS process. There was almost no performance degradation during 4-h maximum power operation. REFERENCES [1] N. O. Sokal and A. D. Sokal, “Class E—A new class of high-efficiency tuned single-ended switching power amplifiers,” IEEE J. Solid-State Circuits, vol. SC-10, no. 6, pp. 168–176, Jun. 1975. [2] F. H. Raab, “Idealized operation of the class E tuned power amplifier,” IEEE Trans. Circuits Syst., vol. CAS-24, no. 12, pp. 725–735, Dec. 1977. [3] N. Kumar, C. Prakash, A. Grebennikov, and A. Mediano, “High-efficiency broadband parallel-circuit class E RF power amplifier with reactance-compensation technique,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 3, pp. 604–612, Mar. 2008. [4] M. Kazimierczuk and K. Puczko, “Exact analysis of class E tuned power amplifier at any and switch duty cycle,” IEEE Trans. Circuits Syst., vol. CAS-34, no. 2, pp. 149–158, Feb. 1987. [5] A. V. Grebennikov, “Class E high-efficiency power amplifiers: Historical aspect and future prospect,” Appl. Microw. Wireless, vol. 14, no. 72, pp. 64–71, Jul.–Aug. 2002. [6] C.-H. Li and Y.-O. Yam, “Maximum frequency and optimum performance of class E power amplifiers,” Proc. Inst. Elect. Eng.—Circuits Devices Syst., vol. 141, pp. 174–184, Jun. 1994. [7] A. J. Wilkinson and K. A. Everard, “Transmission line load network topology for class E power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 6, pp. 1202–1210, Jun. 2001. [8] T. Tuetsugu and M. L. Kazimierczuk, “Analysis and design of class E amplifier with shunt capacitance composed of nonlinear and linear capacitances,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 7, pp. 1261–1268, Jul. 2004. [9] P. Alinikula, K. Choi, and I. Long, “Design of class E power amplifier with nonlinear parasitic output capacitance,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 46, no. 2, pp. 114–119, Feb. 1999. [10] A. Mediano, P. Molina-Gaudó, and C. Bernal, “Design of class E amplifier with nonlinear and linear shunt capacitances for any duty cycle,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 3, pp. 484–492, Mar. 2007.

Q

Yonghoon Song (S’09) received the B.S. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 2007, and is currently working toward the M.S. degree at Seoul National University. His research area is on power efficient transmitter architecture and RF circuits for wireless communications. He is currently involved with linear amplification with nonlinear components (LINC) and highly efficient CMOS PAs.

SONG et al.: CMOS CLASS-E PA WITH VOLTAGE STRESS RELIEF AND ENHANCED EFFICIENCY

Sungho Lee (S’09) received the B.S. and M.S. degrees in electrical engineering from Sogang University, Seoul, Korea, in 1998 and 2000, respectively, and is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University, Seoul, Korea. While working toward the B.S. and M.S. degrees, his focus was on high-speed high-resolution analog-to-digital converters. In 2000, he joined GCT Semiconductor, San Jose, CA, where he has been involved with various RF transceiver developments for wireless communication applications, including WCDMA, PHS, GSM, and S/T DMB. His research interests include RF/analog circuits and transceivers in nanometer CMOS technology.

Eunil Cho received the B.S. degree in electrical engineering from Korea University, Seoul, Korea, in 2008, and is currently working toward the M.S. degree at Seoul National University, Seoul, Korea. His research interest is CMOS RF circuits for wireless communications with a special focus on highly efficient RF PA design.

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Jaejun Lee (S’09) received the B.S. and M.S. degrees in electrical engineering from Sogang University, Seoul, Korea, in 1997 and 1999, respectively, and is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University, Seoul, Korea. While working toward the B.S. and M.S. degrees, his focus was on high-speed off-chip signal integrity. In 1999, he joined Samsung Electronics, Hwasung, Korea, where he is currently Senior Engineer with the Department of the DRAM Design Team. His research interests include off-chip signal integrity, on-chip signal integrity, and high-speed I/O design.

Sangwook Nam (S’87–M’88) received the B.S. degree from Seoul National University, Seoul, Korea, in 1981, the M.S. degree from the Korea Advanced Institute of Science and Technology (KAIST), Seoul, Korea, in 1983, and the Ph.D. degree from The University of Texas at Austin, in 1989, all in electrical engineering. From 1983 to 1986, he was a Researcher with the Gold Star Central Research Laboratory, Seoul, Korea. Since 1990, he has been a Professor with the School of Electrical Engineering and Computer Science, Seoul National University. His research interests include the analysis/design of electromagnetic (EM) structures, antennas, and microwave active/passive circuits.

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A Dual-Band Self-Oscillating Mixer for C -Band and X -Band Applications Brad R. Jackson, Student Member, IEEE, and Carlos E. Saavedra, Senior Member, IEEE

Abstract—A self-oscillating mixer that employs both the fundamental and harmonic signals generated by the oscillator subcircuit in the mixing process is experimentally demonstrated. The resulting circuit is a dual-band down-converting mixer that can operate in -band from 5.0 to 6.0 GHz, or in -band from 9.8 to 11.8 GHz. The oscillator uses active superharmonic coupling to enforce the quadrature relationship of the fundamental outputs. Either the fundamental outputs of the oscillator or the second harmonic oscillator output signals that exists at the common-mode nodes are connected to the mixer via a set of complementary switches. The mixer achieves a conversion gain between 5–12 dB in both frequency bands. The output 1-dB compression points for both modes of the mixer are approximately 5 dBm and the output third-order intercept point for -band and -band operation are 12 and 13 dBm, respectively. The integrated circuit was fabricated in 0.13- m CMOS technology and measures 0.525 mm2 including bonding pads. Index Terms—Dual-band mixer, harmonic self-oscillating mixer (SOM), quadrature oscillator, subharmonic mixer.

I. INTRODUCTION

T

HE DESIRE to realize multifunction wireless communications devices has led to an interest in designing circuits that operate in multiple bands in an attempt to avoid requiring a duplication of the RF circuitry. Often in multiband wireless communications systems, there is a separate RF front-end for each frequency band of operation, consisting of multiple lownoise amplifiers, mixers, and oscillators. Clearly there is significant potential to reduce power consumption and chip area required if some of the RF front-end circuits can be used for more than one frequency band. There have been several demonstrations of dual-band mixer circuits. For example, in [1], a switched inductor matching network was used to match the input impedance in the two bands of interest. Similarly, in [2], an L–C network was used to achieve input and output matching simultaneously in the two desired bands. In [3], a dual-band front-end was demonstrated, but used redundant circuitry as opposed to realizing a dual-band mixer with a single mixer core. A dual-band upconverter was discussed in [4], but also used two mixer cores. In each of these Manuscript received February 04, 2009; revised August 19, 2009. First published January 19, 2010; current version published February 12, 2010. This work was supported in part by the Ontario Centres of Excellence (OCE) and by the Natural Sciences and Engineering Research Council of Canada (NSERC). B. R. Jackson is with the Department of Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON, Canada K7K 7B4 (e-mail: [email protected]). C. E. Saavedra is with the Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada K7L 3N6 (e-mail: Carlos. [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2037865

Fig. 1. Block diagram of the proposed dual-band SOM.

previous designs, multiple local oscillators (LOs) were used or an external LO signal was used as the input to the mixer. In this paper, a fully integrated dual-band self-oscillating mixer (SOM) circuit is demonstrated that uses a single oscillator and a single mixer core. The dual-band performance is achieved by usefully exploiting the fundamental and harmonic signals that are generated by the oscillator subcircuit. In other words, this circuit can function either as a fundamental-mode SOM or as a subharmonic SOM. While there have been previous studies on subharmonic SOMs [5]–[7] and many more on fundamental-mode SOMs, to the best of our knowledge, this study describes the first chip that incorporates both types of SOMs in a single design. As a demonstration of this technique, a chip was fabricated using CMOS 0.13 m technology with dual-band operation in -band and -band. Measurement results are shown that characterize the gain and linearity of the circuit in both states of operation. II. CIRCUIT DESCRIPTION A block diagram of the proposed dual-band SOM is shown in Fig. 1. This figure shows a downconverting mixer with differential RF input and IF output, as well as a reconfigurable LO input. and If an LO is available that has a differential output at both , two pairs of complementary switches can be used to connect the desired LO signal to the mixer. Depending on the state of the switches, the mixer can have an LO input in two different frequency bands, thus permitting two different RF frequency bands at the mixer input while maintaining a constant IF output. The result is a dual-band SOM using a single on-chip quadrature voltage-controlled oscillator (VCO) along with a single mixer circuit. To distinguish between the two states of the dual-band SOM, the term “fundamental mode” will be used to describe the is circuit state where the fundamental oscillator output at connected to the mixer, and the term “subharmonic mode” will signal is connected be used to describe the state where the to the mixer.

0018-9480/$26.00 © 2010 IEEE

JACKSON AND SAAVEDRA: DUAL-BAND SOM FOR

-BAND AND

-BAND APPLICATIONS

There are many types of mixers that have a broadband frequency response. That frequency response, however, is narrowed by the baluns and impedance-matching circuitry that are used to interface with the mixer. In the case of SOMs, the intrinsic broadband response of the mixer is restricted not only by the interface circuitry, but more importantly by the tuning range of the oscillator subcircuit. The design approach used in this paper noticeably extends the useful bandwidth of the SOM because feeding the mixer stage with the second harmonic of the VCO in addition to the fundamental tone expands the operating frequency band of the SOM by a factor of 3. To see how this occurs, note that, in the fundamental mode, the VCO , but at the second harmonic, the has a tuning range of . Since the tuning range frequency swing is doubled to of the oscillator is the determining factor in the frequency response of the chip, the aggregate bandwidth of this SOM is . now

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Fig. 2. Quadrature VCO using superharmonic coupling.

A. Voltage-Controlled Quadrature Oscillator The general topology chosen for the oscillator in this study is the well-known cross-coupled pair oscillator. This basic oscillator circuit uses two cross-coupled transistors to generate that is used to counteract a negative resistance equal to the losses in the L–C tank. The output of this oscillator is differential at the drains of the two cross-coupled field-effect transistors (FETs). In order to use this technique to realize a quadrature oscillator, two identical cross-coupled oscillator circuits can be used along with a connecting circuit that enforces a quadrature relationship between the fundamental outputs. There have been several techniques proposed to enforce quadrature outputs including fundamental coupling circuits [8] and superharmonic coupling circuits [9]–[13]. Superharmonic coupling exploits the existence of even-ordered harmonic signals at the common-mode nodes of an oscillator, the strongest of which is at twice the fundamental frequency. By enforcing a 180 relationship between the second harmonic signals in the two otherwise separate oscillator circuits, a quadrature relationship between the fundamental outputs is obtained. Superharmonic coupling was the natural choice for this work since the second-harmonic signal will also be used for the mixer while in the subharmonic mode. Superharmonic coupling can be achieved using both passive [9]–[11] and active [12], [13] techniques. Active superharmonic coupling was used for the quadrature oscillator in this study because of its significant advantage of requiring much less space on-chip by replacing the transformer with a cross-coupled pair of FETs. The voltage-controlled quadrature oscillator circuit is shown in Fig. 2. Each of the two cross-coupled oscillators will oscillate at the same frequency , where is the inductance shown in Fig. 2, and is the total capacitance including the varactor capacitance , as well as any parasitic capacitance at the output nodes. The nodes labelled CM1 and CM2 in Fig. 2 are examples of common-mode nodes where only the even-order harmonics of the fundamental outputs exist, . An the most dominant of which is the second harmonic at additional cross-coupled pair is used to connect the two oscillators and generate a 180 relationship between the second-order harmonic signals at CM1 and CM2, which enforces a quadrature

Fig. 3. Simplified circuit schematic of the proposed dual-band SOM in subharmonic mode.

relationship between the fundamental outputs. The frequency of the oscillator is tuned via a control voltage on the varactor shown in Fig. 2. An advantage of using the second-harmonic signal for the mixer while in the subharmonic mode is the doubling of the tuning range of the oscillator compared to the fundamental tuning range. Compared to the quadrature oscillator in [13], this oscillator does not use cross-coupled PMOS transistors above the cross-coupled NMOS transistors in order to maximize the signal at the common-mode nodes CM1 and CM2. The bias voltage on the gates of the coupling circuit is set to strongly couple the signal to ensure a differential relationship is established at CM1 and CM2 when the oscillator reaches a steady-state, thus resulting in quadrature fundamental outputs. Source–follower buffers were connected to the four fundamental outputs of the quadrature oscillator (not shown in Fig. 2) so that the effect of connecting the oscillator output to other circuits will be minimal. To reduce the overall power consumption of the proposed dual-band SOM, any low-power buffer circuit architecture could be used to connect the output of the oscillator to the mixer or even straightforward differential pairs. Furthermore, the buffer circuits could be shut off while

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Fig. 4. Circuit schematic of the proposed dual-band SOM.

the circuit is in the subharmonic mode by simply controlling the gate–voltage on the buffer transistors, which could result in a significant power savings. B. Mixer The mixer circuit uses the top half of the traditional Gilbertcell topology. Fig. 3 shows a simplified circuit schematic of the mixer in the subharmonic mode. The common-mode nodes where the second harmonic signal is dominant is connected to the sources of the RF transistors. signals at CM1 and CM2 are 180 out of phase These with each other, which maintains the double-balanced characteristic of the Gilbert cell. The circuit could be implemented as shown in Fig. 3 as a single-band mixer with the doubled LO frequency output. If implemented in this way, the use of an additional frequency doubler circuit connected to the fundamental output could be avoided, thus saving chip space and reducing power consumption. A simplified circuit diagram of the dual-band SOM is shown in Fig. 4. Included in this figure are the four source–follower buffers that are connected to the fundamental quadrature oscilwas selected to equalize the funlator output. The value of damental signal amplitude with the signal amplitude at CM1 and CM2. To select the fundamental mode for the mixer, is set to , turning on switches the control voltage and and turning off switches and . This connects the 0 and 180 fundamental outputs at to the sources of the RF transistors. The 90 and 270 fundamental outputs are connected to identical source–follower buffers as the 0 and 180 outputs to maintain equal loads to the oscillator tank. Note that the 90 and 270 fundamental outputs of the oscillator are not used in the fundamental mode of operation; howsignal at CM2 for ever, they are required to generate the the subharmonic mode, and they could be used elsewhere in the system if needed. For the subharmonic mode, the control voltage V, turning off switches and , and turning on and . This connects the 0 and 180 switches signals to the sources of the RF transistors.

and are Each of the two outputs of the mixer at connected to source–follower buffers and connected to bonding pads. These two signals are combined off-chip and connected to the 50- measurement equipment. The source–follower buffers and combiner were designed such that the output voltage amload of the measurement equipment is plitude across the . equal to Alternative circuit configurations are possible to achieve a similar behavior to that presented in this study. For example, followed by a an oscillator whose fundamental frequency is signal could be used. While frequency divider to generate the the quadrature oscillator approach employed here does lead to a certain overhead in dc power dissipation due to the need for two oscillators, using the frequency-divider method would not necessarily bring significant savings in dc power since frequency dividers can easily consume as much power as a single oscillator. Another possible configuration is to only use the fundamental outputs of the quadrature oscillator along with the subharmonic mixer described in [14] and [15]. In that type of subharmonic mixer, the four transistors in the LO path require quadrature inputs at 0 , 90 , 180 , and 270 , which is precisely what the quadrature oscillator provides. In order to achieve dual-band operation, a series of switches are needed to connect the 0 , 90 , 180 , and 270 signals to the appropriate LO transistors for the subharmonic mode, and only connect the 0 and 180 to the appropriate LO transistors for the fundamental mode. It was found through simulation that greater conversion gain could be achieved by directly using the doubled frequency component already present at the common mode as opposed to using the quadrature fundamental outputs with an LO doubling pair. Furthermore, a lower noise figure was obtained by using the signal directly from the oscillator due to the elimination of the switching noise that accompanies the LO doubling pairs in the subharmonic mixer topology of [14] and [15]. III. MEASUREMENT RESULTS The dual-band SOM was characterized using coplanar-waveguide probes, signal sources, and a spectrum analyzer. The

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Fig. 5. Measured fundamental LO frequency tuning for V

-BAND APPLICATIONS

= 0 0 2:4 V.

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Fig. 8. IM3 measurement for both fundamental and subharmonic mixer modes.

Fig. 6. Conversion gain at various RF input frequencies for a fixed IF frequency of 200 MHz. Fig. 9. IM2 measurement for both fundamental and subharmonic mixer modes.

TABLE I FUNDAMENTAL-MODE AND SUBHARMONIC-MODE LO FEEDTHROUGH MEASUREMENTS

Fig. 7. Measured IF output power at 200 MHz for various RF input power : GHz and subharmonic mode levels for both fundamental mode : GHz .

(RF = 9 8

)

(RF = 5 0

)

supply voltage was set to 1.5 V. The fundamental oscillation frequency was measured at various varactor control , and the results are shown in Fig. 5. As shown voltages in this figure, the oscillation frequency can be tuned from 4.8 to 5.8 GHz as is varied from 0 to 1.5 V. When the circuit

is in the subharmonic mode, this output frequency is doubled, thus giving an LO frequency range from 9.6 to 11.6 GHz. The conversion gain of the mixer was measured in both states at various LO frequencies and the results are shown in Fig. 6. An IF frequency of 200 MHz was used, giving an RF input frequency range from 5.0 to 6.0 GHz and 9.8 to 11.8 GHz for the fundamental and subharmonic modes, respectively. Fig. 6 shows a power conversion gain of between approximately 10 and 12 dB for the fundamental mode of the mixer, and a range from 5 to 12 dB for the subharmonic mode. The decrease in conversion gain at higher RF frequencies for the subharmonic mode is due

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TABLE II COMPARISON OF HARMONIC SOMs

to parasitic capacitances reducing the signal amplitude as the frequency is increased. Since the input RF signal to the circuit is applied directly to the gates of MOSFETs, as shown in Fig. 4, the input is not matched to a 50- system. This situation would likely be the case when the mixer is a subcircuit of a larger RF integrated circuit (RFIC). The voltage conversion gain of the mixer is approximately 6 dB lower than shown in Fig. 6. The RF power performance of the circuit was measured using a fixed LO fundamental frequency of 4.8 GHz GHz , the input RF power was varied, and the output power of the IF signal was measured. The results of the fundamental-mode measurement with an RF frequency of 5.0 GHz and the subharmonic-mode measurements with an RF frequency of 9.8 GHz are shown in Fig. 7. The two curves are very similar, and the output 1-dB compression points both occur at 5 dBm. The third-order intermodulation (IM3) products were also measured using two-tone RF inputs of 5.00 and 5.02 GHz for the fundamental mode, and 9.80 and 9.82 GHz for the subharmonic mode (IM3 signals at 180 and 240 MHz). The results, shown in Fig. 8, display an output third-order intercept point (OIP3) of 12 dBm for the fundamental mode and 13 dBm for the subharmonic mode. The second-order intermodulation (IM2) products were also measured at an IM2 signal frequency of 20 MHz, and the results are shown in Fig. 9. The mixer demonstrates strong linearity with an output second-order intercept point (OIP2) of 40 dBm in fundamental mode and an OIP2 of 50 dBm for the subharmonic mode. The LO feedthrough was measured at the RF and IF ports and the results are shown in Table I. This table shows the output power levels of the and signals at the RF and IF ports for an LO fundamental frequency of 4.8 GHz. In fundamental mode, the LO signal at the RF port is 40.3 dBm, which is an isolation of approximately 40 dB since the oscillator output signal has a power of approximately 0 dBm from simulations. Similarly, the signal at the RF port for subharmonic mode shows about 36 dB of isolation. The RF to IF isolation was measured to be 35 dB for both mixer states. Since the switches are not ideal, some of the signal will leak into the mixer while it is in the fundamental state and signal will leak to the mixer in the subharmonic some of the state. The conversion gain from the undesired LO signal was measured to evaluate the mixer performance in this regard. With the mixer in the fundamental mode GHz , an RF

Fig. 10. Microphotograph of the dual-band SOM chip.

signal input of 25 dBm at 9.8 GHz was used and the power of the output signal at 200 MHz was measured. Ideally, there should be no power at this frequency, but since some of the signal at 9.6 GHz leaks to the mixer, it will produce a 200-MHz IF output from the 9.8-GHz RF signal. The conversion gain for this case was 15.2 dB. Similarly, with the mixer in the subharmonic mode, an RF input of 25 dBm at 5.0 GHz was used to measure the conversion gain due to the leakage of the fundamental LO signal at 4.8 GHz. The conversion gain for this case was 19.7 dB. In both cases, the conversion gain is more than 20 dB below the conversion gain from the desired LO signal. The leakage can be made smaller by using a switch with higher isolation. An example of such a switch is a three-transistor network arranged in a configuration. The phase noise of the VCO could not be measured because there were no pads connected to the oscillator output. However, the DSB noise figure was measured for the mixer in both states and was found to be 8.7 dB for fundamental mode and 10.9 dB for subharmonic mode. The dc power consumption of the quadrature oscillator alone was measured to be 68 mW including the four buffers. The buffers that are connected to the fundamental outputs of the oscillator consume a total of approximately 48 mW (12 mW each). The mixer circuit adds an additional 2 mW approximately in both the fundamental and subharmonic states. A comparison is shown in Table II, which shows the performance of this work along with several harmonic SOMs. The proposed architecture has the largest bandwidth while also achieving conversion gain. A microphotograph of the fabricated chip is shown in Fig. 10. The dimensions of the chip were 875 m 600 m 0.525 mm including bonding pads.

JACKSON AND SAAVEDRA: DUAL-BAND SOM FOR

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-BAND APPLICATIONS

IV. CONCLUSION A new topology for a dual-band SOM has been demonstrated using CMOS 0.13- m technology. This technique uses both the fundamental and second harmonic outputs of a single on-chip quadrature VCO connected to a mixer through complementary switches. For -band operation, switches connect the fundamental oscillator output to the mixer, and for -band operation, switches connect the second harmonic of the oscillator to the mixer. The mixer achieves a conversion gain of at least 5 dB over RF frequencies of 5.0 to 6.0 GHz and from 9.8 to 11.8 GHz while maintaining a constant IF output. This circuit could be used as part of a multistandard system on a chip to reduce the number of circuit elements required, potentially resulting in lower power consumption and reduced costs. This technique could also be very attractive at millimeter-wave frequencies where the use of a frequency-doubler circuit connected to the output of an LO could be avoided and in cases where the use of a broadband mixer circuit is not possible. REFERENCES [1] Y.-S. Hwang et al., “A 2 GHz and 5 GHz dual-band direct conversion RF frontend for multi-standard applications,” in Proc. IEEE Int. SOC Conf., Sep. 2005, pp. 189–192. [2] T. Abdelrheem, H. Elhak, and K. Sharaf, “A concurrent dual-band mixer for 900 MHz/1.8 GHz RF front-ends,” in Proc. 46th IEEE Int. Midwest Circuits Syst. Symp., Dec. 2003, vol. 3, pp. 1291–1294. [3] W. Kim et al., “A dual-band RF front-end of direct conversion receiver for wireless CDMA cellular phones with GPS capability,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2098–2105, May 2006. [4] M. Arasu et al., “A 3 to 9-GHz dual-band up-converter for a DS-UWB transmitter in 0.18-m CMOS,” in IEEE Radio Freq. Integr. Circuits Symp., Jun. 2007, pp. 497–500. [5] M. Fernandez et al., “Nonlinear optimization of wide-band harmonic self-oscillating mixers,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 5, pp. 347–349, May 2008. [6] S. W. Winkler et al., “Integrated receiver based on a high-order subharmonic self-oscillating mixer,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1398–1404, Jun. 2007. [7] M. Roberts, S. Iezekiel, and C. Snowden, “A W -band self-oscillating subharmonic MMIC mixer,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2104–2108, Dec. 1998. [8] A. Rofougaran et al., “A single-chip 900-MHz spread-spectrum wireless transceiver in 1-m CMOS. I. Architecture and transmitter design,” IEEE J. Solid-State Circuits, vol. 33, no. 4, pp. 515–534, Apr. 1998. [9] J. Cabanillas, L. Dussopt, J. Lopez-Villegas, and G. Rebeiz, “A 900 MHz low phase noise CMOS quadrature oscillator,” in IEEE Radio Freq. Integr. Circuits Symp., 2002, pp. 63–66.

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[10] C. Meng, Y. Chang, and S. Tseng, “4.9-GHz low-phase-noise transformer-based superharmonic-coupled GaInP/GaAs HBT QVCO,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 339–341, Jun. 2006. [11] S. Gierkink et al., “A low-phase-noise 5-GHz CMOS quadrature VCO using superharmonic coupling,” IEEE J. Solid-State Circuits, vol. 38, no. 7, pp. 1148–1154, Jul. 2003. [12] T. Hancock and G. Rebeiz, “A novel superharmonic coupling topology for quadrature oscillator design at 6 GHz,” in IEEE Radio Freq. Integr. Circuits Symp. Dig., Jun. 2004, pp. 285–288. [13] B. R. Jackson and C. E. Saavedra, “A 3 GHz CMOS quadrature oscillator using active superharmonic coupling,” in Eur. Microw. Conf., Oct. 2007, pp. 1109–1112. [14] K. Nimmagadda and G. Rebeiz, “A 1.9 GHz double-balanced subharmonic mixer for direct conversion receivers,” in IEEE Radio Freq. Integr. Circuits Symp., Dig., 2001, pp. 253–256. [15] B. R. Jackson and C. E. Saavedra, “A CMOS subharmonic mixer with input and output active baluns,” Microw. Opt. Technol. Lett., vol. 48, pp. 2472–2478, Dec. 2006.

Brad R. Jackson (S’05) received the B.Sc. (Eng.) degree in electrical engineering, M.Sc. (Eng.) degree, and Ph.D. degree in electrical engineering from Queen’s University, Kingston, ON, Canada, in 2002, 2005, and 2009, respectively. He is currently a Postdoctoral Fellow with the Royal Military College of Canada, Kingston, ON, Canada. His research interests are in the field of RF CMOS and RF microelectromechanical systems (MEMS) integrated circuits such as mixers, filters, low-noise amplifiers (LNAs), frequency dividers, and frequency multipliers, as well as antennas and radar systems. Dr. Jackson is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

Carlos E. Saavedra (S’92–M’98–SM’05) received the Ph.D. degree in electrical engineering from Cornell University, Ithaca, NY, in 1998. From 1998 to 2000, he was with the Millitech Corporation, South Deerfield, MA. Since August 2000, he has been with the Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada, where he is currently an Associate Professor and the Coordinator of Graduate Studies. His research interests are in the field of microwave integrated circuits and systems for communications, automotive, and biological applications. Dr. Saavedra is a Registered Professional Engineer (P. Eng.) in the Province of Ontario. He is the vice-chair of the MTT TCC-22 and is a member of the Technical Program Committee of the IEEE RFIC Symposium.

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A Novel Alternating and Outphasing Modulator for Wireless Transmitter Yijun Zhou and Michael Yan-Wah Chia, Member, IEEE

Abstract—This paper describes a novel alternating and outphasing modulator for the generation and amplification of a linear modulation signal. The architecture requires a linear modulation signal to be represented as two outphasing signals with a constant envelope, which are alternating or switching at the input of two nonlinear amplifiers to produce a linear modulation signal. A power combiner can be employed to cancel the mixed components due to the switching. This will minimize the requirements of the output filter, and hence, simplified the design. This new modulation architecture is simple, and hence, is suitable for all-digital integration. The measurement results of the wideband code division multiple access signal are presented and compared with a conventional linear amplification with nonlinear components architecture. Index Terms—All-digital, linear amplification with nonlinear components (LINC), linear modulation, outphasing.

I. INTRODUCTION

M

OBILE terminals have increased rapidly as more users demand wireless connectivity at a low cost. Besides the traditional handheld phone, portable equipment such as the notebook computer, personal digital assistant (PDA), etc. also require wireless communications for Internet connectivity. The different wireless standards such as wideband code division multiple access (WCDMA), worldwide interoperability for microwave access (WiMAX), and wireless local area network (WLAN) are becoming popular and have to coexist on the same terminal. Thus, there is a strong demand for a low-cost, low power consumption, and multistandard compatible transceiver for these applications. Due to the continuous miniaturization of semiconductors, the system integration on a single chip or system-on-chip (SOC) becomes an effective solution to reduce the cost and power consumption of the mobile terminal. The transceiver is the critical part for wireless system integration, and normally this is realized with RF analog circuits. The CMOS silicon process is the most widely applied in the integrated circuit industry and it is aimed for digital circuit design. RF CMOS circuits benefit from the process downscaling as well, and are becoming popular in recent years, but unlike the digital circuit, they are much more complicated to design and integrate on a chip. Most RF CMOS circuits follow the traditional analog circuit design method and have to be redesigned Manuscript received July 15, 2009; revised October 30, 2009. First published January 19, 2010; current version published February 12, 2010. The authors are with the Institute for Infocomm Research, Agency for Science, Technology and Research, (A*STAR), Singapore 138632 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037879

as the process changed. In a SOC design, the digital part tends to follow Moore’s law to reduce size, power consumption, and cost, but the analog part is harder to redesign to follow the process change. This not only increases the costs of time and manpower, but also the difficulty and risk in the product design. Therefore, an all-digital transceiver will be well suited for a modern deep-submicrometer CMOS process, as it owns the programmable and scalable advantages of the digital circuit, and can be easily integrated with other digital units such as a microcontroller, digital signal processor (DSP), etc. Besides, its power consumption is reduced with the down scaling of the semiconductor process. With the reconfigurable digital circuits and the software-defined radio (SDR) technique, the multistandard compatible requirement can be realized as well. However, the high data-rate transmission needs the complex and bandwidth-efficient digital modulation approaches such as orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA). These modulations require a highly linear modulator to generate the signal for bandwidth-efficient transmission. Thus, there is an ongoing need to investigate a new architecture that exploit the digital CMOS process for the all-digital transceiver to generate the linear modulation signal [1]–[3]. Several solutions regarding generation of the linear modulation signal with an all-digital technique, such as the polar modulation technique [2], [4], bandpass delta–sigma modulator [6], [7], linear amplification by sampling technique (LIST) [7], [15], and linear amplification with nonlinear components (LINC) have been reported [5]–[8]. The LINC architecture has recently drawn some attention since it does not require an output filter. Fig. 1 illustrates the architecture of a LINC amplifier, which is based on the vectorial addition of two constant envelope and phase modulated signals [5]–[8]. The two respective constant envelope signals are amplified by a pair of highly efficient, but nonlinear amplifiers. A power combiner is used to recombine these two constant envelope and phase modulated signals to generate the linear modulation signal. The LINC architecture does not need the bandpass filter. However, recent research has revealed the major limitation of LINC, i.e., the stern matching requirement between two branches [6], [7], [10]–[13]. In the LINC architecture, the amplitude modulation is realized by phase cancellation. The matching between two channels requires approximately 0.5 dB for gain and 0.3 for phase [6]. These requirements are extremely difficult to meet without a complex feedback system [1], [13], [14]. Some work has been done regarding the mismatch compensation [9], [12], [13]. This paper introduces a novel architecture for linear modulation signal generation using a new alternating and outphasing

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Fig. 1. (a) Signals in LINC amplifier. (b) Architecture of LINC amplifier. TABLE I FEATURES OF THE INTRODUCED MODULATION METHODS FOR ALL-DIGITAL TRANSCEIVER DESIGN Fig. 2. Architecture of the proposed AOM: (a) with switches in RF and (b) with switches in baseband.

In this paper, we have earlier discussed the motivations for this research in Section I. We will next discuss the principle and provide the analysis of the AOM architecture in Section II. The theory is validated by our designs and experimental results, which are presented in Section III. Conclusions will be delivered in Section IV. II. PRINCIPLE OF AOM

modulator (AOM). By introducing switches at the outphased sources, the alternating and outphasing signals can be generated, and then amplified by nonlinear amplifiers to produce the linear signal modulation and amplification. In addition, with the combination of the two identical branches, the mixed components are removed, and the design of the output filter can be simplified. The proposed modulator has a similar configuration as the LINC modulator, but owns the advantages over the LINC on mismatch tolerance. It has a simple configuration and can provide high linearity. It is easy to be integrated with the all-digital CMOS process. Table I summarizes the above discussions relevant to all-digital transceiver design.

The architecture of the proposed modulator is shown in Fig. 2(a) and (b). The same outphasing signal generator as the conventional LINC amplifier is used in this design. Fig. 2(a) and (b) shows the architecture with RF switches and with baseband switches, respectively. As illustrated in Figs. 1 and 2, RF signal can be separated into two constant and by an envelope and phase modulated signals outphasing signal generator (1) (2) (3) where

and . In Fig. 2(a), the two constant envelope signals and are alternating between the two respective amplifiers by two RF switches SW1 and SW2, which are controlled by switching . Fig. 2(b) realizes the same function by switching signal

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the baseband signals instead. By switching, the phase modulated is alternately multiplied by 1, thus two new consignal and are produced. stant envelope signals Signals and are merely the amplified outputs of and , respectively, (4) (5) where is the gain of the amplifier, and signal with amplitude 1, angle frequency

is a square wave

(6) (7) Substituting (6) into (4),

to be increased. It is also shown from (10) that the output of the combiner is an amplified form of the original or input signal, amplified or multiplied by the gain factor and achieving the linear amplification as well without the usual problem of nonlinearity. The advantages of the use of the combiner are to increase the amplifier’s output and cancel the mixed components to simplify the design of the output filter. Moreover, the linearity of the combiner output is not affected by the mismatches of the two amplification channels. As mentioned, both methods, selecting a switching frequency far away from the signal frequency and using a combiner, can ease the design of output filter. Therefore, in a modulator application, a bandpass filter can remove the mixed components. As compare to the first method, there is a tradeoff between the bandwidth requirement of the amplifier and switching frequency. The following study demonstrates the good linearity characteristics of the proposed design. Assuming there are gain and phase mismatches in the two amplifier branches, from (8)

(11) (8) is then the same as in (9), and then Substituting (6) into (5),

(9) Thus, the combined output

(12) where (10)

It can be shown from (8) and (9) that the output of each amplifier branch consists of and the mixed components of and . By properly selecting , these mixed components can be placed far away from , and removed by the tank circuit of the amplifier and a bandpass filter. Thus, one branch of the amplifier can realize the linear signal generation and amplification. , the requirement for the bandAlthough selecting a high pass filter can be relaxed, the bandwidth of the amplifier needs

(13)

(14) (15) (16)

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Fig. 3. Photograph of the limiting amplifiers and power combiner.

Fig. 5. Data files generated with ADS.

Fig. 4. Measurement setup.

Since the term of is still a constant envelope signal with angle frequency , the mismatch will only affect the cancellation of the mixed components, but not the linearity of the combined output. Thus, the proposed amplifier can tolerate the mismatches in gain and phase of the two branches of amplifiers. Regarding the mixed components, according to (12) and (14), the amplitudes of the mixed components are varied and , and in the case of less than 90 , the with level of the mixed components can be reduced after the combiner. III. EXPERIMENT RESULTS The proposed modulator using AOM architecture is tested and measured using the setup shown in Figs. 3 and 4. A commercial arbitrary waveform generator (AWG) is employed to generate two 2.16-GHz alternating and outphasing signals based on the data file from the WCDMA base-station downlink signal. A spectrum emission mask for the base station with a maximum output power less than 31 dBm is added in the measurement results [16]. The data file is created with commercial tools, i.e., Agilent Technologies’ Advanced Design System and (ADS), which is shown in Fig. 5. Outphasing signals are generated by the outphasing signal generator, and then a 60-MHz signal is applied to switch the two outphasing signals. In Figs. 3 and 4, the two limiting amplifiers ADN2892 from Analog Devices amplify the alternating outphasing signals [17]. As with LINC amplifiers, the voltage mode nonlinear amplifier such as a class-C, class-D, and class-E amplifier can

Fig. 6. Combined output from the AWG. (a) RBW 30 kHz. (b) RBW 300 kHz (to view mixed or higher spectral components).

be used in the proposed architecture. For the all-digital modulator design, the better choice is a class-D amplifier since it is more compatible with an all-digital semiconductor process. Moreover, the limiting amplifier itself can be regarded as the

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Fig. 7. Combined and single-channel outputs from the AWG. (a) RBW 30 kHz. (b) RBW 300 kHz (to view mixed or higher spectral components).

Fig. 8. Combined and single-channel outputs from the limiting amplifier. (a) RBW 30 kHz. (b) RBW 300 kHz (to view mixed or higher spectral components).

output stage for the all-digital modulator. A power combiner ZFRSC-42 from Mini-Circuits [18] is applied to combine the output signals from the AWG directly (route a) or from the limiting amplifiers (route b). Several measured results are provided to show the comparisons between the single-channel output and combined output, the output before and after the amplifier, and the proposed architecture and conventional LINC amplifier. Fig. 6(a) shows the measured result of the combined output from the AWG directly and the WCDMA emission mask. Fig. 6(b) shows the same measurement results in a different frequency span and resolution bandwidth (RBW). In Fig. 6(b), it shows that the mixed components are not fully canceled due to the mismatch of the setup. The measured combined output of the AWG is compared with the single-channel output, and the results are shown in Fig. 7(a) and (b). The measurement results illustrate the linear modulation signal is included in the single-channel output of the alternate outphasing signals. Thus, the linear modulation signal can be generated with a single channel and amplified by a single amplifier, but combining the two alternating outphasing signals can cancel the mixed components, and relax the requirement for the output filter.

The combined and single-channel outputs from the limiting amplifiers are shown in Fig. 8(a) and (b). The mixed components level of the combined output in Fig. 8(b) are higher compared with the mixed components level of the combined output from the AWG directly in Fig. 6(b) due to the mismatch of the two amplification channels and the power combiner. Though mismatch exists between the two amplification channels and power combiner, the measured mixed components level in the combined output is still lower than one in single channel. In order to investigate the tolerance of the proposed architecture to the mismatch of the two channels, the amplitude and timing skew between two channels of the AWG or the limiting amplifier are changed for the following measurements. Case 1) The amplitude of both channels is equal and the time skew between them is zero. Case 2) The amplitude of one channel is 90% of the other channel. The time skew between them is zero. Case 3) The amplitude of one channel is 90% of the other channel. The time skew between them is 100 ps. Fig. 9(a) and (b) shows the measured results of the combined output from the AWG directly in the above three cases. Though

ZHOU AND CHIA: NOVEL AOM FOR WIRELESS TRANSMITTER

Fig. 9. Measured results of the combined output from the AWG. (a) RBW 30 kHz. (b) RBW 300 kHz (to view mixed or higher spectral components).

the mismatch between the two channels affects the cancellation of the mixed component, the linearity of the combined signal is not affected, and this is clearly observed in Fig. 9(a), the measured results of Case 1) and Case 2) are almost identical. In another comparison, the tolerance to the mismatch in terms of nonlinearity distortion is made between the convention LINC architecture and the proposed architecture. Fig. 10(a) and (b) shows the measurement results of Case 3) for the proposed architecture, and Case 1), Case 2), and Case 3) for the LINC architecture. The outputs from the AWG are combined by the power combiner directly in both architectures. Fig. 10(a) and (b) shows that even with the condition of Case 3), the proposed architecture has a better performance in linearity compared with the LINC architecture in all three cases. Figs. 9 and 10 both demonstrate that the linearity of the proposed AOM architecture has not been affected under the mismatched condition, whereas the linearity of the conventional LINC architecture is distorted. In addition, the error vector magnitude (EVM) of the combined and single-channel outputs is also measured. The measured results are summarized in Table II. The modification of the output voltage of the limiting amplifier is realized by changing

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Fig. 10. Comparison of tolerance to the mismatch between the conventional LINC architecture and the proposed architecture. (a) RBW 30 kHz. (b) RBW 300 kHz (to view mixed or higher spectral components).

TABLE II SUMMARY OF THE EVM PERFORMANCE

its supply voltage. In Case 3), the output from the conventional LINC amplifier does not meet the specifications of the WCDMA standard, but the proposed AOM architecture is able to satisfy the specifications. IV. CONCLUSION A novel AOM for linear modulation signal generation and amplification has been introduced. The new modulator can be

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used as a single-channel or combined architecture. The highly linear modulation with nonlinear amplifiers is achieved. The combined architecture can tolerate the mismatch of gain and phase between the two channels and cancel the mixed components. Thus, the requirement for the output filter can be relaxed. The configuration of the proposed modulator is simple and suitable for all-digital integration. ACKNOWLEDGMENT The authors are grateful to the reviewers for their valuable suggestions. The authors would also like to thank their colleague L. S. Weng, Institute for Infocomm Research (I R), Singapore, for his help during the test and measurements. The authors also gratefully acknowledge the support of the Agency for Science, Technology and Research, (A*STAR), Singapore. REFERENCES [1] M. E. Heidari, L. Minjae, and A. A. Abidi, “All-digital outphasing modulator for a software-defined transmitter,” IEEE J. Solid-State Circuits, vol. 44, no. 4, pp. 1260–1271, Apr. 2009. [2] R. B. Staszewski et al., “All-digital PLL and transmitter for mobile phones,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2469–2482, Dec. 2005. [3] Y. Zhou and M. Y.-W. Chia, “High efficiency power amplifier,” PCT patent priority application US61/040754, Mar. 31, 2008. [4] A. W. Hietala, “A quad-band 8PSK/GMSK polar transceiver,” IEEE J. Solid-State Circuits, vol. 41, no. 5, pp. 1133–1141, May 2006. [5] F. H. Raab et al., “Power amplifiers and transmitters for RF and microwave,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 814–826, Mar. 2002. [6] P. M. Asbeck, L. E. Larson, and I. G. Galton, “Synergistic design of DSP and power amplifiers for wireless communications,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 11, pp. 2163–2169, Nov. 2001. [7] P. B. Kenington, High-Linearity RF Amplifier Design. Norwood, MA: Artech House, 2000. [8] D. C. Cox, “Linear amplification with nonlinear components,” IEEE Trans. Commun., vol. COM-22, no. 12, pp. 1942–1945, Dec. 1974. [9] P. Garcia-Ducar, J. de Mingo, and A. Valdovinos, “Improvement in the linearity of a LINC transmitter using genetic algorithms,” IEEE Trans. Wireless Commun., vol. 6, no. 7, pp. 2379–2383, Jul. 2007. [10] L. Sundstrome, “Spectral sensitivity of LINC transmitters to quadrature modulator misalignments,” IEEE Trans. Veh. Technol., vol. 49, no. 4, pp. 1474–1487, Jul. 2000. [11] A. Birafane and A. Kouki, “On the linearity and efficiency of outphasing microwave amplifier,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 7, pp. 1702–1708, Jul. 2004. [12] A. Birafane and A. Kouki, “Phase-only predistortion for LINC amplifiers with Chireix-outphasing combiners,” IEEE Trans. Microw. Theory Tech, vol. 53, no. 6, pp. 2240–2250, Jun. 2005. [13] X. Zhang, L. E. Larson, P. M. Asbeck, and P. Nanawa, “Gain/phase imbalance-minimization techniques for LINC transmitters,” IEEE Trans. Microw. Theory Tech, vol. 49, no. 12, pp. 2507–2516, Jun. 2001. [14] A. Huttunen and R. Kaunisto, “A 20-W Chireix outphasing transmitter for WCDMA base stations,” IEEE Trans. Microw. Theory Tech, vol. 55, no. 12, pp. 2709–2718, Dec. 2007. [15] D. C. Cox, “Linear amplification by sampling techniques: A new application for delta coders,” IEEE Trans. Commun., vol. 23, no. 8, pp. 793–798, Aug. 1975.

[16] Universal Mobile Telecommunication System (UMTS), ETSI TS 125 104 V4.3.0, ETSI, Sophia-Antipolis Cedex, France, 2001–12. [17] “ADN2892 data sheet,” Analog Devices, Norwood, MA, 2005. [Online]. Available: http://www.analog.com/static/imported-files/ data_sheets/ADN2892.pdf [18] “ZFRSC-42 data sheet,” Mini-Circuits, Brooklyn, NY [Online]. Available: http://www.minicircuits.com/pdfs/ZFRSC-42+.pdf, REV. BM108294 ZFRSC-42 HY/TD/CP 090824.

Yijun Zhou received the B.Sc. degree in electronic engineering from Zhejiang University, Hangzhou, China, in 1987, the M.Eng. degree from the Shanghai University of Science and Technology, Shanghai, China, in 1990, and the Ph.D. degree from Lund University, Lund, Sweden, in 2003. From 1990 to 1996, he was a Research and Development Engineer with the Zhejiang Telecommunication Equipment Factory. Since 1996, he has been with the Institute for Infocomm Research (I R), Agency for Science, Technology and Research, (A*STAR), Singapore, where he is a Research and Development Engineer. From 2003, he was a Research Fellow with I R. His current research interests are mixed-signal and RF CMOS circuit design.

Michael Yan-Wah Chia (M’94) was born in Singapore. He has received the B Sc degree (first class honors) and Ph.D. degree from Loughborough University, Loughborough, U.K. In 1994, he has joined the Center for Wireless Communications (CWC), Singapore, as a Member of Technical Staff. He is currently a Principal Scientist and Program Director of Power Aware Wireless Sensor Networks with the Institute for Infocomm Research (I R), Agency for Science, Technology and Research, (A*STAR), Singapore. He also holds an adjunct position with the National University of Singapore. He has held appointments in several technical/advisory committees in industry and national government bodies such as the Infocomm Development Authority, IDA, and SPRING. To date, he has authored or coauthored over 153 publications in international journals and conferences. He holds at least 12 patents. He has led several major wireless research programs in Singapore, particularly in the areas of RF identification (RFID) and ultra-wideband (UWB). He has recently been leading a large research program on terahertz of the Science and Engineering Research Council (SERC), Singapore. He has secured many large projects funded by industry such as EADS, IBM, etc. Since April 2004, his team has also been invited into the IBM Business Partner Program for silicon design. His main research interests are UWB, terahertz, beam steering, wireless broadband, RFID, antennas, transceivers, RF integrated circuits (RFICs), amplifier linearization, and communication and radar system architecture. Dr. Chia has been an active member of organizing committees in various international conferences and was the program cochair of the 2005 IEEE International Workshop of Antenna Technology (IWAT). He was also invited to be a keynote speaker at the 2005 IEEE International Conference of Ultra-Wideband (UWB). He has been the general chair of ICUWB 2007. He has also been a member of the Executive Committee of ICUWB since 2007. He is a member of the Editorial Board of the TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was a recipient of the Overseas Research Student (ORS) Awards presented by U.K. universities and the Research Studentship Award presented by British Aerospace.

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Enhanced Plasma Wave Detection of Terahertz Radiation Using Multiple High Electron-Mobility Transistors Connected in Series Tamer A. Elkhatib, Student Member, IEEE, Valentin Y. Kachorovskii, William J. Stillman, Dmitry B. Veksler, Khaled N. Salama, Member, IEEE, Xi-Cheng Zhang, Fellow, IEEE, and Michael S. Shur, Fellow, IEEE

Abstract—We report on enhanced room-temperature detection of terahertz radiation by several connected field-effect transistors. For this enhanced nonresonant detection, we have designed, fabricated, and tested plasmonic structures consisting of multiple InGaAs/GaAs pseudomorphic high electron-mobility transistors connected in series. Results show a 1.63-THz response that is directly proportional to the number of detecting transistors biased by a direct drain current at the same gate-to-source bias voltages. The responsivity in the saturation regime was found to be 170 V/W with the noise equivalent power in the range of 10 7 W/Hz0 5 . The experimental data are in agreement with the detection mechanism based on the rectification of overdamped plasma waves excited by terahertz radiation in the transistor channel. Index Terms—High electron-mobility transistors (HEMTs), nonresonant detection, plasma waves, room temperature, series-connected transistors, terahertz.

I. INTRODUCTION PPLICATIONS of terahertz technology such as sensing of drugs and explosives materials [1], biomedical imaging [2], and security imaging [3] require terahertz detectors with fast response time. The most common terahertz detectors [4] available now are bolometers [5], pyroelectric detectors, Schottky diodes [6], and photoconductive detectors [7]. Recently, there has been an increasing interest in so-called plasma wave electronics, which uses plasma waves in field-effect transistors (FETs) for emission [8]–[12] and detection [13]–[29] of terahertz radiation. Plasma waves in FETs have a linear dispersion [30], , where is the wave velocity. A structure of gate length

acts for the waves as a resonant “cavity” at frequencies (where ) being harmonics of the fundamental plasma frequency . The quality factor of the FET, where is the based plasma resonator is on the order of momentum relaxation time. The relentless reduction of device dimensions, especially over the last decade, has led to the development of new generations of FETs with very short gates (as 32 nm) and, as a consequence, higher resonance quality factors might be obtained. Such FETs should operate in or close to the ballistic regime [31]. The plasma wave velocity depends on the carrier density in the channel and the gate to channel capaci, where is the electron charge, tance per unit area is the electron effective mass, is the gate-to-channel distance, and is the dielectric constant. In the gradual channel approximation,

A

Manuscript received May 30, 2009; revised August 28, 2009. First published January 22, 2010; current version published February 12, 2010. T. A. Elkhatib, W. J. Stillman, X.-C. Zhang, and M. S. Shur are with the Department of Electrical, Computer, and System Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA (e-mail: [email protected]; stillw2@rpi. edu; [email protected]; [email protected]). V. Y. Kachorovskii is with the Department of the Theory of Electrical and Optical Phenomena in Semiconductors, Ioffe Physical-Technical Institute, St. Petersburg 194021, Russia (e-mail: [email protected]). D. B. Veksler was with the Department of Electrical, Computer, and System Engineering, Rensselaer Polytechnic, Institute, Troy, NY 12180 USA. He is now with the Electrical and Physical Characterization Group, SEMATECH Inc., Albany, NY 12203 USA (e-mail: [email protected]). K. N. Salama was with the Department of Electrical, Computer, and System Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA. He is now with the Electrical Engineering Department, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037872

(1) is the difference between the where gate-to-source voltage and the threshold voltage . Hence, the plasma wave velocity can be easily controlled by the gate voltage (2) , as well as so that the fundamental oscillation frequency its harmonics, may be tuned to be in the terahertz range. The dc current in the FET channel might become unstable with respect to excitation of plasma oscillations [8], thus leading to the generation of gate-tunable terahertz radiation. On the other hand, the excitation by external radiation of plasma oscillations induces a constant source-to-drain voltage due to the nonlinear properties of plasma waves. For FETs having high quality factors, the transistor response, defined as , has a resonant dependence on the radiation frequency with the maxima at , while for a device with a low quality factor, increases with and saturates at some value, which can be controlled by the gate voltage [13] so that detection is nonresonant (at least at relatively small currents). Currently, terahertz detectors based on plasma oscillations in GaAs [16], Si [17], GaN [18], and silicon-on-insulator (SOI) [19] FETs operate over a wide range of subterahertz and terahertz frequencies at high modulation speed. The dependences of the terahertz response on gate and drain bias can be used for

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testing of FETs [28]. Additional information can also be obtained from the spatial dependence of the terahertz response [29]. Plasma wave detectors are tunable and capable of operating at zero drain bias, thus minimizing detector internal noise. On the other hand, dc drain-to-source current dramatically increases the detector response due to the current-driven increase of nonlinear properties of the channel [25]. As was shown in [32] and [33], a dc current might shift such a detector into a resonant detection regime. The predicted responsivity of FET-based detectors depends on their operation regime and is expected to exceed the detectivity of the widely used Schottky diode detectors [13]. To achieve such a level of detectivity, one can increase the responsivity of single FETs or optimize the coupling of the electromagnetic radiation with the FET by using waveguides and/or antenna structures. Even without optimized coupling, single FETs have demonstrated high responsivities (up to 1000 V/W [23], [24]) and a relatively low level of noise equivalent power (NEP) W/Hz [24]). These values approach those (less than 10 of commercially available terahertz detectors operating at room temperature such as micro-bolometers, pyroelectric detectors, and Schottky diodes. A further increase in responsivity (by several orders of magnitude) is expected for FET arrays forming a plasmonic crystal [34], [35]. Such crystals are expected to have much stronger coupling to terahertz radiation than single FETs. One predicts that the responsivity of an FET with unoptimized coupling of the order of 1–10 V/W will increase after optimization of coupling to be of the order of 10 –10 V/W. However, only single transistor structures (albeit some with multiple gates) have been investigated since the first observation of plasma wave detection in FETs. Recently, we have studied the first fabricated multiple transistors structures [36], which might serve as building blocks for a plasmonic crystal detector. In these structures, the transistors were connected in series and were biased separately. We demonstrated that the response of the multiple transistors structure as a whole was equal to the sum of the individual transistor responses. Thus, the overall response was strongly enhanced. In this paper, we present a more detailed study of multiple transistor structures. We demonstrate that the response of each transistor is well described by the plasma wave theory for a single FET [13], [25]. We also report a significant enhancement of the nonresonant detection when the transistors are driven deeper into the saturation region. This paper is organized as follows. Section II summarizes the theoretical background of nonresonant plasma wave detection with emphasis on current-driven effects. The fabricated plasmonic structures of pseudomorphic InGaAs/GaAs HEMTs are described in Section III. We compare the measured and calculated terahertz responses of single transistors in Section IV. Section V presents and discusses the experimental results of detection using multiple transistors connected in series. In Section VI, experimentally determined responsivity and NEP are presented. Finally, our conclusions are drawn in Section VII. II. THEORY OF CURRENT-DRIVEN DETECTION The theory of terahertz detection for was developed in [13] and generalized in [25] to include a nonzero dc current.

In both cases, it was assumed that electron–electron collisions are very fast so that the system can be described by the hydrodynamics equations, i.e., by the Euler equation and the continuity equation as (3) (4) where

is the local value of the gate-to-channel voltage, is the longitudinal electric field in the channel, is the local electron velocity, and is the absolute value of the electron charge. Using the gradual channel approximation, we relate the local carrier density in the electron channel to the local value of the gate-to-channel voltage as (5)

[compare with (1)]. The solution of (3) and (4) requires two boundary conditions. It was assumed, as in both [13] and [25], that the voltage is fixed at the source side of the channel under the gate and the current is fixed at the drain side of the channel and is equal to such that (6) (7) where is the absolute value of the current density is the channel width (since electrons move from source and to drain, the current is negative). Equation (6) implies that the incident terahertz radiation leads to gate voltage oscillations of at frequency . This leads to excitation of electron amplitude density oscillations in the channel with an amplitude, which is fixed at the source by the value . Rectification of these excitations induces the constant source-to-drain voltage (8) For , has a resonant dependence on the radia, while in the nonrestion frequency with the maxima at onant case, where increases with the incident radiation frequency and saturates at some value, which can be controlled by the gate voltage [13]. Both the theory [25] and experiments [15], [25] show that the detection is dramatically enhanced by a dc current (close to the transistor saturation regime) so that the coefficient of proand in (8) increases by a factor of portionality between two magnitude orders compared to the zero current case . In this and paper, we focus on the nonresonant case, when . The latter condition allows neglecting the and terms in (3) (the corresponding criterion is discussed in [25]). Thus, (3) can be simplified into (9) Substituting (9) into (4), we get (10)

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where is the electron mobility. The boundary conditions for (10) follow by assuming terahertz radiation-induced voltage source at the source side of the channel and zero terahertz radiation-induced voltage source due to a large inductive load at the drain side such that (11) (12) , the stationary In the absence of incident radiation voltage–current characteristic is obtained from (10)–(12) as (13) where is the voltage drop across the channel. . At , the electron This expression is valid for concentration at the drain becomes zero and current reaches the value

Fig. 1. Characteristic length L as a function of incident radiation frequency for different gate biases. The electron effective mass and mobility are considered 0:067m and 0.3 m =V 1 s, respectively, for GaAs HEMT.

(14)

of the drain potential induced by the incoming radiation. From (20), we find

is the saturation current in the Shockley model. For , we search the solution of (10) in the form

(23)

where

(15) where we have neglected the contribution of higher harmonics. Following [25], we first separate the oscillating and stationary terms in (10) and (12). The stationary term obeys (16) with the boundary conditions

Therefore, to determine the response, we need to calculate . The analysis of (18) shows that the alternating amplitude decreases exponentially [13], [25] along the channel . When is small on the characteristic scale compared to the length of the gated region , which is is the case at relatively small gate bias voltages (Fig. 1), . Therefore, the response exponentially small compared to , is given by [25] (24)

(17) The spatial dependence of the oscillating amplitude scribed by the following equation:

is de-

Using (13) and (14), one can rewrite (24) as (25)

(18) The boundary conditions for this equation are (19)

Equation (24) and (25) are valid in the above-threshold is positive and large compared to the thermal regime, when voltage. A more general equation valid both above and below threshold is given by [25]

The solution of (16) with boundary conditions (17) is given by (20) The alternating amplitude is proportional to . Since is much smaller than , we can neglect (as well as in (20), which yields

)

(21) where (22) Since , where

, the response is given by is the change

(26) where is the subthreshold ideality factor. The above equations explain the dramatic increase of terahertz response as the applied drain current drives the transistor into the saturation or ), and the denominators in (24) regime ( and (25) become very small. , the reEquations (24) and (25) predict that when sponse should become infinite. Equation (26) removes this divergence by accounting for the finite temperature effects. The velocity saturation in the channel also prevents this divergence (even at zero temperature) [25]. The above theory can be generalized for more realistic boundary conditions by considering

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Fig. 2. Die photographs of the fabricated test structures of: (a) two transistors and (b) four transistors connected in series. The channel length and width of all transistors are 0.5 and 80 m, respectively. The separation distance between all gates is chosen to be 8 m much smaller than the terahertz wavelength. All terminals are labeled showing source (S), drain (D), gates (g ; . . . ; g ), and intermediate nodes (n ; . . . ; n ).

two terahertz radition-induced voltage sources at both source and drain sides of the channel, as was described in [29]. This realistic boundary conditions will be used later in this paper to explain an important new finding of different terahertz coupling to transistors operating in different regimes. III. FABRICATED MULTIPLE TRANSISTORS STRUCTURES We have designed several simple plasmonic structures with two and four 0.5- m enhancement-mode InGaAs/GaAs HEMTs connected in series (Fig. 2). Bonding pads and connecting wires were placed sufficiently distant from the active devices to minimize any coupling interferences. These structures were fabricated by TriQuint Semiconductor, Hillsboro, OR. A significant advantage inherent in this technology is that the relatively high breakdown voltage allows us to bias several series-connected transistors so that each transistor operates in the saturation regime to achieve enhanced terahertz detection. Fig. 3 shows typical current–voltage characteristics for each transistor measured using an Agilent 4156 B semiconductor parameter analyzer. The device threshold voltage, effective electron saturation velocity, mobility, drain and source series resistances, and subthreshold ideality factor were extracted using the technique described in [37]. Following this, the measured characteristics were fitted using Aim-SPICE.1 The fitted data are shown in Fig. 3, and Table I summarizes the parameter values used. We used an optically pumped gas laser beam (Coherent SIFIR-50) as the source of terahertz radiation for our response measurements. The 1.63-THz (184 m) laser beam was modulated by an optical chopper, with a fixed frequency of 100 Hz, and was focused with normal incidence on the transistor surface (Fig. 4). Focusing of the laser beam was achieved by mounting our test structures on a computer-controlled three-axis nanopositioning stage (ThorLabs NanoMax 341). The terahertz laser beam waist was measured and found to be approximately 140- m full width at half maximum (FWHM), while the areas of our multiple transistor designs, including drain and source metallization, were 85 32 m for the two transistors structure and 85 50 m for the four transistors structure. 1[Online].

Available: http://www.aimspice.com

Fig. 3. Measured voltage–current characteristics: (a) I –V and (b) I –V of the fabricated InGaAs/GaAs HEMT at different gate-to-source and drain-to-source voltages, respectively. Dotted lines are the experimentally measured data, while solid lines correspond to Aim-SPICE fitting.

TABLE I EXTRACTED PARAMETERS OF FABRICATED InGaAs/GaAs HEMT

Fig. 4. Experimental setup for measuring terahertz response from our multiple transistors structure.

ELKHATIB et al.: ENHANCED PLASMA WAVE DETECTION OF TERAHERTZ RADIATION

Fig. 5. Terahertz response of InGaAs/GaAS HEMT to 1.63-THz radiation as a function of the applied drain current I at different gate biases V . Solid lines represent the theoretical calculations based on (24) and (26), while the symbols are the experimentally measured data. It is clear that the calculated and measured responses are in good agreement in the linear regime.

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Fig. 6. Open-circuit drain–source voltage induced by incident terahertz radiation as a function of the gate bias. Symmetrical positive and negative responses were obtained by exchanging the transistor’s drain and source terminals for different load resistors.

IV. NONRESONANT RESPONSE OF SINGLE TRANSISTOR The dependence of terahertz response on drain current was measured from single transistors (with other transistors floating), and was compared with theoretical calculations. The dc drain current was applied here using a battery and a series load resistor of 10 k [38] with the gate bias controlled by another battery. Fig. 5 shows the measured nonresonant terahertz response as a function of the applied drain current at different value of gate biases . As expected from the theory, the response increased significantly with the application of the drain current as the transistor was driven from the linear . However, we found that into the saturation regime the terahertz response continued to increase with drain current in the saturation regime without reaching a maximum value and then decreasing, as was the case in [25]. We repeated our measurements using a Keithley source meter in a fashion similar to [25] to understand the difference between results. We found that the saturation of the terahertz response occurs when the source meter reached compliance, resulting in change of the output loading resistance in the source meter. From this, we conclude that the saturation of response reported in [25] was an artifact of the experimental setup. In fact, the terahertz response was increasing in the saturation regime with the drain current. This significant enhancement is observed for the first time in this study. The previous results drew our attention to investigate operating plasma wave HEMT detectors in the deep saturation regime. Two more important new findings were revealed through our experiments. The first finding is that the coupling of terahertz radiation to transistor varies dramatically when the transistor biasing changes from the linear regime into the saturation regime. Secondly, operating the transistor in the saturation regime allows it to detect terahertz radiation with subwavelength sensitivity. We measured the terahertz radiation-induced drain–source voltage as a function of gate bias at zero drain current, and then we exchanged the transistor source and drain terminals and

Fig. 7. Drain–source voltage induced by incident terahertz radiation as a function of the applied drain current with a fixed gate–source bias. Unsymmetrical responses were obtained by exchanging the transistor’s drain and source terminals (one terminal was grounded and the dc drain current was applied through a 100-k load resistor to the other terminal, and then vice versa). The gate bias was fixed at 0.43 V in both cases.

repeated our measurements while keeping the 1.63-THz laser beam focused in the same position on the transistor surface. Fig. 6 summarizes the obtained results, showing symmetrical positive and negative responses for different load resistors. In contrast with these symmetrical responses at zero drain current, the measured terahertz-induced drain–source voltage as a function of the applied drain current (Fig. 7) shows only a positive response when the transistor was driven into the saturation regime. However, a careful look at the measured responses again shows the symmetrical positive and negative responses in the linear regime at very low current values. Moreover, a clear shift ( 10 mV) in terahertz responses was observed in the deep saturation regime (see Fig. 7) after exchanging the source and drain terminals of the device. This shift was produced as a result of moving the coupling point on transistor surface with subwavelength distance under the incident terahertz laser beam. Thus, we conclude that deep saturation regime allows the FET to detect terahertz radiation with

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subwavelength resolution. These advantages enable the series connection of multiple transistors to enhance terahertz detection only if all transistors are operated in the saturation regime, as presented in Section V. The latest results can be interpreted by taking into account two terahertz radiation-induced voltage sources at both the source and drain sides of the transistor channel, as was described by our recent model in [29], where the idealized boundary condition (12) at the transistor’s drain side was replaced by the following equation: (27) Physically, the difference between (12) and (27) is that (12) implies that there is an infinite inductive impedance on the drain side of the device (which is not the case in our experiment), while (27) is more general and considers terahertz radiation-induced voltage source at the drain side. Using boundary conditions (11) and (27), one can find [29] the following expression for the response : (28) With zero applied drain current , and are weak and comparable; thus the detected terahertz response is very sensitive to transistor layout and metallization of source and drain terminals. The symmetrical positive and negative responses obtained in Fig. 6 can be explained easily by exand in (28). On the other hand, the response changing became only positive with increasing the drain current and when the detector was driven into the saturation regime. Thus, we conclude that asymmetry of the device is strongly enhanced by the dc current. Such asymmetry cannot be described neither by theory discussed in the Section II, nor by the theory developed in [29] (see (28)). In our opinion, this happens because both (12) and (27) [as well as (11)] are idealized and one should use a more general boundary conditions to describe experimental situation. This is a quite complicated problem, which should be solved by numerical calculations, taking into account geometric impedances of metallic leads. V. NONRESONANT RESPONSE OF MULTIPLE TRANSISTORS We tested the two transistors structure in three different operating configurations: 1) one transistor operated in the saturation regime while the other floating; 2) one transistor operated in the linear regime and the second, connected in series, operated in saturation; and finally 3) both transistors connected in series and operated in the saturation regime at the same gate-to-source bias voltage. Gate biasing was tuned such that each transistor detected with the maximum responsivity. Fig. 8 presents circuit schematics of the selected operating configurations, showing the dc operating point at each node and dc biasing through a 100-k load resistor with which a higher response was measured [38]. This figure also summarizes the measured linear responsivity for each of these configurations. The results obtained can be interpreted by considering the nonresonant detection of each transistor independently, as shown in Fig. 5. When both transistors are operated with the

Fig. 8. Circuit schematics showing dc operating points for the three testing configurations of the two transistors test structure. (a) Single transistor operated in saturation regime. (b) One transistor operated in the linear regime and the other operated in the saturation regime. (c) Both transistors operated in the saturation regime. The measured responsivities for the three cases are presented in (d).

same gate-to-source value and biased with the same drain current, the responsivities of both transistors are almost identical, and the overall response is doubled. With one transistor operated in the linear regime (with a very small drain-to-source voltage) and the other in saturation, the response of the linear regime transistor is almost negligible in comparison to the other transistor operated in saturation, and the overall response is effectively that of the saturated transistor only. In order to study the response with both transistors operated in saturation, as shown in Fig. 8(c), we raised the second gate bias voltage from 0.44 to 1.2 V while keeping the first gate bias voltage at 0.44 V. Fig. 9 presents the obtained result indicating the linear increase in response as the first transistor moves from the linear regime into saturation. The response is then seen to level off despite further increases in gate bias. These results confirm that the response of each transistor is independent, and that the overall response is the summation of both transistors’ responses. In addition to the two transistors structure, we have tested a structure with four series-connected transistors, all operating

ELKHATIB et al.: ENHANCED PLASMA WAVE DETECTION OF TERAHERTZ RADIATION

Fig. 9. Measured terahertz response versus second gate (g ) bias voltage while the first gate (g ) bias voltage was fixed at 0.44 V for circuit configurations shown in Fig. 8(b) and (c).

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responsivity increases to 170 V/W independent of the number of transistors used. Since the feature size of each transistor is much smaller than the wavelength, a large number of transistors can be stacked in the focal spot of the incident terahertz radiation and a higher responsivity can be realized. An even larger enhancement is expected when the dimension of the transistor chain is such that it exceeds the terahertz wavelength, as predicted in [34] and [35]. Although the 2–3 orders of magnitude gain in responsivity achieved by biasing the plasma wave detectors in the saturation regime, the noise increases much due to the higher saturation ) is the dominant noise current at which the flicker noise ( source. The NEP at 100-Hz modulation frequency was found to be in the range of 10 W/Hz . In contrast, the detector noise is mainly the thermal noise of the transistor’s channel resistance at zero applied drain current and the NEP was about W/Hz . However, the series connection of many tran10 sistors in the saturation regime, as described here, improves the , where overall signal-to-noise ratio (SNR) by a factor of is the number of connected transistors. In addition, the incident terahertz radiation can be modulated electronically above corner frequency to enhance the NEP, as was suggested the in [39]. VII. CONCLUSION

Fig. 10. Measured responsivities of one, two, three, and four transistors connected in series. All transistors were operating in the saturation regime.

in saturation. Fig. 10 summarizes our experimental results showing the measured linear responsivities of one and up to four series-connected transistors. A bias voltage of 30 V through the 100-k load resistor was required for this structure, which underscores importance of high breakdown voltage technology for these multiple transistors structures. We were not able to adjust the gate-to-source biasing of the third and fourth transistors to be exactly similar to the others due to their loading effect. This explains our results in Fig. 10 where the terahertz responses from three and four series-connected transistors were 2.92 and 4.1 , respectively, of one transistor response. Still, these results show that the overall response is approximately proportional to the number of transistors connected in series. VI. RESPONSIVITY AND NEP Estimates of the responsivity of our plasmonic structures were determined by first measuring the maximum power of the focused terahertz laser beam using a Thomas Keating absolute power meter. For a single transistor, operated in the saturation regime, a responsivity of 7 V/W was obtained, corresponding to a maximum laser beam power of 35 mW. This estimate does not consider the much smaller area of our test structure relative to the focused laser beam waist. By such consideration, the

A detailed study of plasma wave detectors operating in the deep saturation regime is absent thus far. In this study, we have experimentally demonstrated for the first time many advantages of operating plasma wave detectors in the saturation regime. Our results showed that the response from several connected transistors increases at least proportionally to the number of transistors placed in series. Future work shall greatly increase the number of the connected transistors in order to take advantage of the improved coupling, and this shall also lead to a much greater increase in responsivity, as predicted in [34]. The achieved subwavelength resolution also shows the possibility of designing 2-D plasmonic FET arrays to sense and image complex distributions of terahertz intensity as a near-field terahertz microscopy. REFERENCES [1] Y. Chen, H. Liu, Y. Deng, D. Veksler, M. Shur, X.-C. Zhang, D. Schauki, M. J. Fitch, R. Osiander, C. Dodson, and J. B. Spicer, “Spectroscopic characterization of explosives in the far infrared region,” Proc. SPIE, vol. 5411, no. 1, pp. 1–8, Oct. 2004. [2] H. Liu, G. Plopper, S. Earley, Y. Chen, B. Ferguson, and X.-C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron., vol. 22, no. 6, pp. 1075–1080, Jan. 2007. [3] S. P. Mickan and X.-C. Zhang, “T-ray sensing and imaging,” Int. J. High Speed Electron. Syst., vol. 13, no. 2, pp. 601–676, Jun. 2003. [4] W. J. Stillman and M. S. Shur, “Closing the gap: Plasma wave electronic terahertz detectors,” J. Nanoelectron. Optoelectron., vol. 2, no. 3, pp. 209–221, Dec. 2007. [5] M. Kroug, S. Cherednichenko, H. Merkel, E. Kollberg, B. Voronov, G. Goltsman, H. W. Huebers, and H. Richter, “NbN hot electron bolometric mixers for terahertz receivers,” IEEE Trans. Appl. Superconduct., vol. 11, no. 1, pp. 962–965, Mar. 2001. [6] S. Barbieri, J. Alton, H. E. Beere, E. H. Linfield, D. A. Ritchie, S. Withington, G. Scalari, L. Ajili, and J. Faist, “Heterodyne mixing of two far-infrared quantum cascade lasers by use of a point-contact Schottky diode,” Opt. Lett., vol. 29, no. 14, pp. 1632–1634, Jul. 2004. [7] J.-Q. Wang, P. L. Richards, J. W. Beeman, and E. E. Haller, “Stressed photoconductive detector for far infrared space applications,” Appl. Opt., vol. 26, no. 22, pp. 4767–4771, Nov. 1987.

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[8] M. Dyakonov and M. S. Shur, “Shallow water analogy for a ballistic field effect transistor: New mechanism of plasma wave generation by dc current,” Phys. Rev. Lett., vol. 71, no. 15, pp. 2465–2468, Oct. 1993. [9] D. C. Tsui, E. Gornik, and R. A. Logan, “Far infrared emission from plasma oscillations of Si inversion layers,” Solid State Commun., vol. 35, no. 11, pp. 875–877, Sep. 1980. [10] A. P. Dmitriev, A. S. Furman, and V. Y. Kachorovskii, “Nonlinear theory of the current instability in a ballistic field-effect transistor,” Phys. Rev. B, Condens. Matter, vol. 54, no. 19, pp. 14020–14025, Nov. 1996. [11] Y. Deng, M. S. Shur, R. Gaska, G. S. Simin, M. A. Khan, and V. Ryzhii, “Millimeter wave emission from GaN high electron mobility transistor,” Appl. Phys. Lett., vol. 84, no. 1, pp. 70–72, Jan. 2004. [12] N. Dyakonova, A. El Fatimy, J. Lusakowski, W. Knap, M. I. Dyakonov, M. A. Poisson, and E. Morvan, “Room-temerature terahertz emission from nanometer field-effect transistor,” Appl. Phys. Lett., vol. 88, no. 14, pp. 141 906–141 908, Apr. 2006. [13] M. Dyakonov and M. S. Shur, “Plasma wave elecronics: Novel terahertz devices using two dimensional electron fluid,” IEEE Trans. Electron Devices, vol. 43, no. 10, pp. 1640–1645, Oct. 1996. [14] X. G. Peralta, S. J. Allen, M. C. Wanke, N. E. Harff, J. A. Simmons, M. P. Lilly, J. L. Reno, P. J. Burke, and J. P. Eisenstein, “Terahertz photoconductivity and plasmon modes in double-quantum-well fieldeffect transistors,” Appl. Phys. Lett., vol. 81, no. 9, pp. 1627–1629, Aug. 2002. [15] J.-Q. Lu and M. S. Shur, “Terahertz detection by high electron mobility transistor: Enhancement by drain bias,” Appl. Phys. Lett., vol. 78, no. 17, pp. 2587–2588, Apr. 2001. [16] W. Knap, V. Kachorovskii, Y. Deng, S. Rumyantsev, J.-Q. Lu, R. Gaska, M. S. Shur, G. Simin, X. Hu, M. A. Khan, C. A. Saylor, and L. C. Brunel, “Nonresonant detection of terahertz radiation in field effect transistors,” J. Appl. Phys., vol. 91, no. 11, pp. 9346–9353, Jun. 2002. [17] W. Knap, Y. Deng, S. Rumyantsev, J.-Q. Lu, M. S. Shur, C. A. Saylor, and L. C. Brunel, “Resonant detection of subterahertz radiation by plasma waves in a submicron field-effect transistor,” Appl. Phys. Lett., vol. 80, no. 18, pp. 3433–3435, May 2002. [18] W. Knap, F. Teppe, Y. Meziani, N. Dyakonova, J. Lusakowski, F. Boeuf, T. Skotnicki, D. K. Maude, S. Rumyantsev, and M. S. Shur, “Plasma wave detection of sub-terahertz and terahertz radiation by silicon field-effect transistors,” Appl. Phys. Lett., vol. 85, no. 4, pp. 675–677, Jul. 2004. [19] N. Pala, F. Teppe, D. Veksler, Y. Deng, M. S. Shur, and R. Gaska, “Nonresonant detection of terahertz radiation by silicon-on-insulator MOSFETs,” Electron. Lett., vol. 41, no. 7, pp. 447–449, Mar. 2005. [20] T. Otsuji, M. Hanabe, and O. Ogawara, “Terahertz plasma wave resonance of two-dimensional electrons in InGaP/InGaAs/GaAs high electron mobility transistors,” Appl. Phys. Lett., vol. 85, no. 11, pp. 2119–2121, Sep. 2004. [21] F. Teppe, M. Orlov, A. E. Fatimy, A. Tiberj, W. Knap, J. Torres, V. Gavrilenko, A. Shchepetov, Y. Roelens, and S. Bollaert, “Room temperature tunable detection of subterahertz radiation by plasma waves in nanometer InGaAs transistors,” Appl. Phys. Lett., vol. 89, no. 22, pp. 222 109-1–222 109-3, Nov. 2006. [22] E. A. Shaner, A. D. Grine, M. C. Wanke, M. Lee, J. L. Reno, and S. J. Allen, “Far-infrared spectrum analysis using plasmon modes in a quantum-well transistor,” IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1925–1927, Sep. 2006. [23] A. V. Antonov, V. I. Gavrilenko, E. V. Demidov, S. V. Morozov, A. A. Dubinov, J. Lusakowski, W. Knap, N. Dyakonova, E. Kaminska, A. Piotrowska, K. Golaszewska, and M. S. Shur, “Electron transport and terahertz radiation detection in submicrometer-sized GaAs/AlGaAs field effect transistors with two- dimensional electron gas,” Phys. Solid State, vol. 46, no. 1, pp. 146–149, Jan. 2004. [24] R. Tauk, F. Teppe, S. Boubanga, D. Coquillat, W. Knap, Y. M. Meziani, C. Gallon, F. Boeuf, T. Skotnicki, C. Fenouillet-Beranger, D. K. Maude, S. Rumyantsev, and M. S. Shur, “Plasma wave detection of terahertz radiation by silicon field effects transistors: Responsivity and noise equivalent power,” Appl. Phys. Lett., vol. 89, no. 25, pp. 253 511-1–253 511-3, Dec. 2006. [25] D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B, Condens. Matter, vol. 73, no. 12, pp. 125 328-1–125 328-10, Mar. 2006. [26] V. Y. Kachorovskii and M. S. Shur, “Field effect transistor as ultrafast tunable detector of terahertz radiation,” Solid State Electron., vol. 52, no. 2, pp. 182–185, Feb. 2008. [27] B. Gershgorin, V. Y. Kachorovskii, Y. V. Lvov, and M. S. Shur, “Field effect transistor as heterodyne terahertz detector,” Electron. Lett., vol. 44, no. 17, pp. 1036–1037, Aug. 2008.

[28] W. Stillman, D. Veksler, T. A. Elkhatib, K. Salama, F. Guarin, and M. S. Shur, “Sub-terahertz testing of silicon MOSFET,” Electron. Lett., vol. 44, no. 22, pp. 1325–1327, Oct. 2008. [29] D. B. Veksler, V. Y. Kachorovskii, A. V. Muravjov, T. A. Elkhatib, K. N. Salama, X.-C. Zhang, and M. S. Shur, “Imaging of field-effect transistors by focused terahertz radiation,” Solid State Electron., vol. 53, no. 6, pp. 571–573, Jun. 2009. [30] A. Chaplik, “Possible crystallization of charge-carriers in low-density inversion layers,” Zh. Eksp. Teor. Fiz., vol. 62, no. 2, pp. 746–753, 1972, (Sov. Phys. JETP, vol. 35, pp. 395–398, 1972). [31] M. S. Shur and L. F. Eastman, “Ballistic transport in semiconductors at low-temperatures for low power high speed logic,” IEEE Trans. Electron Devices, vol. ED-26, no. 11, pp. 1677–1683, Nov. 1979. [32] F. Teppe, W. Knap, D. Veksler, M. S. Shur, A. P. Dmitriev, V. Y. Kachorovskii, and S. Rumyantsev, “Room-temperature plasma waves resonant detection of sub-terahertz radiation by nanometer field-effect transistor,” Appl. Phys. Lett., vol. 87, no. 5, pp. 052 107-1–052 107-3, Jul. 2005. [33] F. Teppe, D. Veksler, V. Y. Kachorovski, A. P. Dmitriev, X. Xie, X.-C. Zhang, S. Rumyantsev, W. Knap, and M. S. Shur, “Plasma wave resonant detection of femtosecond pulsed terahertz radiation by a nanometer field effect transistor,” Appl. Phys. Lett., vol. 87, no. 2, pp. 022 102-1–022 102-3, Jul. 2005. [34] V. V. Popov, G. M. Tsymbalov, and M. S. Shur, “Plasma wave instability and amplification of terahertz radiation in field-effect-transistor arrays,” J. Phys., Condens. Matter, vol. 20, no. 38, pp. 384 2081–384 208-6, Sep. 2008. [35] V. V. Popov, M. S. Shur, G. M. Tsymbalov, and D. V. Fateev, “Higherorder plasmon resonances in GaN-based field-effect transistor arrays,” Int. J. High Speed Electron. Syst., vol. 17, no. 3, pp. 557–566, Sep. 2007. [36] T. A. Elkhatib, D. B. Veksler, K. N. Salama, X.-C. Zhang, and M. S. Shur, “Enhanced terahertz detection using multiple GaAs HEMTs connected in series,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2009, pp. 937–940. [37] K. Lee, M. Shur, T. A. Fjeldly, and T. Ytterdal, Semiconductor Device Modeling for VLSI. Englewood Cliffs, NJ: Prentice-Hall, 1993. [38] W. Stillman, M. S. Shur, D. Veksler, S. Rumyantsev, and F. Guarin, “Device loading effects on nonresonant detection of terahertz radiation by silicon MOSFETs,” Electron. Lett., vol. 43, no. 7, pp. 422–423, Mar. 2007. [39] D. Veksler, A. Muravjov, W. Stillman, N. Pala, and M. Shur, “Detection and homodyne mixing of terahertz gas laser radiation by submicron GaAs/AlGaAs FETs,” in Proc. 6th IEEE Sens. Conf., Atlanta, GA, Oct. 2007, pp. 443–445.

Tamer A. Elkhatib (S’09) received the B.Sc. degree in electronics and communications (with honors) and M.Sc degree in engineering mathematics and physics from Cairo University, Giza, Egypt, in 2002 and 2006, respectively, and is currently working toward the Ph.D. degree in electrical engineering at the Rensselaer Polytechnic Institute, Troy, NY. His current research interests include plasma wave detection of terahertz radiation, terahertz imaging, CMOS image sensors, smart biosensors, and time-of-flight sensors.

Valentin Y. Kachorovskii was born in Leningrad, U.S.S.R., in 1962. He received the Ph.D. degree in semiconductor physics from the Ioffe Physical-Technical Institute, St. Petersburg, Russia, in 1989. He is currently a Senior Researcher with the Department of the Theory of Electrical and Optical Phenomena in Semiconductors, Ioffe Physical-Technical Institute. He has authored or coauthored approximately 70 scientific papers published in refereed journals and conference proceedings. His current research interests include transport in disordered systems, spin-dependent phenomena in low-dimensional structures, dynamics of plasma waves, and terahertz electronics.

ELKHATIB et al.: ENHANCED PLASMA WAVE DETECTION OF TERAHERTZ RADIATION

William J. Stillman received the B.S.E.E,, M.S.E.E., Ph.D. in electrical engineering degrees from the Rensselaer Polytechnic Institute (RPI), Troy, NY, in 1980, 1991, and 2008, respectively. From 1982 to 2007, he was with IBM in various positions, including quality assurance, failure analysis, and inline electrical test and yield diagnostics. He is currently a Post-Doctoral Research Associate with RPI. The focus of his research is on silicon FETs as detectors of terahertz and sub-terahertz radiation, and on application of terahertz radiation to testing of silicon very large scale integration (VLSI) circuits.

Dmitry B. Veksler received the B.S. and M.S. degrees from the Advanced School of General and Applied Physics, Nizhniy Novgorod State University, Nizhniy Novgorod, Russia, in 1996 and 1998, respectively and the Ph.D. degree in physics from the Rensselaer Polytechnic Institute in Troy, NY, in 2007. From 1998 to 2003, he was a Junior Researcher/Staff Researcher with the Institute for Physics of Semiconductors (Russian Academy of Sciences). Following his graduation, he was a Postdoctoral Research Associate with the Electrical, Computer, and System Engineering (ECSE) Department, Rensselaer Polytechnic Institute. In 2009, he joined the Electrical and Physical Characterization Group, SEMATECH Inc., Albany, NY. He has authored or coauthored over 40 scientific papers published in refereed journals and conference proceedings. His research interests include optical and transport phenomena in low-dimensional semiconductor structures; advanced solid-state detectors and emitters of terahertz electromagnetic radiation, including plasma wave electronic devices for terahertz spectroscopy and imaging applications.

Khaled N. Salama (S’98–M’05) received the Bachelors degree in electronics and communications (with honors) from Cairo University, Giza, Egypt, in 1997, and the Masters and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 2000 and 2005, respectively. From 2005 to 2008, he was an Assistant Professor with the Electrical, Computer and Systems Engineering Department, Rensselaer Polytechnic Institute. In 2007, he cofounded Ultrawave Laboratories, a medical imaging startup, and serves as its Vice President of Research and Development. In Fall 2009, he joined the King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia, as an Assistant Professor of Electrical Engineering. He has coauthored 50 papers in the areas of biosensors, low-power mixed-signal circuits for intelligent sensors and medical instrumentation. He holds four patents. His research concerning low-light detection and fully integrated imagers has been funded by the Defense Advanced Research Projects Agency (DARPA) and the National Institutes of Health (NIH). Dr. Salama was the recipient of the Stanford-Berkeley Innovators Challenge Award in biological sciences (recently acquired by Lumina Inc.).

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Xi-Cheng Zhang (M’91–SM’97–F’01) joined the Rensselaer Polytechnic Institute, Troy, NY, in 1992, where he is currently the Eric Josson Professor of Science. He is also currently a Professor with the Department of Physics, Applied Physics and Astronomy, a Professor with the Department of Electrical, Computer and System, and the Founding Director of the Center for Terahertz Research with the Rensselaer Polytechnic Institute. He has authored or coauthored eight books and book chapters and over 350 refereed journal papers He holds 20 U.S. patents. He began his pulsed terahertz research in 1988. Dr. Zhang is a Fellow of the Optical Society of America (OSA) and the American Physics Society. He is the chairman of the North Atlantic Treaty Organization (NATO) SET Terahertz Task Group. He has delivered over 400 colloquium, seminars, invited conference presentations, and 300 contributed conference talks (since 1990).

Michael S. Shur (M’79–SM’83–F’89) received the M.S.E.E. degree (with honors) from the St. Petersburg Electrotechnical Institute, St. Petersburg, Russia, and the Ph.D. and Dr. Sc. degrees from the A. F. Ioffe Institute, St. Petersburg, Russia. He is Roberts Professor, Director of the Broadband Center, Co-Director of the NSF I/UCRC, and Acting Director of the Center for Integrated Electronics. He is cofounder and Vice President of Sensor Electronics Technology Inc. He is Editor-in-Chief of IJHSES and the book series on “Electronics and Systems.” He is Regional Editor of physica status solidi. Dr. Shur is a Life Fellow of the IEEE Antennas and Propagation Society (APS), the ECS, WIF, MRS, and AAAS. He is a member of Eta Kappa Nu, Tau Beta Pi, and ASEE. He is an elected member and former chair of U.S. Commission D and a former member of URSI, a Life Member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), SPIE, Sigma Xi, and the Humboldt Society. He is a member of the Honorary Board of Solid State Electronics and JSTS International Advisory Committee, Vice President for Technical Communications of the IEEE Sensor Council, Distinguished Lecturer of the IEEE Electron Devices Society (EDS). He is a Foreign Member of the Lithuanian Academy of Sciences. He has been the recipient of numerous awards including the Saint Petersburg Technical University Honorary Doctorate, IEEE Donald Fink Best Paper Award, IEEE Kirchmayer Award, Gold Medal of the Russian Education Ministry, Best Paper Awards, van der Ziel Award, Senior Humboldt Research Award, Pioneer Award presented by Compound Semi, RPI Engineering Research Award, and Commendation for Excellence in Technical Communications. He is listed by the Institute of Scientific Information as a Highly Cited Researcher.

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60-GHz Repeater Link for an ISDB-T Gap-Filler System Based on Self-Heterodyne Technique Applying an Adaptive Distortion Suppression Technique Yozo Shoji, Member, IEEE, Chang-Soon Choi, Member, IEEE, and Hiroki Ohta

Abstract—A 60-GHz through-repeater link, which adopts the self-heterodyne transmission technique and a distortion suppression technique, is demonstrated as a solution to cost-effectively develop an Integrated Services Digital Broadcasting for Terrestrial gap-filler system. The transmitter multichip module and the receiver (Rx) multichip module are especially designed to investigate the impact on the link performance when varying the bias voltage injected to the self-heterodyne Rx mixer. It is demonstrated that the adaptive control of the bias voltage depending on the transmission distance is effective in extending the transmittable range even if the transmission power is limited. It is also experimentally shown that the developed 60-GHz repeater link can cover the transmission distance ranging from 23.7 to 110.9 m with a BER less than 10 5 if the adaptive control of the bias voltage is applied, while the repeater link with a fixed bias voltage can cover only a range from 23.7 to 53.1 m. Index Terms—Gap filler, Integrated Services Digital Broadcasting for Terrestrial (ISDB-T), millimeter wave, self-heterodyne, 60 GHz.

I. INTRODUCTION APAN BEGAN the Integrated Services Digital Broadcasting for Terrestrial (ISDB-T) in 2003 and also began a digital broadcasting service for mobile reception in 2006 by using one segment of the ISDB-T signal. It has been reported that more than 60% of families in Japan are receiving the ISDB-T signal.1 It is expected that the ISDB-T signal provides not only a high-quality broadcasting service, but also a stable mobile reception service. However, TV broadcast stations or repeater systems have been basically developed to provide the service for the fixed terminals. It is known that there can be numerous blind zones where the ISDB-T signal cannot reach, i.e., the “gap area.”

J

Manuscript received September 09, 2009; revised November 13, 2009. First published January 19, 2010; current version published February 12, 2010. Y. Shoji and H. Ohta are with the National Institute of Information and Communications Technology, 183-8795 Tokyo, Japan (e-mail: [email protected]; [email protected]). C.-S. Choi is with IHP Microelectronics GmbH, 15236 Frankfurt, Germany (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2037882 1[Online]. Available: http://www.soumu.go.jp/joho_tsusin/pressrelease/ japanese/denki/000922j603.html

The purpose of a gap-filler system is to compensate the gap area, i.e., the gap-filler system must have a function to receive the ISDB-T signal directly from the broadcast station once, and then rebroadcast to the gap area. The gap-filler system usually consists of a receiver (Rx) unit that directly receives the ISDB-T signal from a broadcast station, a repeater link that repeats the received signal to the gap area, and a rebroadcasting unit that rebroadcasts the received signal from the repeater link. It has become more general to use a wired link for the repeater link. However, it is obvious that the development of the wired link is not cost effective and it often restricts the location of antennas for reception and rebroadcasting. This paper proposes the use of a 60-GHz-band through-repeater link for an ISDB-T gap-filler system. The use of an unlicensed 60-GHz band has attracted considerable interest worldwide due to its broad bandwidth availability and common allocation for different countries. An enormous number of studies have then been reported focusing on the use of the 60-GHz band [1]–[7]. As for the standardization of the 60-GHz band, the IEEE Standard Association formed Working Group 802.15.3c2 and almost finalized the document for very high speed wireless personal area network (WPAN) applications. The working group IEEE 802.11ad3 in 802.11 is also discussing next-generation high-throughput wireless local area network (LAN) applications using the 60-GHz band. Therefore, we can expect that the cost of devices for the 60-GHz band system will drastically decrease in the near future. The reasons for selecting the 60-GHz band as the frequency to wirelessly repeat the ISDB-T signals are discussed in more detail in Section II. One of the critical issues to be overcome in the 60-GHz-band system, which has been discussed for 60-GHz-band WPAN and WLAN systems, is the realization of a stable and low phasenoise carrier frequency and the reduction in cost for developing the device. In order to overcome the above issues, we have developed the millimeter-wave self-heterodyne technique and have studied on the effects theoretically and experimentally [8]–[11]. The self-heterodyne technique appears to be the easiest way not only to provide stable carrier transmission, but also to establish a 2[Online]. 3[Online].

Available: http://www.ieee802.org/15/pub/TG3c.html Available: http://www.ieee802.org/11/Reports/vht_update.htm

0018-9480/$26.00 © 2010 IEEE

SHOJI et al.: 60-GHz REPEATER LINK FOR ISDB-T GAP-FILLER SYSTEM

low-cost transceiver architecture. In particular, the use of the self-heterodyne technique can realize a nondata-regenerative repeater link, i.e., a through-repeater system, which does not cause frequency offset and processing delay at all. These features offer significant advantage in developing a gap-filler system for the ISDB-T service if we take into a consideration that the ISDB-T service allows a carrier frequency offset less than 1 Hz among several broadcasting stations to realize a single frequency network (SFN) [13]. The remaining issue to be discussed for a 60-GHz-band repeater link is how to maintain lower distortion characteristics. The ISDB-T signal, which uses an orthogonal frequency-division multiplexing (OFDM) signal format, tends to be significantly degraded due to the nonlinear characteristics. It has been reported that the use of the self-heterodyne technique causes a higher nonlinear distortion on the detected signal because the received RF signals have to be down-converted by using the received weak power local oscillator (LO) carrier [12]. Our previous study [12] has reported that the careful designing of the transmitter (Tx), i.e., appropriately distributing the transmitting signal and local power, can suppress the nonlinear distortion to some extent. We further found that the nonlinear distortion can be suppressed by carefully designing the self-heterodyne Rx mixer, i.e., appropriately designing the bias voltage of the mixer or adaptively controlling it depending on the received RF power. We then developed the 60-GHz through-repeater link that implemented the above functions, i.e., the functions to control the transmitting power distribution between the signal and local power and to control the bias voltage of the self-heterodyne Rx mixer. This paper is organized as follows. Section II provides an overview of the 60-GHz-band repeater link for an ISDB-T gap-filler system and discusses why we designed the 60-GHz through-repeater link for the ISDB-T gap-filler system. Section III describes a theoretical link design and theoretically estimates the link budget. Section IV describes how nonlinear distortion depends on the bias voltage and the transmitting local-to-signal power ratio (LSR). Section V describes the configuration of the developed 60-GHz-band through-repeater link in detail. Section VI describes the link performance we experimentally obtained by using the developed repeater link. II. OVERVIEW OF THE 60-GHz-BAND REPEATER LINK FOR AN ISDB-T GAP-FILLER SYSTEM The concept of an ISDB-T gap-filler system using a wireless repeater link is shown in Fig. 1. A broadcast station transmits TV signals broadly; however, some areas may be blind, i.e., some areas become “gap area,” due to the shadowing of a tall building or any other reason. The basic function required for the gap-filler system is to receive the TV signals from the broadcast station with better condition, repeat these signals wirelessly to the gap area, and then rebroadcast them. Since the ISDB-T specification allows an SFN configuration [13], i.e., the use of the same frequency in an adjacent coverage area, the rebroadcasting in the gapfiller system can use the same frequency as the original received signal from the broadcast station.

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Fig. 1. Concept of a gap-filler system for ISDB-T using a 60-GHz-band repeater link. TABLE I REPRESENTATIVE SPECIFICATIONS OF ISDB-T SIGNAL

The use of a wireless repeater link for the gap-filler system will provide the benefit of a flexible location of the rebroadcasting antenna apart from the antenna to receive the TV signal directly from the broadcast station. Therefore, we can cost-effectively avoid a critical coupling loop interference (CLI) that might happen between the rebroadcasting antenna and the Rx antenna. The CLI can be suppressed by using the CLI canceler [14]. However, the use of the CLI canceler requires a complicated signal processing in the repeater system, and the cost and system complexity tend to increase. Generally, there are two candidates for the wireless repeater link method. One is a regenerative repeater link and the other is a nonregenerative link, i.e., a through-repeater link. Considering the fact that analogous signal degradations can be removed by data regeneration, the regenerative repeater link would be a better choice. However, we still must take care of a possible interference between the signal received directly from the broadcast station and that from the rebroadcasting antenna, which might happen in the area near the gap-filler system. Table I lists the representative specifications of the ISDB-T signal. Mode 3 is currently used in the practical service. We can see from this table that the guard interval for Mode 3 is 126 s, which signifies that the time delay of the interference signal must be less than 126 s. By looking at the current technology level where the signal regeneration processing of ISDB-T signal generally requires an additional processing time much more than 1 ms, we find it difficult to apply the regenerative repeater system for the ISDB-T gap-filler system. We then concluded that we should adopt a through-repeater wireless link for the gap-filler system. The next issues to be discussed are what technique or method should be used for the wireless repeater link and which frequency band should be used. In order to obtain the answers to these questions, we need to consider the following requirements. 1) The wireless repeater link does not interfere with the original ISDB-T signals, i.e., UHF band signals 2) The wireless repeater link can transmit a bandwidth of over 300 MHz at least because the broadcast signal spectrum spreads from 440 to 770 MHz.

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TABLE II A RESULT OF A THEORETICAL LINK BUDGET ESTIMATION AND ASSUMPTIONS

3) The wireless repeater link can be used without license. 4) The wireless repeater link can repeat the ISDB-T signal with a frequency offset less than 1 Hz. A frequency band that can meet requirements 1)–3) is actually only the 60-GHz band, where a wide bandwidth of 7 GHz is available without license. However, the device technology in the 60-GHz band is still under development for it to be used in a through-repeater system and the 60-GHz-band carrier tends to suffer from frequency offset and phase-noise degradations. This indicates that it is difficult for the 60-GHz-band repeater link to meet requirement 4). In order to solve this problem cost effectively, the self-heterodyne transmission technique has been developed [8]. The adoption of the self-heterodyne technique has already been tried for the transmission of the ISDB-T signal and a 0-Hz frequency offset transmission has been demonstrated [8]. However, the previous report has just achieved a very short-range transmission of the ISDB-T signal, i.e., less than 10 m, because it was not designed for the gap-filler system. In fact, we have found through previous self-heterodyne system developments that the self-heterodyne technique suffers from a serious nonlinear distortion on the detected signal at not only the stage of power amplification, but also the stage of self-heterodyne detection. Since the ISDB-T signal, which consists of the OFDM signal, is significantly degraded by nonlinear distortion, we have been required to develop a technique to suppress the nonlinear distortion effect. The manner in which we suppressed the nonlinear distortion is described in Section III. III. THEORETICAL LINK DESIGN The performance of the 60-GHz repeater link can be estimated theoretically. The first important signal degradation factor will be the carrier-to-noise power ratio (CNR). We then made a rough link budget estimation before the 60-GHz repeater link for the ISDB-T gap-filler system was actually developed. Table II lists a result of theoretical link budget estimations and assumptions used in the calculation. We must understand from Table II that the CNR of a detected signal depends on the transmitted LSR when the self-heterodyne transmission technique is used [8]. The CNR is maximized when the LSR is 0 dB, but it still suffers from a 9-dB penalty when compared to the conventional superheterodyne technique. The CNR suffers an additional 5-dB degradation

Fig. 2. Intermodulation distortion characteristics for different bias voltages injected Rx mixer.

when the LSR is 10 dB. From another viewpoint, one of the other previous studies has demonstrated that the best LSR that minimized the third-order intermodulation distortion (IMD3) was approximately 10 dB [12]. Considering the above results of demonstrations, we have assumed to use the LSR of 10 dB in designing the 60-GHz repeater link for the ISDB-T gap-filler system based on the self-heterodyne technique. This causes a total 14-dB CNR penalty when compared to the conventional link budget design, as listed in Table II. The transmission power must be less than 10 dBm from the radio regulation, while a comparatively high gain antenna can be used in the gap-filler application since the target of the wireless repeater link is a point–point transmission link. Although the CNR required for data demodulation is approximately 23 dB, we have assumed a higher required CNR of 40 dB in this table as a rebroadcasting signal quality. We can see from Table II that the link margin of more than 14 dB is obtained even if we assume the LSR of 10 dB and the required CNR of 40 dB. This link margin can be used for the further extension of the range or the bandwidth. IV. NONLINEAR DISTORTION SUPPRESSION BY CONTROLLING THE BIAS VOLTAGE FOR AN RX MIXER As described in Section II, the self-heterodyne detection causes a nonlinear distortion on the detected signal, while it has been reported that the distortion can be suppressed by increasing the LSR [12]. Fig. 2 shows an example of the measured IMD3 power for different gate bias voltages injected to a self-heterodyne Rx mixer when the total received signal power is 30 dBm. The detected fundamental signal power and the carrier-to-intermodulation distortion power ratio (CIR) corresponding to the bias voltage are also shown in this figure.

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Fig. 3. Measurement setup, which was designed to observe the nonlinear distortion only due to a self-heterodyne Rx.

In the above measurement, a 70-GHz-band self-heterodyne Rx multichip module, which we had previously developed for another application, was used to investigate the impact of changing the bias voltage for the Rx mixer on the CIR performance. Fig. 3 illustrates the measurement setup, which was designed to observe the nonlinear distortion only due to a self-heterodyne Rx. Millimeter-wave two-tones composed of 72.52- and 72.53-GHz carriers and a millimeter-wave local carrier of 73 GHz were, respectively, generated by mixing IF carriers of 3.52, 3.53, and 4-GHz with a 69-GHz oscillation signal. The obtained millimeter-wave two-tones plus local carrier were then input to a self-heterodyne Rx module and the detected two-tones and third intermodulation distortion power in the IF band were measured. We can see from Fig. 2 that the CIR depends on not only the LSR, but also the gate bias voltage. The CIR for the condition dB maintained a value higher than that for the of dB when the bias voltage was more condition of dB was maximized and it than 1 [V]. The CIR for achieved 47 [dB] at the bias voltage of 0.6 [V], while the CIR dB at the same condition was only 13 [dB]. for This means that we can expect the CIR improvement of more than 30 dB if we control the bias voltage for the self-heterodyne Rx mixer, although we may sacrifice a conversion gain to some extent. V. CONFIGURATION OF THE DEVELOPED 60-GHz REPEATER LINK A. Overview The developed 60-GHz through-repeater link consists of a Tx unit, which up-converts the received UHF band ISDB-T signals into 60-GHz-band signals, and an Rx unit, which down-converts the received 60-GHz-band signals into the original UHF band ISDB-T signals. An exterior view of the developed Tx unit and Rx unit is shown in Fig. 4. Their main specifications are listed in Table III.

Fig. 4. Exterior view of 60-GHz-band Tx and Rx.

TABLE III MAIN SPECIFICATIONS OF THE DEVELOPED 60-GHz REPEATER LINK

The Tx unit consists of a Tx IF circuit, a 60-GHz Tx-multichip module (Tx-MCM), and a Tx antenna; similarly, the Rx unit consists of an Rx IF circuit, a 60-GHz Rx-MCM, and an Rx antenna. The Tx-MCM and Rx-multichip module (Rx-MCM) are the main parts of the Tx and Rx units, respectively, and they are especially designed for the self-heterodyne transmission technique; the Tx-MCM is designed to transmit the 60-GHz-band local carrier along with the up-converted signals and the Rx-MCM is designed to down-convert the received RF signals by using the received local carrier. B. Configuration and Conversion Characteristics of Tx Unit The schematic configuration of the Tx unit is shown in Fig. 5. A photograph of the main Tx circuit board including the Tx-MCM is shown in Fig. 6. The received UHF band TV signals are treated as IF input signals and they are directly up-converted to 60-GHz-band signals by the Tx-MCM. The Tx unit is designed in such a way so as to control LSR by changing the IF input signal power and/or changing the bias voltage for the self-heterodyne Tx mixer. Increasing the IF input signal power can linearly increase the RF

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Fig. 5. Configuration of 60-GHz-band Tx circuit.

Fig. 6. Photograph of the main Tx circuit board.

output signal power; however, the output LO power cannot be controlled. The bias voltage was adjusted to achieve an appropriate output LO power. Considering the saturation characteristics of the power amplifier included in the developed Tx-MCM, we have basically adjusted the bias voltage for the Tx unit to achieve the output LO power of 7 dBm. Since the IF frequency is extremely lower than the millimeterwave frequency, the Tx-MCM is designed to output the lower sideband (LSB) signal and suppress the image signal, i.e., the upper sideband (USB) signal, by the image rejection mixer technique. Fig. 7 shows the conversion characteristics of a developed Tx unit. The up-converted signal power for the desired signal components, LO and USB, and the undesired signal components, 2LSB, 2USB, and USB, are shown together. We can see from this figure that the LSB signal power increases in proportion to the IF input power; however, the output local carrier power remains to be 7 dBm. The target LSR, which is 10 dB, as described in Section III, is achieved when the IF input power is 13 dBm. We can also see from this figure that the power level of all undesired components, i.e., USB, 2LSB, and 2USB, are effectively suppressed due to the image rejection technique and are less than 10 dBm when the IF input power is 13 dBm. The phase-noise performance of the local carrier implemented in the Tx unit is shown in Fig. 8. We can see from this figure that the phase-noise performance is not as good as

Fig. 7. Output signal power characteristics of a developed Tx module.

Fig. 8. Phase-noise performance of the local carrier implemented in the Tx module.

the one of the recent phase-locked-loop-type millimeter-wave oscillators because a low-cost dielectric resonator oscillator (DRO) is used. We can see from this figure that the phase-noise level at 10-kHz offset is approximately 50.5 dBc Hz.

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Fig. 9. Configuration of 60-GHz-band Rx circuit.

Fig. 10. Photograph of the main Rx circuit board.

C. Configuration and Conversion Characteristics of Rx Unit The schematic configuration of the Rx unit is shown in Fig. 9. A photograph of the main Rx circuit board including the Rx-MCM is shown in Fig. 10. The circuit design of the Rx mixer included in the Rx-MCM is basically the same as what we have developed previously in [11]. However, peripheral/control circuits were newly designed and added in this development. The main feature of this Rx circuit is its capability to control the nonlinear characteristics of the self-heterodyne mixer by changing the bias voltage. We have used a GaAs pseudomorphic HEMT (pHEMT) device for the self-heterodyne down-conversion mixer. As is well known, a comparatively high local oscillation power should be injected to a field-effect transistor (FET)-based Rx mixer generally in a normal operation. Otherwise, the down-converted signal will suffer from high nonlinearity. Expecting the improvement in the CIR performance, we specially developed an mmW Rx board including an Rx monolithic microwave integrated circuit (MMIC) module so as to operate at different bias voltages for the mixing device. Fig. 11 shows the measured relationships between the CNR of the detected IF signal power and the received millimeter-wave signal power for different bias voltage settings for a self-heterodyne mixer (higher and lower). The relationships between the CIR and received RF power are also shown together. We can see from this figure that the CIR performance for the higher bias voltage is superior to that for the lower bias voltage,

Fig. 11. CNR and CIR performance of Rx module.

while the CNR performance for the higher bias voltage is inferior to that for the lower bias voltage. We can guess from the results that the total signal performance considering the CNR and CIR may be maximized by controlling the bias voltage setting. VI. LINK PERFORMANCE IN AN ISDB-T SIGNAL TRANSMISSION A. Measurement Setup and Parameters The Tx and Rx units were connected with WR15 waveguides and a variable power attenuator was inserted to simulate the propagation loss. An ISDB-T signal generator and an ISDB-T signal analyzer are connected with the Tx and Rx units, respectively. The parameters of the ISDB-T signal used for the link performance measurement basically followed those of the practical ISDB-T service. The main parameters are listed in Table IV. B. Confirmation of Phase-Noise Cancellation Effect As described in Section I, the main advantage of using the self-heterodyne technique is the achievability of an extremely

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TABLE IV MAIN PARAMETERS OF ISDB-T SIGNAL USED FOR THE LINK PERFORMANCE MEASUREMENT

Fig. 14. Relationship between BER and propagation loss for different bias voltages of self-heterodyne Rx mixer.

C. Dependency of the Rx Mixer Bias Voltage On BER Performance

Fig. 12. Phase-noise performance of IF signal before mmW transmission.

Fig. 13. Phase-noise performance of IF signal after mmW transmission.

low-frequency offset and phase-noise performance with a lowcost mmW oscillator. Figs. 12 and 13 show the phase-noise performances before and after an mmW transmission, respectively. We can see from these figures that the phase noise of 115 dBc Hz at 10-kHz offset degrades to 92 dBc Hz after the mmW transmission. However, if we consider the local carrier has the phase noise of 50.5 dBc Hz at 10-kHz offset, as shown in Fig. 8, we can say the phase noise is cancelled by using the self-heterodyne technique.

Fig. 14 shows the relationship between the bit error rate (BER) and the propagation loss for different bias voltages of the self-heterodyne Rx mixer, i.e., 205, 689, and 865 mV. The LSR of the transmitted signal was set to 10 dB. We can see from this figure that the BER decreases with the propagation loss, but suddenly increases at a certain propagation loss for all bias conditions. We can define an allowable propagation loss from this figure for each bias voltage once the required BER is assumed. For example, let us assume the required BER is 10 . We can then see the propagation loss from 34.5 to 38.9 dB, i.e., the loss range mV. Similarly, we can of 4.5 dB, is acceptable for see that the propagation loss from 30.5 to 35 dB and 25.5 to 32.5 dB, i.e., the loss range of 4.5 and 7 dB, are accepted for mV and mV, respectively. On the basis of the above results, we can easily assume that an adaptive setting of the Rx bias voltage effectively enlarges the allowable propagation loss from 25.5 to 38.9 dB, i.e., the acceptable loss range can be extended to 13.4 dB if the bias voltage is changed adaptively according to the propagation loss. Since it is easy to know the propagation loss from the received signal power level, the installation of the adaptive bias voltage function into the Rx should be easy. Let us translate the acceptable propagation loss in the decibel unit into a transmittable distance. The propagation loss, [dB], is expressed by (1) where , , , and are the Tx antenna gain, Rx antenna gain, wavelength, and distance, respectively. The corresponding distance can then be calculated by (2) Since we can use the antenna gain of 35 dBi for both the Tx and Rx and the wavelength is approximately 5 mm, the acceptable

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propagation loss from 25.5 to 38.9 dB corresponds to the transmittable distance from 23.7 to 110.9 m (the range is 87.2 m). On the other hand, the transmittable distances were from 67.0 to 110.9 m (the range is 43.9 m), 42.1 to 70.8 m (the range is 28.7 m), and 23.7 to 53.1 m (the range is 29.4 m) unless the adaptive control of the Rx bias voltage is assumed. From these consideration results, we can extend the transmittable distance range to about twice by applying the adaptive bias voltage control for the self-heterodyne Rx mixer. VII. CONCLUSION We have proposed the use of a 60-GHz repeater link for the ISDB-T gap-filler system and the use of a self-heterodyne technique applying a nonlinear distortion suppression technique. We have demonstrated that the 60-GHz repeater link based on the self-heterodyne technique enables a 0-Hz frequency offset through-repeater link with extremely low phase-noise characteristics in a 60-GHz band. We have also proposed to adaptively control the bias voltage for the self-heterodyne Rx mixer to maximize the total signal performance considering both CNR and CIR performances. We have demonstrated that the adaptive bias voltage control for the self-heterodyne Rx mixer is effective to enlarge the acceptable propagation loss, i.e., transmittable distance range. The developed repeater link succeeded in extending the transmittable distance range to 87.2 m by assuming the bias voltage control, while 43.9 m was the maximum transmittable distance range if the fixed bias voltage was assumed. REFERENCES [1] N. Moraitis and P. Constantinou, “Measurements and characterization of wideband indoor radio channel at 60 GHz,” IEEE Trans. Wireless Commun., vol. 5, no. 4, pp. 880–889, Apr. 2006. [2] C. Liu, E. Skafidas, and R. J. Evans, “Characterization of the 60 GHz wireless desktop channel,” IEEE Trans. Antennas Propag., vol. 55, no. 7, pp. 2129–2133, Jul. 2007. [3] R. C. Daniels and R. W. Heath, “60 GHz wireless communications: Emerging requirements and design recommendations,” IEEE Veh. Technol. Mag., vol. 2, no. 3, pp. 41–50, Sep. 2007. [4] H. Singh, O. Jisung, K. C. Kweon, Q. Xiangping, S. Huai-Rong, and N. Chiu, “A 60 GHz wireless network for enabling uncompressed video communication,” IEEE Commun. Mag., vol. 46, no. 12, pp. 71–78, Dec. 2008. [5] Z. Hao, L. Jian, and T. A. Gulliver, “On the capacity of 60 GHz wireless communications,” in Can. Elect. Comput. Eng. Conf., May 2009, pp. 936–939. [6] P. Minyoung and P. Gopalakrishnan, “Analysis on spatial reuse and interference in 60-GHz wireless networks,” IEEE J. Sel. Areas Commun., vol. 27, no. 8, pp. 1443–1452, Oct. 2009. [7] A. Maltsev, R. Maslennikov, A. Sevastyanov, A. Khoryaev, and A. Lomayev, “Experimental investigations of 60 GHz WLAN systems office environment,” IEEE J. Sel. Areas Commun., vol. 27, no. 8, pp. 488–1499, Oct. 2009. [8] Y. Shoji, K. Hamaguchi, and H. Ogawa, “60 GHz band 64 QAM/ OFDM terrestrial digital broadcasting signal tarnsmission by using millimeter-wave self-heterodyne system,” IEEE Trans. Broadcast., vol. 47, no. 3, pp. 218–227, Sep. 2001. [9] Y. Shoji, K. Hamaguchi, and H. Ogawa, “Millimeter-wave remote selfheterodyne system for extremely stable and low-cost broad-band signal transmission,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 6, pp. 1458–1468, Jun. 2002. [10] Y. Shoji and H. Ogawa, “70-GHz-Band MMIC transceiver with integrated antenna diversity system: Application of receiving-module-arrayed self-heterodyne technique,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2541–2549, Nov. 2004.

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[11] Y. Shoji, C. S. Choi, and H. Ogawa, “70-GHz-Band OFDM transceivers based on self-heterodyne scheme for millimeter-wave wireless personal area network,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 10, pp. 3664–3674, Oct. 2006. [12] C.-S. Choi and Y. Shoji, “Third-order intermodulation distortion characteristics of millimeter-wave self-heterodyne transmission techniques,” in Asia–Pacific Microw. Conf., Dec. 2006, pp. 1751–1756. [13] Transmission System for Digital Terrestrial Television Broadcasting, ARIB Standard STD-B31 ver. 1.6, Nov. 2005. [14] K. Shibuya, “Broadcast-wave relay technology for digital terrestrial television broadcasting,” Proc. IEEE, vol. 94, no. 1, pp. 269–273, Jan. 2005.

Yozo Shoji (S’98–M’99) received the B.E. and M.E. degrees in electrical engineering and Dr. Eng. degree in communications engineering from Osaka University, Osaka, Japan, in 1995, 1996, and 1999, respectively. In 1999, he joined the Yokosuka Radio Communications Research Center, Communication Research Laboratory (CRL), Ministry of Posts and Telecommunications, Yokosuka, Japan, as a Researcher; where he was engaged in the research, development, and standardization of millimeter WPAN systems until 2007. He invented a novel millimeter-wave signal transmission technology, which is known as millimeter-wave self-heterodyne transmission technology, to reduce the cost of millimeter-wave devices and to improve stability in communication. He is currently a Senior Researcher with the National Institute of Information and Communications Technology (NICT), Tokyo, Japan, where he is engaged in research on optical and millimeter-wave satellite communications systems. Dr. Shoji is a member of the Institute of Electrical, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 2003 CRL Excellent Achievement Award, the 2000 IEICE Young Researcher’s Award, the 2006 Communications Society Distinguished Contributions Award and the 2007 Electronics Society Award, and the 2008 Minister of Education, Culture, Sports, Science and Technology Young Scientists’ Prize Commendation for Science and Technology.

Chang-Soon Choi (S’02–M’05) received the B.S., M.S., and Ph.D. degrees in electrical and electronic engineering from Yonsei University, Seoul, Korea, in 1999, 2001, and 2005, respectively. His doctoral dissertation concerned fiber-supported millimeter-wave wireless communication systems. From 2005 to 2007, he was with the National Institute of Information and Communications Technology (NICT), Tokyo, Japan, where he was engaged in the development of millimeter-wave wireless communication systems, Gigabit/second WPANs and millimeter-wave photonics systems. Since 2007, he has been with IHP Microelectronics GmbH, Frankfurt, Germany, where he is involved with the development of 60-GHz wireless LANs, particularly multigigabit/s OFDM and millimeter-wave beamforming systems. He has also contributed to IEEE 802.15.3c and IEEE 802.11ad standardization activities.

Hiroki Ohta graduated from the Tokyo Technical High School, Tokyo Institute of Technology,, Tokyo, Japan, in 1979. In 1979, he joined the Communications Research Laboratory (CRL), Ministry of Posts and Telecommunications (MPT) [now the National Institute of Information and Communications Technology (NICT)], Tokyo, Japan, where he is currently a Senior Researcher of the Electromagnetic Compatibility (EMC) Group. His current research interests are digital television broadcasting systems using the OFDM method, and the gap-filler relay station using an SFN. Mr. Ohta is a member of the Institute of Electrical, Information and Communication Engineers (IEICE), Japan, and the Institute of Transportation Engineers (ITE), Japan.

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A 60-GHz 38-pJ/bit 3.5-Gb/s 90-nm CMOS OOK Digital Radio Eric Juntunen, Student Member, IEEE, Matthew Chung-Hin Leung, Member, IEEE, Francesco Barale, Student Member, IEEE, Arun Rachamadugu, Member, IEEE, David A. Yeh, Student Member, IEEE, Bevin George Perumana, Member, IEEE, Padmanava Sen, Member, IEEE, Debasis Dawn, Member, IEEE, Saikat Sarkar, Member, IEEE, Stephane Pinel, Member, IEEE, and Joy Laskar, Fellow, IEEE

Abstract—A 60-GHz fully integrated bits-in bits-out on–off keying (OOK) digital radio has been designed in a standard 90-nm CMOS process technology. The transmitter provides 2 dBm of output power at a 3.5-Gb/s data rate while consuming 156 mW of dc power, including the on-chip 60-GHz frequency synthesizer. A pulse-shaping filter has been integrated to support high data rates while maintaining spectral efficiency. The receiver performs direct-conversion noncoherent demodulation at data rates up to 3.5 Gb/s while consuming 108 mW of dc power, for a total average transceiver energy consumption of 38 pJ/bit in time division duplex operation. To the best of the authors’ knowledge, this is the lowest energy per bit reported to date in the 60-GHz band for fully integrated single-chip CMOS OOK radios. Index Terms—CMOS, digital radio, 90 nm, on–off keying (OOK), 60 GHz, transceiver.

I. INTRODUCTION

E

MERGING “bandwidth hungry” applications such as high-definition video distribution and ultrafast multimedia side-loading have extended the need for multigigabit wireless solutions beyond the reach of conventional wireless local area network (WLAN) technology or even more recently emerging ultra-wideband (UWB) and multiple input/multiple output (MIMO) systems. The availability of 7 GHz of unlicensed bandwidth in the 60-GHz spectrum presents a unique opportunity to address such data-throughput requirements [1]. Moreover, the very stringent low-power specifications for battery operated portable consumer electronics will impose very low energy per bit requirements on these multigigabit links. Manuscript received April 02, 2009; revised June 26, 2009. First published January 19, 2010; current version published February 12, 2010. This work was supported by the National Science Foundation (NSF) and the U.S. Army Communications–Electronics Research, Development, and Engineering Center (CERDEC). E. Juntunen, M. C.-H. Leung, F. Barale, D. A. Yeh, B. G. Perumana, P. Sen, D. Dawn, S. Sarkar, S. Pinel, and J. Laskar are with the School of Electrical and Computer Engineering, Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). A. Rachamadugu is with the Intel Corporation, Hillsboro, OR 97124-5961 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2037867

A 60-GHz multichip module amplitude-shift keying (ASK) solution for fixed point-to-point transmission is reported in [2], which delivers a link greater than 1 Gb/s at a power consumption of 1.55 W. A significant improvement is achieved in [3] with 996-mW dc power consumption for a 2-Gb/s MSK solution. Recently, low-power multigigabit 60-GHz transceivers with varying levels of integration have been reported in [4]–[10]. This study is motivated by short-range multigigabit mobile applications with links on the order of 1 m or less. This paper demonstrates the first fully integrated single-chip 60-GHz CMOS on–off keying (OOK) digital radio with further reduction of transceiver power consumption while maintaining data transmission capabilities up to 3.5 Gb/s. OOK modulation was chosen because it allows for simple low-power modulation and demodulation circuits. A power consumption of only 156 mW in the transmit mode and 108 mW in the receive mode is achieved for up to 3.5-Gb/s data transmission and demodulation, leading to an average energy of 38-pJ/bit in time division duplex (TDD) operation. The transmitter front-end lineup consists of an OOK modulator with integrated 60-GHz frequency synthesizer and a threestage 60-GHz power amplifier (PA) [11]. Digital input buffers are used to drive a 13-tap raised cosine pulse shaping filter with a roll-off factor of 0.25. The filter is integrated for increased spectral efficiency at the demonstrated multigigabit data rates. The transmitter consumes a total of 156-mW dc power for a 2-dBm output. The receiver includes a four-stage 60-GHz low-noise amplifier (LNA), a 60-GHz power detector, and a high-gain baseband amplifier. In addition, a 1-bit comparator and a linear Hodge clock and data recovery (CDR) circuit are integrated to provide a clocked serial digital data output. The total dc power consumption of the receiver has been measured to be 108 mW (an additional 13 mW is consumed by 50- output drivers for measurement purposes) for a total noise figure of 8.5 dB and a sensitivity beyond 40 dBm (without antenna gain) at 1.728 Gb/s for a bit error rate (BER) of less than 10 . BERs less than 10 were measured for higher input power levels. The radio provides a complete bits-in bits-out solution and does not require any additional synchronization or equalization. Section II summarizes the low-power transceiver architecture and describes the design and performance of different building blocks. Section III presents the measurement results of the single-chip digital radio.

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Fig. 3. Cross-coupled 60-GHz VCO schematic.

Fig. 1. Single-chip digital radio architecture.

Fig. 4. Block diagram of the PSF.

Fig. 2. Frequency synthesizer block diagram.

II. 60-GHz 90-nm CMOS OOK SINGLE-CHIP DIGITAL RADIO ARCHITECTURE AND IMPLEMENTATION The architecture of the fully integrated single-chip digital radio is shown in Fig. 1. The transmitter lineup consists of buffered digital clock and data inputs, a pulse-shaping baseband filter with bypass capability, cross-coupled voltage-controlled oscillator (VCO) with phase-locked loop (PLL), single-ended input single-ended output up-converter, and a three-stage 60-GHz PA. The receiver uses direct-conversion architecture with a four-stage 60-GHz LNA, a 60-GHz power detector, baseband amplifier, 1-bit comparator, and a linear Hodge CDR. Performing noncoherent OOK demodulation with a novel 60-GHz power detector saves dc power and complexity in the receiver since no local oscillator (LO) or carrier synchronization scheme is required. The penalty is high conversion loss in the demodulator that reduces the overall receiver sensitivity. To offset the conversion loss of the demodulator, a four-stage high-gain LNA is used. A. Transmitter 1) 60-GHz Frequency Synthesizer: The frequency synthesizer block diagram is shown in Fig. 2. The divider chain employs different divider topologies for different frequency inputs. The 60.48-GHz (for example) VCO output is applied to a divide-by-2 injection-locked divider (ILD) [12]. The ILD output drives a divide-by-8 block consisting of three static master–slave (MS) flip-flop dividers [13]. At this point, the signal is at 3.78 GHz and programmable digital divider blocks are used to achieve a divide-by-140 [14], bringing the signal down to the reference frequency at 27 MHz.

A second-order loop filter is used with a D flip-flop-based phase-frequency detector (PFD) and current-steering charge pump (CP) to drive the VCO control node. A cross-coupled oscillator, shown in Fig. 3, is used to generate a differential 60-GHz signal. The tank inductance is provided by a microstrip transmission line with length optimized from layout parasitic extraction. A small varactor is used for reliable oscillations with a capacitance range of 25–45 fF. The VCO outputs are buffered through source–follower stages to provide isolation to the core. A differential amplifier is used to boost the output signal to 6 dBm on a 50- differential equivalent. The frequency synthesizer exhibits a lockable frequency range of 59.9–61.3 GHz and consumes 65 mW of dc power (30 mW in the PLL). The phase noise is 81 dBc/Hz at a 1-MHz offset. 2) Baseband Processor: The baseband block includes input buffers, analog multiplexers, and a pulse-shaping filter (PSF). Pulse shaping is performed by a 13-tap raised cosine filter, as seen in Fig. 4. A roll-off factor of 0.25 is implemented, which gives a theoretical reduction of 37.5% in the null-to-null bandwidth of an OOK spectrum. The filter consumes 4 mW of dc power. True OOK modulation by the digital input bit stream is also supported by bypassing the PSF. 3) OOK Modulator: The circuit schematic of the 60-GHz dual-gate up-converter used to perform OOK modulation is shown in Fig. 5. The single-ended baseband signal is fed to the gate of one of the upper transistors with the other shorted to ground. The open stub at the baseband port serves the dual purpose of achieving stability of the circuit as well as providing LO rejection for better conversion-loss performance. The differential LO signal is fed to the gates of the lower transistor pair. Matching circuits are provided at the LO port to achieve impedance matching between the output of the VCO to the input of the mixer. The output at the RF port is combined to cancel the LO leakage during the off-state. The matching circuits at the RF output port provide 50- matching to the PA input. This up-converter provides a 15-dBm output at 60 GHz with a 6-dBm differential LO power at an average dc power consumption of less than 5 mW.

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Fig. 7. Output power characteristics of the three-stage 60-GHz PA. From [11].

Fig. 5. Circuit schematic of 60-GHz OOK modulator.

Fig. 8. 60-GHz PA simulated versus measured: (a) jS and (d) jS j. From [11].

j

, (b) jS

j

, (c) jS

j

,

Fig. 6. Three-stage 60-GHz PA. (a) Die photograph. (b) Schematic.

4) PA: The three-stage PA was implemented focusing on low power consumption. A cascode topology was chosen for the first stage to obtain a high gain as well as stability in the entire frequency band of operation. The second and third stages were implemented with single device common-source topologies to maximize linearity. A die photograph and circuit schematic are shown in Fig. 6. The PA achieves a small-signal gain of 17 dB while delivering with 5.8% power-added efficiency (PAE) 5.1-dBm output and 8.4-dBm saturated output power [11]. The measured output power characteristics and -parameter performances are shown in Figs. 7 and 8, respectively. The PA consumes 78 mW of dc power. B. Receiver 1) 60-GHz LNA: The receiver requires a high gain LNA as the first element in the down-conversion chain. The LNA schematic diagram is seen in Fig. 9. The topology is four cascode stages with microstrip transmission line matching. Cascode devices were used to achieve a high gain per stage while maintaining a stable design. Cascode devices have a slightly higher noise contribution than common-source devices; however, the additional gain of each stage helps to reduce the cascaded noise figure. Conjugate to 50- matching was used at the input and output of each stage. Short-circuit stub-matching

Fig. 9. Four-stage 60-GHz LNA schematic.

networks were used so that the gate and drain biases could be brought via the stubs of the input and output matching networks, respectively, of each stage. The noise contributions of the active devices are minimized by biasing them at a current density of 0.2 mA m, which is optimal in terms of noise performance and maximum frequency of [15]. RC networks at the stub ends provide oscillation protection against low-frequency oscillation. A die photograph of a four-stage LNA test structure along with its measured -parameter performance is seen in Fig. 10. The LNA occupies a die area of 0.6 0.75 mm while delivering a peak gain of 24 dB and a 7.5-dB noise figure at a dc power consumption of 64 mW. 2) Direct-Conversion Demodulator: An innovative demodulator circuit, shown in Fig. 11, was designed to extract baseband data from a 60-GHz OOK modulated signal. The circuit is an autocorrelator based upon a dual-gate mixer architecture. using a series-stub microstrip The input is matched to 50 matching network. Power detection is performed by multiplying the 60-GHz input signal by a 180 delayed version of itself. The series transmission line at the port creates a phase delay

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Fig. 12. Small-signal transconductance g M by the source–follower M .

Fig. 10. 60-GHz LNA. (a) Die photograph, simulated versus measured (b) jS j, (c) jS j, and (d) jS j.

Fig. 11. Detector schematic.

between the waveforms at the and ports. Additionally, this line functions as a resonant structure, which provides a voltage gain due to the high impedance loading at the port. This voltage boost, denoted by , was simulated to be a open-circuit stub is a short factor of approximately 1.5. The at 60 GHz to suppress the RF signal at the output. Extraction of the baseband data is described as follows. The small-signal output current given by (1) is the input voltage to multiplied by its small-signal transconductance (1) Shown in (2) is the small-signal transconductance for is the an above-threshold MOSFET, where in the saturation region is delarge-signal transconductance. pendent on the overdrive voltage , whereas in the linear region, it is dependent upon the drain to source . Mixing action can be enabled in (1) if the drain voltage can be modulated via the voltage, and therefore, the , of source–follower stage of (saturation) (linear). (2) The ac waveforms at the gates of and are expressed is a 180 shifted version by (3) and (4), respectively, where is the magnitude of boosted by the series resonator, and of the OOK modulated signal that contains the baseband data (3)

of M modulated at the drain of

(4) The use of direct-conversion multiplication is taken advanand tage of by applying 180 out-of-phase signals at the ports. This allows for a larger swing at the drain of from the constructively interfering voltage outputs of the commonstage and the source–follower stage. This effect source is accounted for by the parameter and has been simulated to nearly twice as large as provide a signal swing at the drain of the case where and are in phase. This effect has a direct increase on the conversion gain, as will be shown in the following discussion. is biased at the edge of the linear/saturation If the drain of , the periodically varying region, i.e., can be described as in (5), where is a half-wave rectified sine wave described by the Fourier series in (6). This action is illustrated in Fig. 12, where (5) (6)

To evaluate the baseband mixing product, only the term in needs to be considered since the high-frequency terms will be filtered by the low-pass nature of the circuit. Therefore, the small-signal output current is given by (7). Expanding and again removing the high-frequency terms yields the smallsignal output current given by (8) as follows:

(7) (8) The voltage conversion gain is defined as the baseband output voltage divided by the magnitude of the input voltage. Assuming , this is given the output resistance is approximately equal to by (9) as follows: (9)

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Fig. 13. Simulated detector conversion gain versus input power for a 60-GHz OOK modulated carrier.

Fig. 16. Baseband amplifier schematic.

The first stage of the amplifier is a single-to-differential ended converter implemented by ac grounding one input terminal of a differential amplifier. The PMOS load is biased through resistors at the output whose design values can be adjusted to tune gain versus bandwidth. These also provide common mode feedback for the first stage, which mitigates dc offset that could otherwise propagate in this dc coupled design to the subsequent stages. The second stage is a pseudodifferential-to-single ended circuit with a PMOS current-mirror load and a parallel RC gain peaking network at the source of the input devices. It can be shown [16] that the RC network creates a zero in the of the second stage, as seen in effective transconductance (11). This creates a peaking effect, which can be tuned to extend the amplifier bandwidth. The amplifier has a peak gain of 20 dB with 2.1-GHz 3-dB bandwidth, and consumes 12.7 mW of dc power

Fig. 14. Detector test structure die photograph.

(11)

III. SINGLE-CHIP DIGITAL RADIO MEASURED RESULTS Fig. 15. Detector test structure measured versus simulated jS

j

A. Transmitter

.

Plugging (8) into (9) shows the voltage conversion gain is proportional to input voltage magnitude, as in (10). Therefore, doubling the LNA gain will quadruple the conversion gain of the entire receiver. The simulated detector conversion gain versus input power is shown in Fig. 13 with the conversion gain at the receiver minimum sensitivity (plus the LNA gain) indicated

Pseudorandom bit-sequence (PRBS) data was input to the transmitter baseband ports and the output spectra observed. Fig. 17(a)–(d) shows the captured output spectra for 1.728 Gb/s without PSF, 1.728 Gb/s with PSF, 3.456 Gb/s without PSF, and 3.456 Gb/s with PSF, respectively. The transmitter consumes 156 mW of dc power while achieving a power output of greater than 2 dBm. B. Receiver

(10) Figs. 14 and 15 show a fabricated detector test structure and performance, respectively. The measured reits measured sults show a very good input matching around 60 GHz with greater than 10-GHz 10-dB input matching bandwidth. The demodulator consumes 16 mW of dc power. The simulated 3-dB RF bandwidth is greater than 4 GHz. 3) Baseband Amplifier: The demodulated signal is amplified through the baseband limiting amplifier, seen in Fig. 16, before digitization. A large gain is required and a low supply voltage is desired for low power operation; therefore, a multistage design is used.

An external 60-GHz OOK modulator with PRBS input was used to perform BER measurements on the receiver for swept power inputs at the above data rates. Fig. 18 shows the BER versus received input power. Fig. 19 shows measured eye diagrams of the digital baseband output for 1.728- and 3.456-Gb/s data. The receiver consumes 108 mW of dc power and exhibits a noise figure of 8.5 dB at 40-dBm input. The minimum sensitivity of the receiver for 1.728-Gb/s data at a BER of less than 10 is 40 dBm at the probing pad. C. Integrated Single-Chip Digital Radio A die photograph of the fabricated single-chip digital radio is 2.3 mm shown in Fig. 20. It occupies a die area of 1.8

JUNTUNEN et al.: 60-GHz 38-pJ/bit 3.5-Gb/s 90-nm CMOS OOK DIGITAL RADIO

Fig. 17. Transmitter output spectra. (a) 1.728 Gb/s without PSF. (b) 1.728 Gb/s with PSF. (c) 3.456 Gb/s without PSF. (d) 3.456 Gb/s with PSF.

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Fig. 20. Fabricated OOK single-chip digital radio. TABLE I TRANSCEIVER COMPARISON

Fig. 18. Receiver BER versus input power.

Fig. 19. Measured eye diagrams for: (a) 1.728- and (b) 3.456-Gb/s data.

including pads. It supports data rates of up to 3.5 Gb/s at a transmitter–receiver TDD average of 38 pJ/bit. Table I summarizes the measured performance alongside other reported 60-GHz OOK transceivers. This fully integrated single-chip digital radio reports minimum power budget with maximum data throughput. The

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reported transceiver provides a completely integrated bits-in bits-out solution, including pulse shaping, ADC, and CDR for very short-range multigigabit wireless transmission. IV. CONCLUSION In this paper, a 90-nm CMOS 60-GHz fully integrated singlechip OOK digital radio for multigigabit data rate short-range wireless communications has been presented for the first time. The receiver has been designed to perform direct-conversion noncoherent demodulation of OOK modulated signals at 1.728-Gb/s data rates, and has been successfully measured up to 3.5 Gb/s. The transmitter provides 60-GHz OOK modulation to a digital baseband input up to 3.5 Gb/s with pulse-shaping capability. This fully integrated single-chip radio operates at only 31-pJ/bit (receiver) and 45-pJ/bit (transmitter), thus reporting the highest level of integration and lowest energy per bit among 60-GHz CMOS OOK radios to the best of the authors’ knowledge. REFERENCES [1] J. Laskar, S. Pinel, D. Dawn, S. Sarkar, B. Perumana, and P. Sen, “The next wireless wave is a millimeter wave,” Microw. J., pp. 22–36, Aug. 2007. [2] 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., 2005, p. 4 pp. [3] B. Floyd et al., “Short course: SiGe BiCMOS transceivers for millimeter-wave,” presented at the IEEE Bipolar/BiCMOS Circuits Technol. Meeting, 2007. [4] S. Pinel, S. Sarkar, P. Sen, B. Perumana, D. Yeh, D. Dawn, and J. Laskar, “A 90 nm CMOS 60 GHz radio,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2008, pp. 130–601. [5] S. Sarkar, P. Sen, B. Perumana, D. Yeh, D. Dawn, S. Pinel, and J. Laskar, “60 GHz single-chip 90 nm CMOS radio with integrated signal processor,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 1167–1170. [6] S. Sarkar and J. Laskar, “A single-chip 25 pJ/bit multi-gigabit 60 GHz receiver module,” in IEEE/MTT-S Int. Microw. Symp. Dig., 2007, pp. 475–478. [7] M. Tanomura et al., “TX and RX front-ends for 60 GHz band in 90 nm standard bulk CMOS,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig. Papers, Feb. 2008, pp. 558–559. [8] A. Tomkins, R. A. Aroca, T. Yamamoto, S. T. Nicolson, Y. Doi, and S. P. Voinigescu, “A zero-IF 60 GHz transceiver in 65 nm CMOS with 3.5 Gb/s links,” in IEEE Custom Integr. Circuits Conf., Sep. 2008, pp. 471–474. [9] J. Lee, Y. Huang, Y. Chen, H. Lu, and C. Chang, “A low-power fully integrated 60 GHz transceiver system with OOK modulation and on-board antenna assembly,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2009, pp. 316–318. [10] C. Marcu et al., “A 90 nm CMOS low-power 60 GHz transceiver with integrated baseband circuitry,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2009, pp. 314–315. [11] D. Dawn, S. Sarkar, P. Sen, B. Perumana, D. Yeh, S. Pinel, and J. Laskar, “17-dB-gain CMOS power amplifier at 60 GHz,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 859–862. [12] M. Tiebout, “A CMOS direct injection-locked oscillator topology as high-frequency low-power frequency divider,” IEEE J. Solid-State Circuits, vol. 39, pp. 1170–1174, 2004. [13] Y. Mo, E. Skafidas, R. Evans, and I. Mareels, “A 40 GHz power efficient static CML frequency divider in 0.13- m CMOS technology for high speed millimeter-wave wireless systems,” in 4th IEEE Int. Circuits Syst. Commun. Conf., May 2008, pp. 812–815. [14] F. Barale, P. Sen, S. Sarkar, S. Pinel, and J. Laskar, “Programmable frequency-divider for millimeter-wave PLL frequency synthesizers,” in 38th Eur. Microw. Conf., Oct. 2008, pp. 460–463. [15] T. Yao, M. Gordon, K. Tang, K. Yau, M.-T. Yang, P. Schvan, and S. Voinigescu, “Algorithmic design of CMOS LNAs and PAs for 60-GHz radio,” IEEE J. Solid-State Circuits, vol. 42, no. 5, pp. 1044–1057, May 2007. [16] B. Razavi, Design of Integrated Circuits for Optical Communications. New York: McGraw-Hill, 2003.

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Eric Juntunen (S’01) received the B.S. degree in electrical engineering from Western Michigan University, Kalamazoo, in 2003, the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2008, and is currently working toward the PhD degree at the Georgia Institute of Technology. In Summer 2009, he was with BAE Systems, Merrimack, NH, where he developed CMOS and SiGe circuits for analog signal processing and RF front ends. He is currently a member of the Microwave Applications Group, Georgia Electronic Design Center (GEDC), Georgia Institute of Technology. His research interests include CMOS RF and millimeter-wave integrated circuit design for high-data-rate wireless transceivers. Matthew Chung-Hin Leung (M’08) received the dual B.S. degree in electrical and computer engineering and physics from the Rensselaer Polytechnic Institute, Troy, NY, and the M.S. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2008. His Master thesis concerned millimeter-wave PA modeling and dc circuitries. He is currently with the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, where his primary involvement is millimeter —wave layout. He is also involved in other dc circuits, digital and analog interface circuits, and printed circuit board (PCB) designs. Francesco Barale (S’07) was born in Viareggio, Italy, in 1982. He received the B.S. and M.S. degrees in electronics engineering from the University of Pisa, Pisa, Italy, in 2004 and 2006, respectively, and is currently working toward the Ph.D. degree in electrical engineering at the Georgia Institute of Technology, Atlanta. His research concerns the development of CMOS fully integrated frequency synthesizers and clock-data recovery circuits for 60-GHz wireless applications. Arun Rachamadugu (M’07) was born in Bengaluru, India, in 1983. He received the B.E degree in electronics and communications from the P.E.S Institute of Technology, Bengaluru, India, in 2004, and the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2008. His M.S. thesis concerned high-speed digital PSFs. From 2004 to 2007, he was a Design Engineer with LSI Technologies, Bengaluru, India. From 2007 to 2008, he was a Graduate Research Assistant with the Microwave Application Group, Georgia Electronic Design Center (GEDC), Georgia Institute of Technology. He is currently a Design Engineer with the Converged Core Development Organization, Intel Corporation, Hillsboro, OR. David A. Yeh (S’99) was born in Taipei, Taiwan. He received the B.Eng. degree in electrical and electronic engineering from the University of Auckland, Auckland, New Zealand, in 2001 the M.S. degree in electrical and computing 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. From 2001 to 2002, he was an Engineering Consultant with Broadcast Communications Limited, Auckland, New Zealand, during which time he was involved with the national deployment of a broadband wireless access (BWA), a pre-WiMAX network. While working toward the Master degree, he held a part-time position with the Broadcom Corporation, Duluth, GA, where he gained experience in noise modeling and distortion analysis for cable modem termination systems. During the summers of 2005 and 2006, he held an internship with Motorola Laboratories, Tempe, AZ, during which time he was involved with the practical implementation of a millimeter-wave imaging system. He is currently a member of the Microwave Application Group, Georgia Electronic Design Center (GEDC), Georgia Institute of Technology. His current areas of research include transceiver architecture, gigabit modems, and system and circuit design for millimeter-wave gigabit wireless systems.

JUNTUNEN et al.: 60-GHz 38-pJ/bit 3.5-Gb/s 90-nm CMOS OOK DIGITAL RADIO

Bevin George Perumana (S’04–M’08) was born in Kottayam, India, in 1980. He received the B.Tech. degree in electrical engineering from the Indian Institute of Technology, Kharagpur, India, in 2002, and the M.S. degree and Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2005 and 2007, respectively. His thesis concerned low-power CMOS front-ends for wireless personal area networks. From 2002 to 2003, he was a Research Consultant with the Advanced Very Large Scale Integration (VLSI) Design Laboratory, Indian Institute of Technology. From 2003 to 2005, he was a Graduate Research Assistant with the Microwave Application Group, Georgia Electronic Design Center (GEDC), Georgia Institute of Technology. From 2005 to 2006, he was an Intern with the Communication Circuits Laboratory, Intel Corporation, Hillsboro, OR. He is currently with the GEDC, where he is involved in the field of integrated CMOS millimeter-wave transceiver development. Padmanava Sen (S’04–M’08) was born in Kolkata, India. He received the B. Tech degree in electronics and electrical communication engineering from the Indian Institute of Technology, Kharagpur, India, in 2003, and the M.S. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 2005 and 2007, respectively. He is currently with the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, where he is involved in the field of CMOS millimeter-wave frequency synthesizer designs and the analysis of millimeter-wave high data-rate low-power wireless integrated systems. He has authored or coauthored over 35 journal and conference papers. Debasis Dawn (M’90) received the B.Engg degree from Jadavpur University, Calcutta, India, in 1986, the M.Tech degree from the Indian Institute of Technology (IIT), Kanpur, India, in 1989, and the Ph.D. degree from Tohoku University, Sendai, Japan in 1993, all in electrical engineering. From 1993 to 1998, he was a Research Associate with Tohoku University, where he was engaged in research on the development of millimeter-wave circuits and millimeter-wave photonic circuits. From 1998 to 2004, he was a Research Engineer with Fujitsu Laboratories Limited, Tokyo, Japan, where he was engaged in millimeter-wave monolithic microwave integrated circuit (MMIC) development and device modeling using compound semiconductors such as GaAs pseudomorphic HEMT (pHEMT) process technology. In 2005, he joined the Sony Corpoation, Tokyo, Japan, where he was a Senior MMIC Design Engineer. Since 2006, he has been a member of the Research Faculty at the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, Atlanta, where he is currently engaged in the development of RF front-end circuits for wireless personal area network (WPAN) applications using CMOS process technology. He has authored or coauthored over 50 papers in international journals and conferences. He holds two U.S. patents. Dr. Dawn was an elected Technical Program Review Committee member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) in PA devices and circuits. He was a session chair of the 2009 IEEE MTT-S IMS, Boston, MA. Saikat Sarkar (S’04–M’08) was born in Asansol, India. He received the B. Tech degree in electronics and electrical communication engineering from the Indian Institute of Technology, Kharagpur, India, in 2003, and the M.S. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 2005 and 2007, respectively. He is currently with the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, where he is involved in the field of CMOS millimeter-wave front-end circuit design, system

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integration, and the analysis of millimeter-wave high data-rate low-power wireless systems. He has authored or coauthored over 35 journal and conference papers. He holds one U.S. patent with two international patents pending Dr. Sarkar was the recipient of the Third Prize of the Student Paper Competition of the 2007 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). Stephane Pinel (M’06) 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’Analyse et d’Architecture des Systemes, Centre National de la Recherche Scientifique (CNRS), Toulouse, France, in 2000. He has worked on the UltraThin Chip Stacking (UTCS) European Project for three years involving Alcatel Space and IMEC, Leuven, Belgium. Since 2001, he has been a member of the research faculty with the Georgia Electronic Design Center (GEDC), Georgia Institute of Technology, Atlanta. Since 2001, he has lead the development of the multigigabit wireless testbed at the GEDC. He has authored or coauthored over 160 journals and proceeding papers, two book chapters, and numerous invited talks. He holds four patents. His research interests include CMOS, silicon-on-insulator (SOI) and SiGe RF and millimeter-waves circuit design, advanced 3-D integration and packaging technologies, RF and millimeter-waves embedded passives (filters, antenna arrays) design using organic and ceramic materials, RF microelectromechanical systems (MEMS) and micromachining techniques, and system-on-package for RF and millimeter-waves front-end module. Dr. Pinel has participated and organized numerous workshops at international conferences such the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) where he was the Technical Program Committee (TPC) vice-chair in 2008. He was the recipient of the First Prize Award of SEE 1998, the Second Prize Award of IMAPS 1999, and the 2002 International Conference on Microwave and Millimeter-Wave Technology Best Paper Award, Beijing, China. Joy Laskar (S’86–M-85–SM’02–F’05) received the B.S. degree in computer engineering (with math/physics minors) (summa cum laude) from Clemson University, Clemson, SC, and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign. Prior to joining the Georgia Institute of Technology in 1995, he was a Visiting Professor with the University of Illinois at Urbana-Champaign, and an Assistant Professor with the University of Hawaii at Manoa. With the Georgia Institute of Technology, he holds the Schlumberger Chair in Microelectronics with the School of Electrical and Computer Engineering. He is also Founder and Director of the Georgia Electronic Design Center (GEDC), where he heads a research group of 50 members and has graduated 41 Ph.D. students since 1995. He has authored or coauthored over 500 papers, several book chapters, and three books (with another book in development). He has given numerous invited talks. He holds over 40 patents issued or pending. He and his research team have founded four companies to date: an advanced WLAN Integrated Circuit (IC) company, RF Solutions, which is now part of Anadgics (NASDAQ: Anad), a next-generation analog CMOS IC company, Quellan, which is develops collaborative signal-processing solutions for the enterprise, video, storage, and wireless markets, and is now part of Intersil (NASDQ: ISIL), and two more companies that are part of the Georgia Institute of Technology’s Venture laboratory process. Dr. Laskar was general chairman of the 2008 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He is an elected member of the IEEE MTT-S Administrative Committee (AdCom), chair of the IEEE MTT-S Education Committee, and vice-chair of the IEEE MTT-S Executive Committee.

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Effects of Geometrical Discontinuities on Distributed Passive Intermodulation in Printed Lines Aleksey P. Shitvov, Member, IEEE, Torbjörn Olsson, Member, IEEE, Benjamin El Banna, Dmitry E. Zelenchuk, Member, IEEE, and Alexander G. Schuchinsky, Senior Member, IEEE

Abstract—This paper presents the results of experimental study of passive intermodulation (PIM) generation in microstrip lines with U-shaped and meandered strips, impedance tapers, and strips with the profiled edges. It is shown that the geometrical discontinuities in printed circuits may have a noticeable impact on distributed PIM generation even when their effect is indiscernible in the linear regime measurements. A consistent interpretation of the observed phenomena has been proposed on the basis of the phase synchronism in the four-wave mixing process. The results of this study reveal new features of PIM production important for the design and characterization of low-PIM microstrip circuits. Index Terms—Distributed nonlinearity, microstrip discontinuities, passive intermodulation (PIM), printed circuits.

I. INTRODUCTION

P

ASSIVE intermodulation (PIM) has been a subject of a number of studies related to signal integrity and reliability of the communication systems. Recently, this topic has gained renewed interest owing to rapidly increasing commercial applications of printed circuit boards (PCB) in high-performance components of wireless communications systems such as printed antennas and phased arrays, interconnects, backpanels, power combiners, etc. [1]–[4]. The principal mechanisms and sources of PIM generation in printed lines fabricated on commercial microwave laminates have been discussed in [5]–[9]. It has been shown, in particular, that the weak distributed nonlinearities of the conductor cladding and substrate dielectric materials present major contributions to PIM generation [10]. Namely, it has been found that the material of printed conductors, quality of the finish coating and edges of etched tracks, and roughness of the conductor-to-substrate interface are the main sources of distributed nonlinearity [5]. It has also been observed that the base dielectric and bonding layers contribute to the substrate nonlinearity [11], [12]. Manuscript received August 04, 2009; revised October 12, 2009. First published January 22, 2010; current version published February 12, 2010. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) under EPSRC Grant EP/C00065X/1. A. P. Shitvov, D. E. Zelenchuk, and A. G. Schuchinsky are with the Institute of Electronics, Communications and Information Technology, Queen’s University of Belfast, BT3 9DT Belfast, U.K. (e-mail: [email protected]; [email protected]; [email protected]). T. Olsson is with Powerwave Technologies Sweden AB, Kista 164 40, Sweden (e-mail: [email protected]). B. El Banna is now with the Laird Technologies, 414 51 Göteborg, Sweden (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038456

From the physical standpoint, the distributed nonlinearity of printed lines can be described as a continuum of the microscopic nonlinear scatterers formed by small structural inhomogeneities, which are exposed to high power carrier signals [8], [13]. As a result of the phase synchronism in the collective response of these microscopic sources, the forward propagating PIM products cumulatively grow along the transmission line (TL), while the distribution of reverse propagating PIM products exhibits periodic undulations along the line length. However, these basic features of the PIM production on the matched straight uniform single-mode TLs are significantly altered by the port mismatch in the finite sections of the TLs, lumped discontinuities, and localized PIM sources [8], [14]. The latter effects obscure the basic patterns of distributed PIM generation by the intrinsic nonlinearities of the printed microstrip lines, and therefore, hamper an accurate characterization of the PIM performance of PCB materials. In addition to the discontinuities of board launches and coaxial-to-microstrip transitions, the realistic printed circuits comprise a number of geometrical discontinuities [15] such as strip bends, U-turns, width steps, etc. Their effect on the PIM generation inside the circuit is far from trivial and requires detailed investigation. From the practical perspective, it is also necessary to understand to what extent the PIM measurements performed on the basic straight uniform microstrip lines are representative of the PIM response of actual circuits with complex conductor layouts. It is necessary to note that the extensive literature devoted to the discontinuities in printed lines has dealt with linear structures only. Existing commercial EM simulators do not provide the tools for modeling discontinuities in the TLs with distributed nonlinearities or PIM analysis. The model of the nonlinear TL [13] successfully employed for the study of distributed PIM generation in the straight uniform sections of printed lines has limited applicability to the analysis of PIM production in complex strip layouts. Development of the rigorous electromagnetic phenomenology of PIM generation by distributed nonlinearities in the TLs with geometrical discontinuities remains an extremely challenging task, which requires thorough preliminary conceptualization based on sound experimental observations. This paper presents the first results of a study aimed at evaluating the impact of the conductor geometry on the PIM production in printed lines and developing the associated basic phenomenology. The experimental methodology, based upon the two-port PIM measurements and near-field PIM probing [16], is outlined in Section II. The effects of geometrical discontinuities on PIM performance of microstrip lines are discussed in Section III for meandered and tapered microstrip lines of vari-

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at Port 1 (reverse PIM3, ) and Port 2 (forward PIM3, ). The residual PIM3 level of the instrument, measured with a low-PIM thru adaptor in place of the DUT, was below 125 dBm. In the linear regime, the VNA or ) and transmission is used to measure the reflection ( or ) for the DUT fed with a single CW carrier of the ( frequency or . For the near-field mapping, see Fig. 1(b), the DUT output port is terminated in the low-PIM matched cable load, and an openis connected to the receiver ended coaxial probe of length port Rx of the PIM analyzer or VNA. The probe scans the board at a constant spacing from the surface, which is maintained by a polyethylene sleeve at the probe tip, see Fig. 1(c). The probe for the PIM products of frequency readings, or the transmission ( or ) at the frequency or in the linear regime, are recorded at each probe position . In order to keep the perturbation caused by the probe low, the probe-to-strip coupling has been maintained below a level of 33.2 dB as measured at the center of the reference strip. III. EFFECTS OF GEOMETRICAL DISCONTINUITIES A. Strip Curvature

Fig. 1. Schematics of the test arrangements for: (a) two-port PIM measurements. (b) Near-field PIM probing. (c) Detailed view of the probe tip.

able width and for the printed lines with uniform and profiled strips containing sharp- and round-edged notches. The main findings are summarized in Section IV. II. EXPERIMENTAL ARRANGEMENTS The test setups for two-port measurements and near-field probing of PIM products used in this study are schematically depicted in Fig. 1. They are based upon the Summitek SI-900B PIM analyzer, which is employed for both two-port PIM testing and near-field PIM mapping. For the sample characterization in the linear regime, a conventional vector network analyzer (VNA) is used instead of the PIM analyzer. Port 1 of the test setup is assigned to input of the device-under-test (DUT), Port 2 to the DUT output, see Fig. 1(a), and the near-field probe output is referred to as Port 3, see Fig. 1(b). The test setup is calibrated at the respective port reference planes. The DUT has been represented by a section of a microstrip line of length with two low-PIM end-launchers (Fig. 1), which are either direct cable or contactless launchers [16]. In the two-port PIM measurements, see Fig. 1(a), the PIM analyzer feeds the DUT with two high-power continuous-wave (CW) carriers ( and ) of frequencies and records the power of the third-order PIM (PIM3) product of frequency

The curved conductor tracks in microstrip circuits represent a typical functional discontinuity that affects not only the linear characteristics [15], but also their PIM performance. In particular, the simulations of superconducting open-loop resonators in [17] have shown significant degradation of the PIM performance and quality factor at smaller ratios of the arc radius to strip width. This effect has been attributed to the redistribution of the electric current density due to the strip curvature [17]. To assess an impact of strip curvature on the PIM performance of printed lines, the two-port PIM3 measurements have been performed on a strip U-turn in the microstrip line, see Fig. 2(a), using the setup of Fig. 1(a). Three replicas of straight and two replicas of U-shaped uniform microstrip lines of the same length of 914 mm, see Fig. 2(a), were fabricated on a commercial Taconic TLX-9–0620-CL1/CL1 laminate of 1.58-mm thickness with the dominant conductor nonlinearity [10]. An annular section of the U-shaped strip had radius substantially larger than the strip width mm . In the GSM900 band (890–960 MHz), both layouts exhibited the linear reflection coefficients dB, see Fig. 2(b). The forward PIM3 measurements have been performed at 2 43 dBm carrier power as the carrier frequency MHz was fixed, while the carrier frequency was swept from 960 to 955 MHz so that the PIM3 frequency increased from 910 to 915 MHz. The plots in Fig. 2(c) show the mean level of the measured PIM3 products, averaged over the number of replicas of each layout, and three mating/de-mating cycles for each specimen. The measurement results show that the average forward PIM3 level in the U-shaped strips is lower than in the straight lines. This observation suggests that generation of the forward PIM3 products is affected by the strip curvature, despite this discontinuity has no discernible effect on the linear scattering parameters of the fundamental tones.

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Fig. 3. Schematic representation of phase variation of the PIM sources located at the inner and outer edges and the center line of the strip annular segment;  . is wavelength at the PIM3 frequency f

Fig. 4. Plan view of the meandered microstrip line. The rectangular area encompassed by the dash line was subjected to near-field probing.

B. Mapping PIM Product Distribution on Strip U-Turn

Fig. 2. Effect of the strip curvature on PIM response of straight and U-shaped microstrip lines. (a) Layout of the printed strip conductors. (b) Input reflection coefficients S of the terminated lines. (c) Mean value of PIM3 products averaged over the specimens and reconnections of each line. Error bars delimit maximum deviations of the PIM3 level from the mean value. The residual PIM3 level represents the noise floor of the test setup.

Although this phenomenon may resemble that in the superconducting resonator [17], it nevertheless has a different nature. In contrast to the asymmetric redistribution of the current density across the annular strip causing PIM changes in [17], the lower level of the forward PIM3 products in the U-shaped printed strip is a result of disruption of the phase synchronism in the annular section. Indeed, unlike the cross section of straight strips, phases of the carriers and PIM3 products at the strip center , and the inner and outer edges differ in the radial cross section of the annular arc. As illustrated in Fig. 3, phase difference between the PIM3 products at the inner and outer strip edges of the annular segment, which are the most significant contributors to the distributed PIM generation, is accrued with central angle . This phase mismatch causes disruption of the phase synchronism in the four-wave mixing process existent on the straight TL [8], [13] and results in the reduced rate of cumulative growth of the forward propagating PIM3 products. To corroborate this mechanism of PIM3 generation on the curved strips, the PIM3 product distribution has been mapped on the U-shaped microstrip lines as detailed in Section III-B.

The near-field probing of the PIM3 products has been performed on the U-shaped section of a 1515-mm-long meandered microstrip line with the annular section of radius (strip width mm) (see Fig. 4). The line was fabricated on a Taconic TLG-30-0300-CL1/CL1 laminate of 0.76-mm thickness with the dominant substrate nonlinearity [10]. The near-field probing was first performed in the linear regime at frequency of 910 MHz using the VNA. The maps shown in Fig. 5(a) and (b) demonof the probe readings strate that the strip curvature does not cause any discernible distortion of the fundamental mode pattern. Furthermore, the cross-sectional field distributions on both the straight strip sections adjacent to the U-turn, see Fig. 5(b), appeared to be nearly identical. Near-field probing of PIM3 products has been performed at MHz and 2 44 dBm carrier power. The frequency surface map in Fig. 5(c) shows the irregular pattern of the PIM3 products along the strip that substantially differs from the respective map obtained in the linear regime, especially noticeable on the annular section, see Fig. 5(a). Moreover, the PIM3 distributions are also dissimilar at the annular and straight sections of the microstrip lines. Such a distortion of the PIM3 patterns is the result of disruption of the phase synchronism [8], [13] in the annular segment of the U-shaped section, as discussed in Section III-A. Thus, the mapped PIM3 product distributions in the meandered line proved to be fully consistent with the results of the two-port PIM measurements shown in Fig. 2 and shed new light on the mechanisms underlying PIM generation in the printed lines.

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Fig. 6. PIM3 product distributions on the microstrip lines of different widths with tapered sections fabricated on the laminate with dominant substrate nonlinearity. (a) Plan view of the printed layouts. (b) Near-field map of the PIM3 product distribution along the line.

Fig. 5. Patterns of the electric field distributions (probe readings) at frequency of 910 MHz in the selected part of the meandered microstrip line shown in Fig. 4. (a) Surface map of the field distribution in the linear regime. (b) Distributions of the field magnitude in the cross sections of straight strips at x x and in cm. (c) Surface map of the the proximity of the annular section at x x PIM3 product distribution.

0 =5

=

C. Tapered Impedance Transformers Printed tapered lines used in impedance transformers are essential elements of the microstrip circuits. The long tapers with smooth edges have been employed in our earlier study of the

effect of strip width on the distributed PIM generation [9], [10]. However, contribution of the nonuniform TL sections to PIM generation has not been duly investigated yet. To address this issue, in this study a set of three 914-mmlong microstrip lines with printed tapers (six-section Klopfenstein transformers) was fabricated on a single board of Taconic TLG-30-0300-CL1/CL1 laminate with dominant substrate nonlinearity, see Fig. 6(a). A reference 914-mm-long uniform 50microstrip line of width mm was made on a separate board of the same material. Each TL contained the uniform central section of length mm placed between two tapered sections of length , which varied depending on the central section width . Two short segments of the 50- lines were located at the TL ends. All the specimens exhibited low reflection, dB , measured in the 890–960-MHz frequency band. The near-field probing of PIM3 products was performed MHz and 2 43 dBm carrier power. at frequency Fig. 6(b) displays the PIM3 product distributions mapped along the strip center line of each specimen shown in Fig. 6(a). The higher PIM3 level has been observed on the wider strips, which is indicative of the dominant substrate nonlinearity [10]. It has also been found that for this type of nonlinearity, the rate of PIM3 growth increases with the strip width of the uniform central sections, as illustrated in Table I. The tapered matching transformers appeared to make little contribution to the mean PIM3 level. However, offset of the undulations in the PIM3 distributions on the strips of different widths suggests that the phase of the PIM3 products is altered at the tapered TL sections. The phase distortion of the PIM3 products generated at the nonuniform strips is also consistent with

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TABLE I LINEAR RATES OF PIM3 GROWTH WITH THE STRIP WIDTH (FIG. 6)

Fig. 7. Forward PIM3 levels measured on the lines with the profiled strips. (a) Plan view of the printed layout. (b) Detailed view of the strip conductors with sharp and rounded corners. (c) Mean levels of the forward PIM3 products measured on the lines with sharp- and round-edged corners averaged over five replicas of each layout. Error bars delimit maximum deviations within each set of five replicas.

the observations that the rate of PIM3 growth is slower on the tapered TL sections with larger variations of the strip width, as demonstrated in Table I. D. Strips With Profiled Edges Abrupt discontinuities of strip conductors, such as width steps and bends, are the typical elements of printed circuits [15]. Since intensity of the fields and currents increases at the sharp edges of strip conductors, they may cause the localized PIM production and also change the phase of carriers, thus altering the distributed PIM production in the printed lines. To investigate this effect, three different layouts of the meandered microstrip lines shown in Fig. 7 were designed, and five replicas of each geometry were fabricated on the substrate with and thickness of 0.76 mm. The reference permittivity configuration contained a uniform 1008-mm-long strip with two

similar broadside strip couplers at the ends [16]. In the other two layouts, the straight sections of the strip were profiled with alternating stubs and notches of equal lengths. Each section conmm tained 126 periodically arranged unit cells of length comprised of the notches and stubs with either sharp or rounded (rounding radius was 0.3 mm) corners, as shown in Fig. 7(b). The total length of the profiled conductor edges was 1.9 times longer than that of the reference uniform strip. The boards were fabricated from the same laminate in a single batch. The numerical modeling of the profiled strips with Ansoft’s High Frequency Structure Simulator (HFSS) has shown that the surface current density of the carriers increases at the sharp inner corners, and its magnitude doubles as compared with the current on the straight segments. Therefore, it was expected that the respective local contributions of the corners to distributed PIM production could be observed in the experiments. The forward PIM3 measurements were carried out in the GSM900 band at 2 43 dBm carrier power using the contactless test fixture [16]. The mean PIM3 level measured on the profiled strips was about 2 dB higher than that on the reference TLs. Since the strip edges make a main contribution to the distributed PIM3 generation [5], this difference is attributed to the shorter length of strip edges on the uniform tracks. Further comparison of the PIM3 performance of the strips with sharp- and round-edged corners, see Fig. 7(c), shows that the differences practically remain within the measurement uncertainty. The commensurate PIM3 levels on the strips with sharp and rounded corners indicate rather small contribution of the localized PIM generation at individual sharp corners. Thus, the effect of the corner sharpness on the PIM production proved to be difficult to identify experimentally. Apparently this effect has been smeared by imperfect etching so that the actual corner vertices have been somewhat rounded. At first glance it looks counter-intuitive that the strips with the profiled edges have a weaker impact on the PIM production than the annular sections of the U-shaped lines with smooth edges. However, the analysis of the conditions of phase synchronism, which is the primary mechanism responsible for the distributed PIM generation in these two conductor layouts, provides a consistent qualitative explanation of these experimental observations. As discussed in Section III-A, the inner and outer edges of annular arc in the U-shaped strip have different lengths, and . As a result, phases of the PIM their difference reaches products generated at the opposite edges of the strip arc differ significantly, as illustrated in Fig. 3. This entails the disruption of the phase synchronism responsible for the distributed PIM production [8], [13] and subsequent reduction of the PIM level. On the profiled strips, the stubs and notches are distributed regularly at both sides of the strip and the unit cell size is small as compared with the wavelength at the PIM3 frequency . Since both edges of the profiled strips have the same length. The average phases of the PIM products generated at the opposite edges of the strip within the unit cell remain equal. As the result, no phase mismatch occurs within a single unit cell, and the gross rate of PIM3 production remains at about the same level as it would be on the uniform strip with the straight edges of the respective length.

SHITVOV et al.: EFFECTS OF GEOMETRICAL DISCONTINUITIES ON DISTRIBUTED PIM IN PRINTED LINES

IV. CONCLUSION The effects of the strip shape and periodic discontinuities in printed lines on distributed PIM generation have been experimentally investigated using the meandered microstrip lines with U-shaped sections, printed tapers, and profiled strips with sharpand rounded-corner stubs. It has been shown that the forward PIM level slightly decreases on the curvilinear strips. This effect has been consistently explained by disruption of the phase synchronism of the PIM products generated on the annular strip segments that was corroborated by the near-field probing of PIM3 product distributions. The results of PIM3 mapping on the straight tapered lines have proven that the rate of cumulative growth of the PIM3 level on weakly nonuniform printed lines is slightly reduced as compared with the uniform lines. This effect has also been attributed to the disruption of the phase synchronism within the tapered sections. Finally, it has been demonstrated that the sharp corners of the strip conductors in the periodically profiled printed microstrip lines with the unit cell much smaller than the wavelength at the PIM frequency do not cause considerable increase of the PIM level. Therefore, such discontinuities can be safely used in the low-PIM printed circuits, provided that the associated electrical discontinuities do not create considerable mismatch and standing waves of the carriers. The presented observations of the distributed PIM generation in printed lines with the strip conductors of different geometrical shapes are of the practical importance for the design of the low-PIM printed components and PIM characterization of high-performance microwave laminates.

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[7] B. El Banna, T. Olsson, and J. Uddin, “Sources of passive intermodulation in base station antenna systems,” in Proc. Antennas Propag. Conf., Loughborough, U.K., 2006, pp. 139–144. [8] A. P. Shitvov, D. E. Zelenchuk, A. G. Schuchinsky, and V. F. Fusco, “Passive intermodulation generation on printed lines: near-field probing and observations,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 3121–3128, Dec. 2008. [9] A. P. Shitvov, D. E. Zelenchuk, A. G. Schuchinsky, and V. F. Fusco, “Passive intermodulation in printed lines: Effects of trace dimensions and substrate,” IET Microw., Antennas, Propag., vol. 3, no. 2, pp. 260–268, Mar. 2009. [10] D. E. Zelenchuk, A. P. Shitvov, A. G. Schuchinsky, and V. F. Fusco, “Discrimination of passive intermodulation sources on microstrip lines,” in Proc. 6th Int. Multipactor, Corona, Passive Intermodulation in Space RF Hardware Workshop, Valencia, Spain, 2008, CD ROM, Paper ID PIM-4, pp. 1–6. [11] D. E. Zelenchuk, A. P. Shitvov, and A. G. Schuchinsky, “Effect of laminate properties on passive intermodulation generation,” in Proc. Antennas Propag. Conf., Loughborough, U.K., 2007, pp. 169–172. [12] J. Francey, “Passive intermodulation study,” Taconic ADD, Petersburgh, NY, Apr. 2002. [13] D. E. Zelenchuk, A. P. Shitvov, A. G. Schuchinsky, and V. F. Fusco, “Passive intermodulation in finite lengths of printed microstrip lines,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2426–2434, Nov. 2008. [14] S. Hienonen and A. V. Raisanen, “Effect of load impedance on passive intermodulation measurements,” Electron. Lett., vol. 40, no. 4, pp. 245–247, Feb. 2004. [15] R. Hoffmann, Handbook of Microwave Integrated Circuits. Norwood, MA: Artech House, 1987. [16] A. P. Shitvov, D. E. Zelenchuk, T. Olsson, A. G. Schuchinsky, and V. F. Fusco, “Transmission/reflection measurement and near-field mapping techniques for passive intermodulation characterisation of printed lines,” in Proc. 6th Int. Multipactor, Corona, Passive Intermodulation in Space RF Hardware Workshop, Valencia, Spain, 2008, CD ROM, Paper ID PIM-6, pp. 1–8. [17] J. Mateu, C. Collado, and J. M. O’Callaghan, “Modeling superconducting transmission line bends and their impact on onlinear effects,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 822–828, May 2007.

ACKNOWLEDGMENT The authors are grateful to Taconic Advanced Dielectric Division, Mullingar, Ireland, Trackwise Designs Ltd., Tewkesbury, U.K., PCTEL Inc., Dublin, Ireland, and Castle Microwave Ltd., Newbury, U.K., for providing the test samples and measurement facilities. Special thanks go to J. Francey, Taconic Advanced Dielectric Division, for his continuous support and consulting and to N. Carroll, PCTEL Inc., for his help with the measurements. REFERENCES [1] H. Arai, “Outdoor and indoor cellular/personal handy phone system base station antenna in Japan,” in Handbook of Antennas in Wireless Communications, L. C. Godara, Ed. Boca Raton, FL: CRC, 2001, pp. 11–1/26. [2] “Smart antenna system architecture and hardware implementation,” in Handbook of Antennas in Wireless Communications. Boca Raton, FL: CRC, 2001, pp. 22–1/32. [3] J. Huang, “Microstrip antennas: Analysis, design and application,” in Modern Antenna Handbook, C. A. Balanis, Ed. Tempe, AZ: Wiley, 2008, pp. 157–200. [4] K. Solbach and M. Böck, “Intermodulation in active receive antennas,” in German Radar Symp., Bonn, Germany, 2002, CD ROM, 5 pp. [5] A. G. Schuchinsky, J. Francey, and V. F. Fusco, “Distributed sources of passive intermodulation on printed lines,” in Proc. IEEE AP-S Int. Symp., 2005, vol. 4B, pp. 447–450. [6] J. V. S. Pérez, F. G. Romero, D. Rönnow, A. Söderbärg, and T. Olsson, “A microstrip passive intermodulation test set-up: Comparison of leaded and lead-free solders and conductor finishing,” in Proc. 5th Int. Multipactor, Corona and Passive Intermodulation Workshop, Noordwijk, The Netherlands, 2005, pp. 215–222.

Aleksey P. Shitvov (M’09) received the Diploma Engineer (Engineer–Physicist) degree in semiconductor devices and microelectronics from the N. I. Lobachevsky State University of Nizhny Novgorod (NNSU), Nizhny Novgorod, Russia, in 1995, and the Ph.D. degree in electronic and electrical engineering from the Queen’s University of Belfast, Belfast, U.K., in 2009. From 2000 to 2004, he was a Research Assistant with the Department of Electronics, NNSU, where he was involved with the design and simulation of surface acoustic wave devices. He is currently a Royal Academy of Engineering/Engineering and Physical Sciences Research Council (EPSRC) Research Fellow with the Queen’s University of Belfast. His research is focused on phenomenology and experimental characterization of PIM in printed circuits and waveguide components. His research interests also include electromagnetic characterization of nanostructured materials and metamaterials.

Torbjörn Olsson (A’97–M’03) was born in Perstorp, Sweden, in 1955. He received the M.Sc. degree in engineering physics and Ph.D. degree in experimental atomic physics from the Chalmers University of Technology, Göteborg, Sweden in 1979 and 1987, respectively. Following post-doctoral positions with the Jesse W. Beams Laboratory, Charlottesville, VA, and the Royal Institute of Technology, Stockholm, Sweden, he joined Allgon System, during which time he was active within the mobile phone industry in 1993. He is currently a member of the Systems Engineering Group, Powerwave Technologies Sweden AB, Kista, Sweden.

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Benjamin El Banna was born in Sollentuna, Sweden, in 1981. He received the M.Sc. degree in electrical engineering from the Royal Institute of Technology, Stockholm, Sweden, in 2006. From 2005 to 2006, he performed his Master thesis on PIM from printed wiring boards at Powerwave Technologies Sweden AB. In 2006, he joined Laird Technologies, Göteborg, Sweden, where he is currently a Senior RF Engineer involved with product development of cellular handset antennas.

Dmitry E. Zelenchuk (S’02–M’05) received the B.Sc. and M.Sc. degrees in physics and Ph.D. degree in radiophysics from Rostov State University, Rostov-on-Don, Russia, in 1999, 2001, and 2004, respectively. From 2003 to 2005, he was a Lecturer with the Department of Applied Electrodynamics and Computer Modelling, Rostov State University. He is currently a Research Fellow with Queen’s University of Belfast, Belfast, U.K. He has authored or coauthored over 40 journal and conference papers. His research interests include numerical and analytical methods for the problems of electromagnetic field theory, numerical modeling of frequency-selective surfaces, linear and nonlinear phenomena in planar circuits and antennas, including PIM, and various physical phenomena of plasmonic and nanostructures. Dr. Zelenchuk was the recipient of the 2001 Medal of the Ministry of Education of the Russian Federation “For the Best Scientific Student Paper” for his paper “Conductor Loss in Superconducting Slot Line.”

Alexander G. Schuchinsky (M’97–SM’05) received the M.Sc. degree in radiophysics from Rostov State University, Rostov-on-Don, Russia, in 1973, and the Ph.D. degree in radiophysics from the Leningrad Electrotechnical Institute, Leningrad, Russia, in 1983. From 1973 to 1994, he was with the Microwave Electrodynamics Laboratory, Rostov State University, where he was a Leading Scientist. From 1994 to 2002, he was with Deltec-Telesystems New Zealand. Since 2002, he has been a Reader with the School of Electronics, Electrical Engineering and Computer Science, Queen’s University of Belfast, Belfast, U.K. He has authored or coauthored over 130 papers in refereed journal and conference proceedings. He is a member of the Editorial Board of Metamaterials. He holds three U.S. patents. His current research interests include physics-based modeling techniques, microwave and optical phenomena in linear and nonlinear complex media and metamaterials, characterization and measurements of electromagnetic materials, and microwave applications of functional materials. Dr. Schuchinsky is a member of the European Physical Society. He was chair of the Steering Committee and general co-chair of an annual series of the International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials).

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Unconditional Stability Boundaries of a Three-Port Network Rong-Fa Kuo and Tah-Hsiung Chu, Member, IEEE

Abstract—An analytical approach for acquiring the explicit expressions of the boundaries concerning the unconditional stability regions of a three-port network is presented. This approach begins with the expressions for the input reflection coefficients 11 and 22 at ports 1 and 2 of a three-port network having port 3 terminated with 03 . 11 = 1 and 22 = 1 then give two stability circles in the 03 -plane. One can graphically determine that the tangent point of these two stability circles is on the boundary of the unconditional stability region for the terminating port. The explicit expressions of the boundary for port 3 are then acquired. This procedure may be followed for the other two ports in order to fully characterize the unconditional stability boundaries of a three-port network. In addition, issues pertaining to uniqueness and continuity in the plotting of unconditional stability boundaries are addressed. Using the Agilent Advanced Design System software tool, the derived expressions of the unconditional stability boundary for the terminating port and related extreme phase values of reflection coefficients of the other two ports are implemented. These derived expressions can then enhance the computer-aided capability on the stability analysis of a three-port network and provide useful information for the microwave circuit designer. Index Terms—Reflection coefficient, stability circle, unconditional stability.

I. INTRODUCTION HE expressions for the unconditional stability of a twoport network are derived based on its reflection coeffiand [1]–[5]. Specifically, the input reflection cocients and , efficients at ports 1 and 2 being unity, -plane of the load port and yields two stability circles in the -plane of the source port. The unconditional stability boundaries of a two-port network can then be identified. By using the stability requirements of a two-port network, the approach in [6] deals with the unconditional stability of a three-port network as three individual two-port networks by terminating one port. The region of the unconditional stability in the termination plane for each port can then be determined from three inequalities so that a total of nine inequalities are used to determine the three unconditional stability regions of a three-port network. The approach in [7] also views a three-port network as three two-port networks, but uses the stability factor [8]–[10] in order to reduce the number of inequalities from nine to three.

T

At this point, the three unconditional stability regions can be plotted based on three inequalities and a root search algorithm. The approaches in [6] and [7] provide the analytical methods used to plot the unconditional stability regions of a three-port network based on inequality equations. This paper begins with the reduction of a three-port network to a two-port network by terminating port 3 with . The unconditional stability requirements are then applied for the input reflection coefficients and at ports 1 and 2 to be less than 1. The input reflection and then yields two coefficients being 1, unconditional stability circles in the -plane. In Section II-A, a graphical method is described to show that the tangent point of these two stability circles is the extreme point satisfying the requirements of two input reflection coefficients to be 1. Therefore, the boundary of the unconditional stability region may be plotted by tracing the tangent points and . through properly varying The explicit expression of the unconditional stability -plane is then derived in Section II-B. boundary in the Additionally, the expressions for the corresponding extreme values in the - and -planes are derived. This then leads to being able to directly plot the unconditional stability boundary instead of using inequality equations to plot the unconditional stability region and then identify the boundary as in [6] and [7]. In addition, the corresponding reflection coefficients for the terminations at ports 1 and 2 to give the unconditional stability boundary can be found as given in Section II-C. It then provides a computationally efficient approach for the microwave circuit designer on the stability analysis of a three-port network. As a result, two boundaries of unconditional stability regions exist. The uniqueness and continuity issues in regard to the unconditional stability boundary are discussed in Sections II-D and E. Since this approach provides the explicit expressions of the unconditional stability boundary of a three-port network, it is relatively simple to implement by microwave circuit designer using software tools, e.g., Agilent Advanced Design System (ADS) [11]. The three-port scattering matrix ( -matrix) of the numerical examples given in [6] and [7] are adopted in Section III to illustrate and verify the effectiveness of the developed analytical approach. Finally, a conclusion is given in Section IV. II. FORMULATION

Manuscript received August 29, 2008. First published January 22, 2010; current version published February 12, 2010. This work was supported by the National Science Council of Taiwan under Grant NSC 97-2221-E-002-057-MY2 and Grant NSC 95-2221-E-002-086-MY3. The authors are with the Graduate Institute of Communication Engineering, National Taiwan University, Taipei 106, Taiwan (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2038660

As shown in Fig. 1, a three-port network as given by its threeis connected with three loads , , and port -matrix , respectively. In order to analyze its stability, this three-port network is treated as a two-port network between ports 1 and and , 2. The input reflection coefficients are given by at port 3 and which are expressed in terms of the termination

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Fig. 1. Three-port network [S

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terminated with three loads 0 , 0 , and 0 .

the three-port network -matrix are given as [6]

. Specifically,

and

(1) (2) In (1) and (2), by

is the cofactor of the th element given , , and , and is the determinant of . The unconditional stability condition for the two-port network given by ports 1 and 2 with port 3 terminated with , as shown in Fig. 1, is known to have (1) and (2) satisfying and for all passive terminations at ports and ) [1]–[3]. The following 1 and 2 (i.e., analysis is focused on deriving the expressions on the boundary of the region in the -plane satisfying the unconditional staand inside the Smith chart. bility requirement for all Note this treatment of a three-port network being a two-port network given by ports 1 and 2 with port 3 terminated with should also be performed for two other cases in order to fully characterize the boundaries of the unconditional stability regions in the termination planes of , , and . One case to give a two-port network for is to terminate port 2 with ports 1 and 3 for the derivation of boundary expressions in the -plane, and the other case is to terminate port 1 with to give a two-port network for ports 2 and 3 for the derivation of boundary expressions in the -plane. A. Unconditional Stability Circles in By squaring and proper manipulation, one can get

-Plane for (1) and (2) and after (3) (4)

where (5) (6)

(7) (8)

Fig. 2. Illustration on the unconditional stability regions in the 0 -plane as: (a) A > 0 and A > 0, (b) A < 0 and A > 0, (c) A > 0 and A < 0, and (d) A < 0 and A < 0.

(9)

(10) Note that (3) and (4) are inequality expressions of two circles in the -plane and are functions of and , respectively. This indicates that a three-port network terminated with is satisfies (3) and (4) for unconditionally stable if and only if all passive terminations at ports 1 and 2. Therefore, for values of and in the - and -planes, one can identify two circles in the -plane to be the unconditional stability and with and as circles (11) (12) In the following, a discussion is described by using graphs in for the two-port Figs. 2 and 3 to find the adequate values of network given by ports 1 and 2 to be unconditionally stable. The approach to determine the explicit expressions on the boundary of the unconditional stability region in -plane ensues. or expressed in (5) or (8) is a positive value, the As exterior region of and is the region of unconditional stability satisfying (3) or (4) in the -plane. On the other hand, the or becomes unconditionally stable as interior region of or is negative. Fig. 2 basically illustrates four possible cases of and in the -plane caused by certain values of and with the shaded region representing the unconditional stability region. and As shown in Fig. 2(a), the exterior region of both denotes the unconditional stability region. However, there is

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and , as shown in Fig. 3(c) until the stability the points is an inscribed circle of , as shown in Fig. 3(d). circle and being Therefore, there are two extreme cases with tangential to one another, as shown in Fig. 3(b) and (d). This leads to the derivation of the boundary expressions of the unand conditional stability region in the -plane for by finding the expressions of the tangent point of stability circles and . Essentially, one can then trace values from these tangent points given by all resulting and by properly changing the and values to yield the boundary of the unconditional stability region in the -plane for a three-port network terminated with at port 3. B. Boundary Expressions

Fig. 3. Two unconditional stability circles and with: (a) circle and circle moving apart until the extreme cases with two circles such as (c) (b) circumscribed and (d) inscribed, respectively.

no intersection of and . This means that one cannot find solution of (11) and (12) to yield an unconditional stable the and . Therefore, the two-port network, as unconditional stability region in the -plane does not exist in this case. However, Fig. 2(b)–(d) shows that there are two intersection and . These two points and give two points between values of satisfying (11) and (12) as the coefficients and , and , and and , respectively. The unconditional stability region of is the shaded region in these three cases. For the case with , , and the shaded region in Fig. 2(b) being the stability region, the intersection points and are on the boundary of the unconditional stability region in the -plane for certain and values. Since we are trying to find the boundary of the unconditional stability region of for and , a stability circle must exist inside , as shown in Fig. 3(a), by properly changing the value to give a smaller stability region . The two intersection points and are then replaced by points and until the two stability circles circumscribe one another, as shown in Fig. 3(b). The resulting tangent point is then a point on the boundary of the unconditional stability region in the -plane for all passive loads at ports 1 and 2 since further movement of the circle value satisfying (11) gives no intersection point or causes no and (12). and , the shaded region For the case with in Fig. 2(c) is similar to the stability region in Fig. 2(b). Therefore, the boundary of the unconditional stability region in the -plane for all passive loads at ports 1 and 2 is also similar to the result of Fig. 3(b). and , as shown in Fig. 2(d) For the case with also exists inside with the stability region , a stability circle by finding another value to give a smaller stability region . The two intersection points and are then replaced by

Based on the graphical results given above, expressions on the boundary of the unconditional stability region can be deand . Note the rived in the -plane for boundaries of the - and -planes for passive loads are the outer circles of the Smith chart with unit magnitude given by and . Therefore, the two extreme cases and , found to be tangential shown in Fig. 3(b) and (d) for to one another, are caused by the proper values of and on the outer circle of Smith chart for and , respectively. and into (11) and (12), By substituting and become the expressions of stability circles (13) (14) The detailed derivation of (13) and (14) and the related parameters are given in Appendix A. Now let and substitute it into (13) and (14) to give (15) (16) where , , , , Appendix A. Subtract (16) from (15) to give

, and

are defined in

(17) Equation (17) is then the expression of the tangent line of and circles given by (13) and (14). By substituting (17) into (16), a quadratic equation can be acquired as (18) where (19) (20) (21)

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Since the intersection point of and is a single point , as shown in Fig. 3(b) and (d), the coefficients of (18) should satisfy the discrimination equation (22) to yield the solution of (18), or the

value of point

the solutions of (28) are

or (30)

, as (23) or

The value of the tangent point can then be acquired by substituting (23) into (17). Therefore, the boundary of the unconditional stability region for and can be traced from (17) and of (23) by knowing and in the - and -planes. In Section and , II-C, the relation of and will be derived to yield which will be two tangent circles based on (22). With the use of this relation, one can directly calculate the corresponding (or ) value by sweeping a single parameter (or ) around the outer circle of the Smith chart. C. Relation Between

and

By substituting (19)–(21) into (22), the following equation of or the phase term of may exist as

(24) and are given in Appendix B and they are where functions of . Next, the triangle identities are applied in (24) to give (25) where

,

, ,

, and . The coefficients of (25) can be shown to satisfy (26) (27) In essence, (25) is a square expression of (28) The proofs of (26) and (27) are tedious and not given; however, they can be an indicator of the correct solution of in (28). By giving the discrimination equation of (28), (29)

(31) Equation (24) is a second-order equation of and and its coefficients are functions of . Therefore, by giving a value for , there are two values of for given by (30) points traced from (17) and and (31). This then leads to two (23). However, the square operation for (24) being (25) gives four possible solutions of (25). Therefore, all four solutions given by (30) and (31) should be substituted into (24) to identify the two correct values. In order to trace the boundary of the unconditional stability region in the -plane, one can first sweep the value over the range from 0 to 360 in the -plane and calculate the two corresponding values of from (30) and (31). Note this computation saving approach by sweeping a single parameter then calculating the value instead of optimally or iteratively finding and values has been applied in the matching network synthesis [12]. By giving and values, two stability boundaries in the -plane can be plotted with the use of (17) and (23). Note the . This criterion termination at port 3 is passive with should then be imposed upon the two boundary regions of to acquire the correct boundary for the unconditional stability region in the -plane. The reason one traces two stability boundaries from (17) and and (23) is because they are based on given by (11) and (12). One boundary then corresponds to the boundary of the unconditional stability region for and , and the other corresponds to the boundary of the or , which is discussed unstable region for in Section III. Alternatively, a similar treatment can be conducted to derive the expression of in terms of as in that of (24). At this point, the expressions are acquired as those of (30) and (31) for values and the boundary of the unconditional stability region is plotted accordingly. D. Uniqueness Since the boundary plotting approach described in value in Section II-C is a one-to-two mapping from one the -plane to two values in the -plane, and then to two values in the -plane, its uniqueness needs to be verified. In this section, it will be proven that the inverse mapping from the boundary of the unconditional stability region in the -plane to the -plane and the consequent -plane is a one-to-one

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mapping. Only one of the boundaries derived in Section II-C is the boundary of the unconditional stability region. and into (3) and (4) and Substituting moving the terms of and to the right side results in (32) (33) where (34) (35) (36) (37) (38) (39) (40) (41) Since (32) and (33) are valid for all and values in the and and -planes, respectively, they imply . In fact, the boundary of the unconditional stability region and with and occurs as . The relation of , , and may be found and as based on (42) (43) Equations (42) and (43) indicate that the corresponding values of and in the - and -planes are uniquely determined from the unconditional stability boundary of in the -plane. Therefore, the criteria of and may be imposed upon the two acquired boundaries described in Section II-C to identify the correct one for the unconditional stability region. E. Continuity In this section, the continuity issue on the plotting of the unconditional stability boundary will be discussed. Since (24) is and , its solutions are cona polynomial equation of tinuous from 0 to 360 . This then leads to the unconditional stability boundary being continuous based on the linear operation of (17) and (23). Similarly, the reverse mapping is also continuous from the -plane to the - and -planes by (42) and (43). Therefore, all solutions of (24), by sweeping the value over the range from 0 to 360 in the -plane, will give a continuous closed curve in the -plane to be the boundary of the unconditional stability region for a three-port network terat the third port. minated with In the following, the continuity issues of the and plots - and -planes. Although there are are discussed in the two solutions of (24) given by (30) and (31), (42) and (43) are one-to-one mappings from the -plane to the - and

Fig. 4. Results of: (a) two stability boundaries in the 0 -plane with the shaded area corresponding to the unconditional stability region in a compressed Smith chart. (b) Enlarged plot of the unconditional stability region.

-planes. The passive termination of with may then limit the available and values over the range from 0 to 360 . In addition, those and values with in (29) do not exist, as evidenced by the example given in Fig. 2(a). Therefore, the plots of and on the outer circle of the Smith chart may become locally continuous. III. EXAMPLES To illustrate the results given by the described analytical approach, one may acquire the three-port -matrix of a testing three-port device through the multiport network analyzer measurement [13] or a reduced port network analyzer measurement [14]. However, three-port -matrices in [6] and [7] are adopted here for two reasons. One is to verify the explicit expressions of the stability boundaries given in Section II. In addition, they are used to illustrate the further useful information acquired from the developed stability analysis. The first example is to use the three-port -matrix in [6] given as

(44) In this following study, all expressions developed in Section II are implemented in Agilent ADS [11] to enhance its computeraided capability of the stability analysis of a three-port network. The procedure for plotting the boundaries of the unconditional stability regions starts with the case of the termination at port 3, as described in Section II. Basically, the value is calculated using (30) and (31) by sweeping the value from 0 to 360 with a step of 0.01 . With the use of (17) and (23), two stability boundaries are then plotted in the -plane, as shown in Fig. 4. Plots of the corresponding values in the -plane and values in the -plane are shown in Fig. 5(a) and (b), respectively. Fig. 4(a) illustrates that there are two closed curves of the stability boundaries in the -plane based on (17) and (23). The one inside the Smith chart with unit magnitude satisfying

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Fig. 5. Results of the corresponding: (a) values in the 0 -plane and (b)  values in the 0 -plane for the unconditional stability boundary given in Fig. 4(b).

and is the boundary of the unconditional stability region. The other one outside the Smith chart with unit magnitude gives and meaning and . Which side of the boundary is the unconditional stability reinto (3) gion must then be identified? By substituting and , and and (4) with can be derived using (A.8) and (A.5) or and . Therefore, they can be used to verify which side of the plotted boundary will be the unconditional stability region in the -plane. For the boundary given in Fig. 4(b), gives and since the origin point , the unconditional stability region then excludes the origin of the Smith chart, as shown in Fig. 4(b), identified via the shaded region. Results of the corresponding values in the -plane and values in the -plane are given in Fig. 5(a) and (b). Note that they are nonclosed curves, as explained in Section II-E, due to in (30) and (31) for certain and values. Therefore, an unconditional stable three-port network can be designed with and , except those on the use of the passive terminations the thick heavy lines given in Fig. 5(a) and (b) and the passive within the shaded region in Fig. 4(b). terminations With the use of the same expressions implemented in Agilent ADS, two other unconditional stability boundaries may be and by properly rearreadily plotted for the terminations ranging the -parameters given, respectively, in (44) as

Fig. 6. Results of: (a) unconditional stability boundary in the 0 -plane and the corresponding (b) values in the 0 -plane and (c)  values in the 0 -plane.

(45) and (46)

Fig. 7. Results of: (a) unconditional stability boundary in the 0 -plane and the corresponding (b) values in the 0 -plane and (c)  values in the 0 -plane.

Results of the unconditional stability boundary and the corat port 2 are responding and values for the termination shown in Fig. 6. The shaded region is the region of unconditional and and it excludes the origin stability verified by and for because of .

Similarly, results of the unconditional stability region and the corresponding and values for the termination at port 1 are shown in Fig. 7. The shaded region is the region of unconditional and , and it includes the origin stability verified by and for because of .

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. Secondly, the results shown in Fig. 8(b) indicate that this three-port -matrix is less stable than that of the first example. However, it shows that an oscillator can be designed by terminating port 1 with a reactive component as a two-port series feedback network. This then provides the microwave circuit designer a computationally efficient approach for active circuit design. IV. CONCLUSION

Fig. 8. Results of: (a) unconditional stability boundary in the 0 -plane and the corresponding (b) values in the 0 -plane and (c)  values in the 0 -plane.

As shown in Figs. 4(b), 6(a), and 7(a), all unconditional staare shown in agreement bility boundaries for , , and with those derived by plotting the unconditional stability regions using nine inequities in [6] or using three inequities with the root-searching algorithm in [7]. With the use of the developed analytical approach, the unconditional stability boundaries can be directly plotted based on closed-form expressions, and they also provide useful information on the corresponding extreme values of and . Moreover, plots of the boundaries of unstable regions can be acquired. One example is the closed curve outside the unit Smith chart, as shown in Fig. 4(a) for the termination . It can provide useful to design an active three-port information on the termination network with passive terminations at ports 1 and 2. The second example is presented by giving the three-port -parameters [7] as

(47) The unconditional stability boundary in the -plane is shown in Fig. 8(a) with the corresponding values in the -plane and values in the -plane, as depicted in Fig. 8(b) and (c). In this example, the boundary shown in Fig. 8(a) is a closed curve within the Smith chart with the shaded region representing the unconditional stability region. In addition, the values are shown with a closed curve, whereas the values give a nonclosed curve. The above example is noteworthy for the following reasons. Firstly, the curve in the -plane being closed has no relation to the curve in the -plane being closed. The closed boundary is determined by the criterion of (29), whereas the closed of region of stable terminations of is verified by and

In this paper, an analytical method to derive the explicit expressions on the unconditional stability boundaries of a threeport network has been presented. Differing from the approaches that use inequality equations to express the unconditional stability regions, this method can be directly implemented in Agilent ADS or commercially available software tools, e.g., Microsoft Excel, for the stability analysis of a three-port network in an effective manner. The unconditional stability boundary for each selected port, e.g., expressed by (17) and (23) in the -plane, is shown to be unique and continuous due to and . In addition, the locally continuous boundaries for the two corresponding terminations, expressed, e.g., by (30) and (31), or (42) and (43) for values in the -plane and values in the -plane to yield the resulting unconditional stability region can be acquired. Therefore, the developed analytical approach can plot the unconditional stability boundaries in a computational-saving manner and also provide useful information for engineers on passive or active three-port network design, as illustrated in the examples. APPENDIX A By substituting they become

and

into (11) and (12), (A.1)

and (A.2) where (A.3) (A.4) (A.5) (A.6) (A.7) (A.8) In (A.3)–(A.8), the following expressions of the corresponding parameters are given: (A.9) (A.10) (A.11) (A.12) (A.13)

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(A.14) (A.15) (A.16) (A.17) (A.18) (A.19) (A.20) (A.21) (A.22)

(B.4)

Therefore, (A.1) and (A.2) can be properly rewritten as (A.23) and (A.24) ,

where ,

, , and

,

. (B.5) APPENDIX B

(B.6) REFERENCES (B.1)

(B.2)

(B.3)

[1] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005, pp. 542–548. [2] G. D. Vendelin, A. M. Pavio, and U. L. Rohde, Microwave Circuit Design Using Linear and Nonlinear Techniques. New York: Wiley, 1990, pp. 45–50. [3] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York: McGraw-Hill, 1992, pp. 735–740. [4] T. Fjallbrant, “Activity and stability of linear networks,” IEEE Trans. Circuit Theory, vol. CT-12, no. 1, pp. 12–17, Mar. 1965. [5] D. Woods, “Reappraisal of the unconditional stability criteria for active 2-port networks in terms of s parameters,” IEEE Trans. Circuits Syst., vol. CAS-23, no. 2, pp. 73–81, Feb. 1976. [6] J. F. Boehm and W. G. Albright, “Unconditional stability of a threeport network characterized with S -parameters,” IEEE Trans. Microw. Theory Tech, vol. MTT-35, no. 6, pp. 582–585, Jun. 1987. [7] E. L. Tan, “Simplified graphical analysis of linear three-port stability,” Proc. Inst. Elect. Eng.—Microw. Antenna Propag., vol. 152, no. 4, pp. 209–213, Aug. 2005. [8] M. L. Edwards and J. H. Sinsky, “A new criterion for linear 2-port stability using a single geometrically derived parameter,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 12, pp. 2303–2311, Dec. 1992. [9] G. Lombardi and B. Neri, “Criteria for the evaluation of unconditional stability of microwave linear two-ports a critical review and new proof,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 746–751, Jun. 1999. [10] E. L. Tan, “Simple derivation and proof of geometrical stability criteria for linear two-ports,” Microw. Opt. Technol. Letters, vol. 40, no. 1, pp. 81–83, Jan. 2004. [11] Advanced Design System (ADS). Agilent Technol., Palo Alto, CA, 2006. [12] B. Kormanyos, “Matching network synthesis for low noise and power amplifiers,” Microw. RF Mag., pp. 105–109, Feb. 1998. [13] T. G. Ruttan, B. Grossman, A. Ferrero, and J. Martens, “Multiport VNA measurements,” Microw. Mag., vol. 9, no. 3, pp. 56–69, Jun. 2008. [14] H. C. Lu and T. H. Chu, “Multiport scattering matrix measurement using a reduced-port network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 5, pp. 1525–1533, May 2003.

KUO AND CHU: UNCONDITIONAL STABILITY BOUNDARIES OF THREE-PORT NETWORK

Rong-Fa Kuo was born in Tainan, Taiwan, in 1969. He received the B.S. degree in electrical engineering from Chung Yuan Christian University, Chung Li, Taiwan, in 1992, the M.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1994, and is currently working toward the Ph.D. degree at National Taiwan University. From 1996 to 2007, he was a Research and Development Engineer for RF integrated circuit (RFIC) and RF circuit design in Hsinchu, Taiwan. His research interests include RF and microwave circuit and subsystem design.

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Tah-Hsiung Chu (M’87) received the B.S. degree from National Taiwan University, Taipei, Taiwan, in 1976, and the M.S. and Ph.D. degrees from the University of Pennsylvania, Philadelphia, in 1980 and 1983, respectively, all in electrical engineering. From 1983 to 1986, he was a Member of Technical Staff with the Microwave Technology Center, RCA David Sarnoff Research Center, Princeton, NJ. Since 1986, he has been a faculty member of the Department of Electrical Engineering, National Taiwan University, where he is currently a Professor of electrical engineering. His research interests include microwave-imaging systems and techniques, microwave circuits and subsystems, microwave measurements, and calibration techniques.

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Analysis and Synthesis of Double-Sided Parallel-Strip Transitions Pedro Luis Carro, Student Member, IEEE, and Jesus de Mingo, Member, IEEE

Abstract—Antenna feeders, mixers, and filters made in doublesided parallel-strip technology usually must be adapted to unbalanced lines like the microstrip structure, needing transitions from asymmetric to symmetric waveguides (baluns). In this paper, we propose a new method for the evaluation of a generic tapered balun based on a conformal-mapping technique and an integral equation. This method, along with the use of an optimization technique such as genetic algorithms, allows for quick evaluation of the return losses of any tapered balun and the synthesizing of specific shapes to achieve desired responses in terms of return losses or impedance values. Index Terms—Baluns, conformal mapping, parallel strips (PSs), passive circuits, ultra-wideband (UWB) technology.

I. INTRODUCTION

P

RINTED parallel-strip (PS) lines, as a balanced type of transmission lines, offer an interesting alternative to other printed transmission lines, such as the coplanar stripline, or to other unbalanced transmission structures such as the common microstrip (MS) line. Although PS topology received important attention more than 40 years ago, other transmission lines like the MS geometry were considered more interesting for millimetric applications. This was because of MS geometry’s outstanding features, including reasonable bandwidth, easy integration with active circuits, compact dimensions, and cheap manufacturing. There has been a growing interest in PS lines in recent years since they have many of the beneficial properties of MS lines. Printed PS lines are naturally balanced, without a ground plane, making them suitable for designing both passive and active microwave circuits. Additionally, they are used in antenna designs when almost omnidirectional radiation patterns are required, avoiding the possible complexities of MS antenna designs in order to achieve those patterns. We have to pay attention to the design process of millimeter integrated circuits with balanced and unbalanced devices since this situation usually implies transitions between both types of circuits called baluns. This may include impedance-matching capabilities, which are required, for example, when a PS antenna is connected to an MS line. Manuscript received November 04, 2008; revised September 22, 2009 and November 01, 2009. First published January 22, 2010; current version published February 12, 2010. This work was supported by the Spanish Government under Project TEC2008-06684-C03-02, MCI, and FEDER, the Gobierno de Aragón for WALQA Technology Park Project, and European IST Project EuWB. The authors are with the Department of Electronics and Communication Engineering, Universidad de Zaragoza, Zaragoza 50018, Spain (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038454

As far as double-sided PS and MS lines are concerned, the first balun geometry was proposed by Climer [1]. Some authors have used this balun for years in order to measure some antennas, couplers, feeding networks, and other balanced circuits. As recent examples of such circuits, printed filters and couplers are designed in [2], a bandpass filter is developed in [3] by inserting a ground plane between the strips, and [4] shows a diplexer based on a similar configuration. In spite of being extensively used in practical devices, there is not an analytical study of this balun in order to characterize its electromagnetic response (namely, the -matrix). In fact, Climer [1] analyzed the problem by estimating the even and odd voltages on the strips, computing the scattering matrix corresponding to two profiles (linear and exponential profiles). In addition, that study only focuses on perfect matching, which occurs when both the MS and PS lines have a characteristic impedance of 50 . Circular or more complex profiles were analyzed by means of an electromagnetic simulator (such as IE3D ) [5]. Alor High Frequency Structure Simulator (HFSS), though this procedure provides accurate results, it does not offer a clear physical interpretation (in terms of impedance variations) and it can be computationally expensive if a specific response is required. This paper introduces a novel fast semianalytical method used for computing the return losses of any PS to MS tapered balun. This approach is based on three different mathematical tools. First, we review the analysis method applied to any tapered transmission line geometry. This approach requires the knowledge of the characteristic impedance, which is, afterwards, worked out under the hypothesis of a quasi-TEM regime operation by applying a conformal mapping to an asymmetric double-sided printed transmission line. Finally, the new closedform formula is combined with the taper analysis method, introducing some examples of the analysis and synthesis of baluns. In terms of the analysis, return losses are computed by means of an integral approximation. The synthesis is carried out by an optimization procedure [using a genetic algorithm (GA)] that takes the analysis method into account, which provides an effective cost function for any desired electromagnetic response in terms of return losses. II. ANALYSIS OF MS TO PS TAPERED BALUNS The MS to double-sided PS tapered transition geometry consists of a (finite) ground plane, which is gradually converted into a strip, as in Fig. 1. The double-sided parallel line is achieved when the final strip is exactly identical in width to the nonground-plane strip. According to the results presented in [1], the electromagnetic performances of this transition depend on the taper applied in the gradual ground plane conversion.

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W

Fig. 3. Geometry cross section and parameters involved in the Schwarz– Christoffel transform ( -plane).

Fig. 1. Geometry of the printed balun transition with a general profile in the ground plane.

Fig. 2. Tapered transmission line parameters.

previously studied and evaluated [14], [15]. Hence, this analysis equation is potentially useful for computing the geometric taper to reach either optimum or specific return losses in a frequency band. The normalized impedance corresponding to the structure seems to be the main drawback in applying the previous formulation. Although the characteristic impedance of several printed transmission lines (including MS and coplanar strip lines and double-sided parallel transmission lines) has been reported in [16]–[19], to the authors’ knowledge, the case of asymmetrical double-sided parallel transmission lines has not yet been published in the literature. In Section III, we approximate such impedance in order to complete the analysis of the transition, applying a conformal-mapping technique. III. ASYMMETRICAL DOUBLE-SIDED TRANSMISSION LINE CHARACTERISTIC IMPEDANCE BY CONFORMAL MAPPING

From the physical point of view, this taper sets the characteristic impedance at any position along the balun. Therefore, the reflected power depends on this variation in . The analysis of nonuniform transmission lines has been studied by many authors, either in the frequency domain [6]–[10] or time domain [11]–[13]. In the case of tapered transmission lines (Fig. 2), the reflection coefficient at any point, , is governed by the nonlinear differential equation [7] (1) where is the propagation constant and is the normalized impedance, which is a function of the distance along the taper. If the condition is assumed and ohmic losses and dispersion are considered negligible in the transmission line , the reflection coefficient at the input is expressible in the form (2) where is the total transition length, is the effective propagation constant, is the frequency, is the speed of light, and is the effective dielectric constant (assumed to remain unchanged as a first approximation). If the PS to MS geometry is analyzed as a particular case of a nonuniform transmission line in quasi-TEM operation, (1) and (2) can be used for computing , or equivalently, , where is the angular frequency. Additionally, some methods relying on adaptive techniques to accomplish desired responses, as well as optimum solutions under certain circumstances, have been

Consider the asymmetrical double-sided strip line of Fig. 3. The dielectric sheet is assumed to be infinitely wide, and the strips are assume to have negligible thickness. The structure has been closed by an infinite ground plane in order to carefully apply the conformal-mapping technique, following a similar process to the one employed in an MS line analysis [20]. in width when The geometry resembles an MS line of , whereas if , the PS line is obtained. The objective is to yield simple closed-form formulas for obtaining the characteristic impedance given a transmission line that has a cross section like that in Fig. 3. Conformal-mapping techniques provide us with a powerful mathematical method to accomplish this task, supposing a quasi-TEM hypothesis. This implies this procedure is only valid up to a few gigahertz (for typical substrates), but this range still includes most wireless applications. Actually, we compute the capacitance per unit length when is determined, we the conformal method is applied. Once can calculate the characteristic impedance and the effective dielectric constant. This technique has been successfully applied to MS and double-sided PS lines, as well as to other complex transmission line geometries of more recent interest. Most cases have focused on symmetrical structures, although some studies deal with asymmetrical structures and finite ground planes [21], [22]. Conformal mapping is applied in [21] to a strip line with two infinite ground planes, introducing an asymmetry respect to the vertical axis, whereas the structures under study in [22] consist of finite ground planes placed in one single face above

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TABLE I COMPLEX POINTS MAPPED BY INVERSE TRANSFORM

Fig. 4. Schwarz–Christoffel mappings represented geometrically. By the direct transform, structures (a) and (b) are equivalent in terms of potential.

a complex plane into a plane , and the second applies direct mapping to transform the complex plane to the plane . In this last plane, the geometry is a simple symmetrical parallel transmission line, but it has a finite substrate. The transformed geometry has an identical capacitance according to the properties of conformal mapping. Unlike the initial structure, the equivalent capacitance is evaluated using the plane capacitor approximation. A. Application of the Inverse Schwarz–Christoffel Transform

the substrate (in rectangular or polar coordinates) with symmetry respect to the same axis. The nonuniform PS line comprises only one single infinite ground plane, and different strip widths are the responsibility of the horizontal asymmetry. As a result, the complex planes used in the conformal mapping contain both finite and asymmetry features. It requires different mapping points and consequently leads to other integral transforms that need to be solved. The total capacitance of the asymmetrical line is obtained ignoring the fringing fields in the corners approximately by

The mathematical analysis begins with the definition of the points involved in the Schwarz–Christoffel transform (Table I). Mapping the -plane into the -plane is evaluated according to such a transformation. This relation is shown in (8) as follows:

(3)

(8)

is the double-sided strip capacitance, defined by a where line of height , and strip widths , and is the MS capacitance, defined by a line of height and a . strip width The analysis of the capacitance per unit length is straightforward in the case of MS geometry due to the widespread use of this transmission line, and consequently, the conformal-mapping study has been already reported. By defining the parameters [20]

defined by the finite complex points 1 and 1, and where correspond to , respectively. The analytical evaluation leads to (9) Taking into account the mapping points (Table I),constants and constrain the final inverse transform as (10)

(4)

(5)

where . and are computed applying this transThe values of formation to the strip corners. These values must fulfill the following equations:

(6)

(11)

and

the MS capacitance is expressed as

where

(12)

is the complete elliptical integral (7)

The most difficult part of the analysis is the estimation of the capacitance of the double-sided structure , which is computed by the Schwarz–Christoffel transform [23], defined in the context of complex analysis. This evaluation requires two mappings (see Fig. 4). The first is an inverse transformation from

which finally lead to (13) These points will be used in the second part of the analysis in order to achieve a finite substrate structure by means of a second mapping.

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The following equations relate the parameters of the geometry of interest with those of the final structure:

TABLE II COMPLEX POINTS MAPPED BY DIRECT TRANSFORM

(19) (20) (21)

B. Application of the Direct Schwarz–Christoffel Transform The direct transform must be applied at this point of the analysis keeping in mind the desired final cross section, which is a complete finite structure. Consequently, the previous computed points (in the -plane) are mapped into new -plane points, as in Table II. The Schwarz–Christoffel transform definition leads to the complex integral

The parameter is the main value required to quantify the capacitance. By using some algebra manipulations on (19)–(21), it holds that (22) In order to simplify (22), we introduce (23) which leads to

(14)

(24) Using this relation, the equivalent height is

where it holds that integration result (15)–(17),

. Using a fundamental (25) Finally, the capacitance is expressed as (26) (15)

C. Closed-Form Impedance Formula The impedance and effective dielectric constant of the whole structure depend on the total capacitance. We find this using (3), (4), and (26)

where

(27) (16)

where and are described in (4) and (5). Finally, the effective permittivity constant is obtained though the quotient (28)

(17)

and the final expression for the asymmetric double-sided line characteristic impedance is (29)

this integral is evaluated to obtain an explicit expression. The constants and are computed by means of the mapping conditions. Additionally, we define the parameter as (18)

This closed-form formula has been compared to the numerical result that comes from the analysis of a simple geometry, computed by means of a full-wave simulation. In order to perform this comparison, we analyzed a single cell (see Fig. 5) of l-mm length. The asymmetric PS line has been simulated

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Fig. 5. Simple transmission line geometry for impedance identification.

using Zeland IE3D, based on the method of moments (MoM). The impedance was estimated for several strip-width values and compared to the analytical results, setting the parameters of the mm, ). In addition, the value FR4 material ( of involved in the MS capacitance was set to with as the substrate height. The numerical impedance value is obtained by means of the return losses (30) where (31) Thus, can be computed from the scattering value , and consequently, the impedance value. As Fig. 6(a) and (b) shows, the estimation in the impedance is very accurate. The maximum error between the closed form and the numerical simulation is about 5 , which is a relative error of about 5%. IV. APPLICATION TO THE ANALYSIS AND SYNTHESIS OF TRANSITIONS As presented in Section II, the transition may be analyzed using an integral approach following (2). However, the practical use of that equation requires the knowledge of the impedance at any point of the transition, which was solved in Section III by means of a conformal-mapping method. Next, both equations must be combined in order to analyze the geometry according to the following steps. , which define Step 1) Given the geometry, and the material parameters, compute using (29). Step 2) For every frequency , compute , using as the mean value of (28) and evaluate using (2). is performed to simplify the approach, The averaging of which leads to slight deviations from the real response. Nevertheless, solving the nonlinear differential equation instead of the . In adintegral equation itself can include the effects of dition, different geometry functions can bring similar results in return losses because the same impedance values (Fig. 3) may be obtained using different combinations of and . On the other hand, the synthesis problem, starting from a required return loss, deals with estimating the values of the geometry functions . This problem

Fig. 6. Comparison of closed-form formula versus full-wave simulations (IE3D) Only one semispace region is plotted, as symmetry with respect to the diagonal holds. (a) Values obtained by means of the proposed method (analytical). (b) Difference between the analytical formula prediction and the full-wave simulation results. (a) Numerical value. (b) Numerical error.

is usually more interesting than the analysis process, as it has an inherent design application. We show here two examples of synthesis where the analysis algorithm is needed: the design of a balun with optimum return losses in a specific frequency band and the synthesis of a Klopfenstein balun [7]. Besides, as in many synthesis algorithms, the use of optimization techniques will be necessary. In this paper, a GA approach is used, although any optimization technique is directly applicable. In addition, as differential geometry functions provide better results in terms of return losses, a spline interpolation method is used for defining the geometry, decreasing the number of variare specified by ables. Thus, sets of two vectors (32) and (33)

CARRO AND DE MINGO: ANALYSIS AND SYNTHESIS OF DOUBLE-SIDED PS TRANSITIONS

These vectors allow for the evaluation of complete geometry functions. The cubic spline method assigns a cubic polynomial to each subinterval

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50–100 . The cost function chosen as

was consequently

(39) (34) satisfying some conditions

(35) (36) (37) Due to these constrains, the geometry function is continuous and differentiable. The constants involved in the polynomials are computed by the GA in order to achieve an optimum according to some cost function. In this study, the set of vectors delineating the geometry functions are established following these rules. 1) The number of points is set to nine in the ground plane layer and two in the top because, in this layer, the geometry function variation is not very wide. , the geometry functions take electrical 2) For values, constrained by the electrical boundary conditions. , where These are denotes the strip widths that lead to and , respectively. values are obtained by sampling uni3) The rest of the . formly in the interval

The convergence toward the optimum [see Fig. 7(a)] is fast, and the GA reaches the optimum in about 80 generations. The optimized geometry functions [see Fig. 7(a)] evolve towards the PS line having several local maxima and minima in the ground plane. In order to evaluate the integral method accuracy, the optimized balun was simulated using the electromagnetic code HFSS based on the finite-element method. The comparison using both approaches [see Fig. 7(b)] shows a reasonably similarity in the target band with return losses below approximately 30 dB in such frequencies. B. Klopfenstein Transition The optimum impedance taper of a fixed length matching section has been analyzed by several authors. Using the integral formulation, Klopfenstein [7] showed the optimum taper in the sense that the minimum reflection coefficient for a passband fulfills

(40) where the function

is defined as

A. Minimum In-Band Return Loss Transition

(41)

The design process of a transition ( mm in length) with minimum return losses in the range between two specified frequencies can be formulated mathematically as a geometry optimization find

such that: (38)

where is the reflection coefficient in frequencies from to . If we want to solve this optimization problem with great accuracy, this requires using a full-wave simulator, which supposes time and resources. This time generally increases when dealing with optimization processes, as they usually require the evaluation of several iterations, and may be reduced using the proposed integral analysis method. In order to solve the problem by a GA, some random geometry functions are built using a natural spline interpolation scheme on the genes of the GA. Afterwards, the analysis algorithm is applied so that the score of each chromosome (transition) is obtained. The optimization process evolves for some in this study), until a requirement is fulgenerations ( filled or it is stopped. The method has been applied successfully to a transition of 25 mm in length in the range from 3.1 to 4.6 GHz. In addition, it was required in the balun matches

being the modified Bessel function, being the value , and defining the passband fulfilling the condition being the bound of the reflection coefficient in the passband. Following the work of Klopfenstein, it is possible to formulate an optimization problem based on impedance synthesis rather than the reflection coefficient as in the previous example. In this context, the utility of the proposed impedance formula is very clear. Mathematically, the optimization problem is as follows: find

such that: (42)

where would be the actual impedance value presented is the theoretby the taper section at the point and ical impedance value the taper must have, computed by means of (39). The optimization problem presented above is intended to force the Klopfenstein impedance taper. The GA uses this equation based on the quadratic error as a cost function. When the GA reaches the convergence point [see Fig. 7(c)], the geometry functions are as close as possible to the Klopfenstein values.

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Fig. 7. Synthesis profile results and electromagnetic performance comparison between full-wave simulations and the proposed technique. (a) Minimum in-band optimization convergence and optimum geometric profile. (b) Minimum in-band optimum frequency response comparison between the integral analysis and a full-wave analysis. (c) Klopfenstein balun synthesis optimization convergence and Klopfenstein geometric profile. (d) Klopfenstein scattering parameters obtained by the proposed method and a full-wave simulator. TABLE III OPTIMUM VALUES GEOMETRY FUNCTIONS

Fig. 8. Comparison between the required impedance and the synthesized impedance by means of a GA.

The obtained impedances (Fig. 8) are near the required values calculated from the Klopfenstein equations. The largest differences lay at the beginning and at the end of the transition,

namely due to the discontinuities required by the Klopfenstein method in contrast to the continuity imposed by the cubic-spline geometry functions. In addition, the full-wave numerical results agree reasonably well compared to our proposed method, as presented in Fig. 7(d). In both synthesis examples, the whole optimization process took about 3 min, whereas a single full-wave transition took about 40 min. Regarding the optimization results, Table III

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Fig. 9. Synthesized test beds and electromagnetic performance comparison between full-wave simulations and the experimental results. (a) Back-to-back Klopfenstein balun. (b) Minimum in-band back-to back test bed. (c) Experimental and simulated Klopfenstein balun scattering parameters. (d) Experimental and simulated wideband balun scattering parameters.

summarizes the obtained values after 200 generations, pointing out the difference between the transition geometry functions. V. EXPERIMENTAL VALIDATION In order to validate the analysis and synthesis method, two test samples corresponding to the presented designs have been fabricated on an FR4 substrate with dielectric constant 4.6. Measurements have been carried out in a back-to-back configuration because of the balanced circuit nature. Since it is not straightforward to characterize by measurements a single balun, we have also performed an electromagnetic simulation of the samples to compare with experimental data, which are obtained by means of the vector network analyzer ANRITSU 37247D. Fig. 9 presents the manufactured boards according to Table III and their simulated and measured scattering parameters. The Klopfenstein design [see Fig. 9(a)] constrains the bandpass ripple to a constant value. The back-to-back measurement [see Fig. 9(c)] shows that the maximum bandpass ripple is about 14 dB, pointing out a high probability of fulfilling the Klopfenstein condition. In addition, it provides a remarkable bandwidth considering the common criteria of dB

to define the operative band, which is verified from 1.7 GHz up to 9.4 GHz. This transition can be used in practice for feeding antenna structures in ultra-wideband (UWB) systems. The wideband transition [see Fig. 9(b)] measurements, shown in Fig. 9(d), agree with the proposed target bandwidth. The goal was to design a transition from 3.1 to 4.6 GHz, and the experimental results are excellent at the required frequency band. The return losses are below 25 dB and achieve extremely low values at 4 GHz ( 40 dB). The conformal-mapping technique can be validated indirectly (at least up to 6 GHz) according to the experimental data and its agreement with our proposal. Slight differences can be explained from the fact that ohmic losses have not been taken into account in our approach. In this case, the method can be applied for designing baluns at any required frequency band. VI. CONCLUSION In this paper, we have proposed a new method based on conformal mapping allowing to evaluate and optimize the return losses of a tapered MS to double-sided PS balun with impedance-matching capabilities. The Swartz–Christoffel

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transform applied to this electromagnetic structure led to impedance and effective dielectric constant closed-form formulas, offering a new approach to analyze and optimize the tapered balun in terms of impedance variations. These expressions have been verified by comparing their predictions to full-wave computation results, showing very small differences. In addition, two case studies have demonstrated the validity of this method, which has been applied in order to design structures with minimum return losses in a specific frequency band and approximate the Klopfenstein geometric shape. The synthesis procedure combines a closed-form impedance formula and an optimization technique (in this case, GAs) providing some advantages: fast convergence toward the optimum solution, small computation cost compared to a full-wave numerical approach, and a better understanding about the electromagnetic balun behavior from the impedance variation point of view. The synthesized proposals have been fabricated and measured using a vector network analyzer, ensuring the validity of the algorithm and confirming indirectly the conformal-mapping approach.

[15] M. Kobayashi and N. Sawada, “Analysis and synthesis of tapered microstrip transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 8, pp. 1642–1646, Aug. 1992. [16] D. Park, “Planar transmission lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-3, no. 3, pp. 8–12, Apr. 1955. [17] H. A. Wheeler, “Transmission-line properties of parallel wide strips by a conformal-mapping approximation,” IEEE Trans. Microw. Theory Tech., vol. MTT-12, no. 3, pp. 280–289, May 1964. [18] H. A. Wheeler, “Transmission-line properties of parallel strips separated by a dielectric sheet,” IEEE Trans. Microw. Theory Tech., vol. MTT-13, no. 2, pp. 172–185, Mar. 1965. [19] H. A. Wheeler, “Transmission-line properties of a strip line between parallel planes,” IEEE Trans. Microw. Theory Tech., vol. MTT-26, no. 11, pp. 866–876, Nov. 1978. [20] C. Nguyen, Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures. New York: Wiley, 2000. [21] J. S. Rao and B. N. Das, “Analysis of asymmetric stripline by conformal mapping,” IEEE Trans. Microw. Theory Tech., vol. MTT-27, no. 4, pp. 299–303, Apr. 1979. [22] M. Duyar, V. Akan, E. Yazgan, and M. Bayrak, “Analyses of elliptical coplanar coupled waveguides and coplanar coupled waveguides with finite ground width,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1388–1395, Jun. 2006. [23] G. D. Zill, A First Course in Complex Analysis With Applications. Bloomfield, NJ: Jones and Bartlett, 2003.

REFERENCES [1] B. Climer, “Analysis of suspended microstrip taper baluns,” Proc. Inst. Elect. Eng., vol. 135, pt. H, pp. 65–69, Apr. 1988. [2] S. Kim and K. Chang, “Ultrawide-band transitions and new microwave components using double-sided parallel-strip lines,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2148–2152, Sep. 2004. [3] C. Jian-Xin, C. H. K. Chin, and X. Quan, “Double-sided parallel-strip line with an inserted conductor plane and its applications,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 9, pp. 1899–1904, Sep. 2007. [4] Q. Xue and J. X. Chen, “Compact diplexer based on double-sided parallel-strip line,” Electron. Lett., vol. 44, no. 2, pp. 123–124, Jan. 2008. [5] P. L. Carro Ceballos and J. de Mingo Sanz, “Ultrawideband tapered balun design with boundary curve interpolation and genetic algorithms,” presented at the IEEE AP-S Int. Symp., Albuquerque, NM, Jul. 9–15, 2006. [6] H. A. Wheeler, “Transmission lines with exponential taper,” Proc. IRE, vol. 27, no. 1, pp. 65–71, Jan. 1939. [7] R. W. Klopfenstein, “A transmission line taper of improved design,” Proc. IRE, vol. 44, no. 1, pp. 31–35, Jan. 1956. [8] R. E. Collin, “The optimum tapered transmission line matching section,” Proc. IRE, vol. 44, no. 4, pp. 539–548, Apr. 1956. [9] R. P. Hecken, “A near-optimum matching section without discontinuities,” IEEE Trans. Microw. Theory Tech., vol. MTT-20, no. 11, pp. 734–739, Nov. 1972. [10] D. C. Youla, “Analysis and synthesis of arbitrarily terminated lossless nonuniform lines,” IEEE Trans. Circuit Theory., vol. 11, no. 3, pp. 363–372, Sep. 1964. [11] J. E. Schutt-Aine, “Transient analysis of nonuniform transmission lines,” IEEE Trans. Circuits Syst., vol. 39, no. 5, pp. 378–385, May 1992. [12] T. Dhaene, L. Martens, and D. De Zutter, “Transient simulation of arbitrary nonuniform interconnection structures characterized by scattering par arne ters,” IEEE Trans. Circuits Syst., vol. 39, no. 11, pp. 928–937, Nov. 1992. [13] W. Bandurski, “Simulation of single and coupled transmission lines using time-domain scattering parameters,” IEEE Trans. Circuits Syst., vol. 47, no. 8, pp. 1224–1234, Aug. 2000. [14] J. P. Mahon and R. S. Elliott, “Tapered transmission lines with a controlled ripple response,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 10, pp. 1415–1420, Oct. 1990.

Pedro Luis Carro (S’06) was born in Zaragoza, Spain, on 1979. He received the Engineer of Telecommunication M.S. degree and Ph.D. degree from the Universidad de Zaragoza, Zaragoza, Spain, in 2003 and 2009, respectively. In 2002, he carried out his Master’s thesis on antennas for mobile communications with the Department of GSM and Antenna Products, Ericsson Microwave Systems AB, Göteborg, Sweden. From 2002 to 2004, he was an Electrical Engineer with the Space and Defense Department RYMSA S.A., where he was involved in the design of antennas and passive microwave devices for satellite communication systems. From 2004 to 2005, he was an RF Engineer with the Research and Development Department Telnet Redes Inteligentes, where he was involved with radio-over-fiber systems. In 2005, he joined the Universidad de Zaragoza, where he was an Associate Professor, and since 2006, an Assistant Professor with the Departamento de Ingeniería Electrónica y Comunicaciones. His research interests are in the area of mobile antenna systems, passive microwave devices, and power amplifiers.

Jesus de Mingo (M’98) was born in Barcelona, Spain, on 1965. He received the Ingeniero de Telecomunicación degree from the Universidad Politécnica de Cataluña (UPC), Barcelona, Spain, in 1991, and the Doctor Ingeniero de Telecomunicación degree from the Universidad de Zaragoza, Zaragoza, Spain, in 1997. In 1991, he joined the Antenas Microondas y Radar Group, Departamento de Teoría de la Señal y Communicationes, Universidad Politénica de Cataluña. In 1992, he was with Mier Comunicaciones S.A., where he was involved with the solid-state power amplifier design until 1993. Since 1993, he has been an Assistant Professor ,and since 2001, a Professor with the Departamento de Ingeniería Electrónica y Comunicaciones, Universidad de Zaragoza. He is a member of the Aragon Institute of Engineering Research (I3A). His research interests are in the area of linearization techniques of power amplifiers, power amplifier design, and mobile antenna systems.

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High-Q RF-MEMS 4–6-GHz Tunable Evanescent-Mode Cavity Filter Sang-June Park, Student Member, IEEE, Isak Reines, Student Member, IEEE, Chirag Patel, Student Member, IEEE, and Gabriel M. Rebeiz, Fellow, IEEE

Abstract—This paper presents a miniature high- tunable evanescent-mode cavity filter using planar capacitive RF microelectromechanical system (MEMS) switch networks and with a frequency coverage of 4.07–5.58 GHz. The two-pole filter, with an internal volume of 1.5 cm3 , results in an insertion loss of 4.91–3.18and a 1-dB bandwidth of 17.8–41.1 MHz, respectively, and an ultimate rejection of 80 dB. RF-MEMS switches with digital/analog tuning capabilities were used in the tunable networks so as to align the two poles together and result in a near-ideal frequency of the filter is 300–500 over the tuning response. The measured range, which is the best reported using RF-MEMS technology. The filter can withstand an acceleration of 55–110 g without affecting its frequency response. The topology can be extended to a multiple-pole design with the use of several RF-MEMS tuning networks inside the evanescent-mode cavity. To our knowledge, these results represent the state-of-the-art in RF-MEMS tunable filters. Index Terms—Capacitive cantilever switch, evanescent mode, tunable filter, RF microelectromechanical systems high(MEMS), waveguide filter.

I. INTRODUCTION

L

Fig. 1. Tunable two-pole evanescent-mode cavity filter (half shown) and equivalent circuit model (after [17]).

Manuscript received October 14, 2009; revised October 23, 2009. First published January 26, 2010; current version published February 12, 2010. This work was supported by the Defense Advanced Research Projects Agency (DARPA) by the ASP Program under a subcontract from Rockwell Collins. S.-J. Park is with Qualcomm Inc., San Diego, CA 92101 USA (e-mail: [email protected]). I. Reines, C. Patel, and G. M. Rebeiz are with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093 USA (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038448

size [13]. These have been extensively used in industry, and recently Joshi et al. showed a 3–6-GHz tunable evanescent-mode filter with external piezoelectric actuators [14]–[16]. This paper presents the first high- (300–500) tunable filter in the 4–6-GHz range based on an evanescent mode cavity and an RF-MEMS switch network [17]. In this design, two 4-bit RF-MEMS capacitance networks are integrated on planar quartz substrates and placed on metal posts inside an evanescent-mode cavity (Fig. 1). A quartz substrate is chosen as opposed to a glass substrate due to its low dielectric loss. The external biaswires pass through miniature channels in the cavity wall and are connected to the quartz substrate at the voltage null location, thereby ensuring minimal disturbance and leakage from the cavity. The input and output coupling sections are realized using the center pins of coaxial connectors, and the inter-resonator coupling is controlled by a fixed iris located at the center of the cavity. A tunable two-pole filter is demonstrated in this study, but the design can be extended to multiple poles with the use of several resonator sections. The cavity is composed of five sections, as outlined in Fig. 1 (input/output sections, resonator sections, coupling section) and is quite modular. On one hand, this ensures easy access to the cavity (iris selection, quartz wafer insertion, etc.), but on the

OW-LOSS tunable filters are essential for multiband radios, and to our knowledge, tunable filters with based on planar fabrication technologies have not yet been reported at 2–6 GHz. In the past few years, there has been a substantial increase in the performance of tunable filters, both using RF microelectromechanical systems (MEMS) and Schottky diode devices [1]–[11], but was still limited by the planar resonators (in the case of RF MEMS) or the Schottky varactor diodes. The can be increased to 300–500 using suspended strip-line configurations, but this occupies a substantial volume [12]. Standard cavity resonators can also be used, but their large volume at 2–10 GHz and incompatibility with fabricated tuning devices limit their usefulness for tunable wireless systems. The volume can be reduced with evanescent-mode of 1000–5000 depending on their designs, which result in

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other hand, assembling the different sections can result in a disturbance in the electric current on the cavity walls. This can be mitigated with the use of multiple screws to tighten the sections all together, and we have found that this was acceptable for a filter of 300–500. An important aspect of this design is that the RF-MEMS capacitance networks are fabricated on the same planar quartz substrate, thereby ensuring high uniformity, diced and pre-tested outside of the filter, and then placed on a large planar surface (the capacitive post) inside the evanescent mode cavity. This simplifies the assembly procedure and ensures high repeatability from filter to filter. II. DESIGN AND IMPLEMENTATION A. Evanescent-Mode Waveguide The characteristic impedance of an evanescent-mode region can either be inductive or capacitive depending on its mode shape, and is for TE mode

(1)

for TM mode

(2)

Fig. 2. (a) (i) T and (ii) 5 equivalent lumped circuit models for an evanescent mode waveguide (length = l , and Z = jX ). (b) Evanescent-mode waveguide filter model.

where (3) (4) For the TE evanescent mode, the wave impedance becomes (5)

where (6) are the waveguide cross-section dimensions. The TE and evanescent-mode and its equivalent model is either a T or a circuit [see Fig. 2(a)]. A filter circuit can be designed using either the T or circuits with the proper amount of series or shunt capacitances. Fig. 2(b) presents a possible filter circuit implemented with shunt capacitances since it is usually easier to realize a shunt capacitance versus a series capacitance in a waveguide implementation. Using the resonance condition, the required shunt capacitance values can be found by (7)

B. Extracting Filter Design Parameters A conceptual evanescent-mode waveguide tunable filter with external coupling and its equivalent-circuit model are shown in Fig. 1. The shunt capacitances are implemented using capacitive posts in the waveguide, and a planar quartz substrate with an

Fig. 3. Evanescent-mode cavity resonator with: (a) inductive post coupling, (b) its equivalent circuit model, and (c) input impedance. (L is a parasitic inductance due the coupling post and L is the coupling inductance).

RF-MEMS tunable switch network is mounted on each side of the posts to tune the resonance frequency. An inductive post coupling scheme is utilized as the external coupling circuit due to its matching characteristics over a wide frequency range. The evanescent mode filter can be simplified to the model in Fig. 3 due to the even- and odd-mode symmetry; the perfect electric conductor/perfect magnetic conductor (PEC/PMC) boundaries represent the even- and odd-mode resonances in the waveguide cavity. The filter design parameters such as the , unloaded even- and odd-mode resonance frequencies

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quality-factor , coupling coefficient , and external qualitycan be extracted from the reflection coefficients of factor this model. The input impedance of the cavity resonator is (8) where (9) is the unloaded resonance frequency and and are the unloaded and loaded resonator , respectively. The complex input reflection coefficient is plotted in is the frequency Fig. 3. The loaded resonance frequency has its minimum. If the coupling where the magnitude of coefficient diminishes to zero, the input reflection coefficient . The vector creates a circle on the Smith becomes chart, and is given by [18] (10)

Fig. 4. Full-wave simulation model of the evanescent-mode cavity resonator with post coupling and an internal volume of 1.5 cm . All dimensions are in in millimeters (after [17]).

where (11) (12) When , the magnitude of the vector specified in (10) has its maximum at (13) The coupling coefficient is then

(14) If the two frequencies and and , respectively, the

are selected to have value from (10) is (15)

and

are then (16) (17)

is the external . where A full-wave simulation with an actual physical model of the evanescent-mode cavity resonator (Fig. 4) is performed to ex, and ( is the RF-MEMS capacitance tract , , , network). A lumped gap port is placed between the cavity wall in the simulaand the post to include the loading capacitor tion in addition to a wave-port at the coaxial input. The coupling is calculated using the pole-splitting coefficient of the filter method and is given by (18)

=

Fig. 5. (a) Extracted C , (b) Q , k versus the resonance frequency with y with x : mm, and (d) k with y mm for the cavity resonator in Fig. 4 with different y and x , respectively. The calculations in (c) and (d) are done at 5 GHz (after [17]).

5 mm, x = 2:5 mm, (c) Q

=25

=5

The symmetry plane of the filter in the resonator is set to PEC or PMC to obtain the even- or odd-mode resonant frequency. , , and values are plotted versus resoThe extracted values of 640–180 fF result in nance frequency in Fig. 5. a resonance frequency of 4.0–6.0 GHz, respectively, and the and values are 170 23 and 0.0062 corresponding 0.0005, respectively. The frequency dependence in shows a constant fractional-bandwidth behavior (23–40 MHz absolute

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3-dB bandwidth at 4–6 GHz), and the filter maintains good impedance matching over the frequency range due to the de. crease in The external coupling of the resonator is controlled by the , and the area between the cavity wall and the coaxial pin inter-resonator coupling can be adjusted by changing the cou. The extracted and values versus pling aperture size and are plotted in Fig. 5. C. High- RF-MEMS Cantilever-Switch Capacitance Network A narrowband filter design requires high- resonators to maintain low loss. A well-known closed-form expression re, lating the fractional bandwidth , unloaded quality factor is [19] and the insertion loss (19) where is the low-pass prototype element value. It can be estimated from (19) that an unloaded of 580–870 is needed to realize a 0.05% two-pole Butterworth filter with an insertion loss of 3.0-2.0 dB (a Butterworth filter response is chosen since we are defining the filter bandwidth at the 3-dB level). An essential component in tunable filter design is the variable impedance network, and its associated loss has a sigof an nificant effect on the resonator . Fig. 6 shows the evanescent-mode cavity with different volumes and variable sein the tuning element . The required at ries resistance 5 GHz for each volume is shown in Fig. 6(b). It can be seen that of the resonator drops from 1150 for a 1.5-cm cavity, the . It is, therefore, esto 350–450 at 5 GHz for sential to build a very high- ( 500) tuning network to realize . The resonator is a low-loss tunable filter with nearly entirely dominated by the of the impedance network [see Fig. 6(c)]. It is also seen that a 2.5–3.0-cm for cavity results in a considerably higher for , – fF). but requires a very low capacitance value ( The 1.5-cm cavity was chosen due to program constraints for minimal filter size, and future work will consider larger cavities with miniature MEMS switched capacitors [20]. Until now, RF MEMS is the only planar tunable technology with such a high at microwave frequencies [21], and this technology is used in this study. 1) Bias Lines and Their Effect on the Resonator : In the tunable filter design, the RF-MEMS capacitance network is usually placed at the peak electric field location in the resonators to ensure maximum frequency tuning. This high resonant electric field can easily couple to the resistive bias lines and greatly deof grade the resonator , as shown in [1]. In this study, the the RF-MEMS filter was 85–170, and the use of an orthogonal biasing network was sufficient to reach this moderate . How, the dissipation in ever, in the design of a filter with the orthogonal bias line can be the dominant loss factor. Full-wave simulations were performed in Ansoft’s High Frequency Structure Simulator (HFSS) [22] with different bias-line configurations, and their effect on the resonator was investigated (Fig. 7). In this case, the RF-MEMS switch was simplified

Fig. 6. (a) Loading capacitance C and (b) unloaded Q versus the volume of the cavity, and (c) Q versus frequency. Q is the quality fF. factor of the impedance network with C

= 350

to a fixed metal–air–metal (MAM) capacitor with fF , ). Even though all the (equivalent bias lines are configured orthogonally to the electric field, still showed a strong dependence on the bias-line resistance and length, and is due to fringing field components, which are tangential to the bias lines. The resistive bias line effect can be significantly reduced using a metal air-bridge cover, as shown in Fig. 7(a). The tangential electric field diminishes to an insignificant level on the metal bridge, and therefore, the electric-field coupling to the bias lines is substantially reduced. For increases from a 400- m-long bias line with 10 k sq, the 500 to 670 for the 1.5-cm cavity, which is lower than the with no bias lines. The difference in is from residual losses in the 10-k sq bias lines due to the current generated on the 60- m-wide thin gold bias lines [see Fig. 7(a)]. 2) Device Matching: For a narrowband tunable filter, it is important to match the resonance frequencies of each resonator. Simulations show that at 6.0 GHz, the two loading capacitance and ) need to be controlled within 1 fF so values (

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Q

Fig. 9. High- RF-MEMS cantilever capacitive switch. (a) Cross section (after [17]). (b) Measured C–V curve. All dimensions are in micrometers.

Fig. 7. (a) Tuner network with an optional metal air bridge covering the resistive bias lines, and a MAM (fixed) RF-MEMS switch model (half circuit shown). The of the evanescent-mode cavity versus (b) bias-line resistance, and (c) bias-line length. The calculations were done at 5 GHz with the cavity of Fig. 4.

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Fig. 8. Simulated filter response with a resonator loading mismatch of at 4.0 fF and 6.0 GHz fF for .

(C = 640 )

(C = 185 ) R = 0:1

1C

as not to degrade the filter response (Fig. 8). At 4.0 GHz, a 2-fF variation is the maximum allowed. This, as well as the high- requirement, puts serious limitations on the design of the RF-MEMS capacitance network.

An RF-MEMS cantilever switch with a digital/analog tuning capability is utilized to fulfill those requirements [23]. The thick plated (3.5–4.0 m) cantilever and its associated zipping effect with a hold-down bias voltage make this switch an ideal candidate for both high- and analog tuning capabilities (Fig. 9). Alternatively, the analog tuning can be achieved by applying a larger once the beam is pulled down, and without any control . The mechanical resonant frequency of the can, and with up-to-down tilever device is 34 kHz with and down-to-up switching speeds of 25 and 50 s, respectively, using a 60-V actuation waveform. The typical spring constant N/m for a uniform load [23]. of the switch is In this study, a single bias line is used per MEMS switch to provide both digital and analog tuning while also simplifying the control line routing, and reducing the amount of RF leakage through the resistive bias lines. The C–V curve can vary from device-to-device due to fabrication tolerances and different residual stress gradients in the plated gold beams. Typical de– fF, a – fF at vices show a measured pull-in, and an analog tuning from 250–320 fF or from 310–350 fF. The cantilever switch used in this study has an up-state and V and 280 fF a down-state capacitance of 40–45 fF ( – V, V), respectively, and its analog capac– V, or – itance coverage is 280–350 fF ( V). The measured is 300 at 6 GHz, even in the down-state position due to the thick gold-plated beam [23]. This device has been tested without failures to 100 bilV) lion cycles (at 16 kHz under partial vacuum with GHz, W). under hot switching conditions ( Such large cycle counts are obtainable because there is always a

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Fig. 11. Simulated loading capacitance of the 4-bit tuner network. There are 16 digital states with analog coverage between most of the states.

Fig. 12. Fabricated tunable evanescent-mode cavity filter with the RF-MEMS cantilever-switch capacitance network chip.

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Fig. 10. (a) Micrograph of the high- 4-bit RF-MEMS capacitive network on a quartz substrate. (b) Half of the equivalent-circuit model. The ground plane is air bridged over the bias lines.

0.4–0.5- m air gap between the cantilever and pull-down electrode, which results in a low electric field and virtually no substrate charging. is 3) 4-bit Impedance Network: The loading capacitor realized using a 4-bit RF-MEMS cantilever-switch capacitance network, and each MEMS switched capacitor is in series with a fixed MAM scaling capacitor (Fig. 10). Two different MAM capacitors with values of 600 and 200 fF are used in order . With the analog tuning to provide a wide variation in network continually covers the capaccapability, the 4-bit itance range of 157–697 fF (Fig. 11), which, in turn, results in a 3.75–6.25-GHz frequency tuning (see Fig. 5). As the RF-MEMS switches are actuated, the overall resistance of the impedance network drops due to the parallel connections of the loading. devices and this maintains a high even with large For this high- resonant cavity, it is important to minimize RF leakage and radiation loss through the biasing channel in the

ground plane, and therefore, an circuit ( k , k for 5–10 k sq and pF) is imand plemented by routing the bias lines underneath the ground plane. The external bias wires go through a small channel in the cavity wall, and are connected to the bias pads on the RF-MEMS chip using silver epoxy before the chips are installed into the modular cavities (Fig. 12). A bias-routing board facilitates independent voltage control for all eight RF-MEMS switches (four switches per chip). The effect of the two 4.2 mm 1 mm slits on the bottom side of the tunable filter, which facilitate the insertion of the quartz chips, were taken into account through full electromagnetic (EM) simulations. The discontinuity created by these slits introduces a small inductance, which is lumped together with the evanescent mode -section (see Fig. 1). III. FABRICATION AND MEASUREMENTS A. Fabrication impedance network is fabricated on a The high, ) 508- m-thick quartz substrate ( using a standard RF-MEMS fabrication process developed at the University of California at San Diego, La Jolla [23]. The MAM capacitors, air bridges, and first ground plane layer are electroplated with 4- m-thick gold and are fabricated with MEMS cantilever beams (1.5 m above the underlying metal). The bias lines are SiCr with a sheet resistance in the range of 3–10 k sq depending on the fabrication run. The ground planes are further electroplated with 4 m of additional gold to reduce conductor losses. The chips are individually diced and critical point drying process. released using a

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Fig. 13. Measured filter responses for two different switched capacitor settings with and without voltage tuning.

Due to typical variations in the C–V curves of the cantilever devices and the stringent filter device matching requirements, the loading capacitance of several chips are first measured and matched in pairs in order to preselect the impedance networks. This is accomplished by measuring the resonant frequencies of a single loaded evanescent-mode cavity resonator using a one-port measurement and replacing the coupling iris with a of a single impedance short-circuited plane. The measured network is 415–528 at 4.5–5.5 GHz for a run with an SiCr resistance of 10 k sq [17].

Fig. 14. Measured: (a) S and (b) S filter using digital and analog tuning.

of the tunable evanescent-mode cavity

B. Filter Measurements Even with preselection, analog voltage tuning is still required to recover from the unequal capacitive loading since must be 1–2 fF for an excellent filter response at 4–6 GHz. This is demonstrated in Fig. 13, which presents two different switched capacitor settings both with and without final voltage tuning. In both cases, the ideal filter response can be recovered at the expense of tuning range. A 4.1-mm-wide coupling iris is used for this filter measurement. -parameter measurements were taken from 3 to 7 GHz with an Agilent E5071B network analyzer and the reference planes are defined at the subminiature A (SMA) connectors. The RF-MEMS capacitive switches were actuated using a 10-kHz bipolar waveform to reduce the effects of substrate charging. The measured filter center frequencies using both digital and analog tuning (range from 4.07 to 5.58 GHz), and demonstrate a tuning range of 31.3% centered at 4.83 GHz (Fig. 14). Note that six out of the eight total RF-MEMS switches actuated, thereby limiting the tuning range 4.07 GHz instead of 3.75 GHz. The measured frequency response shows ranging from 300 to 500 with associated insertion losses a between 3.18–4.91 dB and 1-dB bandwidths ranging from 17.8 to 41.1 MHz (0.44%–0.74%) (see Table I). In this fabrication run, the SiCr resistance was 3–5 k sq. The filter is a constant fractional bandwidth design, and the measured 1-dB bandwidth varies from 0.44% to 0.72% due to nonexact capacitance matching. The upper frequency is 5.58 GHz instead of 6.0 GHz due to a higher than expected RF-MEMS up-state capacitance. The measurements agree and are perfectly with HFSS simulations, once a fitted used in the lumped-port model, and show an ultimate rejection

TABLE I MEASURED RESPONSES OF THE TUNABLE FILTER (BW %, MHz)

of 80 dB with no spurious responses (Fig. 15). To our knowledge, this represents the state-of-the-art in this frequency range. C. Power Handling The power handling of the filter was simulated using both a lumped-element model (see Fig. 1) and a full-wave HFSS simulation with the RF-MEMS 4-bit switch networks connected

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The filter can be designed to have a constant absolute bandwidth by placing a planar MEMS tuning network on the iris plans, or by designing a fixed unsymmetrical iris (for narrowband tuning). A larger cavity can also be used (2.5–3.0 cm ) for a higher , but this necessitates a lower value capacitance network – fF instead of 350 fF at 5 GHz). It is not clear at this ( moment if the 4-bit capacitance network will be the limiting factor in such a design. This will be the subject of future work. V. CONCLUSION

=

Fig. 15. Measured and fitted S -parameters for three filter responses (f : ;f : GHz, C : GHz, C fF, R fF, : : GHz, C : ;f fF, R ). R

= 241 5 58 = 0 27 = 4 08

= 0 33 = 4 85 = 614 = 0 21

= 380

with lumped-element ports. The simulation is performed at 5.58 GHz because the filter is most sensitive to the input power level when all the switches are in the up-state position. Both the lumped-element model and full-wave simulations show that – dBm self-actuation of the cantilever occurs when – V). Note that the voltage required for self-ac( tuation when the force is applied at the tip of the cantilever using an RF voltage waveform [see Fig. 9(c)] is lower than . This is because the defined at the cantilever tip is lower than the defined above the pull-down electrode. As is well known, power handling for high- filters is a challenge since the voltages generated across the tuning devices are very large even at low RF powers. Although the simulated power handling is only 5–6 dBm, the third-order intermodulation intercept point (IIP3) is still 40 dBm since kHz, and the beam simply does not move for –50 kHz. D. G-Sensitivity The acceleration sensitivity is calculated by first simulating the deflection of the cantilever under a uniform load corresponding to the force exerted by acceleration ( , g, N/m) and then calculating the associated change in capacitance . The shift in resonant frequency is then easily found using Fig. 5(c). The filter is most sensitive when all of the RF-MEMS switches are in the up-state position GHz and moves coherently with acceleration. The simulations show that a g force of 55–110 g results in a frequency shift of 10–20 MHz at 5.58 GHz, which is 0.5 the 1-dB bandwidth. This amount of frequency shift is insignificant for most applications. In the down-state position, the acceleration insensitivity is even greater due to the fixing of the free end of the cantilever to the dielectric. IV. DISCUSSION The measured of the tunable filter is 300–500 from 4.07 to 5.57 GHz. When the RF-MEMS switches are in the up-state and is dominated by the losses in the position, 3–5-k sq bias network. If the bias line network is increased to 100 k sq, then [see Fig 7(c)]. In the down-state – and is limited by a composition, the measured of the bination of the device and bias network losses. The MEMS cantilever device can be improved by increasing the bottom metal electrode thickness from 0.3 to 1 m.

This paper has presented the first tunable high- evanescent-mode cavity filter based on a 4-bit RF-MEMS capacitance network. Both tunable resonator and filter measurements indicate the potential of a very high- tuning, and a tunable filter – was achieved from 4.07 to 5.58 GHz with a 1-dB bandwidth of 18–41 MHz, respectively. The design is scalable to multiple poles and to constant absolute-bandwidth designs. ACKNOWLEDGMENT The authors thank R. Newgard, C. Conway, R. Potter, and T. Journot, all with Rockwell Collins, Cedar Rapids, IA, for their valuable technical discussions. REFERENCES [1] S.-J. Park, M. El-Tanani, I. Reines, and G. M. Rebeiz, “Low-loss 4-6-GHz tunable filter with 3-bit high-Q orthogonal bias RF-MEMS capacitance network,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 10, pp. 2348–2355, Oct. 2008. [2] M. Houssini, A. Pothier, A. Crunteanu, and P. Blondy, “A 2-pole digitally tunable filter using local one bit varactors,” in MTT-S Int. Microw. Symp. Dig., Atlanta, GA, Jun. 2008, pp. 37–40. [3] R. M. Young, J. D. Adam, C. R. Vale, T. T. Braggins, S. V. Krishnaswamy, C. E. Milton, D. W. Bever, L. G. Chorosinski, L.-S. Chen, D. E. Crockett, C. B. Freidhoff, S. H. Talisa, E. Capelle, R. Tranchini, J. R. Fende, J. M. Lorthioir, and A. R. Tories, “Low-loss bandpass RF filter using MEMS capacitance switches to achieve a one-octave tuning range and independently variable bandwidth,” in IEEE MTT-S Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 1781–1784. [4] A. Pothier, J.-C. Orlianges, G. Zheng, C. Champeaux, A. Catherinot, P. B. D. Cros, 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. [5] B. Pillans, A. Malczewski, R. Allison, and J. Brank, “6-15 GHz RF MEMS tunable filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Long Beach, CA, Jun. 2005, pp. 919–922. [6] W.-D. Yan and R. R. Mansour, “Tunable dielectric resonator bandpass filter with embedded MEMS tuning elements,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 1, pp. 154–160, Jan. 2007. [7] S. Fouladi, W. D. Yan, and R. R. Mansour, “Microwave tunable bandpass filter with MEMS thermal actuators,” in 38th Eur. Microw. Conf., Oct. 2008, pp. 1509–1512. [8] C. Ong and M. Okoniewski, “MEMS-switchable coupled resonator microwave bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 7, pp. 1747–1755, Jul. 2008. [9] S.-J. Park and G. M. Rebeiz, “Low-loss tunable filters with three different pre-defined bandwidth characteristics,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 5, pp. 1137–1148, May 2008. [10] M. Tanani and G. M. Rebeiz, “A two-pole two-zero tunable filter with improved linearity,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 4, pp. 830–839, Apr. 2009. [11] M. Tanani and G. M. Rebeiz, “Corrugated coupled-lines for constant absolute bandwidth tunable filters,” IEEE Trans. Microw. Theory Tech., Mar. 2009, submitted for publication. [12] I. Reines, A. Brown, M. El-Tanani, A. Grichner, and G. M. Rebeiz, “1.6–2.4-GHz RF-MEMS tunable 3-pole suspended combline filter,” in MTT-S Int. Microw. Symp. Dig., Jun. 2008, pp. 133–136. [13] G. F. Craven and C. K. Mok, “The design of evanescent mode waveguide bandpass filters for a prescribed insertion loss characteristic,” IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 3, pp. 295–308, Mar. 1971.

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[14] C. K. Mok, “Design of evanescent-mode waveguide diplexers,” IEEE Trans. Microw. Theory Tech., vol. MTT-21, no. 1, pp. 43–48, Jan. 1973. [15] R. V. Snyder, “New application of evanescent mode waveguide to filter design,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 12, pp. 1013–1021, Dec. 1977. [16] H. Joshi, H. H. Sigmarsson, D. Peroulis, and W. J. Chappell, “Highly loaded evanescent cavities for widely tunable high- filters,” in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, Jun. 2007, pp. 2133–2136. [17] S.-J. Park, I. Reines, and G. M. Rebeiz, “High- RF-MEMS tunable evanescent-mode cavity filter,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2009, pp. 1145–1148. [18] D. Kajfez and E. J. Hwan, “ -factor measurement with network analyzer,” IEEE Trans. Microw. Theory Tech., vol. MTT-32, no. 7, pp. 666–1984, Jul. 1984. [19] G. L. Matthaei, L. Young, and E. Jones, Microwave Filters Impedance-Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980. [20] B. Lakshminarayan, D. Mercier, and G. M. Rebeiz, “High-reliability miniature RF-MEMS switched capacitors,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 4, pp. 971–981, Apr. 2008. [21] G. M. Rebeiz, RF MEMS Theory, Design, and Technology. New York: Wiley, 2003. [22] HFSS. ver. 10.1, Ansoft Corporation, Pittsburgh, PA, 2006. [23] A. Grichener, B. Lakshminarayanan, and G. M. Rebeiz, “HighRF MEMS capacitor with digital/analog tuning capabilities,” in IEEE MTT-S Int. Microw. Symp. Dig., Atlanta, GA, Jun. 2008, pp. 1283–1286.

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Chirag Patel (S’09) received the B.S. degree in computer engineering from The University of Michigan at Ann Arbor, in 2005, and is currently working toward the Ph.D. degree in electrical engineering at the University of California at San Diego, La Jolla. From 2005 to 2007, he was with the U.S. Navy Space and Naval Warfare Systems Center, San Diego, CA, as a member of the Circuits and Sensors Group. His research interests include RF MEMS and microwave and millimeter-wave systems.

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Gabriel M. Rebeiz (S’86–M’88–SM’93–F’97) received the Ph.D. degree from the California Institute of Technology, Pasadena. He is currently a Professor of electrical and computer engineering at the University of California at San Diego (UCSD), La Jolla. From 1988 to 2004, he was with The University of Michigan at Ann Arbor He has contributed to planar millimeter-wave and terahertz antennas and imaging arrays from 1988 to 1996, and his group has optimized the dielectric-lens antennas, which is the most widely used antenna at millimeter-wave and terahertz frequencies. His group recently developed 6–18- and 30–50-GHz eight- and 16-element phased arrays on a single chip, making them one of the most complex RF integrated circuits (RFICs) at this frequency range. His group also demonstrated high- RF-MEMS tunable 300) and the new angular-based RF-MEMS capacfilters at 4–6 GHz ( itive and metal-contact switches. As a consultant, he developed the 24-GHz -, and -band phased single-chip automotive radar with USM/ViaSat, -, arrays for defense applications, the Radio Frequency Micro Devices (RFMD) RF-MEMS switch , and the Agilent RF-MEMS switch. He leads a group of 18 Ph.D. students and three post-doctoral fellows in the area of millimeter-wave RFIC, microwaves circuits, RF MEMS, planar millimeter-wave antennas, and terahertz systems. He is the Director of the UCSD/Defense Advanced Research Projects Agency (DARPA) Center on RF MEMS Reliability and Design Fundamentals. He authored RF MEMS: Theory, Design and Technology(Wiley, 2003). Prof. Rebeiz is a National Science Foundation (NSF) Presidential Young Investigator. He was an associate editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was a Distinguished Lecturer fo rthe IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and IEEE Antennas and Propagation Society (AP-S). He was a recipient of an URSI Koga Gold Medal, an IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Distinguished Young Engineer (2003), and the IEEE MTT-S 2000 Microwave Prize. He was also the recipient of the 1998 Eta Kappa Nu Professor of the Year Award, the 1998 Amoco Teaching Award given to the best undergraduate teacher at The University of Michigan at Ann Arbor, and the 2008 Teacher of the Year Award of the Jacobs School of Engineering, UCSD. His students have been the recipients of a total of 18 Best Paper Awards presented at IEEE MTT-S, IEEE RFIC, and IEEE AP-S conferences.

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Sang-June Park (S’05) received the B.S. degree in physics from Youngnam University, Kyungsan, Korea, in 1991, and the M.S. and Ph.D. degrees in electrical engineering (with an emphasis in applied electrodynamics and RF circuits) from The University of Michigan at Ann Arbor, in 2004 and 2007, respectively. From 1997 to 2001, he was with the Electromechanics Research and Development Center, Samsung, Suwon, Korea, where he was involved with the development of microwave ceramic filters and low-temperature co-fired ceramic (LTCC) antenna and switch modules. He is currently with Qualcomm Inc., San Diego, CA, where he is involved with RF systems. His current research interests includes RF MEMS for microwave and millimeter-wave applications, tunable filters, antennas, and microwave systems.

Isak Reines (S’07) received the B.S. and M.S. degrees in electrical engineering from the University of New Mexico, Albuquerque, in 2002 and 2004, respectively, and is currently working toward the Ph.D. degree in electrical engineering at The University of California at San Diego, La Jolla. From 2004 to 2006, he was a Member of the Technical Staff with the RF Microsystems Department, Sandia National Laboratories, where he was involved with RF-MEMS-based phase shifters, tunable filters, and switching networks for radar and communications applications. His current research interests include novel RF-MEMS devices development for wireless systems.

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Compact Hybrid Resonator With Series and Shunt Resonances Used in Miniaturized Filters and Balun Filters Tao Yang, Student Member, IEEE, Masaya Tamura, Member, IEEE, and Tatsuo Itoh, Life Fellow, IEEE

Abstract—A hybrid resonant circuit is proposed in this paper. The circuit is a combination of a shunt resonant circuit and series resonant circuit. With this combination, lower resonant frequency is achieved as compared to the single shunt and series resonant circuits. As a result, a compact resonator with smaller size can be achieved as compared to the conventional quarter- and half-wave resonators. Besides the size reduction, the proposed resonant circuit is able to introduce a transmission zero to improve the stopband suppression in filter design. Based on this circuit, a very compact interdigital coupled microstrip resonator is proposed in this paper. The resonator achieves a small length of nearly 1/10 guided wavelength ( ), which has a length reduction of 63% as compared to the conventional uniform quarter-wave resonator. By using the proposed resonator, a second-order 0 128 and a bandpass filter with a small size of 0 144 01 are fourth-order bandpass filter with a size of 0 217 built based on the standard filter synthesis methods. Both good performance and miniaturization are achieved for the proposed filters, and the expected transmission zeros are also observed. In addition to the small filters, the proposed resonator is suitable for miniaturized balun bandpass filters. A novel configuration for a balun bandpass filter is proposed based on the aforementioned resonators. A second-order balun bandpass filter with a size of 0 145 and a fourth-order balun bandpass filter 0 26 0 203 are reported in this paper. with a size of 0 213 Both balun filters achieve good filtering performance, as well as excellent amplitude and phase imbalances, which are less than 1 dB and 1 in the passband, respectively. Index Terms—Balance-to-unbalance (balun) filter, hybrid resonator, interdigital coupled microstrip resonator, miniaturized bandpass filter, transmission zeros.

I. INTRODUCTION N MODERN planar microwave systems, high-quality bandpass filters with small sizes are always in need. Many techniques and structures have been tried to make filters small,

I

Manuscript received July 07, 2009; revised November 20, 2009. First published January 26, 2010; current version published February 12, 2010. This work was supported in part by Panasonic under the University of California (UC) Discovery Grant. The work of T. Yang was supported by the China Scholarship Council. T. Yang is with the Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095 USA, and also with the Department of Electrical Engineering, University of Electronic Science and Technology of China, 610054 Sichuan, Chengdu, China (e-mail: [email protected]). M. Tamura is with the Corporate Components Development Center, Panasonic Electronic Devices Corporation Ltd., 1006 Kadoma, Osaka, Japan (e-mail: [email protected]). T. Itoh is with the Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2038662

Fig. 1. Proposed hybrid resonant circuit.

and many of them have been proposed in recent years [1]–[6]. Generally, most of these filters are based on the resonators that are evolved from the classic quarter- and half-wave resonators. In [1], [2], and [5], filters with an ultra-small size are proposed based on quarter-wave resonators. These filters all achieve good performance. However, the structures of these filters are complicated, as a complicated folding topology and mass of shorted vias are required. In [3], well-performed bandpass filters with a small size are proposed based on half-wave resonators. These filters do not require vias, but the sizes of them are slightly larger than the filters based on the quarter-wave resonators. In addition to the filter size reduction, much effort has also been made to introduce transmission zeros to improve the filter selectivity [7]–[15]. In [7] and [8], general methods for filter synthesis with transmission zeros are proposed. Based on accurate mathematical expression and optimization technology, transmission zeros are introduced by employing cross coupling. In [15], a hybrid series resonant structure is proposed to build filter with transmission zeros. This structure has the intrinsic capability of introducing transmission zeros in the filter design. Thus, no additional cross-coupling is required to produce transmission zeros by using this structure. However, this structure is built in low-temperature co-fired ceramic (LTCC) layers, and the filter synthesis process is based on the image parameter method. The cost for the fabrication is not negligible and the synthesis process is relatively complicated. In modern communication systems, baluns are key components in balanced circuit topologies such as balanced mixers, frequency multipliers, and push–pull amplifiers. In many cases, the input or output of the balanced circuit needs to be connected to a filter for signal selection. Thus, an integration of the balun and filter is necessary to reduce the cost and

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TABLE I NUMERICAL SOLUTION TO (4)

Here, f

= 2! , and f = 2! . !

and ! are the first and second positive roots for (4), respectively.

size of the circuitry used in the systems. Recently, a significant amount of research has been conducted to realize the integration of baluns and filters, and many balun filters have been proposed. One way to integrate a balun and a filter is simply through an inter-matching circuit to combine these two circuits [16]. This method is the simplest, but its circuit topology is very complicated. In [17], a balun filter is realized by building a bandpass filter with a balun function. This kind of balun filter is a simple bandpass filter with an unbalanced input and two balanced output ports. The circuit topology of this method is simpler compared with other solutions, however, it requires some special filter structure. In [18]–[23], symmetrical four-port networks are developed to build balun filters by applying specific boundary conditions. Compact balun filters with high common-mode suppression can be built with this method. Meanwhile, this method can be easily understood by odd- and even-mode analysis. In this paper, a hybrid resonant circuit is proposed. This circuit consists of shunt and series resonance circuits. By combining the shunt and series resonances, a lower resonant frequency is achieved as compared to the single shunt and single series resonance. As a result, compact resonators with smaller size can be obtained based on this circuit. In addition, this circuit has an intrinsic capability of introducing a transmission zero at high frequency and improve the stopband suppression in the filter design. Based on this circuit, an interdigital coupled microstrip resonator is proposed. This in length, resonator is very compact, which is only where is the guided wavelength at the center frequency. Along with the size reduction, the resonator has a superior capability to introduce a transmission zero in filter designs. To demonstrate the miniaturized application of the proposed resonator, a series of miniaturized bandpass filters and balun bandpass filters are reported based on the proposed resonator. All the filters and baluns exhibit good performance, as well as very small sizes. II. HYBIRD RESONATOR WITH SHUNT AND SERIES RESONANCES

Fig. 2. Structure of the proposed interdigital coupled hybrid resonator. TABLE II PHYSICAL SIZE FOR THE PROPOSED INTERDIGITAL COUPLED RESONATOR

admittance follows:

, seen from the open side, can be calculated as

(1) where and represent the shunt and series resonant frequencies and are given as (2) and

is given as follows: (3)

The resonance for the whole circuit in Fig. 1 occurs when . Thus, the resonant frequencies can be obtained by and the roots are given as follows: solving

A. Circuit Analysis The proposed hybrid resonant circuit is shown in Fig. 1. It consists of a conventional series resonant circuit and a conventional shunt resonant circuit, which are connected on the open side and shorted to the ground on the other side. The input

(4) From (4), it is easy to know that there will be four roots in , two of which are positive and the rest are total for negative. In practice, only the two positive roots are desired and

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TABLE III EXTRACTED LUMPED PARAMETERS AND CALCULATED RESONANT FREQUENCIES FOR THE RESONATOR SIZE GIVEN IN Table II

physically representing the resonances of the circuit in Fig. 1. Obviously, these two resonances are different from the shunt and series resonance. Each of them is a function of both the shunt and series branches. To investigate the resonant property, a series of numerical solutions to (4) are given in Table I where the values for the capacitors and inductors are given arbitrarily. From Table I, it can be and . This indieasily found that is always smaller than cates that the fundamental resonant frequency of the proposed resonant circuit is always lower than that of the single shunt and series branches. As a result, the resonator with a combined equivalent circuit of shunt and series resonances in Fig. 1 may achieve smaller size as compared to the conventional quarterand half-wave resonator, which usually have equivalent circuits of single shunt and single series resonant circuits. Besides the size reduction, the proposed circuit configuration can introduce a transmission zero in the filter design. Consid. At this ering the input admittance in (1), there is a pole at frequency, the input admittance of the whole circuit becomes infinite, indicating that the circuit is directly shorted to the ground. Thus, there will be no power transmitted between the resonators , and a transmission zero is introduced as at the frequency of a result. The frequency of this transmission zero is equal to the series resonant frequency.

Fig. 3. Comparison of the uniform quarter-wave resonator, SIR, and proposed resonator.

and Since are satisfied:

are the roots to (1), the following conditions

(5) thus,

and

can be obtained as follows:

(6)

B. Circuit Realization To realize the physical structure of the proposed resonant circuit in Fig. 1, an interdigital coupled structure is proposed in Fig. 2. It is composed of two main segments, one of which is series interdigital metal fingers and the other is a shunt metal line. The resonator is shorted to the ground through metallic vias on one side and is left open on the other side. The interdigital fingers contribute to the series capacitance and inductor , which are corresponding to the series resonance in Fig. 1. The shunt metal line contributes to the shunt inductor . The cais presented by the voltage gradient between the pacitance upper conductor and the bottom ground. This capacitance together with the shunt inductor is corresponding to the shunt resonance in Fig. 1. To investigate the resonant properties of the proposed structure, a lumped parameter extraction process is presented here. Firstly, a short section of microstrip line is added to the open side of the proposed resonator as an input port and simulated in an electromagnetic (EM) simulator [Ansoft High Frequency Structure Simulator (HFSS)]. By de-embedding the phase reference plane and subtracting the phase shift introduced by the additional microstrip line, the input impedance and input admittance are calculated. As a result, the resonant frequencies and , where the input admittance is equal to zero, and the frequency of the potential transmission zero where the input impedance is equal to zero can be obtained.

Once , , and are obtained, it can be found from (2) and (3) that the three pairs of product of the four lumped parameters in the equivalent circuit of Fig. 1 are known. As a result, if one of these four parameters is specified, then the other three is speciwill consequently be determined. For instance, if fied, then the other three parameters can be obtained as follows:

(7) To obtain the interdigital capacitance of , an empirical formula can be used as a starting point [24]. The empirical equation is shown as follows: (8) with pF pF

m m

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TABLE IV COMPARISON BETWEEN THE RESONATORS

where , , , and are the length of the interdigital fingers, width of its finger, number of fingers, and height of the substrate, respectively. By using this empirical formula, an initial can be obtained, and then the other three parameters can be calculated sequentially. It should be noted that (8) is only used . To obtain a more accuto obtain an approximated value of rate value, the method given in [25] can be used. To give an example, Table II provides a group of physical parameters of the proposed structure in Fig. 2. Rogers 5880 with relative permittivity of 2.2 and thickness of 0.508 mm is used as the substrate in this paper. The extracted lumped parameters and calculated resonant frequencies are shown in Table III. It can be found that the fundamental resonant frequency of the proposed structure is smaller than either the shunt and series resonances that comprise the circuit, as is expected. Therefore, the size of the proposed resonator should be smaller than the conventional quarter- and half-wave resonators. Fig. 3 gives a comparison of the uniform quarter-wave microstrip resonator and the stepped-impedance resonator (SIR) with the proposed resonator. Table IV gives the specific dimensions of all three resonators at the same frequency of 2.5 GHz. It can be seen from Table IV that the proposed resonator achieves a length reduction by 63% as compared to the uniform quarter-wave resonator, and by 39.2% as compared to the SIR. of the proposed resonator deThe unloaded quality factor teriorates a little as compared to the conventional quarter-wave resonator. This may be due to the narrow metal lines in the interdigital fingers and shunt metal branch, which introduce some in Table IV, which are metal losses. It should noted that given for the purpose of comparison, are obtained by eigenmode simulation in the EM simulator HFSS. These values are will be the ideal cases for the three resonators. In practice, much smaller than these values because of surface roughness of the metal, corrosion, and other factors that are difficult to accurately predict. To improve the unloaded quality factor of the proposed resonator, a low-loss substrate with a high dielectric constant can be used to reduce the dielectric and radiation losses. Meanwhile, the interdigital fingers and shunt metallic lines can be chosen wider to reduce the metal loss. III. FILTER DESIGN A. Second-Order Bandpass Filter To demonstrate the filter application of the proposed hybrid resonant circuit, a second-order bandpass filter schematic diagram is shown in Fig. 4. It consists of two hybrid resonant circuits with J-inverters of -type capacitance networks. Corresponding

Fig. 4. Schematic diagram of the second-order bandpass filter by using the proposed hybrid resonant circuit.

Fig. 5. Structure of the proposed second-order bandpass filter corresponding to the schematic diagram in Fig. 4.

to this schematic diagram, a physical realization structure is proposed in Fig. 5. It is comprised of two hybrid resonators proposed in Section II. The two resonators are arranged side by side, and shorted to the ground through a row of metallic vias on one side. A gap between these two resonators is used to realize the capacitive coupling. Two parallel coupling lines are placed near the open side of the resonators and along the shunt inductor stub to realize the input/output coupling. 50- microstrip lines are tapped to the coupled lines as input and output ports. For filter design, the following parameters are first specified. • Center frequency : 2.7 GHz. • Transmission zero frequency : 4.6 GHz. • Spurious frequency : 7 GHz. • Filter type: second-order Chebyshev bandpass filter With a ripple of 0.1 dB and a fractional bandwidth of 4.5%.

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TABLE V CALCULATED LUMPED-PARAMETERS AND RESONANT FREQUENCIES FOR THE SECOND-ORDER BANDPASS FILTER

As an initial design, is first chosen as 0.17 pF, and then the other parameters can be calculated by using (7), which are pF, nH, and nH. According to [26], the normalized element values of the second-order Chebyshev low-pass filter prototype with a ripple , of 0.1 dB and a fractional bandwidth of 4.5% are , , and . Thus, the values for the J-inverters can be calculated by using (9)

Fig. 6. Filter performance based on the calculated lumped-parameters of the second-order bandpass filter.

(9) where is the fractional bandwidth, and and are the susceptance slope parameter of the resonator, which can be given by (10) where is the image part of the input admittance of the resonator ,which is given in (1). The capacitor values of the -inverters used in Fig. 4 can be obtained by (11)

Thus, all the parameters in Fig. 4 are obtained, and are shown in Table V. The resulted filter performance is shown in Fig. 6. It can be found that the filter specifications given in advance are well satisfied. The center frequency of the filter is much smaller than both resonant frequencies of the shunt and series resonant branches that comprise the resonator. As is expected, a transmission zero is observed at 4.6 GHz. It should be noted that there are two capacitors with negative values in each J-inverter in Fig. 4. To realize this circuit, the negative capacitor can be absorbed by the adjacent resonator. As a result, the practical resonant frequency of the resonator should be chosen higher than that of the theory value of 2.7 GHz. To synthesize the physical size of the proposed filter, a similar method to the parameter extraction in Section II can be employed here. Firstly, (8) is used to obtain an initial size of the . An optimization interdigital fingers with the initial value of process in the EM simulator is then taken to obtain the final size. The capacitive coupling between the resonators is adjusted by the gap size. Since the input/output capacitive coupling requires a relatively large value, the input/output coupling line is chosen as long as possible to achieve as large capacitance as possible,

and then the gap size is adjusted to get suitable input/output coupling capacitance. The final filter size is shown in Table VI. The simulated and measured results of the optimized filter are shown in Fig. 7. Good agreement between the circuit simulation, EM simulation, and measurement results is observed. The measured responses show a fractional bandwidth of 4.2% at a center frequency of 2.72 GHz. The frequency shift and bandwidth variation may be due to the error between the actual and nominal values of the relative dielectric constant. Measured and simulated minimum insertion losses are 2.3 and 1.4 dB, respectively, in the passband. This deviation may be due to fabrication error such as dielectric loss tangent, metal thickness, effective dielectric constant, and so on. In addition, the measured bandwidth is narrower than the simulated one, which is also one of the deviation reasons. The minimum return losses in the passband of both results are nearly 20 dB. Fig. 7(b) depicts the wide span frequency responses of the . As expected, a transmission zero is simulated and measured observed. The simulated transmission zero happens at 4.6 GHz, while the measured transmission zero happens at around 5 GHz. This variation may be due to fabrication error. This transmission zero improves the suppression in the stopband to a large degree. The measured spurious passband happens at approximately 7.1 GHz. A photograph of the fabricated filter is shown in Fig. 8. The size of the filter is only about 10.8 mm 9.62 mm and is about , where is the guided wavelength in the substrate at 2.7 GHz. As compared to the conventional SIR filter with the same impedance ratio as the SIR in Fig. 3, the filter achieves a size reduction of 25%. B. Fourth-Order Bandpass Filter To further verify the application of the proposed resonator in a miniaturized filter, a fourth-order Chebyshev bandpass filter is designed and tested. Fig. 9 shows the layout of the fourth-order Chebyshev filter. Four resonators are arranged side by side in

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TABLE VI PHYSICAL PARAMETERS FOR THE SECOND-ORDER FILTER

Fig. 9. Structure of the proposed fourth-order bandpass filter. TABLE VII PHYSICAL SIZE FOR THE RESONATOR IN THE FOURTH-ORDER FILTER

Fig. 7. (a) Simulated and measured results of the proposed filter. (b) Wide span frequency responses of the simulated and measured S .

while the gap size between the second and third resonators is . indicated by Instead of the filter design method of the lumped-element approach applied in the second-order bandpass filter, the method of coupled resonator circuits is used to design the fourth-order bandpass filter [26]. A prototype of the fourth-order Chebyshev low-pass filter is applied to the design with a ripple of 0.04 dB and fractional bandwidth of 10%. Firstly, the resonator size is chosen to resonate at a center frequency of 2.45 GHz. The inter-stage coupling coefficients and external quality factor is then extracted in an EM simulator [26]. After that, an initial filter is synthesized, and optimization is applied to the initial filter to get a final performance. The calculated inter-stage couand external quality factor according to the pling matrix low-pass prototype is given in (12) as follows:

(12)

Fig. 8. Photograph of the fabricated second-order bandpass filter.

the filter. Instead of coupled lines used as feeding ports in the second-order filter, tapped lines, which are directly connected to the first and fourth resonators, are used as the input/output ports. The position of the tapped line is indicated by . The gap , size between the first and second resonators is indicated by

Table VII shows the physical size of the resonator in the proposed filter, and Fig. 10 shows the extracted inter-stage coupling coefficients and external quality factor with respect to the physical parameters. The simulated and measured performance of the filter is shown in Fig. 11. As can be seen, the measured and simulated results agree well with each other. The simulated result shows a fractional bandwidth of 10% at a center frequency of 2.45 GHz, and the measured result shows a fractional bandwidth of 9.5% at a center frequency of 2.5 GHz. The minimum insertion loss of the simulated results is 1.23 dB, while the minimum insertion loss of the measurement is 2.03 dB. Small variation between simulation and measurement may be due to the fabrication error. As compared to the insertion loss

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Fig. 12. Simulated and measured group delay of the fourth-order bandpass filter. Fig. 10. Extracted inter-stage coupling and the external quality with respect to the corresponding physical parameters. Dashed line: external quality with respect to the tapped line position t. Dotted line: coupling between the second and third resonator with respect to the gap size of g . Solid line: coupling between the first and the second resonator with respect to the gap size of g .

Fig. 13. Photograph of the fourth-order balun filter.

Fig. 12 shows the simulated and measured group delay of , and the variation are less than 1.5 ns in the passband. Fig. 13 shows a photograph of the fourth-order filter. It occupies a small area of 18.3 mm 8.5 mm, which is , where is the guided wavelength in the substrate at the center frequency. As compared to the conventional quarterwave SIR filter, which has the same resonator size as that in Table IV, the proposed filter can have a size reduction of about 39%. IV. BALUN FILTER DESIGN A. Basic Concept Fig. 11. Simulated and measured results of the proposed filter. (a) Narrow frequency span responses. (b) Wide frequency span responses of the simulated and measured S .

of the second-order filter in Section III-A, the insertion loss of the fourth-order filter is even smaller. This is because that the metallic interdigital line of 0.5 mm is used in this design, while 0.3-mm lines are used in the second-order filter. A wider metallic line will reduce the metal loss. Meanwhile, the wider passband of the fourth-order filter will also give a smaller insertion loss. The first spurious passband appears around 7 GHz, and a transmission zero is observed around 3.3 GHz. This transmission zero is due to the same reason as given in Section III-A.

In [18] and [19], it was stated that a three-port balun can be obtained from the symmetric four-port structure with one of the ports being open. The -matrix of such a three-port balun can be obtained by odd/even-mode analysis in terms of the respective odd/even-mode reflection and transmission coefficients and ), which are illustrated in Fig. 14. The -pa( , , rameters of the three-port balun can be expressed as (13) (14) (15)

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Fig. 14. Schematic diagram of the integrated three-port balun filter.

To obtain a balanced output signal , as well as a good input match , a feasible solution can be as follows: (16)

Fig. 15. Structure of the second-order bandpass balun filter in which g = 0:05 mm, g = 0:5 mm, w = 0:3 mm, l = 10 mm, w = 1:5 mm, l = 3:6 mm, and s = 0:6 mm.

(17) These equations impose the requirements on the three-port balun, which is transformed from a symmetric four-port network with one of the ports being open. Specifically, to obtain a perfectly differential signaling with equal amplitude, a zero transmission should be achieved in the even-mode half-circuit, as is suggested in (16). Besides, to obtain a perfect input match at the unbalanced input port, the input impedance of the corresponding odd-mode half-circuit should be twice the source terminated impedance, as is suggested in (17). By constraints (16) and (17), a well-performed balun can be achieved. However, the filtering characteristic cannot be controlled by only (16) and (17). To achieve a filter characteristic based on the balun, additional constraints must be satisfied. Substituting (16) into (14) and (15), the -parameters of the three-port balun can be simplified as (18) From (18), it can be found that and is proportional . It implies that the transmission characteristics ( and ) of the three-port balun are similar to the transmission characteristic of the odd-mode half-circuit. Specifically, when the odd-mode half-circuit behaves as a bandpass filter, and constraint (17) is satisfied in the passband, (18) becomes to

(19) In the stopband of the filter where nearly 1, (18) becomes

is nearly 0 and

is

(20) From (19), it can be found that the transmission coefficient of the three-port balun is just a scale of the transmission coefficient of the odd-mode half-circuit in the passband. From (20), it can be found that the three-port balun also has a zero transmission in the stopband of the odd-mode half-circuit. Thus, it is possible that a balun filter can be built from the three-port balun, when the odd-mode half-circuit behaves as a bandpass filter.

Fig. 16. Transmission properties of even- and odd-mode half-circuits.

B. Second-Order Balun Bandpass Filter The structure of the proposed second-order balun bandpass filter is shown in Fig. 15. It is constructed by simply making a mirror replication of the second-order bandpass filter proposed in Section III along the shorted side, and at the same time taking away the vias and shorted lines in the middle. Port 1 behaves as the unbalanced port, while ports 2 and 3 are used as the balanced ports, and port 4 is left open. This structure can be viewed as a symmetric four-port structure with a symmetric line in the middle. The half-circuit is analyzed under odd- and even-mode excitation. In the odd-mode excitation, a virtual ground is formed along the symmetric plane. The end side of the resonators in the symmetric line will be shorted to ground through the virtual ground plane. These resonators can be considered the same as the hybrid resonators that have metallic vias to create a short circuit to the ground, which were discussed in detail in Section II. Thus, the odd-mode half-circuit of the proposed structure will behave as the same bandpass filter, as discussed in Section III. Fig. 16 shows the simulated of the odd-mode half-circuit, and a bandpass performance is observed in odd-mode excitation. Under an even-mode excitation, a virtual open is formed in the symmetrical line. In this case, the resonators have open boundaries on both end sides. Hence, they are no longer the proposed hybrid resonators given in Section II. The resonators will actually behave as a conventional half-wavelength

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Fig. 18. Measured phase and amplitude imbalance of the second-order balun bandpass filter.

Fig. 17. Simulated and measured results of the second-order balun bandpass filter.

resonator, and the fundamental resonant frequency of these half-wavelength resonators is much higher than the hybrid resonant frequency in odd-mode excitation. Thus, a stopband will be formed in the even-mode excitation in the frequency range where a passband is formed in odd-mode excitation. Fig. 16 shows the simulated -parameters under the even-mode excitation. It can be seen that it is a stopband in the whole frequency range from 1 to 5 GHz. Based on the discussion above, the proposed structure has a nearly zero transmission in the even-mode half-circuit, which means a balanced output can be achieved, as is suggested in (16). At the same time, the proposed structure achieves a bandpass property in the odd-mode half-circuit, which means a filter characteristics can be obtained, as is suggested in (19) and (20). To obtain a perfect input match at the unbalanced input port, (17) still needs to be satisfied. In the proposed structure, the 50microstrip lines are used as the input/output port and 50- termination impedance is used to test the structure. Thus, the constraint (17) implies the input impedance of port 1 of the balun filter should be twice the input impedance of ports 2 and 3. To achieve these different input impedance values, the coupling gap between port 1 and the adjacent resonator is chosen differently from the one between ports 2 and 3 and the adjacent resonators, as shown in Fig. 15. Optimization in HFSS is employed to obtain optimal match performance. The optimized physical size is listed in Fig. 15. It should be noted that the physical size of the hybrid resonators in the balun filter is the same as in Table VI. The simulated and measured results are shown in Fig. 17. Good agreement between simulation and measurement are observed. The center frequency at about 2.79 GHz shifts slightly higher than that of the second-order bandpass filter proposed in Section III. This shift is due to the vias that are removed from the

Fig. 19. Measured wide span frequency response of the second-order balun filter circuit.

hybrid resonators in the balun filter. For the second-order filter proposed in Section III, the vias in the short side will contribute to the shunt inductance in addition to the shunt metal line of the resonator. For the balun filter, the vias are removed and a virtual ground is utilized in the odd-mode half-circuit. As a result, the resonant frequency of the resonator in the balun filter with a virtual ground will be a little higher than that of the resonator with real metallic vias to ground in the second-order bandpass filter proposed in Section III. and in the The simulated minimum insertion losses of passband are around (3 2) dB. It should be noted that 3 dB here is due to the equal power division to ports 2 and 3, and 2 dB is the actual insertion loss of filter. The measured results are around (3 2.6) dB. The difference between the simulated and measured results may be due to the fabrication error. The measured amplitude and phase imbalance between and in the passband is shown in Fig. 18. As can be observed, good amplitude and phase balances are achieved. The amplitude imbalance is less than 1 dB and the phase imbalance is less than 1 in the passband. The measured wide span frequency response is shown in Fig. 19. There are one transmission zero observed in and two transmission zeros observed in . These transmission zeros are due to the cancellation of the transmission of the even and odd modes. By making (14) and (15) equal to 0, it can be found that the transmission zeros of occur when and , and the transmission zeros of

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Fig. 20. Extracted even- and odd-mode responses.

Fig. 22. Structure of the proposed fourth-order balun bandpass filter.

C. Fourth-Order Balun Bandpass Filter

Fig. 21. Photograph of the fabricated balun filter.

occur when and . In the stopband of the balun filter, both the odd and even modes are suppressed; thus, it is possible that the transmission coefficients of the even and odd modes can be equal. When they are equal and in phase, , and when there will be transmission zeros appearing in they are equal and out of phase, there will be transmission zeros appearing in . Fig. 20 shows the even- and odd-mode transmission coefficients, which are extracted from the measured three-port responses according to formulas proposed in [22] and [27]. Comparing Figs. 19 and 20, one can easily find that the transmission zeros of and occur at the frequencies where the even-mode transmission response intersects with the odd-mode transmission response. At theses intersection points, the transmission coefficient of the even mode is equal to that of the odd mode, and thus, the transmission zeros occur in or . It should be noted that there is a little difference of the evenand odd-mode responses between Figs. 16 and 20. This is because of not taking into account the effect of the open-terminated port 4 for analysis convenience in Fig. 16, while it is actually based on the three-port network in Fig. 20. The photograph of the fabricated balun filter is shown in Fig. 21. It occupies a small area of 20.09 mm 10.96 mm, which is only . It should be noted that due to the symmetrical structure and the virtual ground formed along the symmetrical line in odd-mode excitation, the balun filter is via free and can be fabricated easily in conventional microwave printed circuit board technology.

To further verify the application to the balun filter by using the proposed resonator, a fourth-order balun bandpass filter is designed. The structure of the fourth-order balun filter is shown in Fig. 22. It is also constructed by simply making a mirror replication of the fourth-order bandpass filter proposed in Section III along the shorted side, and at the same time taking away the vias in the middle. Port 1 behaves as the unbalanced port while ports 2 and 3 are used as the balanced ports. Port 4 is left open and can be removed. Since the structure is symmetrical, it can be analyzed by the even/odd-mode method that is the same as the second-order balun bandpass filter. It should be noted that the circular bends at ports 2 and 3 are added only for measurement convenience since the distance between ports 2 and 3 is too small to solder subminiature A (SMA) connectors. In odd-mode excitation, a virtual ground is formed in the symmetrical line. Thus, the odd-mode half-circuit will behave as a bandpass filter, which is similar to the fourth-order bandpass filter in Section III. , the input To satisfy the balun requirement of impedance at port 1 should be twice the source terminated impedance, which is usually 50 . A microstrip line with a characteristic impedance of 100 is chosen as input at port 1, while the microstrip lines at ports 2 and 3 are still kept at 50 . The same design process with the fourth-order bandpass in Section III is then applied to obtain a good bandpass performance in the odd-mode half-circuit. It should be noted that since the impedance of port 1 is changed as compared to the fourth-order bandpass filter in Section III, the position of the tapped line needs to be carefully readjusted to make the external factor at port 1 match to 100 . In even-mode excitation, a virtual open is formed in the symmetrical line, and the resonators that consists of the balun filter are no longer the proposed hybrid resonators. Instead, they act as half-wave resonators, and the passband will be much higher than that of the bandpass filter in the odd-mode half-circuit. Fig. 23 of the structure in odd- and even-mode excitations. shows It can be seen that a bandpass performance in odd-mode excitation is observed while a bandstop performance in even-mode excitation is observed.

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Fig. 23. Transmission properties of even- and odd-mode half-circuits.

Fig. 25. Input impedance of the even-mode half-circuit versus the elec: ,Z , tric length of the tapped input line when Z  : rad,  : rad, and  : rad.

= 0 3264

= 0 459

= 94 2

= 0 47

= 100

Fig. 24. Equivalent circuit of the tapped input section in even-mode half-circuit.

To satisfy , the input impedance of the even-mode needs to be 0. Considering the equivalent circuit half-circuit of tapped input resonator in the even-mode half-circuit shown in Fig. 24, the input impedance can be given in (21), shown at and are the characterthe bottom of this page, in which istic impedances of the tapped input line and interdigital line are the electric length in the resonator, and , , , and of the different microstrip sections. As can be seen from (21), is a function of the length of the 100- input tapped line. by adjusting the length of the Thus, one can achieve input tapped line. Fig. 25 shows the even-mode input impedances with a different length of the input tapped line. The length of the tapped line can be approximately chosen from this figure . It should be noted that the bandpass perforto make mance of the odd-mode half-circuit will not be influenced by adjusting the length of the input tapped. Thus, it is possible to , while . make After all of the requirement of the balun filter is specified, a initial balun can be synthesized, and then a optimization process is applied in the EM simulator to get optimized performance. A fourth-order balun filter with a center frequency of 2.7 GHz is designed, fabricated, and tested. The simulated and measured

Fig. 26. Frequency responses of the fourth-order balun filter.

results are shown in Fig. 26 with all three ports terminated to 50- loads. Good agreement between the measurement and simulation is observed. The measured center frequency is at 2.75 GHz, which shifts slightly higher as compared to the simulated one. The measured 3-dB fractional bandwidth is 10.9%, and the minimum measured insertion loss in the passband is 1.43) dB in each pass path. The center frequency also (3 shifts slightly higher as compared to the fourth-order filter bandpass filter in Section III. This is due to the same reason as given in the second-order balun bandpass filter in Section IV-B. On the other hand, the actual insertion loss here is smaller than that of the fourth-order bandpass filter in Section III, and is partially due to the fact that the balun filter here is via free, while the shorted vias in the bandpass filter in Section III contribute some losses.

(21)

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Fig. 30. Photograph of the fabricated fourth-order balun filter. Fig. 27. Measured wide frequency span responses of the fourth-order balun filter.

testing), which is , and has a size reduction of about 29% and 45%, as compared to the two balun filter proposed in [23]. V. CONCLUSION

Fig. 28. Measured amplitude and phase imbalance of the fourth-order balun bandpass filter.

In this paper, a hybrid resonant circuit has been proposed. Based on the circuit, a compact interdigital coupled microstrip resonator has been proposed. This resonator achieves much smaller size as compared to the conventional quarter- and half-wave resonators. Meanwhile, it has the intrinsic capability of introducing a transmission zero in the filter design. Based on this compact proposed resonator, a second-order bandpass and a fourth-order filter with a small size of were built. bandpass filter with a small size of Both filters exhibit good performance, as well as small size. Beside the bandpass filters, a second-order balun bandpass and a fourth-order balun filter with a size of were built. bandpass filter with a size of Both balun filters achieve good bandpass performance and the amplitude and phase imbalance are all less than 1 dB and 1 in the passband, respectively. In addition, the balun filters are via free and can be easily fabricated in a conventional printed circuit board. It is verified that the proposed resonator can be well used in miniaturized filters and balun filters. REFERENCES

Fig. 29. Measured group delay of S pass filter.

and S

of the fourth-order balun band-

The measured wide frequency span responses are shown in Fig. 27. Good suppression in the stopband is observed. Some transmission zeros are observed, and this is caused by the same reason discussed in the second-order balun bandpass filter. The measured amplitude and phase differences between ports 2 and 3 are shown in Fig. 28. Excellent amplitude and phase imbalances in the passband are obtained, where the amplitude difference is less than 0.2 dB and the phase imbalance is less and , which are than 0.8 . The measured group delay of almost the same in the whole passband, is shown in Fig. 29. The variation of the group delay in the passband is less than 1.5 ns. A photograph of the fabricated fourth-order balun bandpass filter is shown in Fig. 30. It only occupies a small area of 15.2 mm (not including the extended ports for 14.9 mm

[1] C. H. Liang and C. Y. Chang, “Compact wideband bandpass filters using stepped-impedance resonators and interdigital coupling structures,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 9, pp. 551–553, Sep. 2009. [2] C. H. Liang, C. H. Chen, and C. Y. Chang, “Fabrication-tolerant microstrip quarter-wave stepped-impedance resonator filter,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 5, pp. 1163–1172, May 2009. [3] R. J. Mao, X. H. Tang, L. Wang, and G. H. Du, “Miniaturized hexagonal stepped-impedance resonators and their applications to filter,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 440–448, Feb. 2008. [4] T. N. Kuo, S. C. Lin, C. H. Wang, and C. H. Chen, “Compact bandpass filters based on dual-plane microstrip/coplanar waveguide structure with quarter-wave length resoantors,” IEEE Trans. Microw. Theory Tech., vol. MTT-17, no. 3, pp. 178–180, Mar. 2007. [5] C. F. Chen, T. Y. Huang, and R. B. Wu, “Novel compact net-type resonators and their applications to microstrip bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 755–762, Feb. 2006. [6] A. Djaiz and T. A. Denidni, “Compact bandpass filters based on dual-plane microstrip/coplanar waveguide structure with quarter-wave length resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 1929–1936, May. 2006. [7] R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 1–10, Jan. 2003. [8] J. Lee and K. Sarabandi, “Synthesizing microwave resonator filters,” Microw. Mag., vol. 10, no. 1, pp. 57–65, Feb. 2009.

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[9] C. W. Tang and S. F. You, “Design methodologies of LTCC bandpass filters, diplexer, and triplexer with transmission zeros,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 717–723, Feb. 2006. [10] M. M. Mendoza, J. S. G. Diaz, and D. C. Rebenaque, “Design of bandpass transversal filters employing a novel hybrid structure,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2670–2678, Dec. 2007. [11] M. Bekheit, S. Amari, and W. Menzel, “Modeling and optimization of compact microwave bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 420–430, Feb. 2008. [12] S. Amari and G. Macchiarella, “Synthesis of inline filters with arbitrarily placed attenuation poles by using nonresonating nodes,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 10, pp. 3075–3081, Oct. 2005. [13] J. C. Lu, C. K. Liao, and C. Y. Chang, “Microstrip parallel-coupled filters with cascade trisection and quadruplet,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 9, pp. 2101–2111, Sep. 2008. [14] C. L. Hsu and J. T. Kuo, “Design of cross-coupled quarter-wave SIR filters with plural transmission zeros,” in IEEE MTT-S Int Microw. Symp. Dig., 2006, pp. 1205–1208. [15] Y. H. Jeng, S. F. Chang, and H. K. Lin, “A high stopband-rejection LTCC filter with multiple transmission zeros,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 633–6381, Feb. 2006. [16] L. K. Yeung and K. L. Wu, “An integrated RF balanced-filter with enhanced rejection characteristics,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 713–716. [17] E. Y. Jung and H. Y. Hwang, “A balun-BPF using a dual mode ring resonator,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 9, pp. 652–654, Sep. 2007. [18] Y. C. Leong, K. S. Ang, and C. H. Lee, “A derivation of a class of 3-port baluns from symmetrical 4-port networks,” in IEEE MTT-S Int Microw. Symp. Dig., 2002, pp. 1165–1168. [19] K. S. Ang, Y. C. Leong, and C. H. Lee, “Analysis and design of miniaturized lumped-distributed impedance-transforming baluns,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 1009–10179, Mar. 2003. [20] L. K. Yeung and K. L. Wu, “A dual-band coupled-line balun filter,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 2406–2411, Nov. 2007. [21] C. H. Wu, C. H. Wang, and C. H. Chen, “Balanced coupled-resonator bandpass filters using multisection resonators for common-mode suppression and stopband extension,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 8, pp. 1756–1763, Aug. 2007. [22] C. H. Wu, C. H. Wang, and C. H. Chen, “Novel balance coupled-line bandpass filters with common-mode noise suppression,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 2, pp. 287–295, Feb. 2007. [23] C. H. Wu, C. H. Wang, S. Y. Chen, and C. H. Chen, “Balanced-tounbalanced bandpass filters and the antenna application,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2474–2482, Nov. 2008. [24] I. Bahl, Lumped Elements for RF and Microwave Circuits. Boston, MA: Artech House, 2003, pp. 230–235. [25] C. Caloz and T. Itoh, Electromagnetic Metamaterials. New York: Wiley, 2005, pp. 130–134. [26] J. S. Hong and M. J. Lancaster, Microstrip Filter for RF/Microwave Applications. New York: Wiley, 2001, pp. 235–272. [27] D. E. Bockelman and W. R. Eisenstant, “Combiled differential and common-mode scattering parameters: Theory and simulation,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 7, pp. 1530–1539, Jul. 1995.

Tao Yang (S’09) received the B. Eng. degree from the University of Electronic Science and Technology of China, Chengdu, China, in 2005, and is currently working toward the Ph.D. degree at the University of Electronic Science and Technology of China. Since September 2008, he has been a Visiting Student with the University of California at Los Angeles (UCLA). His research is concerned with microwave metamaterials, microwave and millimeter-wave circuit and system design, microwave and millimeterwave application-based on LTCC.

Masaya Tamura (M’07) received the B.E. and M.E. degrees in electrical and electronic engineering from Okayama University, Okayama, Japan, in 2001 and 2003, respectively. In 2003, he joined the Panasonic Electronic Devices Corporation Ltd., Osaka, Japan, where he has been engaged in research and development on microwave components including lightwave, especially microwave filters, metamaterials, and plasmonics. Mr. Tamura is a member of the Institute of Electrical, Information and Communication Engineers (IEICE), Japan. He was the recipient of the IEEE Hiroshima Section Best Research Award presented at the 4th IEEE Hiroshima Student Symposium.

Tatsuo Itoh (S’69–M’69–SM’74–F’82–LF’06) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, in 1969. From September 1966 to April 1976, he was with the Electrical Engineering Department, University of Illinois at Urbana-Champaign. From April 1976 to August 1977, he was a Senior Research Engineer with the Radio Physics Laboratory, SRI International, Menlo Park, CA. From August 1977 to June 1978, he was an Associate Professor with the University of Kentucky, Lexington. In July 1978, he joined the faculty of The University of Texas at Austin, where he became a Professor of electrical engineering in 1981 and Director of the Electrical Engineering Research Laboratory in 1984. During Summer 1979, he was a Guest Researcher with AEG-Telefunken, Ulm, Germany. In September 1983, he was selected to hold the Hayden Head Centennial Professorship of Engineering at The University of Texas at Austin. In September 1984, he became Associate Chairman for Research and Planning of the Electrical and Computer Engineering Department, The University of Texas at Austin. In January 1991, he joined the University of California at Los Angeles (UCLA), as Professor of electrical engineering and Holder of the TRW Endowed Chair in Microwave and Millimeter Wave Electronics (currently the Northrop Grumman Endowed Chair). He was an Honorary Visiting Professor with the Nanjing Institute of Technology, Nanjing, China, and with the Japan Defense Academy. In April 1994, he became an Adjunct Research Officer with the Communications Research Laboratory, Ministry of Post and Telecommunication, Tokyo, Japan. He was a Visiting Professor with The University of Leeds, Leeds, U.K. He has authored or coauthored 375 journal publications and 775 refereed conference presentations. He authored 43 books/book chapters in the area of microwaves, millimeter waves, antennas and numerical electromagnetics. He has generated 70 Ph.D. students. Dr. Itoh was elected to the National Academy of Engineering in 2003 as a member. He is a member of the Institute of Electronics and Communication Engineers of Japan, and Commissions B and D of USNC/URSI. He was the editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES (1983–1985). He serves on the Administrative Committee of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He was vice president of the IEEE MTT-S in 1989 and president in 1990. He was the editor-in-chief of the IEEE MICROWAVE AND GUIDED WAVE LETTERS (1991–1994). He became an Honorary Life Member of the IEEE MTT-S (1994). He was the chairman of USNC/URSI Commission D (1988–1990) and chairman of Commission D of the International URSI (1993–1996). He was chair of the Long Range Planning Committee, URSI. He serves on advisory boards and committees of a number of organizations. He was a Distinguished Microwave Lecturer on Microwave Applications of Metamaterial Structures of the IEEE MTT-S (2004–2006). He was the recipient of numerous awards including the 1998 Shida Award presented by the Japanese Ministry of Post and Telecommunications, the 1998 Japan Microwave Prize, the 2000 IEEE Third Millennium Medal, and the 2000 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Distinguished Educator Award.

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Radio-Optical Dual-Mode Communication Modules Integrated With Planar Antennas Anatoliy O. Boryssenko, Member, IEEE, Jun Liao, Member, IEEE, Juan Zeng, Member, IEEE, Shengling Deng, Member, IEEE, Valencia M. Joyner, Member, IEEE, and Z. Rena Huang, Member, IEEE

Abstract—This paper presents new results on integrated devices for radio and free-space optical dual-mode communication. Two novel hybrid packaging schemes using two different microwave printed antenna designs are presented for the integration of radio-optical front-end circuits on a planar compact printed circuit board with shared electrical and structural components. Full-wave electromagnetic (EM) simulations are presented for antenna optimization to minimize EM interference between the radio and optical circuits. A hybrid radio-optical package design is developed, prototyped, and experimentally studied using a modified quasi-Yagi antenna with split directors to form pads for opto-electronic device integration. Dual-mode link connectivity is investigated in simulations and experiments. A data rate of 2.5 Gb/s is demonstrated for the optical channel despite 15–20-dB signal coupling between the optical and microwave circuits. Index Terms—Antenna, dual-mode wireless communication, integration, optical receiver, optical transmitter, packaging designs.

I. INTRODUCTION HERE IS an increasing interest in hybrid communication systems to combine the advantages of radio and optical free-space signaling for future communication and network technologies with increased bandwidth, reduced power consumption and cost, high adaptability to dynamic operational environment, and other promising features [1]–[3]. Dual-modality imaging incorporating microwave and optical sensors also represents a practical interest for biomedical studies including early breast cancer detection [4]. To reach such goals, new integration and packaging techniques must be advanced to account for several orders of dimensional discrepancy between antenna geometries, measured typically in millimeters at microwaves, and characteristic sub-millimeter dimensions of the active optical components. Several hybrid

T

Manuscript received April 15, 2009; revised September 29, 2009. First published January 19, 2010; current version published February 12, 2010. This work was supported in part by the Rensselaer Polytechnic Institute under an Internal Seed Grant, by the National Science Foundation (NSF) under Grant ECCS-0823946, and by the Collaborative Biomedical Research (CBR) Program Grant, University of Massachusetts, Amherst. A. O. Boryssenko is with the Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003 USA (e-mail:[email protected]). J. Liao, S. Deng, and Z. R. Huang are with the Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA (e-mail: [email protected]; [email protected]; [email protected]). J. Zeng and V. M. Joyner are with the Department of Electrical and Computer Engineering, Tufts University, Medford, MA 02155 USA (e-mail: juan. [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038441

Fig. 1. Two printed antennas used for hybrid radio-optical packaging studies. (a) Quasi-Yagi. (b) Microstrip patch. All dimensions are in millimeters.

integration approaches were demonstrated to solve this challenging problem by employing single-module and single-chip designs [5]–[7]. Here we report results of ongoing multiuniversity research efforts in the design, development, and testing of miniaturized radio-optical transceiver modules for combined radio-optical wireless communications. The research outcome will accelerate deployment of sensor networks by providing agile and reliable connectivity with long standby time and low manufacturing cost. Two hybrid radio-optical packaging schemes are considered, which are based on two versions of the microwave antennas: quasi-Yagi antenna [1], [8], [10] and microstrip patch antenna [9], as shown with their major dimensions in Fig. 1. These designs are tuned to operate around 11 GHz for a narrowband radio link and several gigabit per second data rates for an optical link. Both designs are developed by taking advantage of the dimensional difference between the microwave antenna and optical front-end elements. Specifically, the optical elements share some physical space with microwave circuits to minimize the overall packaging area/volume and align directions of optical and microwave radiation. Both designs with quasi-Yagi antenna [see Fig. 1(a)], and microstrip patch antenna [see Fig. 1(b)], are first analyzed in numerical simulations and then designed, prototyped, and experimentally tested. Coupling from the microwave circuits to the optical transmitter and receiver front-ends is important in the view of

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signal transmission integrity issues due to shared on-board space. Unlike optical modulators that are controlled by electric signals such as Mach–Zehnder modulators [14], the research described here is aiming to create a module to support two separate wireless channels: radio and optical free-space links. It is predictable that the electric signal/power is coupled into the optical subsystem because of packaging in a very tight space with shared structural components. This phenomenon is observed through numerical simulation, namely, commercial full-wave solvers including Ansoft High Frequency Structure Simulator (HFSS) and CST Microwave Studio. By careful design, as shown in this paper, the mutual coupling between the microwave and optical front-end circuits is minimized. It is especially lowered in the case of the microstrip patch assembly. The predicted impact of mutual coupling and link performance degradation are in a good agreement with measured results. The tested radio-optical modules demonstrate a data rate of 2.5 Gb/s in the duplex dual-channel communication configuration regardless of noticeable 15–20-dB coupling between radio and optical channels in the case of the quasi-Yagi antenna assembly. The assembly and testing of optical elements with both the antennas are experimentally demonstrated. The discussion and comparative analysis of optical elements co-integrated with a microstrip patch antenna is built upon previous work presented in [1] and a comparison will be presented in this paper. II. RADIO-OPTICAL HYBRID MODULES WITH QUASI-YAGI ANTENNA A quasi-Yagi antenna [see Fig. 1(a)] is first considered in this study for the hybrid radio-optical packaging because of the convenience in integration of two separate microwave and optical boards at the initial experimental phase [9]. The quasi-Yagi antenna board is printed on an RT/Duriod 6010 substrate with a thickness of 0.635 mm and relative permittivity of 10.2. This antenna is inherently reasonably broadband and exhibits high front-to-end ratio radiation along the antenna axis [7]. For the purpose of this study, the quasi-Yagi antenna design is modified by using split directors to provide options for packaging with both optical photodetectors (optical receiver) and laser diodes (optical transmitter). In addition, the antenna direction of the maximum radiation is altered from the original direction along the antenna axis to the direction that is normal to the antenna board to align the signal propagation directions of optical and microwave radiation. This beam alteration is achieved by backing the antenna board by a metal reflector (ground) at the bottom. This type of design adjustment exhibits a certain degradation of radiation performance [11], which is not critical for the proof-of-concept initial studies, while enabling faster prototyping and testing. In particular, the realized antenna gain of the modified quasi-Yagi is just 0.5 dBi against 4–5 dBi for the same antenna with regular radiation direction, as predicted in HFSS simulations. The HFSS model of the antenna used for this study is shown in Fig. 2. In the model of this package, several optical ports are assigned between external tips of the split directors and the system ground at the board bottom [see Fig. 2(a)] of the

Fig. 2. HFSS computational model of the quasi-Yagi antenna with split directors used concurrently as pads to mount optical diodes. (a) Model overview. (b) Magnified portion highlighting connections to optical circuitry through four assigned optical ports to model mutual coupling between the antenna and optical ports (from [1]).

quasi-Yagi antenna. Bondwires are used for the optical components placed on the pads (directors) to simulate signal return path with optical components added [see Fig. 2(b)]. Full-wave electromagnetic (EM) simulations using either HFSS or CST enables evaluation of the major electrical characteristics of this package, as illustrated in Fig. 3, for some representative component of the 5 5 terminal scattering matrix. The modified quasi-Yagi antenna demonstrates good matching to the feed line according to Fig. 3. This is achieved due to 50- loads applied at the optical ports that, as expected, contribute to the lowering of antenna radiation efficiency from one side, but supports antenna matching on the opposite side at an acceptable level by compensating the effect of the bottom ground plane. This ground plane is used to alter the beam direction as above mentioned. Apparently, EM coupling appears in this layout because the same structural elements are shared as the antenna directors and optical circuit pads. The magnitude of computed coupling between the antenna port (#1) and, e.g., optical ports #2–3 is shown in Fig. 2(b) with respect to the 50- reference impedance. Specifically, the coupling approaches 15–20 dB around the antenna resonance frequency around 11 GHz for the layouts in Fig. 2. This coupling seems negligible in the case of optical transmitters due to the large drive currents measured typically about 100 mA, but might exhibit a perceptible effect in the optical receiver, where weak photocurrent signals of a few A are amplified, as further revealed.

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2

Fig. 3. HFSS predicted component of the 5 5 scattering matrix in decibels including return loss for the antenna port (S 11) and coupling between the antenna port and two optical ports (S 21 and S 31) with slight asymmetry appearing due to difference in shape and position of the bondwires [see Fig. 2(b)]. Optical ports are terminated to 50 .

Fig. 5. CST models of the radio-optical assembly based on microstrip patch 2.54 cm substrate (Duroid: t = 1:5 mm,  = 2:2). antenna. (a) 2.54 (b) Magnified portion highlighting pads for optical component and return signal path formed through vias. The antenna is fed through the antenna radio port and two optical ports #1 and #2 provide connections to optical transmit/receive front-ends.

2

Fig. 4. Measured E - and H -plane antenna radiation patterns (90 reference direction corresponds to the Z -axis in Fig. 2).

The - and -plane sections of the antenna radiation pattern measured using the 1.5 1.5 m near-field NSI scanner are illustrated in Fig. 4, showing good antenna directivity. III. RADIO-OPTICAL HYBRID MODULES WITH MICROSTRIP PATCH ANTENNA The microstrip patch antenna [see Fig. 1(b)] is analyzed in full-wave CST simulations [see Fig. 5(a)] as an alternative design solution with respect to the quasi-Yagi antenna to improve the electrical performance of the latter. In particular, the complete radio-optical design requires a single dielectric substrate and two layers of conductors on both faces of the substrate. Furthermore, this antenna structure conserves surface area for placement of all conductor traces and circuits for radio and optical transmission. In addition, a quasi-Yagi antenna is end-fire, while the laser diodes are surface emitters, thus there is an angle between the maximum radiation directions and the optical axes of the optical elements. The beam direction alteration leads to the antenna efficiency loss as demonstrated and it is avoided in the microstrip design. As a result of numerical studies, the optimized microstrip patch antenna structure [see Fig. 5(a)] occupies a small surface area of 2.54 2.54 cm . The optical circuits are represented by signal traces with dummy resistors to

model the equivalent impedance of the optical components. To conserve area, the optical component pads are located in rectangular notches on opposite sides of the patch conductor. The mutual coupling is expected to be low because the lowest TEM resonance patch mode has a zero field in the area where the optical components will be placed [8]. The two optical ports, one for the transmitter and the other for the receiver, include two microstrip conductor sections. The optical return signal path is supported by the same bottom ground as for the microwave antenna by using the through vias [see Fig. 5(b)]. Using the same ground in a single layer for both radio and optical circuits enables less noise and interference. In a practical design, the dummy component of the optical circuits will be replaced by corresponding optical chips, as further shown in Section IV. The scattering matrix of the radio-optical circuit layout in Fig. 5(b) is numerically predicted in CST simulations and illustrated in Fig. 6. The antenna can be matched to the required operational frequency, e.g., 11 GHz, with very low return loss while providing high realized gain in the range 6–7 dBi shown in the CST simulations. Mutual coupling is nearly 10 dB lower at the antenna resonance frequency compared to this feature of the quasi-Yagi antenna (Fig. 3) that eventually improves signal integrity for this design. The simulated antenna radiation pattern at 11 GHz is shown in Fig. 7 and exhibits high realized gain and radiation efficiency. In particular, the predicted realized gain is about 6.5 dBi compared to just 0.5 dBi simulated for the quasi-Yagi antenna design (Fig. 2) with optical ports loaded in both cases with equivalent resistive loads to model the presence of optical components.

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Fig. 8. Photographs of fabricated radio-optical modules packaged with the quasi-Yagi antenna. (a) Transmitter. (b) Receiver (from [1]).

2

Fig. 6. CST predicted component of the 3 3 scattering matrix in decibels illustrated for return loss at the antenna port (S 11) and coupling between the antenna port and an optical port (S 21 and the same for S 31 due to structural symmetry. Dummy 50- resistors are used to mimic the effect of the optical components.

Fig. 9. Photographs of details to mount the optical die components on the pads shared with the quasi-Yagi antenna. (a) VCSEL on the antenna pad to construct a transmitting radio-optical. (b) p-i-n on the antenna pad to construct the receiver board on PCB (from [1]).

Fig. 7. CST predicted 3-D antenna radiation pattern of the patch antenna at 11 GHz normalized in terms of realized gain with total radiation efficiency of 95% using dummy 50- resistors to simulate the presence of the optical components on pads in shared physical space.

IV. PROTOTYPES OF RADIO-OPTICAL HYBRID TRANSMIT/RECEIVE MODULES Both the design concepts are prototyped for experimental studies including the transmitter and receiver modules for the quasi-Yagi antenna [see Fig. 1(a)] and the receiver module for the microstrip patch antennas [see Fig. 1(b)]. A rationale to consider only the receiver in the second antenna case relies on the fact that the mutual coupling between the optical and radio front-ends affects the hybrid receivers without a notable impact on the hybrid transmitters, as demonstrated in Section VI. A. Transmitter and Receiver Hybrid Modules With Quasi-Yagi Antenna The radio-optical dual mode transmitter and receiver modules with the quasi-Yagi antenna are built on a four-layer FR4 printed circuit board (PCB) and shown in Fig. 8. For free-space optical processing, the use of vertical-cavity surface-emitting

laser (VCSEL) and p-i-n diode devices is attractive for future low-cost hybrid/flip-chip packaging with active silicon complementary metal–oxide semiconductor (CMOS) electronic circuits [12], [13]. CMOS technology enables high levels of integration combining sensitive front-end circuits with digital processing circuits on the same die. For this preliminary study, hybrid integration is achieved by wirebonding bare die opto-electronic devices to commercial optical transmitter and receiver circuits. On the transmitter board, a commercial high-speed current switch laser diode driver (Micrel SY88922V) is employed to drive a bare die VCSEL (Optowell SM85-2N001). The VCSEL is attached to the director of the transmitting quasi-Yagi antenna. On the receiver board, a high-speed transimpedance amplifier chip (MAX3864) is mounted to amplify the single-ended photocurrent signal from a p-i-n diode (Optowell SP85-3N001). The p-i-n is assembled to the director of the receiving quasi-Yagi antenna. The VCSEL on the transmitter board is fabricated on a gallium–arsenide (GaAs) substrate with a peak emission of 2.5 mW nm. The die size of the VCSEL is 300 300 m . at The GaAs p-i-n on the receiver board has a responsivity of 0.6 A/W. The die size of the p-i-n is 250 250 m . The N contacts of both the VCSEL and the p-i-n are attached to antenna director pads by conductive epoxy adhesives (Resinlab SEC 1233). The P contacts of the VCSEL and p-i-n are wirebonded to the remaining antenna director using gold wires with a diameter of 25 m. The antenna director pads are electrically connected to the PCB bonding pads with silver-coated copper wires. The length of the bonding wires are minimized to reduce ringing and peaking induced by the parasitic capacitance and inductance. Details of the optical devices packaged on the antenna director pads are shown in Fig. 9.

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Fig. 11. MATLAB model simulation for weak coupling between the microwave and optical front-ends. (a) Portion of the transmitted 2 1 test PRBS mixed with random phase 10-GHz time–harmonic signal. (b) Computed eye diagram.

0

Fig. 10. Photographs of fabricated radio-optical receiver module packaged with the microstrip patch antenna [see Fig. 1(b)].

B. Receiver Module With Microstrip Patch Antenna The radio-optical dual mode receiver prototype with the microstrip patch antenna is shown in Fig. 10. The assembly consists of the two superimposed boards for quick prototyping similarly to the approach implemented in Fig. 8. Specifically, the optical circuit board is very similar to the board used with the quasi-Yagi antenna [see Fig. 8(b)]. This optical board is also built on a four-layer FR4 PCB using essentially the same electronic components, as indicated above. Both of the boards also have comparable outer dimensions. The microstrip patch antenna board [see Fig. 1(b)] is printed on the RT/Duroid 5880 substrate of dialectical permittivity 2.2 and thickness of 0.8 mm. It is observed that some area conservation is achieved in the receiver design in Fig. 10 compared to the receiver in Fig. 8(b) because of the compact geometry of the microstrip patch antenna. Note that the actual optical front-end in the receiver prototype shown in Fig. 10 is based on a differential network unlike the simplified unbalanced network used in the simulated design in Fig. 5. This fact does not change mutual coupling between the optical and microwave front-end circuits, but enables integration with the differential inputs of the MAX3864 transimpedance amplifier chip. In the case of the board in Fig. 10, the same p-i-n chips and its assembling technology is employed as described above for the board in Fig. 8(b). V. ANALYSIS OF LINK PERFORMANCE UNDER IMPACT OF COUPLING BETWEEN MICROWAVE AND OPTICAL CIRCUITS The bit error rate (BER) performance of the optical link is directly determined by the noise performance of the optical receiver circuit, according to the following expression: (1)

Fig. 12. MATLAB model simulation for strong coupling between the microwave 1 test PRBS mixed and optical front-ends. (a) Portion of the transmitted 2 with random phase 10-GHz time–harmonic signal. (b) Computed eye diagram.

0

where is the BER factor, is the average received optical is the function and can be approximated with power, and high accuracy by (2) and is the detector responsivity in A/W. The square root of the input-referred noise-current spectral density integrated over the receiver’s noise equivalent bandwidth ( ) yields the total mean-square input-referred noise current (3) Thus, mutual coupling between the microwave and opto-electronic front-end circuits will affect the optical link by noise coupling at opto-to-electronic interface. The BER performance will be adversely affected by two noise mechanisms, which are: and 2) input current 1) laser driver current noise corrupting noise at the optical receiver front-end increasing . The eye pattern can be predicted based on the simulated data in Figs. 3 and 6, respectively, for the quasi-Yagi antenna and the microstrip patch antenna using a simple MATLAB model. In 1 pseudorandom bit sequence this model, reception of the 2 (PRBS) optical signal transmitted at a 2.5-Gb/s rate is considered. Additionally, a time–harmonic signal at 11 GHz is mixed with the PRBS signal as a noise component with magnitude corresponding to the predicted magnitudes of the inter-channel coupling and random phase because the optical and radio signals are not locked in phase. For illustrations, two channel conditions are treated for low 25 dB and high 15 dB coupling between the optical and microwave front-end circuits. Re1 PRBS are plotted spective portions of the transmitted 2 in Figs. 11(a) and 12(a), while the respective eye diagrams are shown in Figs. 11(b) and 12(b). Note that the simulated data

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A. Hybrid Receiver Prototype With Quasi-Yagi Antenna

Fig. 13. Measured 2.5-Gb/s eye pattern for receiver prototype board with the quasi-Yagi antenna [see Fig. 8(b)] for the microwave antenna port fed with different power levels. (a) No microwave signal. (b) 0 dBm. (c) 7 dBm. (d) 14 dBm. The time scale is 100 ps/div and magnitude scale is 9.6 mV/div.

In this prototype board [see Fig. 8(b)], the antenna induced current is coupled into the optical channel through the bondwire connecting the optical photodetector to the front-end transimpedance amplifier circuit. As the antenna input power increases, the EM induced current is higher and more noise is coupled into the optical channel, which dramatically degrades the signal-to-noise ratio. The corresponding measured eye diagrams are shown in Fig. 13. As shown in Fig. 13(d), the eye is almost closed when the antenna is fed with 14-dBm power. In general, the measured diagrams are qualitatively similar to the corresponding predicted patterns in the MATLAB model. Specifically, this similarity is respectively observed between the simulated data in Figs. 11(b) and 12(b) from one side, and the measured data in Figs. 13(a) and 13(d) from the other side. However, it is worth noting that for indoor wireless communication, the power fed into the transmission antenna is much lower than 14 dBm. Furthermore, in the presented study, the microwave antenna integrated with a p-i-n diode operates in the receiving mode, which will minimize the microwave noise coupling to the photoreceiver. The phenomenon appearing in Fig. 13(d) accounts for the worst case in terms of radio-optical coupling. For real applications, Fig. 13(a) and (b) is sufficient to study the coupling between the two links. B. Hybrid Receiver Prototype With Microstrip Patch Antenna

Fig. 14. Measured 2.5-Gb/s eye pattern for the receiver prototype board with the microstrip patch antenna [see Fig. 10] for the microwave antenna port fed with different power levels. (a) No microwave signal. (b) 0 dBm. (c) 7 dBm. (d) 14 dBm. The time scale is 100 ps/div and magnitude scale is 20 mV/div.

eye diagram is in a good agreement with measured results under identical conditions and bit rate for the radio-optical receiver, as further shown in Figs. 13 and 14.

The board with the microstrip patch antenna (Fig. 10) is similarly tested as the above case with the Yagi antenna by varying the input microwave power at the antenna port at the same gradual levels. The measured eye diagrams are shown in Fig. 14. Unlike the case in Fig. 13, the derived results for this prototype board do not exhibit a notable impact of the microwave signals on the optical channel. Essentially, the experimental eye diagrams for this case are somewhat analogous to the simulated case in MATLAB for low mutual coupling between the microwave and optical front-ends shown in Fig. 11(b). Thus, the derived results confirm the theoretical prediction that follows from comparison of the simulated dependencies in Figs. 3 and 6. In fact, the receiver board with the microstrip antenna looks much robust with respect to the mutual coupling effects compared to the board based on the quasi-Yagi antenna. C. Hybrid Transmitter Prototype With Quasi-Yagi Antenna

VI. EXPERIMENTAL STUDIES OF HYBRID RECEIVER AND TRANSMITTER PROTOTYPES A set of tests are carried out to assess the impact of the mutual radio-optical coupling in the prototyped hybrid boards in Figs. 8 and 10 by measuring the eye pattern of the optical receiver as the microwave antennas are fed for different input power levels. In particular, the tests are performed for: 1) the hybrid receiver board with the quasi-Yagi antenna [see Fig. 8(b)]; 2) the hybrid receiver board with the microstrip antenna (see Fig. 10); and 3) hybrid transmitter board with the quasi-Yagi antenna [see Fig. 8(a)]. In the receiver cases, the data pattern input to the optical laser driver circuit is 2.5-Gb/s PRBS, similar to the MATLAB link model in Section V.

To evaluate the feasibility of high data-rate optical communication under the impact of inter-channel mutual coupling, the eye diagram of an optical link is tested. The link consists of the radio-optical transmitter [see Fig. 8(a)], receiver [see Fig. 8(b)], and lens alignment system. The data pattern input to the optical 1 PRBS. In this setup, laser driver remains as a 2.5 Gb/s, 2 the microwave signal is fed into the antenna on the transmitter board, while the antenna on the receiver board is connected to a spectrum analyzer to measure the received microwave power. When the transmission antenna is fed with a 14-dBm radio signal at 10 GHz, the received microwave power is 14 dBm. The measured optical link eye pattern under the condition of a nonradiating antenna is shown in Fig. 15(a). Fig. 15(b) displays the eye pattern when the microwave power is delivered

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degradation because of lower coupling between the microwave and optical front-ends. Our ongoing studies are focused on several other perspective integrated radio-optical packaging designs to minimize signal integrity degradation, approach to single-chip solutions, and exploit other types of EM radiators. Our future developments will be focused on providing the same or comparable data throughput for both radio and optical link modalities by exploiting a suitable UWB antenna and signaling scheme. REFERENCES

Fig. 15. Measured eye pattern for optical link when the quasi-Yagi antenna is: (a) turned off and (b) turned on.

to the antenna. As previously discussed, the antenna power leakage in the optical front-end circuits has little effect on the transmitter side and can be neglected on the receiver side if the radio receiving power is low. Therefore, the coupling from the radio channel to optical channel is negligible in this setup and no noticeable change in the eye diagram is observed when the antenna is on or off, validating the theoretical prediction. VII. CONCLUSION Two novel hybrid radio-optical transceiver configurations with different microwave antenna structures are first studied numerically in full-wave HFSS and CST simulations. A set of transmitter and receiver modules for two different microwave printed antennas is developed and implemented in several packaged modules prototyped for an experimental dual-mode radio-optical communication system. Being tested, the new packaging approach reveals that it is feasible to design radio and optical circuits with shared structural components and physical space to tackle dimensional discrepancies between radio and optical devices. In our studies of the packaging design with the quasi-Yagi antenna (Fig. 8), the metal director pads of a planar antenna are used as the mounting pads for optical semiconductor elements, resulting in an ultra-compact hybrid radio-optical package design through the shared areas of the radio and optical transmitter and receivers. Shared electrical interconnections between radio and optical circuit components introduce additional interference signals due to EM coupling. Our analysis also shows that the microwave induced noise is negligible for the transmitter, but might degrade the signal integrity and BER performance of the optical receiver. Experimentally, a dual-mode radio-optical transmitter and receiver pair was demonstrated with an optical transmission rate of 2.5 Gb/s. In our studies of the packaged receiver prototype with the microstrip patch antenna, a different robust scheme is implemented and successfully tested. In particular, the packaged prototype (Fig. 10) occupies less physical space compared to the prototype in Fig. 8(b). It also exhibits notably lower signal integrity

[1] A. O. Boryssenko, J. Liao, J. Zeng, V. Joyner, and Z. R. Huang, “Studies on RF-optical dual mode wireless communication modules,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 805–809. [2] S. D. Milner and C. C. Davis, “Hybrid free space optical/RF networks for tactical operations,” in Proc. IEEE Military Commun. Conf., Nov. 2004, vol. 1, pp. 409–415. [3] S. Deng, J. Liao, Z. H. Rena, M. Hella, and K. Connor, “Wireless connections of sensor network using RF and free space optical links,” Proc. SPIE, vol. 6773, pp. 677307.1–677307.11, 2007. [4] , K. D. Paulsen, P. M. Meaney, and L. Gilman, Eds., Alternative Breast Imaging: Four Model-Based Approaches. New York: Springer, 2005. [5] J. J. Lin, L. Gao, A. Sugavanam, X. Guo, R. Li, J. E. Brewer, and K. O. Kenneth, “Integrated antennas on silicon substrates for communication over free space,” IEEE Electron Device Lett., vol. 25, no. 4, pp. 196–198, Apr. 2004. [6] F. Touati and M. Pons, “On-chip integration of dipole antenna and VCO using standard BiCMOS technology for 10 GHz applications,” in Proc. IEEE Eur. Solid-State Circuits Conf., Sep. 2003, pp. 493–496. [7] B. W. Cook, S. Lanzisera, and K. S. J. Pister, “SoC issues for RF smart dust,” Proc. IEEE, vol. 94, no. 6, pp. 1177–1196, Jun. 2006. [8] W. R. Deal, N. Kaneda, J. Sor, Y. Qian, and T. Itoh, “A new quasi-Yagi antenna for planar active antenna arrays,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 6, pp. 910–918, Jun. 2000. [9] R. Bancroft, Microstrip and Printed Antenna Design. Raleigh, NC: SciTech Publishing, 2008. [10] J. Liao, S. Deng, F. Smith, Z. R. Huang, and K. A. Connor, “Integrated laser diodes and photodetectors with antenna for dual-mode wireless communication,” in Proc. IEEE LEOS Annu. Meeting, Oct. 2007, pp. 264–265. [11] S. E. Melais and T. M. Weller, “A quasi Yagi antenna backed by a metal reflector,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3868–3872, Dec. 2008. [12] C. L. Schow, F. E. Doany, C. Chen, A. V. Rylyakov, C. W. Baks, D. M. Kuchta, R. A. John, and J. A. Kash, “Low-power 16 10 Gb=s bi-directional single chip CMOS optical transceivers operating at 5 mW=Gb=s=link,” IEEE J. Solid-State Circuits, vol. 44, no. 1, pp. 301–313, Jan. 2009. [13] R. Pu, C. Duan, and C. W. Wilmsen, “Hybrid integration of VCSEL’s to CMOS integrated circuits,” IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 2, pp. 201–208, Mar./Apr. 1999. [14] R. Becker, “Broad-band guided-wave electrooptic modulators,” IEEE J. Quantum Electron., vol. 20, no. 7, pp. 723–727, Jul. 1984.



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Anatoliy O. Boryssenko (M’98) received the M.Sc. E.E. and Ph.D. E.E. degrees from the Kiev Polytechnic Institute, Kiev, Ukraine. He was an Associate Professor with the Kiev Polytechnic Institute and a Research and Development Engineer with companies related to millimeter-wave and UWB communication and sensor systems. Since 2000, he has been with the University of Massachusetts, Amherst, where he is currently a Research Associate Professor with the Department of Electrical and Computer Engineering. His research interests include subsurface radar imaging, broadband and UWB antenna and array design, applied and computational electromagnetics, and signal processing and system design for radar, sensing and imaging.

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Jun Liao (M’07) received the B.S. degree from the Beijing University of Posts and Telecommunications, Beijing, China, in 2006, and is currently working toward the Ph.D. degree in electrical, computer and systems engineering at the Rensselaer Polytechnic Institute, Troy, NY. His research interest includes RF/opto hybrid packing, planar antenna design, and free-space optical communication.

Juan Zeng (M’03) received the B.S. degree in electronic science and technology from the Harbin Institute of Technology (HIT), Harbin, China in 2007, and is currently working toward the M.S. degree in electrical engineering at Tufts University, Medford, MA. Her research interests include CMOS circuits for broadband wireless applications. Ms. Zeng was the recipient of the MediaTek Inc. and Wu Ta-You Scholar Award presented by the Harbin Institute of Technology in 2006 and the Dean’s Fellowship presented by Tufts University in 2007.

Shengling Deng (M’08) received the B.S. in physics from Nanjing University, Nanjing, China in 2002, the M.S. in electrical engineering from the University of Florida, Gainesville, in 2005, and is currently working toward the Ph.D. degree at the Rensselaer Polytechnic Institute, Troy, NY. His research interest includes III–V metal–semiconductor–metal (MSM) integration, Si-based electrooptic (EO) modulators, and integrated optics on silicon-on-insulator (SOI).

Valencia M. Joyner (M’98) received the S.B. and M.Eng. degrees in electrical engineering and computer science from the Massachusetts Institute of Technology, Cambridge, in 1998 and 1999, respectively, and the Ph.D. degree from the University of Cambridge, Cambridge, U.K., in 2003. She is currently an Assistant Professor with Tufts University, Medford, MA, where she leads the Advanced Integrated Circuits and Systems Group. Her current research interests include opto-electronic integrated circuit design for high-speed optical and RF wireless networks and biomedical imaging applications. Dr. Joyner was the recipient of a Marshall Scholarship and National Science Foundation (NSF) Graduate Research Fellowship.

Z. Rena Huang (M’99) received the B.S. degree from the Beijing Institute of Technology, Beijing, China, in 1995, and the M.Sc. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 1999 and 2003, respectively. She is currently an Assistant Professor with the Rensselaer Polytechnic Institute, Troy, NY. Her current research focus includes RF/opto packaging for high-speed low-power wireless communication, and integrated photonics for next-generation lightwave technology.

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A Generalized Formulation for Permittivity Extraction of Low-to-High-Loss Materials From Transmission Measurement Ugur Cem Hasar, Member, IEEE

Abstract—We have derived a one-variable metric function for fast computations of the relative complex permittivity of low-tohigh-loss materials from 21 measurement at one frequency. We present how this function can be applied for different applications (e.g., relative complex permittivity measurement of a thin low-loss material). In addition, it can be applied as a measurement tool in broadband applications for samples with substantiate lengths, which demonstrate low-loss property at lower frequency bands and high-loss property at higher frequency bands. The derived expressions can work very well in limited frequency-band applications or for dispersive materials since it is based on point-by-point (or frequency-by-frequency) extraction. We measured the relative complex permittivity of two test samples (a low- and high-loss sample) for validation of the derived expressions. Index Terms—Materials testing, microwave measurements, permittivity.

I. INTRODUCTION ERMITTIVITY measurements and their relation with some materials parameters by microwave techniques are becoming more and more important for many applications during recent years such as agriculture, food engineering, medical treatments, bioengineering, and the concrete industry [1]. These techniques can roughly be divided into two groups as: 1) resonant methods and 2) nonresonant methods [1]. Resonant methods have much better accuracy and sensitivity than nonresonant methods [1] at discrete frequencies. They are applied for characterization of low-loss materials, as well as high-loss materials [3]. On the other hand, nonresonant methods have relatively higher accuracy over a broad frequency band and necessitate less sample preparation compared to resonant methods [1], [4]. They allow the frequency- or time-domain analysis, or both. Owing to their relative simplicity, broad frequency coverage, and higher accuracy, transmission–reflection method (a kind of nonresonant method) are widely utilized for characterization of materials [4]–[13]. Measured reflection and/or transmission scattering - parameters can be utilized for broadband relative complex permitextraction. However, measured transmission -pativity

P

Manuscript received March 01, 2009; revised June 03, 2009. First published January 19, 2010; current version published February 12, 2010. The author is with the Department of Electrical and Electronics Engineering, Ataturk University, 25240 Erzurum, Turkey, and also with the Department of Electrical and Computer Engineering, Binghamton University, Binghamton, NY 13902 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038443

has several advantages over measured reflection rameter -parameter such as: 1) it provides longitudinal averaging of variations in sample properties, which is particularly important for relatively high-loss heterogeneous materials such as moist coal and other powdered materials [14]–[16]; 2) it does not suffer much from surface roughness at high frequencies [17]–[19]; 3) it is more sensitive to the dielectric properties of high-loss samples [14]; 4) it offers a wide dynamic range for measurements [14]; and 5) it does not have any problem achieving accurate measurements for both high- and low-reflection coefficients with standard calibration techniques [20]. measurements, For characterization of materials from single- or multiple-pass techniques can be employed. The single-pass technique assumes that the sample under test is and approach the first reflection lossy enough that and transmission coefficients of the sample, respectively. The single-pass technique greatly simplifies the theoretical formumeasurement [11], lations and eventually allows unique [16], [18]–[24]. However, it can be applied only under certain conditions such as: 1) the duration of the test pulse is smaller than the pulse travel time through the slab (by eliminating the portions of the signal due to multiple reflections inside the sample by means of a time-gating feature in time-domain measurements [21]–[23]) or 2) the sample under test possesses at least 10-dB attenuation for frequency-domain measurements [11], [16], [18], [24]. On the other hand, multiple-pass technique assumes that the sample under test is not lossy (low lossy) so that three are multiple reflections inside the sample and . This technique is general and that contribute to the determined by this technique is more exact. However, it of a low-loss sample from results in multiple solutions for measurement at one frequency. This is because measured of the effect of nonunique retrieval of the phase part of the propagation factor [10], [25]. Zero-search algorithms such as Newton’s method [26], Muller’s method [27], Davidenko’s method [28]–[30], Cauchy integral method [31], [32], genetic algorithms, sequential quadratic programming, and globalized at Nelder–Mead methods [33]–[35] will not yield a unique one frequency since they output local solutions. Various techniques have been proposed to obtain unique using measurements [1], [4], [6], [13]–[15], [25], [36]–[39]. While these techniques are attractive, they either assume that does not significantly vary within the measured range [1], [6], [13]–[15], [25], [36], [37] or test samples are identical [1], [4], [38], [39], require extra measurements [17], or may yield erroneous results in limited frequency bands and require a consider-

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[48]. The electric vector potential can then be written for regions I–III as (3) (4) (5) Fig. 1. Illustration of the problem: permittivity determination of low-to-highloss materials from S measurements inside a rectangular waveguide.

able amount of time for integral computations [25]. In addition, from measurement, different formufor measuring the lations have recently been derived for different purposes [40], [41]. While the method in [41] assumes that the sample is low loss and thin, the method in [40] uses a second-order approximation to derive a one-variable function for fast computations. In recent years, we have also proposed different methods for measurement for various applications. While some of them and/or for unique measurement use amplitudes of using single- or multiple-pass techniques [11], [13], [16], [36], [42], [43], others utilize their complex measurements using the same techniques [10], [12], [44]–[47]. However, none of them extraction of a wide range of materials is applicable for measurements. (low-to-high-loss materials) from only Such an application, at some instances, is a necessity for measurements of low- or medium-loss samples over a wide frequency range. In addition, in these applications, fast extraction becomes important as equally as unique determination and the methods in [31] and [32] are limited in this respect. The motivation of this study is to derive a metric function for fast determination of low-to-high-loss materials from measurement at one frequency with no prior assumption for the problem (e.g., thin sample). The expressions in the metric function can easily be modified for determination for various applications. The advantage of these expressions is that they allow fast computations. II. BACKGROUND

where (6) are the complex values, and Here, correspond to the free-space and cutoff wavelengths, , , and are the operating and cutoff frequencies and the speed of light, is the relative permittivity of respectively, and the sample. Using the electric vector potentials in (3)–(5), electric and magnetic fields can be determined from (1) and (2). Applying boundary conditions at interfaces I–II and II–III, reflection and transmission -parameters can be derived as [4]–[7] (7) (8) where denotes the magnitude of expressions and and are, respectively, the reflection coefficient when the sample is semi-infinite in length and the propagation factor. Their corresponding equations are (9)

III. COMPLEX PERMITTIVITY DETERMINATION A. Demonstration of the Problem

The problem for measurement of a low-to-high-loss inside a waveguide sample holder is sample with length depicted in Fig. 1. In the analysis, it is assumed that the sample is isotropic, symmetric, and homogenous. While regions I and III correspond to air, region II denotes the sample. The expressions of electric and magnetic fields can be derived from their vector potentials (or Hertzian vectors) and such as [48]

It is clear that direct inversion of is not possible from (8). In addition, it is well known that there is no unique solution for due to complex exponential . We have lately demonstrated that and meaa unique solution can be possible from approaches zero [13]. surements at the frequency when at the same Here, the question is: will we extract unique frequency? and measurements, we obtain [6] From complex

(1) (2) where and denote, respectively, the curl and divergence and and are the complex permittivity and permeability of the medium. Assuming that the rectangular waveguide operates in , we have and the dominant mode

(10)

(11)

HASAR: GENERALIZED FORMULATION FOR PERMITTIVITY EXTRACTION OF LOW-TO-HIGH-LOSS MATERIALS

Substituting in (10) and in (11) into shown at the bottom of this page. When (12) reduces to

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, one obtains (12), approaches zero,

approaches zero, we can At certain frequencies where and [13]. Substituting approximate these approximations into (17), we find

(13)

(20)

It is clear from (13) that, from complex measurements, we still obtain multiple solutions. In addition, it is obvious that approaches or one when goes to zero [4], [7]. Second, we want to show that, at this frequency, although transcendental terms can be approximated to certain values [13], from measurements. To this we will not obtain unique end, we define the following variables [13]:

. In a similar where we have approximated fashion, we obtain a function with no transcendental terms since from (16). However, there is no unique solution for has multiple solutions. This problem occurs for both waveguide and free-space measurements since the problem maker term is not . As a demonstration of the problem, we apply a graphical method [16], [24], [42], which works as follows. First, an initial estimate for is substituted into (16) and (17) for computation and where the subscript denotes computed exof pressions. These computed values are then compared with meaand values. Next, if the difference is less than sured the desired tolerance, we save this (possible complex permittivity). This whole process is repeated for all possible values. The graph of saved produces the constant value curves ( and ). Finally, the intersection of these curves is analyzed for permittivity determination of the sample. For instance, Fig. 2 and for two test fredemonstrates the dependency of quencies ( GHz and GHz) of a sample with and mm. It is assumed that GHz ( -band waveguide). While GHz (or corresponds to the frequency that results in maximum minimum for a passive sample), GHz is an arbitrarily selected frequency. It is seen from Fig. 2(a) and (b) that there are two solutions and ) over and . (intersection of We observed that if the ranges of and are increased, more than two solutions can be obtained. It is noted that similar results (multiple solutions) are obtained when we applied Newton’s search algorithm [26] with different initial values. This clearly from demonstrates that there is more than one solution for measurements even at frequencies that result in maximum . This is an opposite case noted in [13]. or minimum

(14)

(15) The definition of new variables changed the inverse problem from determination into and determination. Substituting these variables into (8), we obtain [10] (16) (17) where

B. Polynomial Function for Fast Computations (18)

(19)

In this section, our purpose is to derive a metric function that can be utilized for fast determination in various applications. Since the transcendental terms, which are functions of , have multiple solutions, we express in terms of as follows. Since it is not possible to derive a polynomial expression solely based on a real exponential , we decide to eliminate this term from (16)–(19). Expressing in (16) and (17) in terms of and ,

(12)

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Fig. 2. Dependency of constant value curves of jS : 0j : L a low-loss sample with " (b) f  : GHz.

= 8 65

= 7 34

j

and  (C and C ) of mm. (a) f GHz.

0 005 = 20

=9

we find expressions in (21) and (22), shown at the bottom of this page, where (23) Only the solution for with a negative sign in (21) is valid (the proof is given in the Appendix ). Equating the expressions in (21) and (22), we derive a polynomial function in as

(24)

Fig. 3. Dependency of constant value curves of jS j 0 jS j and 0 j using F ;  in (24) for a low-loss sample with " j : 0j : L mm. (a) f GHz. (b) f  : GHz.

7 34

( ) 0 005 = 20

=9

= 8 65

=

where the polynomial coefficients are given in (25)–(33), shown at the bottom of the following page. It is seen from (24) that has ten roots. These roots can be found from the “roots” function of MATLAB. We observed in (24). In the sethat only one of the roots proves and lection of the correct root of , we consider that is real [13]. Substituting this chosen into either (16) or (17), we can efficiently and quickly compute . For example, Fig. 3 and demonstrates the dependencies of over using the polynomial function in (24) at difGHz and GHz) for a test ferent frequencies ( sample with the same parameters used in Fig. 2. It is assumed GHz ( -band waveguide). that It is seen in Fig. 3(a) and (b) that there are multiple solutions at one frequency, for of a low-loss sample from measured

(21)

(22)

HASAR: GENERALIZED FORMULATION FOR PERMITTIVITY EXTRACTION OF LOW-TO-HIGH-LOSS MATERIALS

which validates the conclusion drawn before. In addition, we note that if the initial guess for is reasonably good, correct socan be obtained as simultaneous interseclution tion of and where denotes the minimum absolute value. In this way, without the need of searching for possible values by any 2-D root-search algorithm, one can directly use the polynomial function in (24) and and/or . can then be calculated from (24) measured with the aid of the “roots” function of MATLAB and using computed . Finally, from (14), will be (34)

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C. About Applications of the Derived Polynomial Function Depending on the accuracy of computation and the problem in (24) for various purat hand, one can manipulate poses. For instance, one can assume that the sample under investigation is low loss and has a substantial thickness. In this circumstance, we can approximate as (35) where subscript denotes the approximation. The closed-form solution for the quartic equation in (35) can be found in the literature [36], [49]. The selection of correct choice for can be done as well by using constraints and [13]. By

(25) (26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

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substituting into (16) and/or (17), one can then accurately and uniquely compute with its good initial guess. In a similar fashion, for low-loss thin samples, one can utilize in (35) and assume that (36) (37) Substituting these linearized approximations into (16) and/or (17) will allow one to compute rapidly since, for computations of any trigonometric or exponential functions, each computational method needs to use different approximations such as Taylor-series expansion [50]. It is noted that, for fast, accurate, and efficient computations, one can compare the calculated value using our derived polynomial function with the one from the approximated expressions in (35)–(37) at a given frequency. If the comparison is in the limit of tolerance, one can use those approximations for the remaining frequencies. In this way, our derived polynomial function can be used as a self-checking technique as well. It should also be discussed that the derivations in (23)–(33) measurement of lossy materials since can be employed for they are general. If the sample possesses at least 10-dB attenuation, we can assume in (23)–(33) that and simplify these expressions. This approximation for will eliminate the oscillatory behavior of trigonometric terms in (23)–(33) and allow one to uniquely compute [11], [16], [18], [19], [24], [36], [42]. However, it should be kept in mind that, for lossy samples, in (24) must directly be used, as will be shown from measurements in Section IV. We also want to point out that the expressions given in (23)–(33) are valid for waveguide measurements with only the mode, as well as free-space measurements. Therefore, in this respect, they are more general than the expressions and formulations given in [14], [15], [36], [40], and [41]. If needed, the expressions given between (23) and (34) can be adapted for free-space or air-line coaxial measurements by letting or by using a different formulation for wave impedance. IV. MEASUREMENT RESULTS A general-purpose waveguide measurement setup is used for validation of the proposed method [13]. An HP8720C vector network analyzer (VNA) is utilized as a source and measurement equipment. It has a 1-Hz frequency resolution (with option 001) and eight parts per million (ppm) frequency accuracy. The waveguide used in measurements has a width of 22.86 mm GHz . Several factors contribute to the uncertainty in determination in waveguide measurements [4], [7], namely: 1) the uncertainty in measured -parameters; 2) errors in the sample length and the holder length; 3) the uncertainty in reference plane positions; 4) guide losses and conductor mismatches; 5) air gaps between the external surfaces of the sample (and holder) and inner walls of waveguides; and 6) higher order modes. All these uncertainties are extensively treated in the literature [4], [7]–[10], [12], [51]. Care can be given to limit the uncertainties due to the sample position, calibration, and air gaps. Using calibration techniques, uncertainties in reference plane positions can be minimized. Preparing the sample and using a sample holder

Fig. 4. Measured " of a 10-mm-long PTFE sample by the proposed method using two different polynomial degrees of F (;  ) and by the method in [10].

Fig. 5. Measured " of distilled water by the proposed method using two different polynomial degrees of F (;  ) and the method in [12]. The parameters for the Debye model are " = 5:2 and " = 78:5, and relexation time  = 8:3 ps at ordinary room temperature [55].

with no scratches, nicks, or cracks, and machining the sample to fit precisely into the waveguide will increase the measurement accuracy and reduce the effect of air gaps [4], [7]. Accordingly, the uncertainty analysis can be restricted to measurements. Since such an analysis has recently been done in [10], in this paper we will not focus on uncertainty analysis. Instead, we will present measurement results of two samples (one low loss and one high loss) by using different approximations for the polynomial function in (24). For calibration of the setup, the thru-reflect-line calibration technique [52] is utilized. We used a waveguide short and the 44.38-mm-long waveguide spacer for reflect and line standards, respectively. The line has a 70 maximum offset from 90 between 9.7–11.7 GHz. After calibration of the setup, we utilized two test samples (a 10-mm-long polytetrafluoro-ethyle (PTFE) sample as a low-loss material and 3-mm-long distilled water as a lossy material). In the measurement of the liquid sample, we utilized two identical low-loss dielectric plugs [9] (two 10-mmlong PTFE samples) to remove the effect of meniscus formation on the performance and accuracy of measurements and to keep the liquid in place in order to eliminate any errors arising from the deformation of the calibration-plane flatness. Since the formulations and approximations for measurements from the -parameter in [40] and [41] are not valid for waveguide (dispersive medium) measurements, we decided to monitor the effect of using different approximations for (24) and compare the results of the proposed method with the methods in the literature. For example, Figs. 4 and 5 demonstrate the measured of the test samples by the proposed method and the

HASAR: GENERALIZED FORMULATION FOR PERMITTIVITY EXTRACTION OF LOW-TO-HIGH-LOSS MATERIALS

methods in [10] and [12]. An initial guess for of these samples for the proposed method is provided with the available data in the literature [53]–[55]. It is seen from Fig. 4 that the extracted of the PTFE sample by the derived metric function with different degrees are in good agreement with the results obtained from the method in [10] and the data in the literature [53], [54]. At 10 GHz, the of the PTFE sample given by von Hippel is [53]. We note that using with various polynomial degrees does not affect the results of of the PTFE sample much. This is because, for low-loss materials, we can neglect the terms with degrees greater than 2. These results are in good agreement with those in [40] and [41]. However, this is not the case for lossy materials, as shown in Fig. 5. In this figure, the effect of using different degrees can easily be noticed. While the results using the with a degree of 10 are similar to those obtained from the Debye model [55] and the method in [12], those using the with a degree of 6 are different than the theoretical and measurement values [12], [55] because, for lossy materials, the contribution of in the measurement becomes important. V. CONCLUSION A metric function, which depends on only one variable, has been derived for fast relative complex permittivity determination of low-to-high-loss materials. The expressions in this function can be simplified depending on the nature of the problem, which can even permit fast permittivity computations. This function can be applied for free-space or coaxial-line measurements (theoretically zero cutoff frequency), as well as mode. In addition, waveguide measurements operating at it is useful in permittivity determination of materials in broadband applications since it does not assume that the sample be low loss or high loss. The derived metric function has been validated by permittivity measurements of a low- and high-loss sample. APPENDIX from (21) Selection of the correct choice of the root of is done as follows. Since is a real exponential quantity and greater than zero, and are both real quantities, and the overall sum of the quantities inside the square root in (21) must be must be less than greater than zero to yield a real value, zero. In addition, because is a function of whose value depends on the loss of the sample, its value should be less than or equal to one. Therefore, the expression of in (21) can be written as (38) The expression in the square root in (38) can then be written as (39) Since and for clearly enforces the condition that

, then

. This from

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(39). Finally, application of this condition to (38) proves that only the minus sign before the square root in (21) satisfies the correct root of . REFERENCES [1] L. F. Chen, C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave Electronics: Measurement and Materials Characterization. West Sussex, U.K.: Wiley, 2004. [2] R. Zoughi, Microwave Non-destructive Testing and Evaluation. Dordrecht, The Netherlands: Kluwer, 2000. [3] C. L. P. Rubinger and L. C. Costa, “Building a resonant cavity for the measurement of microwave dielectric permittivity of high loss materials,” Microw. Opt. Technol. Lett., vol. 49, pp. 1687–1690, 2007. [4] J. Baker-Jarvis, M. D. Janezic, J. H. Grosvenor, Jr., and R. G. Geyer, “Transmission/reflection and short-circuit line methods for measuring permittivity and permeability,” NIST, Boulder, CO, Tech. Note 1355, 1992. [5] A. M. Nicolson and G. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Trans. Instrum. Meas., vol. IM-19, no. 4, pp. 377–382, Nov. 1970. [6] W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE, vol. 62, no. 1, pp. 33–36, Jan. 1974. [7] J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 4, pp. 1096–1103, Aug. 1990. [8] T. C. Williams, M. A. Stuchly, and P. Saville, “Modified transmissionreflection method for measuring constitutive parameters of thin flexible high-loss materials,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 5, pp. 1560–1566, May 2003. [9] K. J. Bois, L. F. Handjojo, A. D. Benally, K. Mubarak, and R. Zoughi, “Dielectric plug-loaded two-port transmission line measurement technique for dielectric property characterization of granular and liquid materials,” IEEE Trans. Instrum. Meas., vol. 48, no. 6, pp. 1141–1148, Dec. 1999. [10] U. C. Hasar and C. R. Westgate, “A broadband and stable method for unique complex permittivity determination of low-loss materials,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 2, pp. 471–477, Feb. 2009. [11] U. C. Hasar, “A fast and accurate amplitude-only transmission-reflection method for complex permittivity determination of lossy materials,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 9, pp. 2129–2135, Sep. 2008. [12] U. C. Hasar, “A microwave method for noniterative constitutive parameters determination of thin low-loss or lossy materials,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 6, pp. 1595–1601, Jun. 2009. [13] U. C. Hasar, “Two novel amplitude-only methods for complex permittivity determination of medium- and low-loss materials,” Meas. Sci. Techol., vol. 19, no. 5, May 2008, 055 706 (10 pp). [14] J. Ness, “Broad-band permittivity measurements using the semi-automatic network analyzer,” IEEE Trans. Microw. Theory Tech., vol. MTT-33, no. 11, pp. 1222–1226, Nov. 1985. [15] J. A. R. Ball and B. Horsfield, “Resolving ambiguity in broadband waveguide permittivity measurements on moist materials,” IEEE Trans. Instrum. Meas., vol. 47, no. 2, pp. 390–392, Apr. 1998. [16] S. N. Kharkovsky, M. F. Akay, U. C. Hasar, and C. D. Atis, “Measurement and monitoring of microwave reflection and transmission properties of cement-based specimens,” IEEE Trans. Instrum. Meas., vol. 51, no. 6, pp. 1210–1218, Dec. 2002. [17] O. Buyukozturk, T.-Y. Yu, and J. A. Ortega, “A methodology for determining complex permittivity of construction materials based on transmission-only coherent, wide-bandwidth free-space measurements,” Cement Concrete Composites, vol. 28, pp. 349–359, 2006. [18] U. C. Hasar, “Free-space nondestructive characterization of young mortar samples,” J. Mater. Civ. Eng., vol. 19, no. 8, pp. 674–682, 2007. [19] U. C. Hasar, “Non-destructive testing of hardened cement specimens at microwave frequencies using a simple free-space method,” NDT&E Int., vol. 42, no. 6, pp. 550–557, Sep. 2009. [20] G. R. Cobb, J. Fitzpatrick, and J. Williams, “ANA techniques differ,” Microw. Syst. News II, pp. 27–35, 1981. [21] D. Kralj and L. Carin, “Ultra-wideband characterization of lossy materials: Short-pulse microwave measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, vol. 13, pp. 1239–1242.

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[22] A. Khosrowbeygi, H. D. Griffiths, and A. L. Cullen, “A new free-wave dielectric and magnetic properties measurement system at millimetre wavelengths,” in IEEE MTT-S Int. Microw. Symp. Dig., 1994, vol. 14, pp. 1461–1464. [23] A. Muqaibel, A. Safaai-Jazi, A. Bayram, A. M. Attiya, and S. M. Riad, “Ultrawideband through-the-wall propagation,” Proc. Inst. Elect. Eng. —Microw. Antennas Propag., vol. 152, no. 6, pp. 581–588, 2005. [24] Z. Ma and S. Okamura, “Permittivity determination using amplitudes of transmission and reflection coefficients at microwave frequency,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 5, pp. 546–550, May 1999. [25] V. V. Varadan and R. Ro, “Unique retrieval of complex permittivity and permeability of dispersive materials from reflection and transmitted fields by enforcing causality,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 10, pp. 2224–2230, Oct. 2007. [26] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. New York: Cambridge Univ. Press, 1992. [27] D. E. Muller, “A method for solving algebraic equations using an automatic computer,” Math. Tables Aids of Comput., vol. 10, pp. 208–215, 1965. [28] W. E. Schiesser, Computational Mathematics in Engineering and Applied Science: ODEs, DAEs and PDEs. Boca Raton, FL: CRC, 1994. [29] S. H. Talisa, “Application of Davidenko’s method to the solution of dispersion relations in lossy waveguiding systems,” IEEE Trans. Microw. Theory Tech., vol. MTT-33, no. 10, pp. 967–971, Oct. 1985. [30] H. A. N. Hejase, “On the use of Davidenko’s method in complex root search,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 1, pp. 141–143, Jan. 1993. [31] F. L. Penaranda-Foix, J. M. Catala-Civera, M. Contelles-Cervera, and A. J. Canos-Marin, “Solving the cut-off wave numbers in partially filled rectangular waveguides by the Cauchy integral method,” Int. J. RF Microw. Comput.-Aided Eng., vol. 16, pp. 502–509, 2006. [32] R. Rodrigez-Berral, F. Mesa, and F. Medina, “Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides,” Int. J. RF Microw. Comput.-Aided Eng., vol. 14, pp. 73–83, 2004. [33] M. E. Baginski, D. L. Faircloth, and M. D. Deshpande, “Comparison of two optimization techniques for the estimation of complex permittivities of multilayered structures using waveguide measurements,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 10, pp. 3251–3259, Oct. 2005. [34] M. A. Luersen and R. Le Riche, “Globalized Nelder–Mead method for engineering optimization,” Comput. Struct., vol. 82, no. 23–26, pp. 2251–2260, 2004. [35] R. Olmi, M. Tedesco, C. Riminesi, and A. Ignesti, “Thickness-indepenband,” dent measurement of the permittivity of thin samples in the Meas. Sci. Technol., vol. 13, no. 4, pp. 503–509, Apr. 2002. [36] U. C. Hasar, “Elimination of the multiple-solutions ambiguity in permittivity extraction from transmission-only measurements of lossy materials,” Microw. Opt. Technol. Lett., vol. 51, no. 2, pp. 337–341, Feb. 2009. [37] S. Trabelsi, A. W. Kraszewski, and S. O. Nelson, “Phase-shift ambiguity in microwave dielectric properties measurements,” IEEE Trans. Instrum. Meas., vol. 49, no. 1, pp. 56–60, Feb. 2000. [38] M. Rodriguez-Vidal and E. Martin, “Contribution to numerical methods for calculation of complex dielectric permittivities,” Electron. Lett., vol. 6, no. 16, p. 510, 1970. [39] H. Altschuler, “Dielectric constant,” in Handbook of Microwave Measurements, J. Fox and M. Sucher, Eds. Brooklyn, NY: Polytech. Press, 1963, vol. 3. [40] A. H. Muqaibel and A. Safaai-Jazi, “A new formulation for characterization of materials based on measured insertion transfer function,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 8, pp. 1946–1951, Aug. 2003. [41] J. D. Mahony, “Measurements to estimate the relative permittivity and loss tangent of thin, low-loss materials,” IEEE Antennas Propag. Mag., vol. 47, no. 3, pp. 83–87, Mar. 2005.

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[42] U. C. Hasar, M. F. Akay, and S. N. Kharkovsky, “Determination of complex dielectric permittivity of loss materials at microwave frequencies,” J. Math. Comput. Appl., vol. 8, pp. 319–326, 2003. [43] U. C. Hasar and O. Simsek, “An accurate complex permittivity method for thin dielectric materials,” Progr. Electromagn. Res., vol. 91, pp. 123–138, 2009. [44] U. C. Hasar, “Thickness-independent automated constitutive parameters extraction of thin solid and liquid materials from waveguide measurements,” Progr. Electromagn. Res., vol. 92, pp. 17–32, 2009. [45] U. C. Hasar, “Simple calibration plane-invariant method for complex permittivity determination of dispersive and non-dispersive low-loss materials,” IET Microw. Antennas Propag., vol. 3, no. 4, pp. 630–637, Jun. 2009. [46] U. C. Hasar and O. Simsek, “A calibration-independent microwave method for position-insensitive and nonsingular dielectric measurements of solid materials,” J. Phys. D, Appl. Phys., vol. 42, no. 7, Mar. 2009, 075 403 (10 pp). [47] U. C. Hasar, “A new calibration-independent method for complex permittivity extraction of solid dielectric materials,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, pp. 788–790, Dec. 2008. [48] C. A. Balanis, Advanced Engineering Electromagnetics. Hoboken, NJ: Wiley, 1989. [49] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972, pp. 17–18. [50] J. H. Mathews and K. D. Fink, Numerical Methods using MATLAB, 4th ed. Englewood Cliffs, NJ: Prentice-Hall, 2004. [51] E. Ni, “An uncertainty analysis for the measurement of intrinsic properties of materials by the combined transmission-reflection method,” IEEE Trans. Instrum. Meas., vol. 41, no. 4, pp. 495–499, Aug. 1992. [52] G. F. Engen and C. A. Hoer, “Thru-reflect-line: An improved technique for calibrating the dual six-port automatic network analyzer,” IEEE Microw. Theory Tech., vol. MTT-27, no. 12, pp. 987–993, Dec. 1979. [53] A. R. Von Hippel, Dielectric Materials and Applications. New York: Wiley, 1954. [54] G. Y. Chin and E. A. Mechtly, “Properties of materials,” in Reference Data for Engineering: Radio, Electronics, Computer, and Communications, E. C. Jordan, Ed. Indianapolis, IN: H. W. Sams & Co., 1986, pp. 4-20–4-23. [55] J. B. Hasted, Aqueous Dielectrics. London, U.K.: Chapman & Hall, 1973.

Ugur Cem Hasar (M’00) was born in Kadirli, Adana, Turkey, in 1977. He received the B.Sc. and M.Sc. degrees (with honors) in electrical and electronics engineering from Cukurova University, Adana, Turkey, in 2000 and 2002, respectively, and the Ph.D. degree in electrical engineering from Binghamton University, Binghamton, NY, in 2008. From 2000 to 2005, he was a Research and Teaching Assistant with the Department of Electrical and Electronics Engineering, Cukurova University. From 2005 to 2008, he was a Research Assistant with the Department of Electrical and Electronics Engineering, Ataturk University, Erzurum, Turkey. He is currently an Assistant Professor with Ataturk University. His main research interest includes nondestructive testing and evaluation of materials using microwaves and novel calibration-dependent and calibration-independent techniques for the electrical and physical (thickness, delamination, etc.) characterization of materials. Dr. Hasar was the recipient of The Scientific and Technological Research Council of Turkey (TUBITAK) Münir Birsel National Doctorate Scholarship, The Higher Education Council of Turkey (YOK) Doctorate Scholarship, The Outstanding Young Scientist Award in Electromagnetics of the Leopold B. Felsen Fund, Binghamton University Distinguished Dissertation Award, and Binghamton University Graduate Student Award for Excellence in Research.

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A New 12-Term Open–Short–Load De-Embedding Method for Accurate On-Wafer Characterization of RF MOSFET Structures Luuk F. Tiemeijer, Ralf M. T. Pijper, J. Anne van Steenwijk, and Edwin van der Heijden

Abstract—A new algorithm for open–short–load de-embedding of on-wafer -parameter measurements is presented. Since in typical on-wafer RF transistor test-structures the imperfect grounding of the internal ports is the dominant source of crosstalk between ports, our proposed open–short–load approach resolving a 12-term error model is equally accurate as the current more general 15-term approach, which requires five dummy structures. To demonstrate this, experimental results obtained for six different increasingly sophisticated on-wafer correction schemes using 2–8 different de-embedding standards and resolving between 8–22 error terms, using -parameter data taken up to 110 GHz on 65and 45-nm node MOSFET devices are compared. Index Terms—Calibration, 45-nm node CMOS, integrated circuits, on-wafer microwave measurements, open–short–load de-embedding.

I. INTRODUCTION

A

CCURATE on-wafer -parameter measurements are essential to build and verify RF-MOSFET device models suitable for high-frequency design. To be able to verify the extremely high intrinsic cutoff and maximum oscillation frequencies available in today’s deep-submicrometer MOSFET devices, high- gate capacitances in the order of tens of femtofarads need to be reliably separated from large measurement pad parasitics and possible calibration inaccuracies. This de-embedding process, together with test-structure design considerations, has over the years been the topic of many publications. Starting with relatively straightforward physics-based correction schemes [1]–[15], and inspired by algorithms originally developed for network analyzer calibration [16]–[18], part of the field has evolved toward a more mathematical four-port approach [19]–[26], aiming for the correction of all relevant on-wafer test-structure parasitics in a general manner without requiring any a-priori assumptions on the test-structure equivalent circuit whatsoever. However, increasing the number of calibration measurements on de-embedding standards does not necessarily enhance the overall de-embedding accuracy due to the increased number of probe contacts to be made, and

Manuscript received June 08, 2009. First published January 22, 2010; current version published February 12, 2010. L. F. Tiemeijer, R. M. T. Pijper, and E. van der Heijden are with the NXPTSMC Research Centre, 5656 AE Eindhoven, The Netherlands (e-mail: Luuk. [email protected]) J. A. van Steenwijk is with NXP RF Power and Basestations, 6534 AE Nijmegen, The Netherlands. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038453

the difficulties in properly characterizing these de-embedding standards. In Section II, we introduce a new algorithm for an equally general approach, which requires only three de-embedding standards. In Section III, we demonstrate that since the imperfect grounding of the internal ports is the dominant source of crosstalk between ports in typical on-wafer RF transistor test-structures, our 12-term approach is equally accurate as the most general mathematical four-port approach, which requires at least five dummy structures to resolve its full 15-term error model. We illustrate this by comparing experimental results obtained for six different increasingly sophisticated on-wafer correction schemes using 2–8 different de-embedding standards and resolving between 8–22 error terms, to see whether the use of extra de-embedding standards brings any sizable improvements over the more conventional approaches when applied to reasonably well designed test-structures. This is completed with a description of our method to de-embed down to the gate-finger level. -parameter data taken up to 110 GHz on 65- and 45-nm node MOSFET devices are used for the experimental validations reported in Section IV. II. OPEN–SHORT–LOAD DE-EMBEDDING A. Introduction Extracting the internal -parameters of the device-under-test (DUT) from measurements taken on on-wafer test structures is a central problem in high-frequency characterization and modeling. Fig. 1 shows an overview of the correction problem for a typical RF MOSFET device in an advanced CMOS process. The parasitic capacitances, resistances, and inductances of the contact pads and interconnect of the on-wafer test-structure are represented by a nine-terminal network, with four external terminals for the probe 1 and 2 signal (S , S ) and ground (G , G ) pads, four internal terminals to connect to the source (S), drain (D), gate (G), and bulk (B) nodes of the MOSFET, and one substrate terminal at the back of the wafer. The two ground pins of the commonly used ground-signal-ground RF-probes are treated as one. Although the grounds of the RF probes and the chuck carrying the wafer under test are connected to a global instrument ground, already at megahertz frequencies asymmetric currents [10] in the ground conductor of the RF-probe start to see prohibitively high inductances, while at gigahertz frequencies, one (Fig. 1) seen by these asymfinds that the impedance metric currents saturates at about 100 [27]. In properly designed test-structures with a low resistive connection between

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Fig. 1. Overview of the on-wafer test-structure parasitics correction (de-embedding) problem.

the opposite ground pads where the capacitive coupling of the internal DUT to the global instrument ground is negligible compared to that to the internal ground of the test structure, the impact of an asymmetric current system, as described in [10], will be hardly noticed. Furthermore, as far as it does play a role, all reference impedance standards used in the de-embedding process are equally affected, and this asymmetric current system will be de-embedded. After conventional line–reflect–reflect–match (LRRM) network analyzer calibration [28], [29], the impedance reference plane for two-port -parameter measurements is located at the tips of the RF probes. To fully characterize a four-terminal MOSFET device, a three-port description would be required, taking for instance the source as a ground reference. However, since one cannot de-embed three-port -parameter data from two-port -parameter measurements, two internal terminals, usually those connected to the source and bulk nodes, and sometimes those connected to the gate and bulk nodes are merged and used to define the internal ground reference of the test structure. Since there are no cross-connections between the external and internal terminals, there is no need to know the actual value of the internal ground reference. Therefore, the general correction problem depicted in Fig. 1 can be described by a single four-port network [see Fig. 2(a)] linking the measured two-port -parameters to those seen at the internal ports. B. Theoretic Framework To describe the new open–short–load de-embedding algorithm, we will work with the I–V relationships between the measurement and internal ports [see Fig. 2(a)], which can be expressed in a 4 4 -matrix as

Fig. 2. Physical four-port model for the interconnect between the external and internal ports. (a) Port definitions. (b) 11-element equivalent-circuit model.

to represent the measured voltage and current vectors, and (3) to represent the internal voltage and current vectors. This simplifies the above equation to (4) where measured and

and -parameters

are four 2 2 matrices. The provide the relation between

(5) while the internal -parameters and

provide the relation between

(6) where a minus sign is needed for the proper direction of the internal currents. A general equivalent circuit for the passive reciprocal network between the internal and the measurement ports is shown in Fig. 2(b), where we have chosen a resistor symbol for a connection, and a capacitor symbol where we expect to see only a parasitic capacitance. For this 11-element circuit, we find

(1)

rather than using power wave relationships or -parameter matrices. The notation is simplified by defining (2)

(7) Since the actual value of the internal ground voltage is not required for the de-embedding process, it might as well be set to zero by removing the impedance . This provides us with the

TIEMEIJER et al.: NEW 12-TERM OPEN–SHORT–LOAD DE-EMBEDDING METHOD

simplest possible equivalent circuit for the general reciprocal 4 4 -matrix. Generally however, and as shown in our exand are of minor periments, the physical capacitances importance, and assuming is a more realistic . This gives simplification than taking (8) and (9) and (10) Basically all on-wafer test-structure equivalent circuits in use today [1]–[14] can be mapped on this nine-element core circuit by standard internal node reduction techniques when the impedances and capacitances in this equivalent circuit are allowed to be complex frequency-dependent quantities. C. Reduction of Dummy Structures When we have measurements on five different suitable dummy structures available, the elements of the 4 4 -matrix can be found without any a-priori assumption on the actual parasitic network, and its reciprocity at all [24] (see the Appendix, Section B.). To see whether we can achieve the same results with a smaller amount of dummy structures, we and , the internal continue as in [21]. Using and the measured -parameters device -parameters can be related as

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and introducing rearranged into

and

, this can be

(17) where the left side of the equation contains a product of meaand the sured quantities, and the right side only contains unknown matrices and . At low frequencies, where open–short de-embedding is supposed to be correct, we ex. Assuming reciprocal interconnect, pect ), we are able to find the four elements (i.e., of these unknown matrices using only two additional “left” and “right” resistive dummy structures [21], [25] (see the Appendix, Section A.). It is, however, an interesting question whether it is worth the effort to try to resolve any possible and . Given that all on-wafer differences between test-structure equivalent circuits in use today consider imperfect grounding of the internal ports as the main source of crosstalk between the input and output ports, and furthermore , using the nine-element core equivalent assume circuit of Fig. 2(b) might be sufficient. Furthermore, even if , we expect that . To continue, we therefore define (18) and (19) which allows us to rearrange (17) into (20) where

(11) (21) The well known “open–short” de-embedding method [2] uses two dummy structures: an “open” with , and a short . Applying this, one obtains with

is a correction term accounting for any difference between and . Since we expect that , we subsequently neglect the correction term and rearrange (20) into

(12)

(22)

and (13) In the “open–short” method, the de-embedded device parameters are calculated by [2] (14) After substituting (11)–(13) in (14) and fairly extensive matrix manipulations, it is found that the result of this method can be related to the internal device -parameters as [21] (15) After defining (16)

from which we can solve (23) where the notion of square root is extended from numbers to matrices. In this case, only one additional calibration measureis sufficient ment taken on a load standard with to find , and after that fully resolve the 4 4 -matrix by ap. The two load impedances proximating in this standard do not have to be equal and they do not have to be pure 50- resistances, as long as their impedances are accurately known and do not differ too much from the preferred 50reference impedance. On the contrary, more common dummy structures like the “short1,” “short2,” and thru, as used for instance in [3], [5], and [13], are useless here since their infinite incause numerical problems in (23), which ternal admittances will remain finite, given that their measured counterpart

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would result in . Similarly, a “left” or a “right” resistive dummy [21] only allows us to find two elements of . in (4) reduces the We thus see that assuming number of unique elements in the 4 4 -matrix from 15 (see the Appendix, Section B.) to 12, which can be directly solved from the data measured on only three dummy structures. To continue, (22) is written as (24) with and are four different solutions for

. There , where (25)

where (26) Fig. 3. Overview of the de-embedding standards and their internal equivalent circuits which were used in this study. (a) DUT. (b) OPEN. (c) SHORT. (d) LOAD. (e) LEFT. (f) RIGHT. (g) THRU. (h) Capacitance, (i) Inductance.

and where (27) Although all four solutions can be used for open–short–load de-embedding, there is only one solution, which gives . This is the solution where the sign of is selected to maxand the sign of is chosen to put in or close to imize the first quadrant of the complex plane, giving it a positive real and imaginary part. After that, in this new “open–short–load” are calcumethod, the de-embedded device parameters lated by (28) where

When imperfect open and short standards are used, this three-step de-embedding procedure will correct for both the on-wafer, as well as for the standard parasitics, and thus, lead to a slight over de-embedding. When the imperfections of the open and short standards are known, a second four-port network describing these standard imperfections might be used to correct for this by embedding the de-embedded result with the standard imperfections, and moving the impedance reference plane exactly to where the internal DUT is thought to be located, should this be a concern [12].

. III. EXPERIMENTS

D. Final Remarks When

, relation (11) can be rearranged into

A. Introduction (29)

showing that rather than using (28), the de-embedded device parameters can also be recovered using

(30) This is a three-step de-embedding procedure where the external admittances , the series impedances , and the are subsequently subtracted internal admittances . This three-step procedure from the measured -parameters is particularly attractive for noise de-embedding [30], which is the process of deriving the internal transistor noise parameters from the noise parameters measured at the contact pads. To get the desired internal transistor noise parameters, the interconnect parasitics are assumed to have added current or voltage thermal noises proportional to the real parts of their respective admittances or impedances, which when working with the proper representations of the noise correlation matrices [31] can readily be subtracted from the measured transistor noise parameters.

To compare our new open–short–load de-embedding method with existing methods, -parameter measurements were taken up to 110 GHz with an LRRM [28], [29] calibrated Agilent 8510XF network analyzer on two sets of different transistor and dummy test-structures realized in 65- and 45-nm node CMOS technology, respectively. For the 65-nm node, in addition to the usual open and short dummy structures, (full) load, left (i.e., load-open), right (i.e., open-load), thru, capacitance, and inductance dummies, as shown in Fig. 3, were available for comparing different correction techniques. The capacitance and inductance dummies were actually open and short dummies designed to de-embed down to the individual MOSFET gate-finger level (see the Appendix, Section D.). For the second 45-nm node set, the pad capacitances were reduced as much as possible, while we restricted ourselves to the three essential open, short, and load de-embedding standards. The measured open dummy capacitance and short dummy inductance are shown in Figs. 4 and 5, respectively. For the 65-nm node, reasonable agreement is obtained with (Sonnet) electromagnetic (EM) simulations. The remaining differences illustrate the difficulty of properly capturing the complicated EM interaction between the RF probes

TIEMEIJER et al.: NEW 12-TERM OPEN–SHORT–LOAD DE-EMBEDDING METHOD

Fig. 4. Measured and EM simulated open dummy capacitance = Y =! versus frequency.

(

)

C =

423

j (from short, see text) and jY Fig. 6. Estimated value of jY (from open, see text) versus frequency.

j

j

by and in (7). This is helpful in judging whether the asis justified. Based on the equivalent cirsumption measured on the open cuit depicted in Fig. 2(b), the value of standard is (31) while the value of

measured on the short standard is (32)

From (7), we recall that (33) Fig. 5. Measured and EM simulated short dummy inductance : =! versus frequency. = Y

((( ) ) 11)

and contains contributions from both and we use with the fairly crude assumption that may approximate

L = neglecting

and the test-structure interconnect in such a simulation [32]. Nevertheless this type of EM simulations is very useful to check the validity of the assumptions made in the different de-embedding procedures compared in this paper and to verify that they are programmed correctly. B. Test-Structure Equivalent Circuit Up to a certain extent, the connections between the signal pad and internal devices can be considered as small transmission line sections. Based on the measurements taken on the open and short dummy structures, their characteristic impedances and delays are found to be about 13 and 28 , and 0.8 and 0.5 ps, for the 65- and 45-nm node structures, respectively. This implies that the first quarter-wavelength resonance of these fairly capacitive lines is in the 300–500-GHz region. The main concern for proper teststructure design is therefore to ensure that the intrinsic transistor capacitances are not overwhelmed by that of the signal pads. The -parameter measurements taken on the open and short standards allow us to get a rough estimate for the relative importance of the potentially asymmetric capacitive crosstalk caused

and and

. If instead of together , we (34)

to evaluate the impact of both contributions, and use (35) to get an approximate measure for just the amount of capaci, as roughly estimated from tive crosstalk. In Fig. 6, the crosstalk measured on the open standard, is compared to as found from the crosstalk measured on the the full short standard. It is seen that even using the crude assumption , the level of capacitive crosstalk that and in (7) remains orders of magnitudes below caused by the crosstalk caused by the imperfect grounding of the internal ports, which is by nature symmetric, and justifies that we take in order to reduce the number of dummy structures required for de-embedding from 5 to 3. C. Extraction of the De-Embedding Standards Before the de-embedding standards depicted in Fig. 3 can be used, their lumped element internal equivalent circuits, which

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Fig. 7. De-embedding standard characterization scheme used in this paper.

are supposed to consist of simple frequency-independent capacitors, resistors, and inductors, must be extracted with high accuracy. This in itself cannot be done without applying some simple de-embedding steps, and therefore, the internal de-embedding standard extraction procedure is an essential part of any de-embedding technique involving more than just an open and a short standard. The de-embedding standard characterization scheme used in this study is schematically depicted in Fig. 7. After assuming ideal open and short de-embedding standards, open–short and short–open de-embedding are used to find the internal equivalent circuits of the load and left and right standards. Provided that the size of the resistances in the load, left and right standards has been chosen small enough that the roll-off due to parasitic capacitances to the substrate occurs beyond our frequencies of interest, these resistances can be assumed to be frequency independent, and open–short de-embedding is sufficient to extract these internal resistance values from low-frequency results. To also get an estimate for the residual parasitic capacitances in these standards, (see Fig. 3), we can use pad–short–open de-embedding [21] or approximate its intrinsic behavior by a weighted average of the open–short and short–open results [7] (36) Typically a weight factor of 0.7 flattens the resistance exin the frequency range up tracted from the real part of to 20 GHz. This is consistent with the EM simulation showing that the on-wafer pad parasitic capacitances can be divided approximately with a 30/70 ratio between internal and external ports. After that, open–short–load de-embedding is used to find the internal equivalent circuits of the thru, capacitance, and inductance standards. D. De-Embedding Uncertainty In order to benchmark our new open–short–load de-embedding method against existing alternatives, and to see whether the use of a sophisticated scheme with many de-embedding standards pays off, the measurement uncertainty at the internal ports should be compared. This de-embedding uncertainty is a combination of random errors caused by the finite signal-to-noise ratio of the -parameter measurements, and the systematic errors caused by improper simplifications made in the de-embedding process. To get a realistic estimate for the de-embedding uncertainty, the errors made after measuring and de-embedding a suitable collection of internal impedance

Fig. 8. De-embedding uncertainty (see text) found for six different de-embedding methods.

standards are averaged. When the de-embedding procedure requires solving an over-determined system of equations (see the Appendices, Sections A.–C.), this can be done using the same impedance standards as used for extracting the error model. However, for open–short and open–short–load de-embedding, it is essential to include at least some de-embedding standards that were not used in the de-embedding algorithm. For all de-embedding algorithms compared in this section, we therefore define the de-embedding uncertainty (37) as the rms average of the differences found between all four internal -parameters and de-embedded -parameters of the nine different de-embedding standards (Fig. 3, using two different capacitance standards) available for this study. This de-embedding uncertainty is plotted versus frequency in Fig. 8 for six different de-embedding methods employing different amounts of extra de-embedding standards, as shown in Table I. These methods are open–short , the new open–short–load de-emde-embedding introduced in this paper, assuming bedding , the open–short–leftt–right de-embedding of , see the Appendix, Section A.), as[21] ( suming reciprocal interconnect, and a full four-port least square fit using either the minimal required five dummies (open–short–left–right–thru) or the complete set of eight and , see the dummies ( Appendix, Section B.), and finally, a full 22-term in-situ calibration (ISC) procedure (see the Appendix, Section C.). The comparison between the four four-port methods OSL, OSLR, OSLRT, and OSLLRTCI is the most interesting one since the differences in de-embedding uncertainty for these four approaches are marginal, and do not reveal any substantial benefit from increasing the number of de-embedding standards from 3 to 8 (Table I). This confirms our idea that these four methods basically all extract the same nine-element core

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TABLE I EXTRA DE-EMBEDDING STANDARDS ADDED TO IMPROVE THE BASIC OPEN–SHORT (OS) METHODOLOGY

equivalent circuit for the interconnect parasitics. This becomes evident when they are compared with the de-embedding uncertainty obtained for the open–short method, which is visibly higher since only an incomplete equivalent circuit is extracted. When compared to the de-embedding uncertainty found using a full 22-term ISC procedure (see the Appendix, Section C.) capable of taking port mismatch differences into account by resolving separate error networks for forward and reverse excitation, this is put into further perspective. When verified with simulated data, all de-embedding algorithms shown in Fig. 8, with the obvious exception of open–short de-embedding, reproduced the de-embedded standards within 10 , demonstrating that the contribution from numerical noise is negligible in Fig. 8. With the same exception of open–short de-embedding, the general increase of the internal measurement uncertainty with frequency seen in Fig. 8 is therefore attributed to the decrease in system dynamic range of the Agilent 8510XF network analyzer used for this study, which reduces from about 80 dB at 10 GHz to about 40 dB at 100 GHz, rather than to imperfections in the de-embedding algorithm. E.

Fig. 9. Comparison of the extracted values for Z ; Z and Z using the three dummy analytical open–short–load procedure and the five dummy fourport fit versus frequency. The measured Z values are included for reference.

-Parameter Matrix Elements

When the elements of the 4 4 parameter matrix extracted with the general five standards method are compared to those , and using the open–short–load obtained assuming de-embedding algorithm, only marginal differences are seen. We, therefore, restrict ourselves to comparing the extracted and with the measured in order values for made in the to verify that the assumption that open–short–load de-embedding algorithm is justified. As shown in Fig. 9, at low frequency an excellent agreement between the and and the measured is found, while at extracted higher frequencies, a small, but systematic, difference starts to and occur. At high frequency, the off-diagonal elements of extracted using the OSLRT four-port fit get fairly noisy, and show, for instance, no indication that assuming would have been more realistic than assuming . To study this in more detail, the differences (38) are plotted in Fig. 10, and the results obtained with the open–short–load method are compared to those obtained using a full least squares fit using either five or eight de-embedding standards. As illustrated in Fig. 10, the off-diagonal differences obtained after the OSLRT and OSLLRTCI four-port fits have collected a considerable amount of measurement noise, whereas compared to that, the differences obtained after

Fig. 10.

Z

difference (see text) versus frequency.

open–short–load de-embedding are extremely smooth and well behaved, and almost disappear below 10 GHz. IV. MOSFET DEVICE CHARACTERISTICS A. Single MOSFET Devices To ensure that MOSFET devices can be characterized with good accuracy, it is desirable that the intrinsic MOSFET capacitances are at least of similar size as that of the test-structure pads and interconnect, which requires that we restrict ourselves to fairly big multifinger devices. We will start with a 45-nm node MOSFET device, employing 64 gate fingers of 0.7- m width contacted from both sides in parallel. For this device, we compare several device characteristics obtained after open–short and open–short–load de-embedding to get an indication for the frequencies where the more sophisticated de-embedding schemes start to pay off. Fig. 11 shows a plot of the trans-conductance and output conductance versus freand , when quency extracted from the real parts of

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Fig. 11. Trans-conductance and output conductance versus frequency for a V V. 45-nm node MOSFET biased at V

=

Fig. 12. MOS capacitances C ; C 45-nm node MOSFET biased at V

=1

; C ; and C

= V = 1 V.

Fig. 13. Input resistance versus frequency for a 45-nm node MOSFET biased V at V V.

=

=1

versus frequency for a

biased at V. As indicated by the dashed lines, these quantities are expected to be flat with frequency, which is indeed the case after open–short–load de-embedding. The increase in trans-conductance with frequency after open–short de-embedding is clearly a de-embedding artifact since, at high frequency, eventually MOSFET models predict a roll-off rather than an increase. Fig. 12 shows a plot of the intrinsic MOS capacitances obtained after dividing the imaginary parts of the MOSFET -parameters by the frequency, and which again are expected to be flat with frequency. Although not entirely flat, the result obtained after open–short–load de-embedding is better behaved. Fig. 13 shows a plot of the input series over frequency. resistance extracted from the real part of Open–short–load de-embedding reveals a lower input resistance value, which is more constant over frequency. Finally, Fig. 14 shows the plots of the current gain and the unilateral (Mason’s) power gain [33] versus frequency, from which, in this case, the (180 GHz) and (300 GHz) can be cutoff frequencies obtained by extrapolation. The ITRS Roadmap recommends is extrapolated that the maximum oscillation frequency using a 20-dB per decade slope from the unilateral power gain measured at 40 GHz. If this would have been done based on the

Fig. 14. Small-signal current gain and unilateral power gain versus frequency V V. The cutoff frequencies for a 45-nm node MOSFET biased at V f and f are 180 and 300 GHz, respectively.

=

=1

open–short de-embedded data, one would have underestimated by almost a factor of 2. B. Down to the MOSFET Gate-Finger Level From a device modeling perspective, it is desirable to remove as much as possible interconnect parasitic capacitances from the measured data, and to de-embed the measurements down to the individual MOSFET gate-finger level [34], [35]. This requires an extra dedicated (D) short–open correction step, as described in the Appendix, Section D., mainly to take the local interconnect capacitance into account, and division by the number of gate fingers. Fig. 15 shows a comparison of the trans-conductances and output conductances versus frequency extracted from the real and for a 65-nm node MOSFET technology parts of 3 m 55 nm gate finger, again contacted from both sides and biased at V. These results were derived from measurements on a structure containing 80 of these gate fingers in parallel. With the dedicated (D) short–open correction step, the results obtained after open–short (OSD), open–short–load

TIEMEIJER et al.: NEW 12-TERM OPEN–SHORT–LOAD DE-EMBEDDING METHOD

Fig. 15. Trans-conductance and output conductance versus frequency for a V V. 3 m 55 nm MOSFET gate finger biased at V

2

=

Fig. 16. MOS capacitance versus frequency for a 3 m V V. finger biased at V

=

=1

=1

2 55 nm MOSFET gate

427

Fig. 17. MOS capacitance versus frequency for a 3 m V V. finger biased at V

=

=1

Fig. 18. Input resistance versus frequency for a 3 m V V. finger biased at V

=

=1

2 55 nm MOSFET gate

2 55 nm MOSFET gate

C. Symmetrical Devices (OSLD), and four-port (OSLRTD) de-embedding are largely flat with frequency, whereas the result obtained after a conventional open–short (OS) de-embedding, where all capacitances are assumed to be in the bondpads, clearly is not. Fig. 16 shows a and obcomparison of the intrinsic MOS capacitances tained after OSD, OSLD, and OSLRTD de-embedding, where the latter two results are slightly better behaved than the OSD result. Fig. 17 shows a similar comparison of the intrinsic MOS and . Finally, in Fig. 18, the input series recapacitances sistance extracted after the different de-embedding procedures are compared. The results are noisy and differ considerably, and there is no clear winner, apart from the fact that once a multitude of impedance standards are available, the OSLLRTCID four-port least square fit procedure employing data measured on all these standards seems to provide the most consistent result up to 80 GHz. We finally mention that the ISC method employing separate parasitic networks for forward and reverse excitation produced considerable noisier results for these MOSFET fingers and was, therefore, omitted from our comparison plots for clarity.

In [21], a simplified version of the open–short–load de-embedding procedure was presented for use with symmetrical passive devices like differential inductors. When applied to clearly asymmetric active devices like transistors or even weakly asymmetric passive devices like certain fringe capacitor structures, this procedure gives erroneous results since the matrix multiplications cannot be commuted. However, as illustrated in Fig. 19, when applied to highly symmetric differential inductors, the simplified and general open–short–load de-embedding algorithms produce almost indiscernible results. V. CONCLUSION We have presented a new 12-term three-standard open–short–load de-embedding method and have demonstrated it to be equally accurate as the current most general 15-term de-embedding scheme, which requires at least five impedance standards. When multiple open and short de-embedding standards are already available, for instance, to separate the internal and external parasitic capacitances, and to allow de-embedding down to the individual MOSFET gate-finger

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needed in (39), and to keep the mathematics simple, we assume complementary left and right standards with internal load impedances (41) and (42) and . Substitution in where (39) provides us with an overdetermined system of six nonlinear equations for the four elements of (43) (44) (45) (46)

Q

Fig. 19. Differential factor versus frequency for a 0.5-nH single-turn octagonal inductor in 45-nm node CMOS technology. For this symmetrical device, the results obtained after the simplified [21] and general open–short–load de-embedding are indiscernible.

(47) level, the end result can already be fairly accurate without adding load standards. Similarly for symmetrical passive devices like differential inductors, the simple open–short–load de-embedding algorithm we presented in [21] already gives the correct result. For all other cases, the possibility to achieve a full correction of all on-wafer parasitics without any a-priori assumption regarding their relative distribution as, for instance, needed for the industry standard open–short de-embedding method, with only three well-defined impedance standards, will allow a considerable saving of wafer area and test time, particularly when de-embedding standards cannot be shared between different devices. We have included a large amount of experimental results to illustrate our findings and have included in the Appendix a full description of the alternative de-embedding methods compared in this paper in order that our benchmarks can be repeated.

and

(48) Substraction of (44) from (43) provides us with (49) which allows us to eliminate from (43) and find . Sim. Although (43)–(46) ilarly, (45) and (46) allow us to find and , these parameters can be can also provide us with more accurately solved from (47) and (48) once and are known. Substraction of (48) from (47) provides us with

(50) APPENDIX A. Open–Short–Left–Right De-Embedding Open–short–left–right de-embedding assumes reciprocal interconnect, which, strictly spoken, reduces the number of unique elements of the full 4 4 parameter matrix to 10. However, , the method again extracts since we only need to use a 12-term error model. Since the solutions presented in [21] and [25] require ideal crosstalk-free internal left (L) and right (R) standards, in this paper, a more general approach is introduced, applicable for any complementary set of left and right standards. , (15) can be simplified into [21] Using (39) where

. To solve the

matrix (40)

yielding a relation between and . After elimination of from (47), can be found. Selecting the correct roots in solving the quadratic equations is fairly straightforward since the matrix reflects the deviation from the open–short de-embedded result, and should therefore approximately equal the unity matrix. After that, in the “open–short–left–right” method, are calculated by the de-embedded device parameters (51) B. Open–Short–Left–Right-Thru De-Embedding To find the full 4 4 -parameter matrix without any a-priori assumptions at all, at least five de-embedding standards are required, leading to an overdetermined system of equations. To minimize the de-embedding residuals in (37), we prefer to work with the linear wave relationships [16], [24] rather than the voltage and current relationships [26] or the methods given in [20] and [25] since it allows us to extract the

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where

(60) and (61) Fig. 20. Scheme of the four-port de-embedding in wave representation.

(62) on-wafer parasitics network using constant weight linear least squares minimization. In this method, the reflected and incident waves at the four-port parasitics network (Fig. 20) are assumed to be related through a 4 4 matrix as

(63) (64) and (65)

(52)

where the notation is simplified defining (53)

Obviously we cannot solve 15 unknowns from only four equations. However, the calibration measurements taken on the five open, short, left, right, and thru standards recommended in [24] provide us with an overdetermined system of 20 equations from which the elements of can be solved. To find the vector , which minimizes the de-embedding uncertainty

for the measured waves and (66) (54) we request

for the internal waves, which allows us to write

(67)

(55)

for all elements of . The resulting set of 15 linear equations The measured and

-parameters

provide the relation between (68) (56)

while the internal -parameters and

provide the relation between

allows us to solve

from (69)

(57) where Substitution allows us to derive the linear equation (70)

(58) which can be used for a least squares fit of the elements of the matrix using known values of and . Since we only need to relate external and internal -parameters using the above equa, which means that we can set tions, it is sufficient to know , to unity, leaving one of the elements of the matrix, here 15 unique matrix elements left to be determined. We see that (58) provides us with four equations (59)

and (71) We found that it was not necessary to revert to singular value decomposition (SVD), as in [16] and [24], to solve since tests with simulated data confirmed the numerical noise to be already level using this classical approach, nine orders of at the 10 magnitude below the typical de-embedding uncertainty depicted

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in Fig. 8. Once the matrix has been found, the de-embedded -parameters can be found using (72) , for Due to the fitting process, we only have any DUT, including the standards used for finding the matrix. The measurements taken on the load, capacitance, and inductance de-embedding standards provide us with 12 additional equations, which can be used to reduce the impact of the measurement noise on the 15 extracted error coefficients. The result of this eight-dummy de-embedding procedure will be referred . To obtain the corresponding 4 4 -paramto as eter matrix, (55) is rearranged into (73) where

(74) and which we recognize as the 4 4 -parameter matrix of the on-wafer parasitics network, from which we can obtain the 4 4 -parameter matrix using (75) where is the identity matrix. We may select such that to get a more physical on-wafer parasitics network. However, we can only make one of the off-diagonal -parameters reciprocal, and will after that, typically find that due to measurement noise, the remaining off-diagonal -parameters are slightly nonreciprocal. For the four-port -parameters, the same findings apply [25]. C. ISC All de-embedding recipes published to date assume the probe tips have been properly calibrated at their impedance reference plane. Inspired by its perceived completeness in [25], it was postulated that the four-port de-embedding algorithm could even work without a proper network analyzer calibration, and that it could be attractive to combine the network analyzer calibration and the de-embedding steps into one general ISC procedure. The historical separation of the network analyzer calibration and the subsequent on-wafer de-embedding did not come along without good reason however, since there are some fundamental differences between network analyzer calibration and on-wafer de-embedding. First of all, in today’s advanced network analyzers, the signals measured by four receivers are not only used to move the calibration reference plane to the probe tips, but also to correct for port mismatch errors, which generally will be different for forward and reverse excitation. On the other hand, the network analyzer calibration algorithms in use today assume that crosstalk between the measurement ports can be neglected,

Fig. 21. Simplified block diagram of the error networks assumed for a threemeasurement channel network analyzer.

in order to reduce the number of calibration standards, and the extent that their behavior must be known before hand. Typically a seven-error term model [28] is used to derive the -parameters seen at the probe tips from the incident and reflected waves measured by the network analyzer. These calibrated -parameters are then the starting point for the subsequent de-embedding process, which aims to eliminate the on-wafer parasitics. When we prefer to perform an ISC instead, we have the choice of either using the signals measured by the four receivers of the network analyzer or work with the -parameters read from the network analyzer. In either case, we now do need to account for leakage errors between the measurement ports. The classical theory of calibrating a network analyzer in the presence of leakage errors can be found in [16]–[18], where it is shown that five calibration standards are needed in order to resolve a 15-error term model relating the ( ) incident and ( ) reflected waves measured by the four receivers of the network analyzer to those seen at the probe tips. Using the raw -parameters instead, as suggested in [25], things get more difficult. Mathematically this problem is equivalent to calibrating a leaky network analyzer, which has only three measurement channels [18], and where we need to find separate solutions for the error for forward and reverse excitation since the port network mismatch errors have become part of the error network. Since for each excitation direction one of the waves is set to zero, and we are furthermore only interested in the ratio’s between the different waves depicted in Fig. 21, we need to resolve 22 errors terms in this approach [18]. To establish whether such an ISC scheme can provide a more profound correction of systematic measurements errors, it is not required to work with the raw -parameters. To be able to make a one-to-one comparison with the different four-port schemes described in this paper, it is instead much more practical to work with the same calibrated -parameter measurements. Approximately following the notation used in [18] and referring to Fig. 21, the incident and reflected power waves at the internal DUT are again related as in (57) (76) Using and to denote the signal waves under forward and backward excitation, respectively, the measured -parameters are now (77)

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431

where . Subsequently separate error networks are introduced relating the signal waves at the measurement and internal ports for forward and backward excitation. For forward excitation, we have Fig. 22. Wiring scheme for a parallel MOSFET test-structure.

(78)

whereas for backward excitation, we have

(79)

Since again it is sufficient to know , we can set one of the elements of the matrices to unity, leaving 2 11 matrix elements to be determined. After combining (76)–(79) as in [18], it is seen that each measured dummy structure provides two linear equations of the form (80) for both forward and reverse excitation, where again the and coefficients are products of different combinations of known quantities and the coefficients are the unknown elements of the error matrix . According to [18], the measurements taken on six different de-embedding standards should be sufficient to extract the error matrices . We found, however, that we needed to use the data taken on all our eight de-embedding standards to achieve a better internal measurement uncertainty as found for the four-port methods (Fig. 8). To get a best (least squares) fit for , we must minimize the total error (81)

finger, this local interconnect also has to be de-embedded. Although each finger will see a slightly different wiring resistance, these differences are small enough that first-order corrections are sufficient. A dedicated open dummy structure containing all interconnect down to the lowest metal level allows to correct for all wiring and local interconnect capacitances seen in the test-structures. However, a dedicated short structure where all gate fingers have been replaced by full shorts will show a parasitic series impedance for the gate and drain connections, which is less than that seen by most gate fingers. This can be solved when a dedicated short structure where only the end fingers are replaced by a full short is used. Subtracting the impedance measured on a standard short structure provides the interconnect series impedance seen between the center (1) and the end fingers ( ). Assuming the wiring resistance is small enough that all gate fingers are biased identically, they will consume equal ac currents, and then according to transmission line theory, the effective series impedances seen in the lines connecting to G, D, and S B will be 1/3 of the total series impedance seen between the center and end fingers. Combined with conventional open–short de-embedding, a three-step de-embedding procedure is obtained, as used in [34] and [35]. In this de-embedding of each internal device is calprocedure, the admittance culated from that measured on the DUT using (83) where where

denotes the number of devices placed in parallel, (84)

by setting of 11 linear equations

for all 11 values of , resulting in a set where (82)

which are solved by matrix inversion. After that, the de-embedding is performed as in [18], yielding . Due to the inclusion of the port match variations, interpretation of this 22-error term model in terms of a parasitic equivalent circuit is not possible anymore. D. De-Embedding Down to the Gate-Finger Level From a device modeling perspective, it is desirable to remove as much as possible of the interconnect parasitic capacitances from the measured data, and to be able to de-embed the measurements down to the individual MOSFET gate-finger level [34], [35]. Fig. 22 shows the typical local interconnect wiring scheme required to connect gate fingers to the internal ports of the test-structure. To retrieve the -parameters of an individual gate

was defined in (12), where

was defined in (16), (85)

is calculated from a dedicated short structure where the end device ( ) is replaced by a full short, and where (86) is calculated from the dedicated open dummy structure containing all interconnect down to the lowest metal level. Since is very small, the impact of the corrections provided by rather than using a separate short structure each time the local interconnect length between the first and last devices changes, in (84), a tuning factor is used to capture the differences. This saves costly wafer space. As explained, the three-step de-embedding procedure to retrieve the MOSFET performance at the gate-finger level exists of a general open–short de-embedding step for removing the pads and the global interconnect followed by a dedicated short–open de-embedding step for removing the

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local interconnect. To make a fair comparison, whether the introduction of the new open–short–load method, or one of the more elaborate four-port de-embedding schemes could improve the de-embedded results at the gate-finger level, the general open–short step was replaced by one of these four-port de-embedding steps. After a similar dedicated short–open step, the adand are obtained. mittances ACKNOWLEDGMENT The authors wish to acknowledge R. van der Hout, VU University Amsterdam, Amsterdam, The Netherlands, for valuable suggestions regarding some of the matrix calculations used in this work. REFERENCES [1] P. J. van Wijnen, H. R. Claessen, and E. A. Wolsheimer, “A new straightforward calibration and correction procedure for ‘on-wafer’ high frequency S -parameter measurements (45 MHz–18 GHz),” in Proc. IEEE Bipolar/BiCMOS Circuits Technol. Meeting, Sep. 1987, pp. 70–73. [2] M. C. A. M. Koolen, J. A. M. Geelen, and M. P. J. G. Versleijen, “An improved de-embedding technique for on-wafer high frequency characterization,” in Proc. IEEE Bipolar/BiCMOS Circuits Technol. Meeting, Sep. 1991, pp. 188–191. [3] H. Cho and D. Burk, “A three step method for the de-embedding of high frequency S -parameter measurements,” IEEE Trans. Electron. Devices, vol. 38, no. 6, pp. 1371–1375, Jun. 1991. [4] T. E. Kolding, “A four-step method for de-embedding gigahertz on-wafer CMOS measurements,” IEEE Trans. Electron. Devices, vol. 47, no. 4, pp. 734–740, Apr. 2000. [5] E. P. Vandamme, D. M. M.-P. Schreurs, and C. van Dinther, “Improved three-step de-embedding method to accurately account for the influence of pad parasitics in silicon on-wafer RF test-structures,” IEEE Trans. Electron. Devices, vol. 48, no. 4, pp. 737–742, Apr. 2001. [6] C. H. Chen and M. J. Deen, “A general noise and S -parameter deembedding procedure for on-wafer high-frequency noise measurements of MOSFETs,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 5, pp. 1004–1005, May 2001. [7] L. F. Tiemeijer and R. J. Havens, “A calibrated lumped-element de-embedding technique for on-wafer RF characterisation of high-quality inductors and high speed transistors,” IEEE Trans. Electron. Devices, vol. 50, no. 3, pp. 822–829, Mar. 2003. [8] C. Andrei, D. Gloria, F. Danneville, and G. Dambrine, “Efficient de-embedding technique for 110 GHz deep-channel-MOSFET characterization,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 4, pp. 301–303, Apr. 2007. [9] A. Issaoun, Y. Z. Xiong, J. Shi, J. Brinkhoff, and F. Lin, “On the deembedding issue of CMOS multigigahertz measurements,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 9, pp. 1813–1823, Sep. 2007. [10] B. Rejaei, A. Akhnoukh, M. Spirito, and L. Hayden, “Effect of local ground and probe radiation on the microwave characterization of integrated inductors,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 10, pp. 2240–2247, Oct. 2007. [11] J. Cha, J. Cha, and S. Lee, “Uncertainty analysis of two-step and threestep methods for de-embedding on-wafer RF transistor measurements,” IEEE Trans. Electron. Devices, vol. 55, no. 8, pp. 2195–2201, Aug. 2008. [12] S.-M. Kuo and M. N. Tutt, “Improvement on de-embedding accuracy by removing parasitics of short standards,” in Proc. IEEE Bipolar/ BiCMOS Circuits Technol. Meeting, Sep. 2008, pp. 240–243. [13] M. Ferndahl, C. Fager, K. Andersson, P. Linner, H.-O. Vickes, and H. Zirath, “A general statistical equivalent-circuit-based de-embedding procedure for high-frequency measurements,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 2692–2700, Dec. 2008. [14] M.-H. Cho, D. Chen, R. Lee, A.-S. Peng, L.-K. Wu, and C.-S. Yeh, “Geometry-scalable parasitic deembedding methodology for on-wafer microwave characterization of MOSFETs,” IEEE Trans. Electron. Devices, vol. 56, no. 2, pp. 299–305, Feb. 2009. [15] I. M. Kang, S.-J. Jung, T.-H. Choi, J.-H. Jung, C. Chung, H.-S. Kim, H. Oh, H. W. Lee, G. Jo, Y.-K. Kim, H.-G. Kim, and K.-M. Choi, “Five-step (pad–pad short–pad open–short–open) de-embedding method and its verification,” IEEE Electron. Device Lett., vol. 30, no. 4, pp. 398–400, Apr. 2009.

[16] J. V. Butler, D. K. Rytting, M. F. Iskander, R. D. Pollard, and M. V. Bossche, “16-term error model and calibration procedure for on-wafer network analysis measurements,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 2211–2217, Dec. 1991. [17] K. J. Silvonen, “Calibration of 16-term error model,” Electron. Lett., vol. 29, no. 17, pp. 1544–1545, Aug. 1993. [18] H. Heuermann and B. Schiek, “Results of network analyzer measurements with leakage errors—Corrected with direct calibration techniques,” IEEE Trans. Instrum. Meas., vol. 46, no. 5, pp. 1120–1127, Oct. 1997. [19] N. L. Wang, W. J. Ho, and J. A. Higgins, “New de-embedding method for millimetre-wave bipolar transistor S -parameter measurement,” Electron. Lett., vol. 27, no. 18, pp. 1611–1612, Aug. 1991. [20] Q. Liang, J. D. Cressler, G. Niu, Y. Lu, G. Freeman, D. C. Ahlgren, R. M. Malladi, K. Newton, and D. L. Harame, “A simple four-port parasistic deembedding methodology for high-frequency scattering parameter and noise characterization of SiGe HBTs,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 11, pp. 2165–2174, Nov. 2003. [21] L. F. Tiemeijer, R. J. Havens, A. B. M. Jansman, and Y. Bouttement, “Comparison of the ‘pad-open–short’ and ‘open–short–load’ de-embedding techniques for accurate on-wafer RF characterisation of high quality passives,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 723–729, Feb. 2005. [22] S. Lee, L. Wagner, B. Jagannathan, S. Csutak, J. Pekarik, N. Zamdmer, M. Breitwisch, R. Ramachandran, and G. Freeman, “Record RF performance of sub-46 nm Lgate NFETs in microprocessor SOI CMOS technologies,” in IEEE Int. Electron. Devices Meeting Tech. Dig., Dec. 2005, pp. 251–254. [23] R. Groves, J. Wang, L. Wagner, and A. Wan, “Quantitative analysis of errors in on-wafer S -parameter de-embedding techniques for high frequency device modeling,” in Proc. IEEE Bipolar/BiCMOS Circuits Technol. Meeting, Sep. 2006, pp. 92–95. [24] X. Wei, G. Niu, S. L. Sweeney, and S. S. Taylor, “Singular-value-decomposition based four port de-embedding and single-step error calibration for on-chip measurement,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 3–8, 2007, pp. 1497–1500. [25] X. Wei, G. Niu, S. L. Sweeney, Q. Liang, X. Wang, and S. S. Taylor, “A general 4-port solution for 110 GHz on-wafer transistor measurements with or without impedance standard substrate (ISS) calibration,” IEEE Trans. Electron. Devices, vol. 54, no. 10, pp. 2706–2714, Oct. 2007. [26] K. Silvonen, N. H. Zhu, and Y. Liu, “A 16-term error model based on linear equations of voltage and current variables,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1464–1469, Apr. 2006. [27] L. F. Tiemeijer, R. M. T. Pijper, R. J. Havens, and O. Hubert, “Low-loss patterned ground shield interconnect transmission lines in advanced IC processes,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 3, pp. 561–570, Mar. 2007. [28] L. Hayden, “An enhanced line–reflect–reflect–match calibration,” in 67th ARFTG Conf. Dig., Jun. 2006, pp. 143–149. [29] F. Purroy and L. Pradell, “New theoretical analysis of the LRRM calibration technique for vector network analyzers,” IEEE Trans. Instrum. Meas., vol. 50, no. 5, pp. 1307–1314, Oct. 2001. [30] T. E. Kolding and C. R. Iversen, “Simple noise deembedding technique for on-wafer shield-based test fixtures,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 11–15, Jan. 2003. [31] H. Hillbrand and P. H. Russer, “An efficient method for computer aided noise analysis of linear amplifier networks,” IEEE Trans. Circuits Syst., vol. CAS-23, no. 4, pp. 235–238, Apr. 1976. [32] C. Andrei, D. Gloria, F. Danneville, P. Scheer, and G. Dambrine, “Coupling on-wafer measurement errors and their impact on calibration and de-embedding up to 110 GHz for CMOS millimeter wave characterizations,” in Proc. IEEE Int. Microelectron. Test Structures Conf., Mar. 2007, pp. 253–256. [33] M. S. Gupta, “Power gain in feedback amplifiers, a classic revisited,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 5, pp. 864–878, May 1992. [34] L. F. Tiemeijer, H. J. M. Boots, R. J. Havens, A. J. Scholten, P. W. H. de Vreede, P. H. Woerlee, A. Heringa, and D. B. M. Klaassen, “A record high 150 GHz fmax realized at 0.18 m gate length in an industrial RF-CMOS technology,” in IEEE Int. Electron. Devices Meeting Tech. Dig., Dec. 2001, pp. 223–226. [35] L. F. Tiemeijer, R. J. Havens, R. de Kort, A. J. Scholten, R. van Langevelde, D. B. M. Klaassen, G. T. Sasse, Y. Bouttement, C. Petot, S. Bardy, D. Gloria, P. Scheer, S. Boret, B. Van Haaren, C. Clement, J.-F. Larchanche, I.-S. Lim, A. Zlotnicka, and A. Duvallet, “Record RF performance of standard 90 nm CMOS technology,” in IEEE Int. Electron. Devices Meeting Tech. Dig., Dec. 2004, pp. 441–444.

TIEMEIJER et al.: NEW 12-TERM OPEN–SHORT–LOAD DE-EMBEDDING METHOD

Luuk F. Tiemeijer was born in Son en Breugel, The Netherlands, in 1961. He received the M.S. degree in experimental physics from the State University of Utrecht, Utrecht, The Netherlands, in 1986, and the Ph.D. degree in electronics from the Technical University of Delft, Delft, The Netherlands, in 1992. His dissertation was entitled “Optical properties of semiconductor lasers and laser amplifiers for fiber optical communication.” He was with Philips Research Laboratories, Eindhoven, The Netherlands, where he conducted research on InGaAsP semiconductor lasers and optical amplifiers. Since 1996, he has been involved in the RF characterization and modeling of advanced integrated circuit (IC) processes. In October 2006, he joined NXP Semiconductors, Eindhoven, The Netherlands. He has coauthored over 130 scientific publications. He is a coinventor on over 20 patent applications.

Ralf M. T. Pijper was born in Holtum, The Netherlands, in 1977. He received the M.Sc. degree in applied physics from the Technical University of Eindhoven, Eindhoven, The Netherlands, in 2003. In 2005, he joined Philips Research Laboratories, Eindhoven, The Netherlands, where he was involved with RF characterization of advanced integrated-circuit technologies. In October 2006 he joined NXP Semiconductors, Eindhoven, The Netherlands.

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Jan Anne van Steenwijk was born in Leiden, The Netherlands, in 1951. He received the M.S. degree in electrical engineering from the Delft University of Technology, Delft, The Netherlands, in 1978. He then joined the Philips Research Laboratory, Eindhoven, The Netherlands, where he was engaged in research on high-speed integrated circuits for optical telecommunication systems, light propagation in optical fibers, and modeling and characterization of MOS transistors. In 1991, he was with the Quality Engineering Group, Philips Consumer Electronics. In 1994, he was with the Reliability Group, Philips Applied Technologies. Within both groups, he was involved in the field of robust design and compact modeling for circuit simulation. In 1998, he joined Philips Semiconductors (now NXP Semiconductors), Nijmegen, The Netherlands. His main research interest is characterization and modeling of RF-LDMOS devices for base-station, broadcast, and microwave applications.

Edwin van der Heijden was born in Eindhoven, The Netherlands, in 1970. He received the a degree in electrical engineering from the Eindhoven Polytechnic College, Eindhoven, The Netherlands, in 1994. In 1996, he joined Philips Research Laboratories, Eindhoven, The Netherlands, where he conducted research on high-frequency load–pull characterisation of RF power transistors and on-wafer RF characterization of various active and passive devices in advanced IC processes. Since 1998, he has been involved in RF IC design on integrated transceivers. In 2006, he joined NXP Semiconductors, Eindhoven, The Netherlands.

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On a Method to Reduce Uncertainties in Bulk Property Measurements of Two-Component Composites Christian Engström

Abstract—For two-component composites, we address the inverse problem of estimating the structural parameters and decrease measurement errors in bulk property measurements. A measurement of the effective permittivity at one frequency gives microstructural information about the composite that is used in cross-property bounds to estimate the effective permittivity at other frequencies. We use this information and inverse bounds on microstructural parameters to tighten error bars on permittivity measurements at microwave frequencies. The method can be used in the design of random and periodic composite materials for a large variety of applications. We apply the method to a composite material used in radar applications. Index Terms—Composites, inverse bounds, microwave, permittivity, quasi-static.

I. INTRODUCTION EASUREMENTS of composites effective dielectric, thermal, and magnetic properties are of fundamental importance in physics and engineering. The design of composite materials with novel physical properties is important owning to the many technical applications. The predictions of the properties of these new materials are often based on experiments, which frequently have large or unknown uncertainties. Therefore, it is highly desirable to develop a systematic and reliable method to verify the measured values and to reduce measurement uncertainties. Classical effective medium approximations and mixing formulas such as the Maxwell Garnett formula [1] and the Bruggeman formula [1] are frequently used to model random composites. The Maxwell Garnett formula is exact for the Hashin structure in which the two materials for all volume fractions are well separated coated spheres [1]. Real composites, however, do not have the Hashin structure, but the Maxell Garnett formula is, in many cases, a good approximation when small volume fractions are considered and when the microstructure is similar to the Hashin structure [1], [2]. The Bruggeman formula is exact for the Milton structure [1] and the formula predicts, in three dimensions, the critical volume fraction 1/3, above which a connected path through the structure exists.

M

Manuscript received June 11, 2009. First published January 19, 2010; current version published February 12, 2010. The author is with the Laboratory for Electromagnetic Fields and Microwave Electronics, ETH Zürich, Zürich, Switzerland (e-mail: [email protected]. ch). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038656

The volume fraction above which percolation occurs is highly sensitive to the microstructure, whereby the critical volume fraction is, in general, not 1/3 [1], [2]. Bruggemans formula is, in some cases, a better approximation than the Maxwell Garnett formula for larger volume fractions, but only for specific microstructures [1]. The classical mixing formulas and effective medium approximations depend only on a few parameters, but the effective permittivity is, in general, a function of -point correlation func[1], [2]. The Maxwell Garnett formula, for tions instance, assumes that the composite is isotropic and depends only on the volume fraction of the components and the dimension. This corresponds to knowledge about the one-point correlation function (the volume fraction) and the two-point correlation function (isotropic). The applications of mixing formulas are limited since they do not take into account higher order correlation functions. That is, they ignore the detailed geometrical structure of the composite [1], [2]. The quasi-static effective permittivity can be calculated exactly when the values on the components are known and the microstructure of the composite is periodic and known [3], [4]. A rigorous theory also exists in the random case and the effective permittivity can, in principle, be determined from Monte Carlo simulations. It is possible to simulate materials with thousands of inclusions, which give accurate estimations of the effective permittivity [4]–[9]. However, a complete statistical knowledge of the geometry is rarely available. The Bergman–Milton theory can be used when the microstructure is partly unknown [1], [3]. This theory provides rigorous bounds on the complex effective permittivity that become progressively narrower as more detailed geometrical information is used. Based on the Bergman–Milton theory [1] for random twocomponent composites and the inverse bounds [10]–[12], we present an inverse method that results in a reduction of measurement uncertainties, i.e., tightens the error bars, when the volume fractions of an isotropic two-component composite material is well determined. We show that this method can be used even with a low number of measurement points, and in cases, when the accuracy in the measurements is low. The method is applied to measurement data from two epoxy-aluminum oxide composites at 10.3 and 11.3 GHz. II. BERGMAN–MILTON THEORY In this paper, the composite materials consist of two homogeneous and isotropic phases with relative permittivity and .

0018-9480/$26.00 © 2010 IEEE

ENGSTRÖM: ON A METHOD TO REDUCE UNCERTAINTIES IN BULK PROPERTY MEASUREMENTS OF TWO-COMPONENT COMPOSITES

Let be one of the eigenvalues of the effective permittivity matrix . In a two-component mixture (random or periodic), the effective permittivity has the integral representation [13], [14]

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of the Stieltjes series in the form of Padé approximants can be Padé approximant to is defined by the equation used. The (8)

(1) where and are polynomials of degree at most and , respectively [15]. This equation gives us an approximation of the effective permittivity by the rational function

where (2)

(9) The integral representation (1) is derived from a quasi-static assumption and has accordingly the same validity range [1]. The nonnegative function is the spectral density function, which is a purely geometric quantity that depends on the structure, but not on the values of the components. For example, the 2-D checkerboard structure [1], [2] has the effective permittivity , which corresponds to the spectral density function

, the Padé approximant of the expansion When (6) gives the lower bound (10) . where Padé approximant of (4) gives an upper bound on the The effective permittivity

(3) (11) This spectral density function also corresponds to Bruggeman’s formula for 2-D structures at the percolation threshold, which occurs at volume fraction 1/2, and classical mixing formulas such as the Maxwell Garnett formula are special cases of (2). If the microstructure is only partly known, we can get bounds on the effective permittivity from a power series expansion. We use the Stieltjes series expansion [14], [15] of the scaled permittivity (4) where cients

These bounds were first derived by Milton [21]. In the isotropic case, , the two-point bounds (10) and (11) are equivalent to the Hashin–Shtrikman bounds [22]. For this reason, we call the anisotropy parameter. Milton and Bergman extended the real-valued Hashin–Shtrikman bounds (10) and (11) to the comdenote the arc of a plex case [17], [20]. Let and , which when extended circle joining the end points passes through . Such an arc is described by (12)

is the contrast and the coeffiare given by the moments (5)

Since (5) do not depend on the values of the phases, the constants depend on the microstructure, but not on the values of the two components. The moments are also called structural parameters since they characterize the geometry and are related to the -point correlation functions [2]. The scaled inverse permittivity has the representation [15], [16] (6) where the coefficients according to

and

in the two series are related

(7) The coefficient is the volume fraction of component 1 and is the volume fraction of component 2. A general method for obtaining a hierarchy of bounds using the analytic properties of the effective permittivity was developed by Bergman [17]–[19] and Milton [20], [21]. Alternatively known lower and upper bounds

The effective permittivity by the lens-shaped region

is in the complex case bounded

(13) where and are the harmonic and arithmetic means, respectively. Milton also derived tighter bounds on the effective permittivity in the complex plane, which depend on higher order [1]. Alternatively, we can desribe the bounds in moments [10]. terms of the structural parameters III. CROSS-PROPERTY BOUNDS The extension of the Hashin–Shtrikman bounds to a complex effective permittivity (13) is considerably improved if we have information from measurements on the effective permittivity at a different frequency or on other related parameters such as the magnetic permeability or the thermal conductivity. These additional information from measurements can be used as long as the microstructure is identical. We infer tight bounds on the effecat the frequency when the measured tive permittivity and at the frequenpermittivity of the two components and , and the effective permittivity of the composite cies at are available. These bounds are called cross-property bounds, as they incorporate knowledge from measurements of

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a related parameter or measurements on the material at a different frequency [21], [23], [24]. The effective permittivity is in the complex case bounded by the lens-shaped region

TABLE I MEASURED VALUES AND THE CORRECTED VALUES AT 10.3 GHz

(14) where the two- and three-point cross-property bounds are [10], [24] (15) (16) (17) (18) The coefficients and and the volume fraction are mi, crostructural parameters and . The coefficients , and , are lower and upper bounds on the parameters and . Notice that we only and and not require bounds on the structural parameters exact values. IV. REDUCTION OF MEASUREMENT ERRORS The task in inverse homogenization is to calculate the mi, or the spectral function crostructural parameters from measurement data [25]–[32]. A general method to derive bounds on structural parameters from complex-valued measurement data has been presented [11]. In this paper, we assume , and that the composite is 3-D and isotropic, [11], which is related to use the bounds on the parameter the three-point correlation function [33]. We use these inverse and the cross-property bounds (14) to improve bounds on the accuracy of measurement data. We assume that the volume fraction is bounded between and and that we know error estimates for the permittivity of the two components and of the composite. A probability distribution for the errors needs to be specified, or alternatively, a region in the complex plane, which contains the permittivity, has to be given. Below we will maximize/minimize functions that depend on the permittivity of the two phases. The maximum/minimum is commonly attended for permittivity values at the boundary of the specified regions. However, this is not always the case and we therefore numerically maximize/minimize the functions over the entire regions. A key point in this paper is that these error bars can be large, which is of special importance when, for example, the imaginary part of one of the components is unknown. As we do not know the probability distribution function and the measurements might contain systematic errors, we use large error bars and generate independent random numbers for the real and imaginary parts of the measured values with uniformly distributed errors. Require that the parameter for a fixed value on in the range satisfy (19)

where and , given in the Appendix, depend on the complex numbers , , and . This requirement gives restricand on the possible values tions on the possible values on on the permittivity of the two components, and bounds on the effective permittivity of the composite. The geometry indepenare and dent bounds on , [10]. We use data from two epoxy-aluminum oxide composites, composed of the same two components, but with different volume fractions. All effective permittivity values were obtained from waveguide measurements at room temperature. The aluminum oxide Al O is a fine powder where the particles are flakes with a characteristic length not larger than 5 m. The complex permittivity of the two components and the two epoxy–aluminum–oxide samples were measured at 10.3 GHz. Let and denote the real and imaginary parts, respectively. The measured values on aluminum oxide are and , and the measured and . values on epoxy are The volume fraction of aluminum oxide of the two samples were measured to 0.2025 0.005 and 0.3036 0.005. The real part of the effective permittivity was fairly well determined, but the imaginary parts fluctuate heavily, and are in some cases unrealistic. For example, the measured value on the imaginary part of the permittivity is for the 20% sample 0.001, which should not be negative. Therefore, we use large error bars on the measured values on the imaginary parts of the permittivity. The effective permittivity of the two composites with error bars , , are , and , where subscripts 20 and 30 denotes the measured volume fraction in percentage. The inverse algorithm, based on the inequality (19) and the inverse bounds in [11], is used to analyze the measured values. To guarantee accurate results for all cases, we generate . With for each sample 10 random sets of the inverse method, we reduce the measurement errors on the imaginary part of the measured value on epoxy and on the effective permittivity of the two samples (Table I). The structural parameter is for all isotropic and 3-D composites bounded between and , . These bounds on all isotropic comwhere for a 20% sample and posites are for a 30% sample. The inverse method gives the tighter bounds and for the and for 20% sample and the bounds the 30% sample. give us the possibility The knowledge of the bounds on to use the cross-property bounds (14) and bound the effective permittivity at a different frequency. The measured values on and aluminum oxide at 11.3 GHz are , and the measured values on epoxy are

ENGSTRÖM: ON A METHOD TO REDUCE UNCERTAINTIES IN BULK PROPERTY MEASUREMENTS OF TWO-COMPONENT COMPOSITES

Fig. 1. Five lens-shaped regions correspond to different realizations of : : , the cross-property bounds (14) at 11.3 GHz when c c : , and c : .

= 0 023

= 0 061

= 0 3036 6 0 005

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at 11.3 GHz and from the cross-property bounds (14). Furthermore, with knowledge of the measured effective permittivity, we can also use the inverse method in the same way as for the measurements at 10.3 GHz. In this case, the algorithm slightly improves the bounds on the imaginary part of the effective permittivity. The intersection of the cross-property bounds and the improved bounds on the measured effective permittivity at 11.3 GHz is, for the 30% sample, and . In all cases, the inverse method gives significant improvements of the bounds on the imaginary part of the effective permittivity of the composite. The method reduces the error bars on the permittivity of epoxy, but not on the aluminum–oxide powder. A higher volume fraction of the aluminum–oxide powder would be an advantage for the presented inverse method, but a composite with a large portion of the powder is difficult to manufacture. V. CONCLUSIONS We have shown that the inverse bounds derived in [11] and cross-property bounds [10], [21], [23], [24] can be used to estimate the effective permittivity and to reduce measurement errors. This can be very useful when the error bars on one of the components are large and the method can still be used when the permittivity of one of the components is unknown. The proposed method was successfully applied to measurement data with low accuracy. We also showed that it is possible to estimate the structural parameter , which is related to the three-point correlation function, even when the uncertainties in the measurements are large.

Fig. 2. Dashed lines bounds all possible realizations of the cross-property bounds (14). The solid lines correspond to the known bound from a measurement. The intersection of the dashed and solid rectangle is the improved bounds on  at 11.3 GHz when c : .

= 0 3036

and . The complex cross-property bounds (14) are tight for fixed values on the components and , but it is necessary to take in to account the measurement errors. Fig. 1 show the cross-property bounds (14) from five at 11.3 GHz when the volume fraction realizations is measured to and the bounds on are and . The spreading is large due to the large error bars on the measurement values. Using 10 random sets of , the cross-property bounds (14) is maximized. The calculated bounds on the effective permittivity at 11.3 GHz is and for the 30% sample , which give narrow bounds on the imaginary part of the effective permittivity, but wide bounds on (see Fig. 2). We now consider the case when in addition we have information from a measurement of the effective permittivity at 11.3 GHz. The measured values on the effective permittivity, with error bars, are and . In this case are the error bars on the real part of the effective permittivity being tight, but the error bars on are wide. Fig. 2 shows the intersection of the allowed values on the effective permittivity from the measurement of

APPENDIX Let and denote the real and imaginary parts of the complex number and denote the effective permittivity by . It was and lower bound on shown in [11] that an upper bound can be calculated from the equations (20) and are the Padé approximant (9) to (4) where and (6), respectively. Explicitly, a lower bound on is given by (21) where

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An upper bound

on

is given by (22)

where (23) and

(24)

ACKNOWLEDGMENT The author is grateful to J. Fagerström and A. Jänis, both with the Swedish Defense Research Agency, Linköping, Sweden, for providing the measurement data of the epoxy-aluminum oxide composite and to A. Wolf, Institute of Terrestrial Ecosystems, ETH Zürich, Zürich, Switzerland, for helpful comments on this paper. REFERENCES [1] G. W. Milton, The Theory of Composites. Cambridge, U.K.: Cambridge Univ. Press, 2002. [2] S. Torquato, Random Heterogeneous Materials: Microstructure and Microscopic Properties. Berlin, Germany: Springer-Verlag, 2002. [3] V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Berlin, Germany: Springer- Verlag, 1994.

[4] O. Ouchetto, S. Zouhdi, A. Bossavit, G. Griso, and B. Miara, “Modeling of 3-D periodic multiphase composites by homogenization,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2615–2619, Jun., 2006. [5] J. Helsing, “Thin bridges in isotropic electrostatics,” J. Comput. Phys., vol. 127, no. 1, pp. 142–151, 1996. [6] F. Wu and K. W. Whites, “Quasi-static effective permittivity of periodic composites containing complex shaped dielectric particles,” IEEE Trans. Antennas Propag., vol. 49, no. 8, pp. 1174–1182, Aug. 2001. [7] K. W. Whites and F. Wu, “Effects of particle shape on the effective permittivity of composite materials with measurements for lattices of cubes,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 7, pp. 1723–1727, Jul. 2002. [8] V. Myroshnychenko and C. Brosseau, “Finite-element modeling method for the prediction of the complex effective permittivity of two-phase random statistically isotropic heterostructures,” J. Appl. Phys., vol. 97, 2005, Art. ID 044101. [9] X. Chen, Y. Cheng, K. Wu, Y. Meng, and S. Wu, “Calculations of dielectric constant of two-phase disordered composites by using FEM,” in IEEE Int. Elect. Insulation Symp., 2008, pp. 215–218. [10] C. Engström, “Bounds on the effective tensor and the structural parameters for anisotropic two-phase composite material,” J. Phys. D, Appl. Phys., vol. 38, pp. 3695–3702, 2005. [11] C. Engström, “Inverse bounds and bulk properties of complex-valued twocomponent composites,” SIAM J. Appl. Math., vol. 67, no. 1, pp. 194–213, 2006. [12] C. Engström, “Structural information of nanocomposites from measured optical properties,” J. Phys., Condens. Matter, vol. 19, 2007, Art. ID 106212. [13] D. J. Bergman, “The dielectric constant of a composite material—A problem in classical physics,” Phys. Rep., vol. 43, no. 9, pp. 377–407, 1978. [14] K. Golden and G. Papanicolaou, “Bounds for effective parameters of heterogeneous media by analytic continuation,” Commun. Math. Phys., vol. 90, pp. 473–491, 1983. [15] G. A. Baker, Essentials of Padé Approximants. New York: Academic, 1975. [16] D. J. Bergman, “Hierarchies of Stieltjes functions and their application to the calculation of bounds for the dielectric constant of a two-component composite medium,” SIAM J. Appl. Math., vol. 53, no. 4, pp. 915–930, 1993. [17] D. J. Bergman, “Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of a two-component composite material,” Phys. Rev. Lett., vol. 44, no. 19, pp. 1285–1287, 1980. [18] D. J. Bergman, “Bounds for the complex dielectric constant of a twocomponent composite material,” Phys. Rev. B, Condens. Matter, vol. 23, no. 6, pp. 3058–3065, 1981. [19] D. J. Bergman, “Rigorous bounds for the complex dielectric constant of a two component composite,” Ann. Phys., vol. 138, pp. 78–114, 1982. [20] G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett., vol. 37, no. 3, pp. 300–302, 1980. [21] G. W. Milton, “Bounds on the transport and optical properties of two-component composite material,” J. Appl. Phys., vol. 52, no. 8, pp. 5294–5304, 1981. [22] Z. Hashin and S. Shtrikman, “A variational approach to the theory of the effective magnetic permeability of multiphase materials,” J. Appl. Phys., vol. 33, no. 10, pp. 3125–3131, 1962. [23] S. Prager, “Improved variational bounds on some bulk properties of a two-phase random medium,” J. Chem. Phys., vol. 50, no. 10, pp. 4305–4312, 1969. [24] D. J. Bergman, “Variational bounds on some bulk properties of a twophase composite material,” Phys. Rev. B, Condens. Matter, vol. 14, no. 4, pp. 1531–1542, 1976. [25] R. C. McPhedran, D. R. McKenzie, and G. W. Milton, “Extraction of structural information from measured transport properties of composites,” Appl. Phys. A, vol. 29, no. 1, pp. 19–27, 1982. [26] E. Cherkaeva and A. C. Tripp, “Inverse conductivity for inaccurate measurements,” Inverse Prob., vol. 12, pp. 869–883, 1996. [27] A. R. Day and M. F. Thorpe, “The spectral function of random resistor networks,” J. Phys., Condens. Matter, vol. 8, pp. 4389–4409, 1996. [28] E. Cherkaeva, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Prob., vol. 17, pp. 1203–1218, 2001. [29] A. R. Day, M. F. Thorpe, A. R. Grant, and A. J. Sievers, “Spectral function of composites from reflectivity measurements,” Phys. Rev. Lett., vol. 84, no. 9, pp. 1978–1981, 2000. [30] D. Eyre, G. Milton, and R. Lakes, “Bounds for interpolating complex effective moduli of viscoelastic materials from measured data,” Rheol. Acta, vol. 41, pp. 461–470, 2002.

ENGSTRÖM: ON A METHOD TO REDUCE UNCERTAINTIES IN BULK PROPERTY MEASUREMENTS OF TWO-COMPONENT COMPOSITES

[31] E. Tuncer, “Extracting the spectral density function of a binary composite without a priori assumption,” Phys. Rev. B, Condens. Matter, vol. 71, no. 1, 2005, Art. ID 012101. [32] D. Zhang and E. Cherkaev, “Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations,” J. Comput. Phys., vol. 228, no. 15, pp. 5390–5409, 2009. [33] A. K. Sen and S. Torquato, “Effective conductivity of anisotropic twophase composite media,” Phys. Rev. B, Condens. Matter, vol. 39, no. 7, pp. 4504–4515, 1989.

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Christian Engström received the Masters degree in mathematics from Växjö University, Växjö, Sweden, in 1998, and the Ph.D. degree in electrical engineering from Lund University, Lund, Sweden, in 2006. From 1998 to 2002, he was a Teacher in mathematics. From 2007 to 2008, he was Post-Doctoral Researcher with the Department of Mathematics, Karlsruhe University, Karlsruhe, Germany. Since 2009, he has been a Research Associate with the Laboratory for Electromagnetic Fields and Microwave Electronics (IFH), ETH Zürich, Zürich, Switzerland. His main research interests include computational electromagnetics and effective material properties.

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Extended Through-Short-Delay Technique for the Calibration of Vector Network Analyzers With Nonmating Waveguide Ports Oscar Antonio Peverini, Giuseppe Addamo, Riccardo Tascone, Member, IEEE, Giuseppe Virone, and Renato Orta, Senior Member, IEEE

Abstract—The extension of the through-short-delay (TSD) technique to the calibration of two-port vector network analyzers (VNAs) with nonmating waveguide ports is reported. The method retains the well-known high accuracy of the basic TSD technique while it enables to calibrate VNAs using two waveguide ports with different cross sections. Comparisons with the reciprocal-short–open–load technique commonly adopted to calibrate VNAs with nonconnectable ports and with theoretical data are reported. The present method can be adopted as either a one- or a two-tier calibration technique. Index Terms—Microwave measurements, scattering parameters measurements, waveguide components.

I. INTRODUCTION

C

OMPLEXITY OF microwave and millimeter-wave systems is continuously increasing in order to meet more and more severe design specifications. Depending on the specific application, waveguide devices may have input ports with different cross sections, e.g., multiplexing orthomode transducers (OMTs) for satellite communication [1]. In the experimental characterization of this class of components, vector network analyzers (VNAs) with nonmating waveguide ports have to be used, for which specific calibration techniques have been developed [2], [3]. In the adapter removal technique, the VNA calibration is performed by exploiting an adapter that has to be measured with great accuracy [4], [5]. To this end, two VNA calibrations are required. In 1992, Ferrero and Pisani introduced the reciprocal-short– open–load (RSOL) calibration technique that overcomes the problem of the complete characterization of the adapter [6], [7]. Indeed, in the RSOL technique, the thru standard (i.e., the adapter or the DUT itself) is completely unknown and it has to satisfy only the reciprocity condition. For this reason, this technique is also referred to as the unknown thru method. As in the traditional short–open–load–thru (SOLT) technique, this method requires the manufacturing of three known one-port standards for each VNA waveguide port, i.e., a matched load, a

Manuscript received December 03, 2009. First published January 22, 2010; current version published February 12, 2010. This work was supported in part by Thales-Alenia Space Italia, Rome, Italy, under research projects aimed at the development of satellite communications RF equipment. The authors are with the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT), Italian National Research Council (CNR), Dipartimento di Elettronica, Politecnico di Torino, 10129 Turin, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2038455

short, and an open. The latter can be realized by shifting back the short standard by a line of known length (approximately a quarter-wavelength). Although the short standard can be implemented in waveguide technology with great accuracy (losses can be minimized by silver-plating), the accuracy of the RSOL calibration may be actually limited by a poor model description of the matched load standards. Conversely, thru-reflection-line (TRL) and through-short-delay (TSD) techniques are widely recognized as the most precise means of calibration of VNAs with connectable waveguide ports since they fully exploit the self-calibrating capabilities of the standards adopted in the calibration process [8]. Moreover, multiple-line TRL methods can be adopted in order to widen the bandwidth and to improve the accuracy of the calibration [9] of single-mode and multimode VNAs [10]. In order to exploit the accuracy of self-calibrating standards also in the measurement of noninsertable devices, multiport VNAs can be used, for which generalizations of the TSD procedure [11] and even more general calibration approaches [12] are available. In this paper, an extension of the TSD procedure to the measurement of noninsertable devices via commonly available twoport VNAs is presented. The procedure is almost as simple as the standard TSD for insertable devices, while providing the same level of accuracy. Moreover, the number of waveguide transitions used in the measurements is minimized since multiport VNAs are not required. The method can be applied to measure any type of device, but it proves to be particularly effective in the measurement of waveguide components, for which it is presented. The method can be applied either as a one- or two-tier calibration procedure. Comparisons of theoretical data with the -, -, and -bands by measurements carried out in the applying the present technique, the RSOL technique, and the procedure presented in [13] validate the method presented. II. THEORY As in standard TRL/TSD techniques, the present method is derived by assuming the eight-term error model depicted in Fig. 1, according to which no leakage between the errors boxes occurs. This model applies very well to waveguide or coaxial setups, while only very leaky on-wafer setups significantly depart from this assumption [14]. A. One-Tier Calibration Procedure In the one-tier version of the calibration procedure, the raw data measured by an uncalibrated VNA are considered. All

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Fig. 1. Eight-term error model used in the derivation of the present VNA calibration method. Ports 1 and 2 of the DUT are not connectable since they have different cross sections.

Ku=K

Fig. 2. -band VNA waveguide setup with a circular waveguide at port 1 and a square waveguide at port 2.

the measurements are meant to be switch corrected by using a four-sampler VNA, in order to compensate for the effect of forward- and reverse-source load matching and switch imperfections [15]. In the switch-correction technique, the four VNA readings performed in the forward-direction (i.e., drive port 1) (1) are combined with those in the reverse-direction (i.e., drive port 2)

Ka

Fig. 3. -band VNA waveguide setup with a rectangular waveguide at port 1 and a square waveguide at port 2.

(2) in order to obtain the scattering matrix test (DUT) by

of any device-under-

(3) is related The corresponding measured transmission matrix to the actual transmission matrix of the DUT via (4) and are the unknown transmission matrices of where and , respectively. the two error blocks For the sake of clearness and without loss of generality, the method is presented by considering a waveguide setup similar to those depicted in Figs. 2 and 3 consisting of two waveguide ports with different cross sections and with the same flange. The formulation derived in the following can also be extended to more general setups, as described in the last part of this section. The direct connection of two waveguide ports with different cross sections corresponding to the thru condition [see Fig. 4 ( )] gives rise to a waveguide step of zero length. The corresponding measured transmission matrix is (5) Under the assumption of single-mode interaction between the error blocks and the standards, the 2 2 transmission matrix contains four calibration unknowns. Since of the step the thru condition corresponds to a fully unknown standard, the basic 12-term TSD technique [8] yields an underdetermined

Fig. 4. Standards adopted in the present extension of the TSD technique for the calibration of VNAs with nonmating waveguide ports. ( 1) Thru. ( 2) Line1 at port 1. ( 3) Line2 at port 2. ( 4) Short at both ports.

S

S

S

S

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system containing 13 unknown coefficients. In order to overcome this underdetermination and to exploit the same kind of standards used in the TSD procedure, the two measurement conand depicted in Fig. 4 are considered, where two ditions different waveguide lines are inserted at ports 1 and 2, respectively. The length of each waveguide line is unknown, although it has to be approximately a quarter-wavelength, and its cross section coincides with that of the corresponding waveguide port. The corresponding measured transmission matrices are

By defining the three coefficients (still to be evaluated) (19) the following formulas can be derived from (14) and (15) for the scattering parameters of the error box : (20)

(6) (7)

(21)

By combining (5)–(7), it is possible to eliminate the unknown as follows: matrix

(22)

(8)

(23)

(9) Application of the spectral decomposition to matrices yields

and

and of the error box (24)

(10) (11)

(25)

and eigenvector and eigenvalues matrices. being Under the assumption of ideally matched waveguide lines, and are diagonal matrices, and hence, the following formulas can be derived:

(26) (27)

(12) (13) (14) (15) and are 2 2 diagonal matrices containing where the unknown parameters and , respectively. The waveguide lines prove to be self-calibrating standards since, from (12) and (13), their phase shift can be estimated via

parameters are introduced. Inserting (14) and (15) where the in (4), the transmission matrix of a generic DUT can be evaluated as (28) where

is a known matrix determined via (29)

(16) (17)

Equations (28) and (29) correspond to the following formulas for the scattering parameters of the DUT:

Since the reciprocity condition is not enforced in the line standards, the procedure provides two figure-of-merits concerning the assumption of ideally matched lines and the repeatability of the standards connection

(30)

(18)

(32)

Indeed, on the basis of the first-order analysis reported in [9], where the eigenvalue sensitivity to connection errors is investigated for TRL-type techniques, it can be straightforwardly derived that these figure-of-merits are an estimate of the standard deviation of the errors introduced in the line measurements (see the Appendix).

(31)

(33) It can be noted that, as is well known, the measurement of the DUT requires the knowledge of the two error boxes apart from ). a 1-D ambiguity (i.e.,

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As in the TSD technique, two highly reflecting one-port standards [see Fig. 4 ( )] can be adopted in order to obtain two additional calibration equations

TABLE I BASIC TSD TECHNIQUE APPLICABLE TO INSERTABLE DEVICES

(34) (35) where are the reflection coefficients measured are the known reflection coeffiat both ports and cients of the highly reflecting standards. In the RSOL technique, the reciprocity condition of either the adapter or the DUT is exploited to derive a further calibration equation. As far as a waveguide setup similar to those depicted in Figs. 2 and 3 is concerned, this condition is always satisfied of Fig. 4, which by the three two-port standards , , and may be regarded as three reciprocal adapters. The corresponding equation is

TABLE II EXTENDED-TSD TECHNIQUE APPLICABLE TO NONINSERTABLE DEVICES

(36) is obtained by inserting in (29) the measurement where for one of the three two-port standards. Equations (34)–(36) can be solved for the unknown calibration coefficients (19) obtaining (37) and denote the right-hand sides of (34)–(36), and . As evident in (30)–(33), the sign ambiguity affects only the DUT scattering parameters of the transmission type and it can be eliminated by a rough estimation of the phase delay of one of the two-port standards. Once all the unknown coefficients have been computed, it is possible to apply the calibration procedure to any DUT, inused in the cluding the three two-port standards , , and of the two procedure. By deriving the transmission matrix standards not used for enforcing the reciprocity condition, two further figures-of-merit of the calibration performance can be defined as where

(38) which, for a good calibration, should be as small as possible. The key properties (i.e., standards, number of unknowns, number of equations) of the basic TSD technique applicable to insertable devices and of its present extension to noninsertable devices are listed in Tables I and II, respectively. Since the procedure suggested is not overdetermined, the redundancies provided by the calibrating equations are fully exploited in order to minimize the number of known standards. The procedure previously described can also be applied to other setups, where the direct connection between the two nonmating ports is not possible. In this case, the thru condition does not refer to the waveguide step, but to a reciprocal adapter or DUT. Since in the latter case the DUT replaces the waveof Fig. 4, the present method guide step as the standard

Fig. 5. VNA waveguide setup with nonmating ports under calibration in the -band. Circular waveguide radius at port 1 mm. Square wavemm. guide side at port 2

K=Ku

a = 15:950

r = 8:900

and the basic TSD technique require the same number of standard measurements. However, cable bending and movements are also minimized in the measurement of a complex DUT since the short and line standards are inserted at both ports with the cables already mounted in the reference position for the measurement of the DUT. The RSOL technique exhibits the same property, but additional cable movements can be necessary to accommodate the matched load standards, which in waveguide technology can be rather long depending on the frequency range of interest. For example, matched loads exhibiting a return loss higher than 35 dB are approximately six wavelength long. B. Two-Tier Calibration Procedure When a two-tier calibration is adopted to experimentally characterize the transitions used in the measurement setup of Fig. 5, a first calibration of the VNA is performed at two connectable ports, e.g., coaxial or rectangular waveguides. Hence, if the procedure illustrated in Section II-A is applied, the two and actually represent the transitions to error boxes be de-embedded. The complete knowledge of the boxes and demands the evaluation of the unknown coefficient . Since waveguide transitions commonly adopted satisfy the reciprocity property, this condition can be enforced on

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or

, yielding, respectively, the following two

(39) (40) where the sign ambiguity is related to the nondirect accessibility to the reference port of Fig. 4. Since the reciprocity of only one box is enforced, a figure-of-merit of the type of (38) can be applied to the other box in order to estimate the accuracy of the two-tier calibration. III. EXPERIMENTAL RESULTS The effectiveness of the calibration procedure described in Section II has been assessed by considering both the -band and the -band waveguide setups of Figs. 2 and 3, respectively. In all the measurements, the present technique has been applied by assuming an ideal short circuit as the standard . Indeed, the deviation of a silver-plated waveguide short circuit from its ideal response in the microwave range is lower than 0.005 dB and 0.02 for the magnitude and phase, respectively. A.

-Band Waveguide Setup

-band is detailed in Fig. 5. The setup used in the The nominal values of the circular waveguide radius at port mm) and of square waveguide side at port 2 1 ( mm) have been chosen in order to meet the ( single-mode condition in the [10.5, 19.0] GHz frequency range under the assumption of a two-axis symmetry of the setup in the transverse plane. The symmetry of the measurement setup is confirmed by the absence of resonance peaks in all the measured data, which could be generated by spurious modes coupled by low mechanical asymmetries. Two different sets of transitions from the circular (square) waveguide to standard rectangular waveguide have been used in order to cover all the band. The setup operating at [10.5, 15.5] GHz consists of WR75 transitions, whereas two WR42 transitions have been mounted in the setup used in the [15.5, 19.0] GHz band. In the experimental validation of the present extension of the TSD technique to nonconnectable ports, the waveguide step arising from the direct connection of the circular and of square ports corresponding to the unknown standard Fig. 4 has been used as DUT. Indeed, since the waveguide step can be accurately simulated, manufactured, and mechanically measured, the comparison between its measured and computed scattering parameters is both simple and meaningful. The scattering parameters of the step have been evaluated by the method of moments with a number of basis functions that guarantees the convergence of the method beyond the accuracy of the measurement setup. The step also provides the adapter necessary in the RSOL calibration procedure used to further validate the present technique. The RSOL technique has been implemented by using ideal short circuits, the short circuits shifted back by the waveguide lines experimentally characterized by the present technique (as detailed in the following), and

Fig. 6. Scattering reflection coefficient S of the step arising from the direct connection of the circular and square ports of the setup of Fig. 5. Comparison between the values measured with the present technique and with the RSOL technique. Theoretical data simulated by the method of moments are reported as well. The vertical dashed–dotted line defines the frequency ranges [10.5, 15.5] GHz and [15.5, 19.0] GHz relative to the different waveguide transitions used in the setup of Fig. 5. (a) Magnitude. (b) Phase.

two 120-mm-long matched-load standards exhibiting a residual reflection coefficient better than 35 dB in all the measurement band. In order to enhance the accuracy of the RSOL technique, both the sliding-load and offset-short techniques have been implemented yielding an overdetermined system solved by the least square method. and of the unknown stanThe scattering parameters extracted via the method presented and the RSOL techdard nique are compared with the simulated data in Figs. 6 and 7. The advantages coming from the use of self-calibrating standards are evident in these measurements. Indeed, the ripples and the higher discrepancy with respect to the simulated data exhibited by the RSOL measurements are mainly due to the residual reflection coefficient of the matched load standards and to the additional cable movements necessary to accommodate them during the calibration process. Since the insertion losses of waveguide steps arising from the direct connection of waveguide ports with different cross sections are lower than 0.005 dB in the microwave range, the evaluation of the quantity for these discontinuities provides a significant measure of the accuracy of the calibration process. Indeed, would be zero for a lossless device, since its scattering matrix is unitary. Fig. 8 reports the values of for the step measured by the present method and the RSOL technique. The simulated

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Fig. 9. Difference between each of the two measured values obtained via (16) and theoretical value of the phase shift introduced by line1 used in the measurement setup at [10.5, 15.5] GHz. This theoretical value refers to a circular waveguide with radius r : mm and length l : mm (nominal : mm and l : mm). values: r

= 8 900

= 8 900 = 8 000

= 8 002

Fig. 10. Difference between each of the two measured values obtained via (17) and theoretical value of the phase shift introduced by line2 used in the measurement setup at [10.5, 15.5] GHz. This theoretical value refers to a square wave: mm and length l : mm (nominal values: guide with side a a : mm and l : mm).

= 15 955

Fig. 7. Scattering transmission coefficient S of the step arising from the direct connection of the circular and square ports of the setup of Fig. 5. Comparison between the values measured with the present technique and with the RSOL technique. Theoretical data simulated by the method of moments are reported as well. The vertical dashed–dotted line defines the frequency ranges [10.5, 15.5] GHz and [15.5, 19.0] GHz relative to the different waveguide transitions used in the setup of Fig. 5. (a) Magnitude. (b) Phase.

Fig. 8. Plot of the quantity , defined in the text, for the step arising from the direct connection of the circular and square ports of the setup of Fig. 5. Comparison between the values measured with the present technique and with the RSOL technique. Theoretical data simulated by the method of moments are reported as well. The vertical dashed–dotted line defines the frequency ranges [10.5, 15.5] GHz and [15.5, 19.0] GHz relative to the different waveguide transitions used in the setup of Fig. 5.

data are shown as well. Several runs of the present calibration technique have been carried out in order to confirm the repeatability of the results reported in Figs. 6–8.

= 15 955 = 8 000

= 8 010

An indicator of the quality of the procedure described is the agreement between theoretical and measured phase shifts introduced by the lines. In particular, the measured phase shifts are extracted according to (16) and (17). Ideally, the two eigenand should provide the same value of phase values shift for each line. As a matter of fact, the measurements produce two different values. For the lines used in the two setups at [10.5, 15.5] GHz and [15.5, 19.0] GHz, the difference between each measured phase shift and the corresponding theoretical value is reported in Figs. 9–12 (the waveguide dimensions used in the simulations are indicated in each figure). The quality of the calibration procedure is confirmed by the very small deviations of the measured phase shifts from theoretical values. Moreover, the difference between the two measured phase shifts associated to the same line is within 0.05 . In order to verify the assumption of ideally matched lines and the repeatability of the connections defining the three standards , , and of Fig. 4, the two figures-of-merit and defined in (18) have been evaluated for the two setups. The average value of these parameters is approximately 70 dB, which is of the same order of magnitude of that provided by the basic TSD technique for insertable devices. Indeed, the line matching and the connection repeatability has been guaranteed by using high-precision alignment pins. Finally, the quality of the complete one-tier procedure has and , as been verified by evaluating the figures-of-merit defined in (38), which concern the reciprocity of standards and when the reciprocity condition is enforced on the thru standard . Values of these figures-of-merit lower than 60 dB have been obtained for the two waveguide setups operating at [10.5, 15.5] and [15.5, 19.0] GHz.

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Fig. 11. Difference between each of the two measured values obtained via (16) and theoretical value of the phase shift introduced by line1 used in the measurement setup at [15.5, 19.0] GHz. This theoretical value refers to a circular waveguide with radius r : mm and length l : mm (nominal values: r : mmand l : mm).

= 8 900

= 8 914 = 4 000

= 4 003

Fig. 13. Exploded view of the three-cavity WR75-to-circular waveguide transition used in the measurement setup operating at [10.5, 15.5] GHz.

Fig. 12. Difference between each of the two measured values obtained via (17) and theoretical value of the phase shift introduced by line2 used in the measurement setup at [15.5, 19.0] GHz. This theoretical value refers to a square wave: mm and length l mm (nominal values: : guide with side a mm and l a : : mm).

= 15 955

= 16 103 = 4 000

= 3 982

The waveguide transitions used in the two setups have been experimentally characterized by applying the two-tier procedure described in Section II-B. In the setups operating in the [10.5, 15.5] and [15.5, 19.0] GHz bands, the VNA has been calibrated via a TRL procedure applied at the WR75 and WR42 rectangular ports of the transitions, respectively. Subsequently, the present extension of the TSD procedure has been carried out at the circular/square ports of the setups. In order to asses the de-embedding capabilities of this process, waveguide transitions exhibiting very low values of reflection coefficient have been considered. They have been designed according to the procedure reported in [16], which allows the synthesis of an arbitrary frequency response, and simulated via a reduced-order technique based on the method of moments applied in the spectral domain [17]. In order to enhance manufacturing accuracy, the transitions have been realized with the split-block technique, where each discontinuity arises from the connection of simple rectangular/circular waveguide blocks. Each block has been realized by high-precision electro-erosion and, subsequently, silver-plated. Assembling accuracy has been enhanced by inserting high-precision dowels, which guarantee a mounting uncertainty less than 0.004 mm. The mechanical design adopted is clarified in Fig. 13, where an exploded view of the WR75-to-circular waveguide transition is reported. The comparison between the measured and simulated scattering coefficients of the transitions used in the two setups operating at [10.5, 15.5] and [15.5, 19.0] GHz are reported in Figs. 14 and 15, respectively. The agreement between measurements and simulations is significant with respect to both the level and the zeros position of the frequency responses, which confirms the

Fig. 14. Comparison between simulated and measured scattering reflection coefficients of the transitions used in the measurement setup at [10.5, 15.5] GHz. The measurements refer to the two-tier version of the present technique as described in the text, whereas the simulations have been carried out by means of the method of moments. (a) Reflection coefficient at the circular port of the WR75-to-circular waveguide transition. (b) Reflection coefficient at the square port of the WR75-to-square waveguide transition. (c) Transmission coefficient of the WR75-to-circular waveguide transition. (d) Transmission coefficient of the WR75-to-square waveguide transition.

validity of the two-tier calibration procedure. The design procedure applied fully exploits the degrees of freedom of the geometries. Indeed, the three cavities of the WR75-to-circular waveguide transition (Fig. 13) have been defined in order to place three zeros of the reflection coefficient in the band of interest

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Fig. 15. Comparison between simulated and measured scattering reflection coefficients of the transitions used in the measurement setup at [15.5, 19.0] GHz. The measurements refer to the two-tier version of the present technique as described in the text, whereas the simulations have been carried out by means of the method of moments. (a) Reflection coefficient at the circular port of the WR42-to-circular waveguide transition. (b) Reflection coefficient at the square port of the WR42-to-square waveguide transition. (c) Transmission coefficient of the WR42-to-circular waveguide transition. (d) Transmission coefficient of the WR42-to-square waveguide transition.

[see Fig. 14(a)]. In this regard, it has to be remarked that the WR75-to-square waveguide exhibits two reflection zeros [see Fig. 14(b)] since this transition consists of only two cavities. The validity of the two-tier calibration procedure has also been verified by evaluating the reciprocity of the transition for which this condition is not enforced. The measured average value of this figure-of-merit is in the order of 65 dB for both the setups. B.

-Band Waveguide Setup

The present technique has been further validated by measuring the scattering parameters of a -band OMT based on the architecture reported in [18]. The reflection and transmission coefficients at the rectangular and square ports of the OMT for the vertical polarization have also been measured with the RSOL technique and the specific procedure for the characterization of OMTs described in [13]. The waveguide setup used in the measurements from 27 to 35 GHz consists of a standard WR28 rectangular waveguide at port 1 and a 6-mm-side square

Fig. 16. Scattering reflection coefficients of the step arising from the direct -band setup depicted connection of the rectangular and square ports of the in Fig. 3. Comparison between the values measured with the present technique and theoretical data simulated by the method of moments. (a) and (b) Reflection coefficient at the rectangular port. (c) and (d) Transmission coefficient.

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waveguide at port 2 (Fig. 3). Fig. 16 reports the scattering parameters of the unknown waveguide step arising from the direct connection of the rectangular and square ports after the calibration of the setup by the present technique. The simulated data shown in Fig. 16 can be reliably used as the reference values of the scattering parameters of the unknown standard. Indeed, as discussed in Section III-A, waveguide steps arising from the direct connection of waveguides with different cross sections can be very precisely simulated and realized. The discrepancies between the measured and computed data for both the coefficients are within 0.02 dB and 0.01 for the magnitude and phase, respectively.

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Fig. 17. Scattering reflection coefficients for the vertical polarization of the -band OMT. Comparison between the values measured with the present technique, the RSOL technique and the procedure described in [13]. Theoretical data computed by the method of moments are reported as well. (a) Reflection coefficient at the rectangular port. (b) Reflection coefficient at the square port.

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Fig. 18. Scattering transmission coefficient from the rectangular port to the square port for the vertical polarization of the -band OMT. Comparison between the values measured with the present technique, the RSOL technique and the procedure described in [13]. theoretical data computed by the method of moments are reported as well. (a) Insertion loss. (b) Group delay.

The scattering parameters of the OMT measured by the three different techniques are reported in Figs. 17 and 18. The values computed by the method of moments are reported as well. Fig. 17 shows the reflection coefficients at the rectangular and square ports, whereas Fig. 18 reports the insertion loss and the group delay associated to the transmission from the rectangular port to the square port. A good agreement between the three measurement techniques is achieved, although a stronger deviation in the RSOL data can be observed. This is due to the residual reflection coefficient of the nonideal matched loads (in the order of 30 dB) and to the additional cable movements performed during the RSOL calibration process necessary to connect these 70-mm-long loads. A significant agreement within 0.02 dB between the values of insertion losses measured by the present technique and the procedure described in [13] is achieved. Indeed, the latter procedure is carried out by connecting five different loads at the square common port of the OMT without moving the cables, which are connected to the two OMT rectangular waveguide ports.

standard. Remarkably, the manufacturing of the latter standard can be avoided by adopting the same flange at the nonmating ports of waveguide setups. The present extended version of the TSD technique introduced for the calibration of VNA with two nonconnectable waveguide ports can also be accommodated to multiport systems.

IV. CONCLUSION The procedure presented combines the advantages of the basic TSD technique, i.e., adoption of self-calibrating standards, with those of the RSOL technique, i.e., the unknown thru

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APPENDIX The relationship between the figures-of-merit (18) and the errors in the line measurements is derived in the following according to the first-order error analysis reported in [9]. Since no assumption, apart from reciprocity, is made about the transmission matrix of the step, the nonideality of the lines and repeatability of the standard connections can be equivalently included in the model by representing each line by a transmission matrix . According to [9], this matrix can be approximated to first order as (41) where the matrices and contain the error terms and representing the imperfections associated

PEVERINI et al.: EXTENDED TSD TECHNIQUE FOR CALIBRATION OF VNAs

with ports 1 and 2 of the line , respectively. Hence, the actual and are expressions for the matrices (42) (43) is no longer a diagonal matrix, the problem Although can be studied as a resulting perturbation for the eigenvalues of since the error terms are much smaller than 1 [9]. To first order,

(44) which, according to [9, Sec. II-A], leads to the following formulas for the two eigenvalues of the nonideal lines: (45) (46) By defining the terms and and inserting (45) and (46) in (18) yields

(47) where the symbol indicates the expectation value. The and represent errors affecting ports 1 and 2, terms respectively. As discussed in [9, Sec. III-B], these errors can be either uncorrelated or correlated according to whether they are due only to imperfect repeatability of the standard connections or also to imperfections of the line standards. Under the assumption of uncorrelated errors with the same standard deviation [9], (47) becomes

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[2] R. A. Speciale, R. E. Grabowski, and N. R. Franzen, “Accurate scattering parameter measurements on non-connectable microwave networks,” in Proc. 6th Eur. Microw. Conf., Rome, Italy, Oct. 1976, pp. 210–214. [3] C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas., vol. 36, no. 2, pp. 524–529, Jun. 1987. [4] “Measuring noninsertable devices,” Agilent Technol., Santa Clara, CA, Agilent 85-10-13 Product Note, 2006. [5] J. Randa, W. Wiatr, and R. L. Billinger, “Comparison of adapter characterization methods,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2613–2620, Dec. 1999. [6] A. Ferrero and U. Pisani, “Two-port network analyzer calibration using an unknown “Thru”,” IEEE Microw. Guided Wave Lett., vol. 2, no. 12, pp. 505–507, Dec. 1992. [7] K. Wong, “The ‘unknown thru’ calibration advantage,” in 63rd ARFTG Conf. Dig., Fort Worth, TX, Jun. 2004, pp. 73–81. [8] H. J. Eul and B. Schiek, “A generalized theory and new calibration procedures for network analyzer self-calibration,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 4, pp. 724–731, Apr. 1991. [9] R. B. Marks, “A multiline method of network analyzer calibration,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 7, pp. 1205–1215, Jul. 1991. [10] C. Seguinot, P. Kennis, J. F. Legier, F. Huret, E. Paleczny, and L. Hayden, “Multimode TRL—A new concept in microwave measurements: Theory and experimental verification,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 5, pp. 536–542, May 1998. [11] R. A. Speciale, “A generalization of the TSD network-analyzer calibration procedure, covering n-port scattering-parameter measurements, affected by leakage errors,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 12, pp. 1100–1115, Dec. 1977. [12] A. Ferrero, F. Sanpietro, and U. Pisani, “Multiport vector network analyzer calibration: A general formulation,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp. 2455–2461, Dec. 1994. [13] O. A. Peverini, R. Tascone, A. Olivieri, M. Baralis, R. Orta, and G. Virone, “A microwave measurement procedure for a full characterization of ortho-mode transducers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 4, pp. 1207–1213, Apr. 2003. [14] A. Ferrero, U. Pisani, and K. J. Kerwin, “A new implementation of a mutiport automatic network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 11, pp. 2078–2085, Nov. 1992. [15] K. Silvonen, “LMR 16—A self-calibration procedure for a leaky network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 7, pp. 1041–1049, Jul. 1997. [16] R. Tascone, P. Savi, D. Trinchero, and R. Orta, “Scattering matrix approch for the design of microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 3, pp. 423–430, Mar. 2000. [17] O. A. Peverini, R. Tascone, M. Baralis, G. Virone, D. Trinchero, and R. Orta, “Reduced-order optimized mode-matching CAD of microwave waveguide components,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 311–318, Jan. 2004. [18] O. A. Peverini, R. Tascone, G. Virone, A. Olivieri, and R. Orta, “Orthomode transducer for millimeter-wave correlation receivers,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2042–2049, May 2006.

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ACKNOWLEDGMENT The authors would like to thank V. Teppati and A. Ferrero, both with the Electronic Department of Politecnico di Torino, Turin, Italy, for valuable discussions about VNA calibration techniques. REFERENCES [1] P. Cecchini, R. Mizzoni, R. Ravanelli, G. Addamo, O. Peverini, R. Tascone, and G. Virone, “Wideband diplexed feed chains for FSS BSS applications,” in Proc. Eur. Antennas Propag. Conf., Berlin, Germany, Mar. 2009, pp. 3095–3099.

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Oscar Antonio Peverini was born in Lisbon, Portugal, in 1972. He received the Laurea degree (summa cum laude) in telecommunications engineering and Ph.D. degree in electronic and communication engineering from the Politecnico di Torino, Turin, Italy, in 1997 and 2001, respectively. From August 1999 to March 2000, he was a Visiting Member of the Applied Pysics/Integrated Optics Department, University of Paderborn, Paderborn, Germany. In February 2001, he joined the Istituto di Ricerca sull’Ingegneria delle Telecomunicazioni e dell’Informazione (IRITI-CNR Institute), Italian National Research Council (CNR). Since December 2001, he has been a Researcher with the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT-CNR institute), CNR. He teaches courses on electromagnetic field theory and applied mathematics with the Politecnico di Torino. His research interests include modeling, design, and measurement techniques of microwave passive devices and integrated acoustooptical components for communication and scientific equipment.

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Giuseppe Addamo was born in Messina, Italy, in 1979. He received the Laurea degree (summa cum laude) in electronic engineering and Ph.D. degree in electronic and communication engineering from the Politecnico di Torino, Turin, Italy, in 2003 and 2007, respectively. In January 2007, he joined the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT), an institute of the Italian National Research Council (CNR), Turin, Italy, as a Research Fellow. He teaches practical classes in courses on electromagnetic field theory and mathematical analysis with the Politecnico di Torino. His main research interests are numerical simulation of microwave antennas and components, and dielectric permittivity measurements.

Riccardo Tascone (M’03) was born in Genoa, Italy, in 1955. He received the Laurea degree (summa cum laude) in electronic engineering from the Politecnico di Torino, Turin, Italy, in 1980. From 1980 to 1982, he was with the Centro Studi e Laboratori Telecomunicazioni (CSELT), Turin, Italy, where his research mainly dealt with frequency-selective surfaces, waveguide discontinuities, and microwave antennas. In 1982, he joined the Centro Studi Propagatione e Antenne (CESPA), Italian National Research Council (CNR), Turin, Italy, where he was initially as a Researcher, and since 1991, a Senior Scientist (Dirigente di Ricerca). He has been Head of the Applied Electromagnetics Section, Istituto di Ricerca sull’Ingeneria delle Telecomunicazioni e dell’Informazione (IRITI), Turin, Italy, an institute of the CNR, and since September 2002 of the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT), Turin, Italy, a newly established institute of the CNR. Since April 2009, he has been the Head of the IEIIT-CNR. He has held various teaching positions in the area of electromagnetics with the Politecnico di Torino. His current research activities are in the areas of microwave antennas, dielectric radomes, frequency-selective surfaces, radar cross section, waveguide discontinuities, microwave filters, multiplexers, optical passive devices, and radiometers for astrophysical observations.

Giuseppe Virone was born in Turin, Italy, in 1977. He received the Electronic Engineering degree in (summa cum laude) and Ph.D. degree in electronic and communication engineering from the Politecnico di Torino, Turin, Italy, in 2001 and 2006, respectively. He is currently a Researcher with the Istituto di Elettronica e di Ingegneria Informatica e delle Telecomunicazioni (IEIIT), Italian National Research Council (CNR), Turin, Italy. He joined the IEIIT as a Research Assistant in 2002. His activities concern the design and numerical analysis of microwave and millimeter waveguide passive components for feed systems, antennas, frequency-selective surfaces, compensated dielectric radomes, and industrial applications.

Renato Orta (M’92–SM’99) received the Laurea degree in electronic engineering from the Politecnico di Torino, Turin, Italy, in 1974. Since 1974, he has been a member of the Department of Electronics, Politecnico di Torino, initially as an Assistant Professor, then as and Associate Professor, and since 1999, as a Full Professor. In 1998, he was a Visiting Professor (CLUSTER Chair) with the Technical University of Eindhoven, Eindhoven, The Netherlands. He currently teaches courses on electromagnetic field theory and optical components. His research interests include the areas of microwave and optical components, radiation and scattering of electromagnetic and elastic waves, and numerical techniques.

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Accurate Complex Permittivity Inversion From Measurements of a Sample Partially Filling a Waveguide Aperture Ugur Cem Hasar, Member, IEEE

Abstract—In this paper, we propose a microwave method, which eliminates the necessity of precise knowledge of sample thickness for accurate permittivity determination of thin materials partially filling the waveguide aperture. The method utilizes propagation constant measurements at two different frequencies for this goal. To facilitate the proposed method for dispersive and nondispersive dielectric materials, we have employed a power series representation of the complex permittivity. We have validated the proposed method from permittivity measurements of prepared thin samples by different methods. We have also noted that the accuracy of the proposed method can be increased by the enhancements in the measurement accuracy of conventional methods, which require complete sample filling into the waveguide aperture. Index Terms—Materials testing, microwave measurements, partially filling, permittivity.

I. INTRODUCTION

M

ATERIAL characterization is an important issue in many material production, processing, and management applications in agriculture, food engineering, medical treatments, bioengineering, and the concrete industry [1], [2]. In addition, microwave engineering requires precise knowledge on electromagnetic properties of materials at microwave frequencies since microwave communications are playing more and more important roles in military, industrial, and civilian life [1]. For these reasons, various microwave techniques, each with its unique advantages and constraints [1], are introduced to characterize the electrical properties of materials. Electrical characterization of thin materials is needed for several reasons. For instance, the dielectric constant of vegetation has a direct effect on radar backscatter measured by airborne and space-borne microwave sensors. A good understanding of the dielectric properties of vegetation leaves is vital for extraction of useful information from the remotely sensed data for earth resources monitoring and management [3]. In the field of electronics, it has also been a lasting key issue to evaluate the relaof thin dielectric materials such tive complex permittivity as high-density packaging [4]. Permittivity measurements of thin materials can be performed by using nondestructive methods such as open-ended waveguide Manuscript received June 24, 2009. First published January 22, 2010; current version published February 12, 2010. The author is with the Department of Electrical and Electronics Engineering, Ataturk University, 25240 Erzurum, Turkey, and also with the Department of Electrical and Computer Engineering, Binghamton University, Binghamton, NY 13902 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2009.2038444

and coaxial methods [5], [6]. In order to accurately measure for these methods, samples with larger apertures should be prepared. Besides, the sample must be sufficiently thick so that the interaction of the electromagnetic field with the noncontacting boundaries or sample holder is negligible [3]. Furthermore, any air gap between the waveguide or coaxial aperture and the sample surface may degrade the accuracy of measurements [7]. Finally, for open-ended waveguides and coaxial probes with a lift-off distance, thin samples may sag, and thus, alter the theoretical computations [8]. Free-space methods, as another nondestructive method, do not require that the sample thickness be moderate. However, it suffers from the diffraction at the edges of the sample. In order to reduce this effect, the transverse dimensions (height and width) of the sample can be selected sufficiently large. However, for thin materials, such a solution may decrease the performance of measurements as a result of sagging. As another solution, spot focusing horn-lens antennas can be employed [9]. Nonetheless, the bandwidth of this antenna system is limited due to focusing nature of the lens. As a final solution, a calibration procedure, which takes into account the diffraction effects, can be incorporated to the measurement system [10], [11]. The accuracy of this approach, however, is not so high since the energy density of electromagnetic waves decreases with distance. Resonant methods have much better accuracy and sensitivity than nonresonant methods [1]. They are generally applied to characterization of low-loss materials. In a recent study, it has been shown that they are also applicable to high-loss materials provided that very small samples are prepared or higher volume cavities are constructed [12], though a meticulous sample preparation is needed before measurements. In addition, for an analysis over a broad frequency band, a new measurement setup (a cavity) must be made. This is not feasible from a practical point of view. Tunable resonators can be used for a wider frequency band analysis; nonetheless, they are expensive and an increase in the frequency bandwidth accompanies a decrease in the accuracy. Due to their relative simplicity, nonresonant waveguide transmission/reflection methods are presently the most widely used broadband measurement techniques [13]. These methods have of thin materials effectively been applied to determine the [3], [7], [14]–[16]. It is not generally possible to locate thin samples to fill a coaxial line or rectangular waveguide section completely. In this circumstance, the transformation of scattering ( -) parameters from the calibration plane to the sample end surfaces (measurement plane) has to be done [13]. Such a transfor-

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mation may result in enormous errors for phase measurement of reflection -parameters. On the other hand, transmission -parameter measurements are not affected if the sample length and the sample holder length both are known [7], [14], [15]. This is because transmission measurements take longitudinal averaging of variations in sample properties [17]. To overcome the problems arising from reflection -parameters, transmissionor amplitude-only measurements can be employed [3], [16], [18]–[21]. Although some of these methods are attractive in determining accurate permittivity, they require that the sample be precisely fitted into the waveguide aperture [7], [13]–[15], [17]–[26]. In some instances, the presence of air gaps between sample surfaces, which are contact with the waveguide walls, and inner waveguide walls may procedure higher order modes or decrease the accuracy and performance of the proposed technique [16], [27], [28]. A promising solution to this problem is to partially fill the sample inside the waveguide aperture. Recently, different techniques have been proposed for permittivity determination using this approach [16], [27]–[30]. While the methods in [16], [27], and [29] are suitable for thin and moderately thin solid materials, those in [28] and [30] are designed for the measurement of liquid materials sandwiched by two plugs and low-loss dielectric materials. Although these methods [16], [27], [29], [30] are accurate, they require precise knowledge of the thickness of the sample for accurate measurements. The accuracy may lower for thin samples since the accuracy of thickness measurements of these samples significantly decreases with a decrease in their thicknesses. Therefore, any method that eliminates the dependence of sample thickness on measurements will be helpful in partially loaded waveguides. To obtain thickness-independent measurements of thin materials partially filling a waveguide aperture and located at the center of the waveguide aperture, in this paper, we utilize propagation constant measurements at two different frequencies. The proposed method does not require any knowledge on sample thickness for inversion.

Fig. 1. Depiction of the problem: permittivity determination of a thin sample partially filling the waveguide section.

In the analysis, we assume that electromagnetic waves propagate into waveguide region II in the -direction with the dominant mode from region I. In addition, we assume that the sample has a flat surface over the -axis at locations of and and its surfaces are parallel to the left and right mode has an elecinner walls of the waveguide. Since the tric field dependency solely in the -direction, only the modes will propagate through waveguide region II. For these and where modes, we can utilize superscript in parenthesis denotes region II [31]. If we, re, , and for the -components spectively, denote of the of the left and right air- and dielectric-filled portions in region II, the scalar wave equation (Helmholtz equation) for each portion in region II is given as (1) where (2) , which satisfies the Helmholtz equation in Solutions for (1), are in the form [33] (3)

II. METHOD (4) A. Background The problem under investigation is depicted in Fig. 1. In this figure, the thin dielectric sample with a thickness of partially filling the waveguide section is asymmetrically located into the waveguide aperture for its permittivity determination. For region II in Fig. 1, either transverse electric to -direction modes or transverse magnetic to -direction modes cannot satisfy the boundary conditions individually [31]. Therefore, the solution will not be unique according to the uniqueness theorem [31], [32]. In this region, field configurations that are combinations of and modes can be solutions and satisfy the boundary conditions of such a partially filled waveguide [31], [32]. In general, in region II, is a function of transverse elecor longitudinal section electric to -ditric to -direction ( rection– ) and transverse magnetic to -direction ( or longitudinal section magnetic to -direction– ) modes [31], [33]. Electric and magnetic field components for each region in Fig. 1 can be found from their vector potentials and (or Hertzian vectors) [31].

(5) where , , and are complex or real constants, , , , and are, respectively, the wavenumbers of air- and dielectric-filled portions in the - and -directions, which will be determined by boundary conditions, and and are the propagation constants of air- and dielectric-filled portions in the -direction. Applying boundary conditions (the continuation of electric and magnetic fields at air–dielectric interfaces), we obtain the following eigenvalues and eigenequations as (6) (7) and

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where and is the wavenumber of electromagnetic waves propagating in an unbounded free-space region. Equation (6) comes from the fact that boundary conditions are satisfied at specific values and are valid for all and values at the interfaces. Furthermore, the derivation of the eigenexpression in (8) can be directly obtained from the transverse-resonance method [33], [34].

where (12) Utilizing (11) and assuming can obtain

and

, we

B. Thickness-Independent Permittivity Determination In this section, we will consider a symmetrically loaded thin sample at the cross section in Fig. 1 , although the following procedure for determination can easily be extended to asymmetrical filling of materials. It is instructive to note that, for symmetrical sample fillings, the expressions of electric vector potentials (or electric and magnetic fields) can simply be obmodes in region II where tained from considering only is an odd number, as a consequence of symmetry about over the aperture [35]. From (8), for a symmetric position of the sample into the waveguide, we have

(13) (14) where, in (14), we use (15) Using (7), we arrange (14) as

(16)

(9) (10) where (9) and (10) correspond to symmetric and asymmetric modes, which result in a short circuit and an open circuit at , respectively. For thin samples, one can assume that only the dominant where ) mode in region II ( will propagate. The frequency bandwidth for the dominant mode will be limited by the appearance of the first higher order . The dependency of this bandwidth over sample mode thickness is analyzed in [36], and it was shown that, for a , the bandwidth in the partially relative width of filled waveguide, as shown in Fig. 1, significantly increases. Therefore, we can assume that, for thin samples with lower mode will propadielectric permittivity values, only the gate along the -axis and the effects of higher order modes can be eliminated. As a result, we will only focus on symmetric modes. The cotangent term on the left-hand side of (9) can be written as (11)

It is obvious from (16) that, for a known thickness of the can be determined from a sample and a given frequency, propagation constant measurement at that frequency. However, for very thin samples, the accuracy of thickness measurement of the sample seriously decreases and this situation can result in significant measurement errors. In this paper, our purpose is of thin samples with no information on their to determine thicknesses using propagation constant measurements at two different frequencies. For the measured propagation constants at two different frequencies and , using the metric function in (16), the sample thickness can be obtained as shown in (17) at bottom of this page, where the superscript denotes the quantities at . Substituting in (17) into (16) or (9), one can compute . Since we use approximations in (15) for the thickness-inof thin samples, the computed dependent measurement of will be fairly accurate. For more precise values of , one can apply the least squares minimization technique [37] to our problem, which is given by for where

(18) denotes the tolerance or error of minimization.

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C. Approximations for a Change in Permittivity Over Frequency changes over frequency, we have to evaluate that Since change in our determination. For very small frequency shifts, we can approximate , where is the second frequency and [38]. We refer to this approximation as “frequency independent” for the remainder of this paper. reduces (17) to (19), shown Assuming at the bottom of this page. Substituting in (19) into (16) or (9), we can find accurate frequency-independent . Although the assumption that slightly changes over the frequency shifts is valid for nondispersive materials, it is not suitable for dispersive materials. Therefore, for dispersive materials, a new approach should be adapted. As a solution, a powerseries representation of can be used [18] Fig. 2. Measurement setup.

(20) where ’s are the unknown complex quantities and is the , the equation in (20) degree of approximation. When will reduce to the case we used for frequency-independent determination [38]. If the degree of power series is selected , it corresponds to the first-order approximation as (linear interpolation) to the permittivity [39]. In the same way, is chosen, then the extended Debye relaxation model if will be used as an approximation to permittivity over frequency changes [40]. The degree of approximation can even be increased to take into consideration higher order power-series terms. It is clearly seen from (20) that power-series represennecessitates an initial guess of at least . We tation of the also need an initial guess for . These guesses can be obtained by using (16)–(19). III. MEASUREMENTS We constructed a general-purpose waveguide measurement setup [18] for validation of the proposed method, as shown in Fig. 2. The setup consists of an HP8720C vector network analyzer (VNA), two flexible coaxial cables, two coaxial-to-waveguide adapters, a 44.38-mm-long nonreflecting measurement cell (a waveguide section), and some nonreflecting extra cells (some waveguide sections) with different lengths. The VNA is connected as a source and measurement equipment. It has a 1-Hz frequency resolution (with option 001) and eight parts per million (ppm) frequency accuracy. The waveguide sections and GHz . adapters operate at -band in reIn order to ensure single-mode transmission gion II in Fig. 1, we utilized two extra waveguide sections with

lengths greater than ( is the free-space wavelength) between the sample holder and coaxial-to-waveguide adapters. These sections will eliminate not only higher order modes such in region II in Fig. 1, but also evanescent as modes in regions I and III in Fig. 1. This is because evanescent modes in regions I and III in Fig. 1 will die out drastically a short distance away from region II and real measurements are performed at waveguide adapters. To calibrate the measurement setup to the calibration planes in Fig. 2, we applied the thru-reflect-line (TRL) calibration technique [41]. We used a waveguide short and the shortest waveguide spacer (44.38 mm) in our laboratory for reflect and line standards, respectively. The line has a 70 maximum offset from 90 between 9.7–11.7 GHz. We prepared two thin low-loss Plexiglas and polyvinyl mm and mm chloride (PVC) samples each with for validation of the proposed method and located them at the center of the waveguide aperture into the sample holder (a 44.38-mm-long waveguide section). Measurements of propagation constants and then of samples are carried out as follows. First, forward and reverse transmission and reflection complex -parameters are measured. By transforming the measurements from the calibration planes to measurement planes, as shown in Fig. 2, we measured the propagation constant at a given frequency as (21)

(22)

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(23)

(24) , , , and are, respectively, the forwhere ward and reverse reflection and transmission -parameters, and are the averaged-out measured reflection and transmission -parameters, , , and are, respectively, the distances between the sample and terminals of the cell and the width of the is the phase constant of the mode for sample in Fig. 2, the region between sample end surfaces and calibration planes, and and are the first reflection coefficient and the propagation factor of the sample. It is clear that (21) and (24) are extensions of those in [27]. of these Next, we determined the frequency-independent samples from propagation constant measurements at two closely separated frequencies using (16), (18), and (19). This gives its approximate value over 9.7–11.7 GHz. We then as an initial guess in (20) and refined it with utilized this using (16), (18), and (19). We continued this process with larger values until the refined with present and previous values are approximately the same. It is noted that the extracted of each sample output very close values for and . Therefore, we stopped the refining process using bigger values. The accuracy of the aforementioned procedure for measurements of at a given frequency mainly depends on how preand are known. To remove the ercisely the distances rors arising from inaccurate knowledge of these distances, in the literature, different methods can be employed [19], [21], [42]–[44]. While the methods in [21] and [42] are applicable to constitutive parameters measurement, those in [19], [43], and measurement. When com[44] can only be employed for pared to the method in [42], the advantage of our method in [21] is that it does not require any knowledge of sample length for constitutive parameter measurement. In this paper, however, we use the broadband and stable method in [19] for measurements since this method is not affected by phase uncertainty in reflection -parameter measurements. To apply it to our problem, any 3-D numerical technique such as the Newton–Raphson method [37] and/or graphical method [18] can be utilized. We utilized both methods to ensure that the determined is accurate. of the Plexiglas Figs. 3 and 4 demonstrate the measured and PVC samples by our proposed method using the propagation constant measurements from (21) and (24). To validate our of the method and compare its accuracy, we also measured Plexiglas sample by the method in [16]. It is seen from Fig. 3 that the extracted of the Plexiglas sample by two methods are in good agreement with one another and the data in literature of a Plexiglas sample [45]. At ordinary room temperature, at 10 GHz given by Von Hippel is approximately [45]. For comparison of the results of our method with those of

Fig. 3. Measured real and imaginary parts of the " of a 2-mm-long Plexiglas sample (l = 20 mm) using the method in [16] and the proposed method.

Fig. 4. Comparison between the method requiring complete filling of the sample into the waveguide aperture [19] and the proposed method for the PVC sample.

the methods that require insertion of the sample into the waveguide aperture completely, we also measured of another PVC mm by the method in [19]. We also note that sample the reconstructed values by our proposed method and by the method in [19] are in good agreement with each other and the reference data in the literature (at ordinary room temperature, of the PVC sample given by Von Hippel is approximately at 3 GHz [45]). The measured values of the PVC and Plexiglas samples by the proposed method shown in Figs. 3 and 4 are dependent on the accuracy of measured and . To validate and compare the results in Figs. 3 and 4, we also measured of the Plexiglas sample using measurements following the procedure in [19]. The result is shown in Fig. 5. It is seen from Fig. 5 that there is a good agreement with the values of the Plexiglas sample measured from propagation constant measurements using two different approaches. It is noted that while (21)–(24) require an accurate knowledge of and , the procedure in [19] eliminates this necessity. Furthermore, we note that the extracted using the procedure in [19] has a spectral dependency smoother than that using the extended procedure in [27]. This is because the accuracy of the procedure in [19] is not much affected by any sharp phase changes in reflection -parameters. It is obvious from (16)–(24) that the proposed method needs propagation constant measurements at two frequencies yielding and/or values. The general procedure used different

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justing the degree of power series representation of the complex permittivity; and 3) its accuracy can be increased by improving the accuracy of permittivity measurements in conventional techniques that require complete sample filling to the waveguide aperture. The proposed method has been verified with complex permittivity measurements of two thin samples by different methods in the literature. REFERENCES

Fig. 5. Comparison between the procedure in [19] and the extended procedure in [27] for the Plexiglas sample.

for measuring the propagation constants in (21)–(24) is similar to that utilized for conventional propagation constant measurements of a sample that completely fills the entire aperture of the waveguide or coaxial line. We have demonstrated in Fig. 5 that the results of the conventional procedure [19] and procedure given in (21)–(24) are closely related [16], [27]. Therefore, any improvement in the conventional propagation constant measurements will be helpful in accurate measurements by the proposed method in this paper. It is important to discuss the effects of sample irregularity and surface roughness on the accuracy of measurements since the theoretical formulations in Section II do not consider these effects. These parameters influence the evaluation in a commeasurements will plex manner. However, we expect that measurements since reflection propbe affected more than erties are predominantly dependent on surface characteristics, whereas transmission properties are mainly dependent upon internal properties of the sample. Since our method utilizes both and measurements, the aforementioned parameters can seriously limit the accuracy of measurements. Increasing the sample length, however, may alleviate this drawback since it may partially eliminate the sample inhomogeneity. Since the method relies on calibrated measurements of and and does not consider higher order modes, in the future, we would like to apply a calibration-independent method that can effectively eliminate the need of calibration and any errors arising from calibration and remove the effect of higher order terms by accounting for them in error boxes [46]–[48]. IV. CONCLUSION A microwave method has been proposed for accurate permittivity measurements of thin dielectric materials. The materials do not need to fill the total aperture of their holders (a waveguide or coaxial line section). We have derived simple expressions to measure the complex permittivity of thin materials, not completely filling the waveguide aperture, using propagation constant measurements at two different frequencies. The advantages of the proposed method are that: 1) it eliminates the requirement of precise knowledge on the thickness of thin samples, which, in turn, augments the accuracy of permittivity measurements by decreasing the sample thickness uncertainty; 2) it can be adapted to dispersive and nondispersive materials by ad-

[1] L. F. Chen, C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave Electronics: Measurement and Materials Characterization. West Sussex, U.K.: Wiley, 2004. [2] R. Zoughi, Microwave Non-Destructive Testing and Evaluation. Dordrecht, The Netherlands: Kluwer, 2000. [3] B.-K. Chung, “Dielectric constant measurement for thin material at microwave frequencies,” Prog. Electromagn. Res., vol. PIER 75, pp. 239–252, 2007. [4] K. A. Murata, A. Hanawa, and R. Nozaki, “Broadband complex permittivity measurement techniques of materials with thin configuration at microwave frequencies,” J. Appl. Phys., vol. 98, pp. 084 107-01–084 107-8, 2005. [5] M. C. Decreton and F. E. Gardiol, “Simple nondestructive method for the measurement of complex permittivity,” IEEE Trans. Instrum. Meas., vol. IM-23, no. 4, pp. 434–438, Dec. 1974. [6] H. Zhang, S. Y. Tan, and H. S. Tan, “An improved method for microwave nondestructive dielectric measurement of layered media,” Prog. Electromagn. Res. B, vol. 10, pp. 145–161, 2008. [7] R. Olmi, M. Tedesco, C. Riminesi, and A. Ignesti, “Thickness-indepenband,” dent measurement of the permittivity of thin samples in the Meas. Sci. Technol., vol. 13, no. 4, pp. 503–509, Apr. 2002. [8] J. Baker-Jarvis, M. D. Janezic, P. D. Domich, and R. G. Geyer, “Analysis of an open-ended coaxial probe with lift-off for nondestructive testing,” IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp. 711–718, Oct. 1994. [9] D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan, “Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 39, no. 2, pp. 387–394, Apr. 1990. [10] K. M. Hock, “Error correction for diffraction and multiple scattering in free-space microwave measurement of materials,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 648–659, Feb. 2006. [11] U. C. Hasar, “A microcontroller-based microwave free-space measurement system for permittivity determination of lossy liquid materials,” Rev. Sci. Instrum., vol. 80, no. 5, pp. 056 103-1–056 103-3, 2009. [12] C. L. P. Rubinger and L. C. Costa, “Building a resonant cavity for the measurement of microwave dielectric permittivity of high loss materials,” Microw. Opt. Technol. Lett., vol. 49, pp. 1687–1690, 2007. [13] J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 8, pp. 1096–1103, Aug. 1990. [14] K. Sarabandi and F. T. Ulaby, “Technique for measuring the dielectric constant of thin materials,” IEEE Trans. Instrum. Meas., vol. 37, no. 4, pp. 631–636, Dec. 1988. [15] E. D. Kenneth and L. J. Buckley, “Dielectric materials measurement of thin samples at millimeter wavelengths,” IEEE Trans. Instrum. Meas., vol. 41, no. 5, pp. 723–725, Oct. 1992. [16] B.-K. Chung, “A convenient method for complex permittivity measurement of thin materials at microwave frequencies,” J. Phys. D, Appl. Phys., vol. 39, pp. 1926–1931, 2006. [17] U. C. Hasar, “Elimination of the multiple-solutions ambiguity in permittivity extraction from transmission-only measurements of lossy materials,” Microw. Opt. Technol. Lett., vol. 51, no. 2, pp. 337–341, Feb. 2009. [18] U. C. Hasar, “Two novel amplitude-only methods for complex permittivity determination of medium- and low-loss materials,” Meas. Sci. Techol., vol. 19, no. 5, May 2008, 055 706 (10 pp). [19] U. C. Hasar and C. R. Westgate, “A broadband and stable method for unique complex permittivity determination of low-loss materials,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 2, pp. 471–477, Feb. 2009. [20] U. C. Hasar, “A fast and accurate amplitude-only transmission-reflection method for complex permittivity determination of lossy materials,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 9, pp. 2129–2135, Sep. 2008.

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[21] U. C. Hasar, “Thickness-independent automated constitutive parameters extraction of thin solid and liquid materials from waveguide measurements,” Prog. Electromagn. Res., vol. 92, pp. 17–32, 2009. [22] U. C. Hasar, “A generalized formulation for permittivity extraction of low-to-high-loss materials from transmission measurement,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 2, pp. 411–418, Feb. 2009. [23] T. C. Williams, M. A. Stuchly, and P. Saville, “Modified transmissionreflection method for measuring constitutive parameters of thin flexible high-loss materials,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 5, pp. 1560–1566, May 2003. [24] W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE, vol. 62, no. 1, pp. 33–36, Jan. 1974. [25] A. M. Nicolson and G. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Trans. Instrum. Meas., vol. IM-19, no. 4, pp. 377–382, Nov. 1970. [26] U. C. Hasar and O. Simsek, “An accurate complex permittivity method for thin dielectric materials,” Prog. Electromagn. Res., vol. 91, pp. 123–138, 2009. [27] J. M. Catala-Civera, A. J. Canos, F. L. Penaranda-Foix, and E. de los Reyes Davo, “Accurate determination of the complex permittivity of materials with transmission reflection measurements in partially filled rectangular waveguides,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 16–24, Jan. 2003. [28] J. M. Akhtar, L. E. Feher, and M. Thumm, “Noninvasive procedure for measuring the complex permittivity of resins, catalysts, and other liquids using a partially filled rectangular waveguide structure,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 2, pp. 458–470, Feb. 2009. [29] J. Pitarch, M. Contelles-Cervera, F. L. Penaranda-Foix, and J. M. Catala-Civera, “Determination of the permittivity and permeability for waveguides partially loaded with isotropic samples,” Meas. Sci. Technol., vol. 17, pp. 145–152, 2006. [30] M. J. Akhtar, L. E. Feher, and M. Thumm, “A closed-form solution for reconstruction of permittivity of dielectric slabs placed at the center of a rectangular waveguide,” IEEE Geosci. Remote Sens. Lett., vol. 4, no. 1, pp. 122–126, Jan. 2007. [31] C. A. Balanis, Advanced Engineering Electromagnetics. Hoboken, NJ: Wiley, 1989. [32] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: Wiley/IEEE Press, 2001. [33] R. E. Collin, Field Theory of Guided Waves. New York: IEEE Press, 1991. [34] Waveguide Handbook, N. Marcuvitz, Ed. New York: McGraw-Hill, 1951. [35] D. M. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 2005. [36] P. H. Vartanian, W. P. Ayres, and A. L. Helgesson, “Propagation in dielectric slab loaded rectangular waveguide,” IRE Trans. Microw. Theory Tech., vol. MTT-5, no. 2, pp. 215–222, Apr. 1958. [37] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. New York: Cambridge Univ. Press, 1992. [38] Y. Huang and M. Nakhkash, “Characterization of layered dielectric medium using reflection coefficient,” Electron. Lett., vol. 34, pp. 1207–1208, 1998. [39] S. Wang, M. Niu, and D. Xu, “A frequency-varying method for simultaneous measurement of complex permittivity and permeability with an open-ended coaxial probe,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 12, pp. 2145–2147, Dec. 1998.

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[40] J. Baker-Jarvis, R. G. Geyer, and P. D. Domich, “A nonlinear least-squares solution with causality constraints applied to transmission line permittivity and permeability determination,” IEEE Trans. Instrum. Meas., vol. 41, no. 5, pp. 646–652, Oct. 1992. [41] G. F. Engen and C. A. Hoer, “‘Thru-reflect-line’: An improved technique for calibrating the dual six-port automatic network analyzer,” IEEE Microw. Theory Tech., vol. MTT-27, no. 12, pp. 987–993, Dec. 1979. [42] K. Chalapat, K. Savala, J. Li, and G. S. Paraoanu, “Wideband reference-plane invariant method measuring electromagnetic parameters of materials,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 9, pp. 2257–2267, Sep. 2009. [43] U. C. Hasar and O. E. Inan, “Elimination of the dependency of the calibration plane and the sample thickness from complex permittivity measurements of thin materials,” Microw. Opt. Technol. Lett., vol. 51, no. 7, pp. 1642–1646, Jul. 2009. [44] U. C. Hasar, “Simple calibration plane-invariant method for complex permittivity determination of dispersive and non-dispersive low-loss materials,” IET Microw. Antennas Propag., vol. 3, no. 4, pp. 630–637, Jun. 2009. [45] A. R. Von Hippel, Dielectric Materials and Applications. New York: Wiley, 1954. [46] U. C. Hasar, “A new calibration-independent method for complex permittivity extraction of solid dielectric materials,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, pp. 788–790, Dec. 2008. [47] U. C. Hasar and O. Simsek, “A calibration-independent microwave method for position-insensitive and nonsingular dielectric measurements of solid materials,” J. Phys. D, Appl. Phys., vol. 42, no. 7, pp. 075 403–075 412, 2009. [48] U. C. Hasar, “A new microwave method for electrical characterization of low-loss materials,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 12, pp. 801–803, Dec. 2009.

Ugur Cem Hasar (M’00) was born in Kadirli, Adana, Turkey, in 1977. He received the B.Sc. and M.Sc. degrees (with honors) in electrical and electronics engineering from Cukurova University, Adana, Turkey, in 2000 and 2002, respectively, and the Ph.D. degree in electrical engineering from Binghamton University, Binghamton, NY, in 2008. From 2000 to 2005, he was a Research and Teaching Assistant with the Department of Electrical and Electronics Engineering, Cukurova University. From 2005 to 2008, he was a Research Assistant with the Department of Electrical and Electronics Engineering, Ataturk University, Erzurum, Turkey. He is currently an Assistant Professor with Ataturk University. His main research interest includes nondestructive testing and evaluation of materials using microwaves and novel calibration-dependent and calibration-independent techniques for the electrical and physical (thickness, delamination, etc.) characterization of materials. Dr. Hasar was the recipient of The Scientific and Technological Research Council of Turkey (TUBITAK) Münir Birsel National Doctorate Scholarship, The Higher Education Council of Turkey (YOK) Doctorate Scholarship, The Outstanding Young Scientist Award in Electromagnetics of the Leopold B. Felsen Fund, Binghamton University Distinguished Dissertation Award, and Binghamton University Graduate Student Award for Excellence in Research.

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Measurement Bandwidth Extension Using Multisine Signals: Propagation of Error Kate A. Remley, Senior Member, IEEE, Dylan F. Williams, Fellow, IEEE, Dominique Schreurs, Senior Member, IEEE, and Maciej Myslinski

Abstract—We describe a post-processing technique that extends the effective measurement bandwidth of narrowband vector receivers by phase aligning overlapping measurements. We study the repeatability of the method and the propagation of errors as increasing numbers of bands are stitched together. The method can be used to find phase errors both in the excitation band of frequencies, as well as in distortion products, for periodic multisine signals. Index Terms—Broadband wireless communications, digitally modulated signal, large-signal network analyzer (LSNA), multisine signal, phase alignment, phase detrending, relative phase, sampling oscilloscope, vector signal analyzer (VSA).

I. INTRODUCTION

O

NE TECHNIQUE for extending the useful measurement bandwidth of vector receivers is based on “stitching” together a series of overlapping frequency bands using the overlapping tones for phase alignment. A well-known issue with stitching methods is that phase errors in the measurement increase as more bands are stitched together unless an external reference signal is used. When an external reference signal is not used, measurement errors depend on the characteristics of the receiver, including its sensitivity and phase measurement accuracy. These quantities may, in turn, depend on characteristics of the measured signal, such as its peak-to-average-power ratio, the rise and fall times of transitions, and random noise introduced during transmission. To understand the interaction of these factors, we study the propagation of error as bands are stitched together in the context of a stitching method based on phase detrending of multisine signals. Stitching methods are used to extend the measurement bandwidth of vector receivers such as vector signal analyzers (VSAs) [1], large-signal network analyzers (LSNAs) [2], and real-time spectrum analyzers [3].1 These vector receivers maintain the phase relationships between measured frequency components Manuscript received June 30, 2009; revised November 18, 2009. First published January 22, 2010; current version published February 12, 2010. K. A. Remley and D. F. Williams are with the National Institute of Standards and Technology, Boulder, CO 80305 USA (e-mail: [email protected]; [email protected]). D. Schreurs and M. Myslinski are with ESAT-Telemic, Katholieke Universiteit Leuven (K.U. Leuven), Leuven 3001, Belgium (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038655

1Commercial products are identified solely for completeness of description; such identification does not constitute an endorsement by the National Institute of Standards and Technology (NIST). Other products may work as well or better.

using methods such as real-time sampling or sampling downconversion. Accurate measurement of the phase components of signals and distortion products is critical for characterization of telecommunication systems that use complex modulation schemes, as well as for development and verification of measurement-based behavioral models of electronic circuits and systems [4]–[6]. The measurement bandwidths of commercially available instruments have increased from around 10 MHz only a few years ago to over 100 MHz today. However, even more bandwidth is needed for a complete vector characterization of distortion products several hundred megahertz from the carrier. This is necessary, for example, in measurements of broadband wireless signals at millimeter-wave frequencies. Full-bandwidth instruments such as digital sampling oscilloscopes [7], [8] offer broadband capability and may be fully calibrated, but typically do not offer the dynamic range of narrowband vector receivers. Consequently, development of bandwidth extension methods that maintain phase relationships between measured frequency components using high dynamic-range instruments has been the subject of a great deal of research. One class of methods that has been proposed for measuring the phases of frequency components in broadband scenarios is based on the use of an alignment signal whose characteristics are known or assumed a priori. Examples may be found in [9]–[13]. These methods are generally restricted to measurement of simple signals such as two- or three-tone signals and their distortion products, or are limited in measurement bandwidth by vector signal generators or receivers. LSNAs based on sampling downconversion, but modified for broadband measurements, have been proposed in [14]–[16]. These modified instruments are not currently available commercially, although the necessary modifications are described in the references. A commercially available VNA-based instrument is described in [17]. The instruments of [14], [16], and [17] utilize a comb generator with a narrow frequency spacing as a phase reference, providing a known alignment signal that enables the measurement of signals that are more complex than those of [9]–[13]. The instrument of [15] adds a switch to allow the samplers to step through the envelope of a broadband modulated signal. In addition to requiring specialized hardware, the instruments of [14]–[17] may not provide the frequency resolution of an instrument such as a VSA, which can have resolution bandwidths comparable to a spectrum analyzer in the kilohertz or hertz range. A second class of bandwidth extension method [18], [19] is not hardware based. These methods stitch together sequentially

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REMLEY et al.: MEASUREMENT BANDWIDTH EXTENSION USING MULTISINE SIGNALS

measured frequency bands that are offset in center frequency by up to half of the measurement bandwidth. Overlapping frequency components of a periodic signal are aligned by maximizing a cross-correlation function [18] or minimizing an error function [19]. Subsampling may be used to optimize the alignment between measured samples. One advantage of these techniques is that they do not require the use of additional hardware or instrumentation. The stitching technique discussed here is similar to the methods of [18] and [19] in that overlapping measurement bands are joined together by aligning individual measurements. The method described here uses an efficient alignment procedure based on minimization of an analytic error function operating on only the phase components of the measured signal. Alignment may be carried out using as few as two overlapping frequency components and is not restricted to sampled time steps. This method is particularly well suited for use with multisine excitations [6], [7], [15], [16], [20]–[24], where a test signal is engineered to have a certain peak-to-average-power ratio by specifying certain phase relationships. The use of multisines also allows us to easily study the propagation of errors in the method as the number of stitched bands increases because the magnitude and phase of each frequency component can be readily specified. The difference between the measured and specified phases then provides a simple metric for studying the errors in stitching methods. Our bandwidth extension method is described in Section II, and measurement results for a two-port circuit are described in Section III. We study the propagation of error in Section IV, including the sensitivity of the method to phase measurement errors as a function of the peak-to-average-power ratio of the signal, the number of overlapping frequency components, and the severity of the initial measured phase error. We also compare the repeatability of the method to that from measurements made with a calibrated sampling oscilloscope. II. BANDWIDTH EXTENSION BASED ON PHASE ALIGNMENT The bandwidth extension method described here, like those described in [18] and [19], aligns overlapping frequency bands of sequential measurements to achieve bandwidths several times wider than that of the narrowband vector receiver itself. In our multisine-based method, measurements are collected that overlap in frequency by a minimum of two tones in order to phase align adjacent bands [24]. These measurements do not need to be collected simultaneously, although collecting them within a reasonably short period will minimize instrumentation drift. that minimizes the We first determine a reference time difference between a set of “target” phase values (for example, phase values provided by the user to the signal generator) and those that were measured, shown by “M1” in Fig. 1. Determination of a reference time is necessary because the relative phase relationships between frequency components depend on where the signal is sampled within the envelope period. We provide an overview of this phase alignment (or “detrending”) procedure in the Appendix, and the method is described in detail in [24].

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Fig. 1. Illustration of the bandwidth extension method. The phases of the tones in the excitation band are the first to be aligned (shown in the top graph labeled M1). In the second measurement (M2), P overlapping tones are used as targets for phase aligning the lower-adjacent band of frequencies.

The aligned phases in the first measurement band are then used as target values for aligning the phases in the upper and lower adjacent frequency bands, as shown by “M2” in Fig. 1. We continue a sequential process of phase alignment while moving to further adjacent frequency bands until the last band is reached. The user-specified target phases only need to be provided in the first measurement band where the excitation signal is generated. Since we use a common reference time to align all measurements, phase alignment is automatic for frequency components for which there are no targets, such as intermodulation distortion products. This is one of the key strengths of our method. Mathematically, if the phases of the frequency components in , we use a the th measured band are given by the vector of these phases at the edge of the measured band as subset of th measured targets for phase alignment in the adjacent band. An analytic expression provides a rough estimate of the reference time. More precise phase alignment is then carried out that expresses the mean by minimizing an error function square error in the difference between the known target values in the th band and the measured frequency components in the th band (1) where and are the overlapping tones measured in the th th acquisition (denoted by “overlap” in Fig. 1). We and at time points around the rough initial guess and calculate select as the time that provides the minimum error between the measured and target phase values. By minimizing the error, rather than setting the phase of a measured frequency component to an ideal value [25], our phase alignment procedure provides a realistic picture of the nonidealities of the signal generation and measurement instruments. For both upper and lower adjacent frequency bands, we carry detrending operations, where is out the number of bandwidths to be joined together on either side of the carrier. Note that this method requires initial experiment design such that the measured overlapping components fall on the same frequency values.

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Fig. 2. LSNA measurements of a nine-tone low peak-to-average-power ratio multisine applied to a broadband amplifier. In (a) and (b), the top graph is magnitude and the bottom graph is the detrended phase. (a) Output for a low-power input signal. (b) Output for a high-power input signal. Vertical dashed lines show the center frequency of each measurement. The measured bandwidth is 30 MHz, over four times the bandwidth of the LSNA we used.

III. TWO-PORT DISTORTION MEASUREMENT

is where is the number of tones in the multisine signal and the phase of the th tone in radians. Use of low peak-to-averagepower ratio multisines allows us to test system distortion under modulated-signal conditions separately from tests of the effects of distortion induced by transient peaks. Other algorithms for low peak-to-average power ratios can be found, for example, in [23], [26]. The vertical dashed lines in Fig. 2 represent the center frequency of each of the ten stitched measurement bands. The excitation band covers a 5-MHz band around the center frequency. These nine tones are the only frequency components for which we have target phase values. To minimize phase dispersion, we used only the inner 4 MHz of the LSNA’s 8-MHz measurement bandwidth in the stitching procedure. The phases shown in the bottom graphs of Fig. 2(a) and (b) determined by the excitation signal were found from a components. The phases of the distortion components were as well. As an example of the phase change found using this in the output wave variable when the amplifier was driven into at the carrier frequency had compression, the component of a measured phase value of 38.6 for both low and high input powers. At the output, this frequency component had a phase value of 141.4 for the lower power and 121.2 for the higher power. This change in phase of the output signal components was relative to the input, not just relative to each other. The ability to measure this system-level phase shift demonstrates the utility of a full vector two-port measurement. Toward the edges of the measured frequency band, Fig. 2(a) shows that, for the lower input power level, the distortion products are buried in the system measurement noise. As a result, the magnitudes and phases measured in adjacent bands do not overlay well. At higher power levels, Fig. 2(b) shows that the distortion products have significant energy, and a distinct structure is discernable for both magnitude and phase outside the excitation band of frequencies.

The method described above can be applied to two-port measurements providing that the signals at both ports are sampled simultaneously. We phase align the signals at the output port using determined from the input port tones for the reference time which we have target values. Once the time alignment is carried out, we can characterize the time delay through the system under test and phase align distortion products generated by the system under test as well. As an example, Fig. 2(a) and (b) shows measurements of at the output port of a broadband amplithe wave variable fier having a gain of approximately 10. Two different excitation power levels are shown: low power ( 15 dBm) in Fig. 2(a) and high power ( 5 dBm) in Fig. 2(b). Eleven LSNA measurements were made: one in the center band and five stitched above and below. The top graph in each figure shows the magnitude and the bottom graph shows the detrended phase. The excitation was a nine-tone Schroeder multisine [20], [23] having a frequency spacing of 500 kHz and a carrier frequency of 2.4 GHz. The relative phases in a Schroeder multisine are designed for a low peak-to-average-power ratio and are defined as

Errors in stitching methods that use measured data for phase alignment, rather than an alignment signal, are affected by the characteristics of the measured signals, as well as by the number of overlapping tones used. A signal with a high peak-to-average-power ratio can introduce distortion into both the measurement instrument and the system under test, making the phase detrending procedure less accurate. Noise in the received signal may also introduce errors. Measurement errors in one band will propagate through to subsequent bands, and the severity of phase measurement errors in the initial band of frequencies can affect the outcome in a nonlinear manner. In this section, we study these effects as increasing number of bands are stitched together. Even though the absolute value of the errors in other measurement scenarios and using other stitching methods will be different from those reported here, this study provides the user with information on the interaction of these effects and their relative importance.

(2)

We compare measurements of a wideband multisine made using a reference instrument to those made using a

IV. PROPAGATION OF ERROR

A. Measurement Comparison

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stitched-VSA measurement procedure. Our reference measurement is made with a digital sampling oscilloscope having a 20-GHz acquisition bandwidth. The measurement comparison described in [7] gives us sufficient confidence to use the oscilloscope as a broadband reference measurement instrument. For our comparison, we made 50 repeat measurements on both the oscilloscope and the VSA because it was determined in [7] that the mean and standard deviation of 50 measurements converged to a steady-state value in the measurement of similar multisines. The oscilloscope’s time-base distortion was corrected using the method of [8]. The data were then transformed to the frequency domain and the phases were detrended using all of the tones in the multisine as targets. Thus aligned, the measured waveforms were averaged in the time domain to reduce the measurement noise floor, as described in [7]. The VSA was automated to acquire five 20-MHz-wide bands that were subsequently stitched together. The experiment was designed with five overlapping tones. In the discussion that follows, we compare the propagation of error when two, three, or all five of these overlapping tones were used as targets in the phase alignment procedure. Use of two targets is desirable because it allows coverage of a broader frequency range with the fewest stitched bands, but using five targets provides the most data for stitching. We acquired 12 801 points in each measured band giving a resolution bandwidth of just over 1.56 kHz. The experiment was designed to minimize spectral leakage by setting the acquisition where time window to a multiple of the envelope period is the spacing between tones in the multisine, as described in [27]. We extracted the frequency components corresponding to the multisine frequencies and carried out the phase alignment/ stitching procedure described in Section II. B. Peak-to-Average-Power Ratio Because stitching is carried out using measured data, distortion caused by signals having higher peak-to-average-power ratios may affect the ability of the receiver to accurately measure the phase. This will, in turn, affect the ability of the stitching method to align overlapping signals. To study this effect, we again utilized a low peak-to-average-power ratio Schroeder multisine. We compared this to a more realistic multisine signal with a probability density function designed to mimic a 64-QAM digitally modulated signal using the method of [6], [28]. The peak-to-average-power ratio for the 64-QAM-like multisine was approximately 10 dB. Both multisines were 80-MHz wide and consisted of 33 tones, giving a MHz. A vector signal generator was tone spacing of used to produce the signals with a carrier frequency of 1 GHz. We connected our receivers to the output port through a coaxial cable. Fig. 3(a) and (b) shows the spectra of the oscilloscope-measured Schroeder and 64-QAM-like signals, respectively. We see a small amount of second-harmonic distortion, as well as intermodulation distortion near the passband of the signals. These effects were studied previously [7] and are due to the signal generator used.

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Fig. 3. Spectra of two 80-MHz-wide 33-tone multisine signals measured using a digital sampling oscilloscope. (a) Schroeder multisine. (b) 64-QAM-like multisine. The inset shows the 100-MHz spectrum around the 1-GHz carrier frequency.

Fig. 4 shows the difference between the specified and measured phases (denoted “Phase Error”) for the low peak-to-average-power ratio Schroeder multisine [see Fig. 4(a)] and the 64-QAM-like multisine [see Fig. 4(b)] measured by the oscilloscope and VSA. For the latter, five bands containing 13 tones each were stitched together using three target phases; 50 measurements are shown. Note that this phase error quantifies the phase distortion introduced by the system under test (in this case, the signal generator) and is the quantity of interest for this measurement. We see that both receivers report phase errors on the order of 20 at the edges of the 80-MHz passband of the signal, which is consistent with the results of [7] for this signal generator. The curve labeled “Difference” in Fig. 4(a) and (b) denotes the measurement phase error in the stitching method when the oscilloscope is used as the reference receiver. This value increases toward the edges of the measurement, as expected. Fig. 4(b) shows that the spread around the mean of the 50 oscilloscope measurements is broader at some frequencies than at others. This is because some of the frequency components in the 64-QAM-like signal were of lower amplitude than others, and these lower amplitude components were affected by the dynamic range of the oscilloscope. In practice, we would typically average all 50 time-domain waveforms from the oscilloscope to reduce this effect.

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Fig. 5. Difference between the mean of 50 oscilloscope measurements and 50 stitched-VSA measurements for different numbers of target phase values. The Schroeder multisine is shown, although the results were comparable for the 64-QAM-like signal.

However, the number of target phases does have an effect on the standard deviation of the repeat measurements. We calculate the standard deviation in the measurement of the th frequency as component (3) Fig. 4. Thick lines show the mean of 50 repeat measurements of the phase error in the: (a) Schroeder and (b) 64-QAM-like multisines measured by the oscilloscope (solid) and the stitched-VSA procedure (dashed). Individual measurements are shown by dots (oscilloscope) and ’s (VSA). The difference between the two, the phase measurement error in the stitching method, is shown by the thin dashed–dotted line. Three target phases were used in stitching.

2

C. Number of Overlapping Tones and Repeatability A greater number of overlapping tones used in the stitching method means that more target values will be used in the phase detrending procedure. Fig. 5 shows the difference between the oscilloscope and the stitched-VSA measurements for the mean of 50 measurements (shown by the thin line labeled “Difference” in Fig. 4). We see that this difference is less than 8 at the edges of the passband when two, three, or five targets were used in the phase alignment/stitching process. This represents the maximum measured error in the stitched-VSA method for this measurement, significantly less than the measured quantity of interest, which was the phase error in the signal generator itself. The difference was less than 8 for the 64-QAM-like multisine as well, as indicated in Fig. 4(b). The asymmetry in the difference curves occurs because we used initial-guess targets that were not centered at the carrier frequency. The signal generator we used can have significant carrier leakthrough, and thus, we avoid the use of the carrier in the initial analytic solution. The number of target phases used in the phase alignment procedure did not have a significant effect on the difference between the mean value of the VSA measurement and the oscilloscope measurement of the phase error in the vector signal generator.

where is the th measured value of the th frequency component, is the mean over all measurements of that frequency measurements were made. component, and Fig. 6(a) and (b) shows the standard deviation for 50 repeat measurements for different numbers of targets. Each repeat is the difference between the specified and the measured phase. The lowest standard deviation occurs when five targets are used, covering almost half of the stitched frequency band. The use of fewer targets enables the use of fewer measured frequency bands, although it results in an increased standard deviation. Fig. 6(b) also shows that standard deviation in the oscilloscope measurements is highest for tones in the 64-QAM-like multisine that have lower amplitudes, as mentioned above. We do not see a corresponding increase in the standard deviation of the stitched-VSA measurements since each measurement uses the full dynamic range of the instrument. Fig. 6(a) and (b) shows that the value of the standard deviation in the stitched VSA measurements increases further from the center frequency. This increase is approximately linear within a given measurement band and the increase is smaller when greater numbers of tones are used as targets. This variability can be caused by, for example, phase measurement errors in the receiver, or additive noise in the transmitted signal, as discussed in Section IV-D. D. Measurement Errors and Additive Noise To study the effects of additive-noise-based phase errors on the method as increasing numbers of bands are stitched together, we conducted a Monte Carlo simulation where Gaussian-distributed noise was introduced into the phase of

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Fig. 6. Standard deviation in 50 oscilloscope (light dotted line) and stitched-VSA (dashed and solid lines) measurements of the signal generator’s phase error in: (a) the Schroeder multisine and (b) the 64-QAM-like multisine. Different numbers of targets were used in the phase-alignment procedure, as noted. The peaks in the standard deviation in (b) correspond to the lower signal levels shown in the inset of Fig. 3(b).

each frequency component in the multisine excitation. In this study, the phase alignment procedure had to “overcome” a given level of phase distortion in the form of additive noise during the stitching process. This additive noise could represent a random process introduced by the vector receiver such as its noise floor when weak signals are received, or random noise introduced on the signal during transmission. Our unperturbed data was one set of the stitched-VSA measurement data for the 64-QAM multisine. We study the difference in phase error for small and large values of additive noise relative to the input signal. 1) Small Errors: We first used a value of simulated additive noise representative of a real laboratory-based measurement. For this, we used the maximum standard deviation of the 50 measurements discussed in Section IV-C. Since this measurement setup consisted of a signal generator connected directly to a signal analyzer, the variance between measurements was internally generated by the instrumentation. From an examination of the data in Section IV-C, the standard deviation of our raw measurements was never greater than 0.15 for any of the 13 frequency components in the five frequency bands for the 50 repeat measurements we made using five targets. We

Fig. 7. (a) Difference between measurement and 500 Monte Carlo simulations where Gaussian-distributed noise with a standard deviation of 0.15 was introduced into each frequency component before stitching. (b) Distribution of phase error at 970 MHz. (c) Standard deviation of measured and simulated phase errors.

conducted 500 Monte Carlo simulations using this standard deviation. Fig. 7(a) shows the difference between the unperturbed phases and the Monte Carlo simulations when five target phases were used in the stitching procedure. The repeatability of the stitching procedure is less than 1 for this level of additive noise. Fig. 7(b) shows the distribution of phases at the frequency of 970 MHz, essentially a vertical slice in the graph of Fig. 7(a). Here we see an approximately Gaussian-distributed phase difference between the unperturbed and perturbed simulated phases. This is expected because we used Gaussian-distributed additive noise in the simulations.

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Fig. 8. (a) Difference between measurement and 500 Monte Carlo simulations where Gaussian-distributed noise with a standard deviation of 0.5 was introduced into each frequency component before stitching. (b) Distribution of phase error at 970 MHz. Five target phases were used.

In Fig. 7(c), we compare the standard deviation in the phase error from the 50 measurements [also shown in Fig. 6(b)] to that of the Monte Carlo simulations. We used the maximum standard deviation at any frequency over all of our measurements as the standard deviation in our Monte Carlo simulation. As a result, the Monte Carlo simulation displays a higher overall standard deviation than do the measurements. However, the order-of-magnitude agreement between the two indicates that the Monte Carlo simulation approximates the measurement well for a standard deviation close to that of the measurements. 2) Large Errors: We next used the Monte Carlo simulations to predict how errors propagate in the stitching method for larger values of phase error. We again carried out 500 Monte Carlo simulations of the 64-QAM-like multisine. As before, 13 frequency components were included in each stitched band, and five bands were stitched together. The standard deviation in the Gaussian-distributed noise was 0.5 , larger than noise that would be introduced by most instrumentation, but this value of additive noise is certainly possible for measurements made in the field. Figs. 8 and 9 show the difference between the unperturbed phases and the Monte Carlo simulations (top graphs) and the distribution of phases at 970 MHz (bottom graphs) when five target phases were used (Fig. 8) and when two target phases were used (Fig. 9).

Fig. 9. (a) Difference between measurement and 500 Monte Carlo simulations where Gaussian-distributed noise with a standard deviation of 0.5 was introduced into each frequency component before stitching. (b) Distribution of phase error at 970 MHz. Two target phases were used.

We again see approximately Gaussian-distributed phase errors, but in both cases the errors are sometimes spaced around an offset phase value. This offset in phase is regularly spaced and increases linearly away from the center 13-tone band of frequencies. The value of the offset is an integer multiple of approximately 7 at 970 MHz. The source of the regularly spaced clusters of phase solutions can be traced to the error function, given in (1), used in the phase alignment procedure. The stitching procedure solution finds the global minimum of the error function. However, the error function contains many local minima, one corresponding to each cycle of the carrier frequency. If the phase error is large enough, the algorithm may converge to an adjacent local minimum, resulting in the clustering of errors seen in Figs. 8 and 9. The number of local minima is related to the envelope period by (4) Here, GHz and MHz, and thus, there are 400 cycles of the carrier in each envelope period, and 400 local minima in the error function. Fig. 10 shows a plot of the local minima for the unperturbed 64-QAM-like multisine when two and five target phases are used. Two complete envelope cycles are shown in Fig. 10(a). The close-up view of the global minimum in Fig. 10(b) shows that the broad valley of local minima for the two-target case can lead to a bad choice of global minimum when noise is introduced into the stitched frequency com-

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V. CONCLUSION

Fig. 10. Plot of the minima of the error function for each RF cycle in the envelope period for the 33-tone 64-QAM-like multisine. (a) Two envelope cycles. (b) Close-up around the global minimum.

ponents. The steeper slope in the five-target case makes it more immune to additive noise. The clustering of phase errors shown in Figs. 8(a) and 9(a) corresponds to the selection of the wrong global minimum. To confirm this, we estimate the phase offset represented by each local minimum. Each local minimum represents one 360 phase change of the carrier frequency , but some other value of phase change for other frequencies . We can find this phase difference from (5) For a frequency of 970 MHz, (5) gives a phase offset of approximately 11 , close to the offset in the clusters seen in Figs. 8(b) and 9(b). The offset is not exact because the increase in offset is not linear within the center band of frequencies, as can be seen in Figs. 8(a) and 9(a). Results of this study indicate that when a high level of additive noise or random measurement error is expected in a measurement scenario, the user would be advised to use a larger number of overlapping tones for the stitching procedure. Note that overcoming this random component of measurement error is separate from the method’s ability to find systematic phase errors, such as the 20 phase error introduced by the vector signal generator in the examples of Fig. 4.

We described a method for extending the measurement bandwidth of vector receivers while maintaining the phase relationships between frequency components. The method presented here enables measurement of wideband signals using narrowband receivers, providing a higher dynamic range than many wideband receivers. The bandwidth extension involves phase alignment of adjacent frequency bands by using overlapping tones as target phases. We demonstrated the use of the method in finding the phase of distortion products at the output port of an amplifier relative to the input port phases over a bandwidth more than four times that of our LSNA. We also used the method to characterize the phase error in a multisine signal generated by a vector signal generator over a frequency band more than three times broader than that of a VSA. For the signals we studied, the peak-to-average-power ratio had little effect on errors in the stitching method. A study of the number of targets used in the phase alignment procedure showed that, while the error in the method remains relatively constant when two, three, or five overlapping tones are used as targets, the standard deviation of the measurements decreases with an increasing number of targets. Monte Carlo simulations were used to model the effects of additive noise on the stitched VSA measurements. These simulations helped to illustrate how errors propagate when both small and large values of additive-noise-based phase errors are encountered. We saw that the use of an error function that minimizes the mean-square error between known target phases and measured phases, while computationally efficient, can also lead to clustering in the calculation of phase error for a measured signal when the phase errors are large. This example demonstrated that when the additive noise is expected to be large, the user may wish to use a larger number of target phases. Our study of propagation of errors in stitching methods that use measured signals for phase alignment provides an understanding on the relative importance of various parameters. We illustrated how these parameters interact with each other in typical measurement scenarios. APPENDIX PHASE ALIGNMENT The measured relative phase between frequency components of a periodic signal is a function of the time during the signal’s envelope period when it was sampled. Time delays introduced into a measurement by cables, random instrument sampling times (including jitter), and other effects can make it difficult to compare the measured phases with the ones specified by the user unless alignment is carried out. This effect is illustrated in Fig. 11, where we see a three-component multisine signal that was specified to have a 0 relative-phase offset between its frequency components. As shown in Fig. 11 and discussed in more detail in [24], at the instant the signal is generated , the relative phase relationships between the frequency components ideally match those specified by the user. However, if the signal is sampled at a time later in the envelope period, the relative phase relationship between

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=

Fig. 11. Illustration of relative phase alignment. At time t t , the phase relationships between the three tones are all 0. The phase relationships are other  than 0 when the signal is sampled at a later time (from [24]).

tones can be significantly different from 0 . Even a slight time offset can give the appearance of increased phase distortion in a measurement. The phase alignment procedure we use [24] first develops and the time an analytic estimate of the difference between . If the signal generator and receiver were perfect, this anaexactly. However, systematic lytic expression would give errors in signal generators, analyzers, and random errors such as jitter and drift mean that the analytic estimate needs to be refined. This is done by minimizing an error function that expresses the mean-square error between the known target values and the corresponding measured frequency components. Rather than assuming the signal emitted from the signal generator is perfect, the minimization procedure accounts for the nonidealities of the signal generation and measurement processes as well. All sampled frequency components in the measurement bandwidth may be phase aligned to the reference time. This includes frequency components for which no target phase values exist such as distortion products, harmonics, and measurements at the second port of a nonlinear two-port device. ACKNOWLEDGMENT The authors acknowledge P. Hale, National Institute of Standards and Technology (NIST), Boulder, CO, for assistance with the oscilloscope measurements and calibrations. REFERENCES [1] “Agilent vector signal analysis basics,” Agilent Technol., Santa Clara, CA, Appl. Note 150-15, Jul. 2004. [2] T. Van den Broeck and J. Verspecht, “Calibrated vectorial nonlinear-network analyzers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1994, pp. 1069–1072. [3] Tektronix, “Fundamentals of real-time spectrum analysis,” Primer, 2004. [4] D. Schreurs, “Capabilities of vectorial large-signal measurements to validate RF large-signal device models,” in 58th ARFTG Conf. Dig., Nov. 2001, pp. 169–174. [5] D. E. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata, “Broad-band poly-harmonic distortion (PHD) behavioral models from fast automated simulations and large-signal vectorial network measurements,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3656–3664, Nov. 2005.

[6] M. Myslinski, D. Schreurs, B. Nauwelaers, K. A. Remley, and M. D. McKinley, “Large-signal behavioral model of a packaged RF amplifier based on QPSK-like multisine measurements,” in Eur. Gallium Arsenide and Other Semiconduct. Appl. Symp., Oct. 2005, pp. 185–188. [7] K. A. Remley, P. D. Hale, D. I. Bergman, and D. Keenan, “Comparison of multisine measurements from instrumentation capable of nonlinear system characterization,” in 66th ARFTG Conf. Dig., Dec. 2005, pp. 34–43. [8] P. D. Hale, C. M. Wang, D. F. Williams, K. A. Remley, and J. Wepman, “Compensation of random and systematic timing errors in sampling oscilloscopes,” IEEE Trans. Instrum. Meas., vol. 55, no. 6, pp. 2146–2154, Dec. 2006. (Time-base correction software download available online.) [Online]. Available: http://boulder.nist.gov/div815/HSM_Project/HSMP.htm [9] 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. [10] P. Draxler, I. Langmore, T. P. Hung, and P. M. Asbeck, “Time domain characterization of power amplifiers with memory effects,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 803–806. [11] J. Dunsmore and D. Goldberg, “Novel two-tone intermodulation phase measurement for evaluating amplifier memory effects,” in 33rd Eur. Microw. Conf. Dig., Oct. 2003, pp. 235–238. [12] J. C. Pedro, J. P. Martins, and P. M. Cabral, “New method for phase characterization of nonlinear distortion products,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 971–974. [13] K. A. Remley, D. Schreurs, D. F. Williams, and J. Wood, “Broadband identification of long-term memory effects,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, pp. 1739–1742. [14] J. Verspecht, “The return of the sampling frequency convertor,” in 62nd ARFTG Conf. Dig., Dec. 2003, pp. 155–164. [15] W. Van Moer and Y. Rolain, “An improved broadband conversion scheme for the large signal network analyzer,” IEEE Trans. Instrum. Meas., vol. 2, no. 58, pp. 483–487, Feb. 2009. [16] M. El Yaagoubi, G. Neveux, D. Barataud, T. Reveyrand, J.-M. Nebus, F. Verbeyst, F. Gizard, and J. Puech, “Time-domain calibrated measurements of wideband multisines using a large-signal network analyzer,” IEEE Trans. Microw. Theory Tech, vol. 56, no. 5, pp. 1180–1192, May 2008. [17] P. Blockley, D. Gunyan, and J. B. Scott, “Mixer-based, vector-corrected, vector signal/network analyzer offering 300 kHz-20 GHz bandwidth and traceable response,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 1497–1500. [18] D. Wisell, D. Rönnow, and P. Händel, “A technique to extend the bandwidth of an RF power amplifier test bed,” IEEE Trans. Instrum. Meas., vol. 56, no. 4, pp. 1488–1494, Aug. 2007. [19] M. El Yaagoubi, G. Neveux, D. Barataud, J. M. Nebus, and J. Verspecht, “Accurate phase measurements of broadband multitone signals using a specific configuration of a large-signal network analyzer,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2006, pp. 1448–1451. [20] K. A. Remley, “Multisine excitation for ACPR measurements,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 2141–2144. [21] N. B. Carvalho, K. A. Remley, D. Schreurs, and K. G. Gard, “Multisine signals for wireless system test and design,” IEEE Microw. Mag., vol. 9, no. 3, pp. 122–138, Jun. 2008. [22] J. C. Pedro and N. B. Carvalho, “On the use of multitone techniques for assessing RF components’ intermodulation distortion,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2393–2402, Dec. 1999. [23] R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach. New York: Wiley, 2001. [24] K. A. Remley, D. F. Williams, D. Schreurs, G. Loglio, and A. Cidronali, “Phase detrending for measured multisine signals,” in 61st ARFTG Conf. Dig., Jun. 2003, pp. 73–83. [25] P. S. Blockley, J. B. Scott, D. Gunyan, and A. E. Parker, “Noise considerations when determining phase of large-signal microwave measurements,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 8, pp. 3182–3190, Aug. 2006. [26] E. van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak factor minimization using time—Frequency domain swapping algorithm,” IEEE Trans. Instrum. Meas., vol. 37, no. 1, pp. 144–147, Jan. 1988. [27] M. D. McKinley, K. A. Remley, M. Myslinski, and J. S. Kenney, “Eliminating FFT artifacts in vector signal analyzer spectra,” Microw. J., vol. 49, no. 10, pp. 156–164, Oct. 2006. [28] J. C. Pedro and N. B. Carvalho, “Designing band-pass multisine excitations for microwave behavioral model identification,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, pp. 791–794.

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Kate A. Remley (S’92–M’99–SM’06) was born in Ann Arbor, MI. She received the Ph.D. degree in electrical and computer engineering from Oregon State University, Corvallis, in 1999. From 1983 to 1992, she was a Broadcast Engineer in Eugene, OR, serving as Chief Engineer of an AM/FM broadcast station from 1989 to 1991. In 1999, she joined the Electromagnetics Division, National Institute of Standards and Technology (NIST), Boulder, CO, as an Electronics Engineer. Her research activities include metrology for wireless systems, characterizing the link between nonlinear circuits and system performance, and developing methods for improved radio communications for the public-safety community. Dr. Remley is currently editor-in-chief of IEEE Microwave Magazine and chair of the MTT-11 Technical Committee on Microwave Measurements. She was the recipient of the Department of Commerce Bronze and Silver Medals and an Automatic RF Techniques Group (ARFTG) Best Paper Award.

Dominique Schreurs (S’90–M’97–SM’02) received the MSc. and Ph.D. degrees in electronic engineering from the Katholieke Universiteit Leuven (K.U.Leuven), Leuven, Belgium. She is currently an Associate Professor with K.U.Leuven. She was a Visiting Scientist with Agilent Technologies, ETH Zürich, and the National Institute of Standards and Technology (NIST). Her main research interests concern the (non-)linear characterization and modeling of active microwave and millimeter-wave devices and circuits, and (non-)linear hybrid and integrated circuit design. Dr. Schreurs serves on the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Administrative Committee (AdCom). She is vice-chair of the MTT-S TCC. She also serves as education chair on the Executive Committee of the Automatic RF Techniques Group (ARFTG). She was general chair of the 2007 Spring ARFTG Conference and co-chair of the 2008 European Microwave Conference.

Dylan F. Williams (M’80–SM’90–F’02) received the Ph.D. degree in electrical engineering from the University of California at Berkeley, in 1986. He joined the Electromagnetic Fields Division, National Institute of Standards and Technology (NIST). Boulder, CO, in 1989. He develops metrology for the characterization of monolithic microwave integrated circuits and electronic interconnects. He has authored or coauthored over 80 technical papers. Dr. Williams is the editor-in-chief of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He was the recipient of the Department of Commerce Bronze and Silver Medals, the Electrical Engineering Laboratory’s Outstanding Paper Award, two Automatic RF Techniques Group (ARFTG) Best Paper Awards, the ARFTG Automated Measurements Technology Award, and the IEEE Morris E. Leeds Award.

Maciej Myslinski was born in Warsaw, Poland, in 1978. He received the Master degree in electronics engineering from the Warsaw University of Technology, Warsaw, Poland, in 2003, and the Ph.D. degree from the Katholieke Univeristeit Leuven (K.U.Leuven), Leuven, Belgium, in 2008. Since December 2008, he has been a Post-Doctoral Fellow with the ESAT-TELEMIC Research Group, K.U.Leuven. His research interests include practical large-signal measurement-based modeling of high-frequency nonlinear components. Dr. Myslinski was the recipient of the 2005 Automatic RF Techniques Group (ARFTG) Student Fellowship.

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Phase-Noise Measurement of Microwave Oscillators Using Phase-Shifterless Delay-Line Discriminator Hamed Gheidi, Student Member, IEEE, and Ali Banai, Member, IEEE

Abstract—In this paper, a modified method based on the frequency discriminator technique for measuring phase noise of microwave oscillators is presented. In the proposed method, the phase shifter is omitted. In contrast, a 90 hybrid with one more channel containing a phase detector, and a low-noise amplifier is added to the measurement setup. It can be said that an in-phase/quadrature phase-noise detection has been developed. With the proposed method, tuning of the variable phase shifter is not needed anymore. Therefore, the measurement is done automatically, and as a result, the measurement time is decreased. Another considerable advantage of this method is that the method is theoretically self-calibrated. For verifying the accuracy of the method, a measurement setup based on the proposed method was established. Two relatively low phase-noise phase-locked oscillators at frequencies of 2.8 and 4.9 GHz were designed. Their phase noise was measured by the proposed method, the conventional delay-line method, and the two-oscillator technique. Comparison of the measured data of the three methods shows the validity of the proposed method. Index Terms—Delay line, FM discriminator, microwave oscillators, phase-noise measurement.

I. INTRODUCTION SCILLATORS are one of the most important parts of any electronic and communication system. They carry out different roles such as reference clock sources, local oscillators (LOs) (for up and down conversion in transceivers), and signal generators in test and measurement systems. Oscillators can appear in different types such as crystal, ceramic resonator, dielectric resonator, voltage controlled, YIG oscillators, etc. Output of an ideal oscillator is modeled mathematically as a sinusoidal signal with constant amplitude and frequency, but in real world, due to the presence of different types of electronic noises, both amplitude and phase of the oscillator are perturbed. Thus, a simple model for a noisy signal is

O

(1) where and are the nominal amplitude and angular freand are the instantaneous quency, respectively, and amplitude and phase fluctuations of the signal. Generally, oscillators have an inherent mechanism for amplitude noise reduction. Thus, the amount of amplitude noise is often sufficiently less than phase noise and the phase noise is dominant. Manuscript received December 03, 2009. First published January 22, 2010; current version published February 12, 2010. The authors are with the School of Electrical Engineering, Sharif University of Technology, 11155-4363 Tehran, Iran (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038452

Phase noise can dramatically influence the performance of communication and radar systems [1]. In digital communication systems, especially those utilizing phase modulation, phase noise of LOs can corrupt the IF signal, and consequently, increase the bit error rate. In Doppler radar, the phase noise of RF signal has a great effect on velocity recognition of low-speed targets [2]. In test and measurement instruments, the measurement quality and accuracy are affected by the phase noise of sources. There have been many studies on the analysis of the phase noise in oscillators, and different models such as linear timeinvariant [3], linear time-variant [4], and the nonlinear model [5] have been introduced and discussed in the literature, but none of these models can exactly predict the oscillator phase noise; therefore, accurate measurement of the oscillator phase noise is of great importance. In Section II, a brief review of the conventional phase-noise measurement techniques and their corresponding characteristics is given. The basis of phase-shifterless method was first presented in [6]. In Section III, a modified and more complete analysis of the procedure of the phase-shifterless method for phase-noise measurement is performed. Further, the advantages of the proposed method will be addressed. In Section IV, error sources of measurement setup, which was not presented in previous work, will be introduced. In Section VI, the experimental setup for evaluation and verification of the proposed method is explained. The procedure of phase-noise floor determination of the proposed method is presented in this section. Finally measurement results of two different phase-locked oscillators (PLOs) using the proposed technique is given and compared with the results of a standard phase-noise meter test set from Agilent Technologies Inc., Santa Clara, CA. II. REVIEW OVER THE CONVENTIONAL TECHNIQUES We can categorize different techniques of phase-noise measurement into three basic techniques, which are: 1) direct-spectrum reading; 2) two-oscillator method; and 3) single-oscillator method. Direct-spectrum reading is the easiest method for phase-noise measurement, which can be performed using a spectrum analyzer. In this method, the effect of resolution bandwidth, equivalent noise bandwidth, and logarithmic detection of the spectrum analyzer on the measurement should be considered. In modern spectrum analyzers, these effects and necessary corrections are performed automatically. Direct-spectrum reading has some drawbacks. Spectrum analyzers can only measure phase noise of locked or very stable oscillators. Phase noise of freerunning oscillators cannot be measured due to spectrum variation resulting from frequency instability. The phase noise of the internal LO of the spectrum analyzers also limits the phase-

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noise floor of the measurement. In addition, since a spectrum analyzer cannot distinguish the amplitude noise from the phase noise, errors may be caused if the amplitude noise is considerable compared to the phase noise. In the two-oscillator technique [7], a second oscillator, called the reference oscillator, is used for mixing with the oscillator under test. A double-balanced mixer is used as the phase detector. The reference oscillator should be a very low phase-noise oscillator, which locks to the oscillator under test. The two-oscillator technique is sometimes referred to as the phase detector method or the phase-locked loop (PLL) method. In the lock situation, the signals at the inputs of the phase detector are phase quadratic. The voltage detected at the phase detector output is proportional to the phase noise of the oscillator under test. After amplification, the output of the phase detector is applied to a spectrum analyzer or a digital fast Fourier transform (FFT) analyzer. By performing necessary calibration, we can reach the phase noise of the oscillator. This method provides the best sensitivity among all methods at the expense of more hardware and more complexity. For free-running oscillators with low stability, using this method especially for close to carrier offsets (with regard to the effect of PLL bandwidth on measurable offset frequencies) needs more consideration, and sometimes phase-noise measurement is impossible. Single-oscillator phase-noise measurement is based on the measurement of frequency fluctuations using frequency discrimination techniques. Therefore, the single-oscillator technique is sometimes referred to as frequency discriminator technique [7], [8]. In this method, there is no need to use another pure reference oscillator. The signal of the oscillator under test splits into two channels. One channel is called the reference channel and includes a variable phase shifter. The signal of the reference channel is applied to the LO port of a double-balanced mixer, which acts as a phase detector. The other channel, including a discriminator, which is usually a delay line or a high- resonator, is connected to the RF port of the double-balance mixer. The phase shifter is used for making phase quadrature at the phase detector inputs. In this situation, the phase detector output is a fluctuating voltage analogous to frequency fluctuations of the oscillator under test. A low-pass filter, a low-noise amplifier (LNA), and finally a spectrum or FFT analyzer are needed to measure the phase noise. In this method, the FM noise of the oscillator is detected. The PM noise can be calculated using the relationship between the FM noise and PM noise and the necessary calibration. Implementation of the single-oscillator technique is much easier and less expensive compared to the two-oscillator technique. In addition, this technique can be easily used for measuring phase noise of any kind of oscillators including free-running, unstable, and locked oscillators. This is the main advantage of the single-oscillator technique over the two-oscillator technique, but the phase-noise floor in this technique is higher than in the two-oscillator technique, especially in close to carrier offsets because of FM noise detection instead of PM noise detection. Using the cross-correlation technique between two similar channels, one can improve the phase-noise floor of the measurement setup up to 20 dB [7]–[9]. This technique can be used either with the two-oscillator technique or FM discriminator technique.

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Fig. 1. Conventional frequency discriminator technique for phase-noise measurement [6].

The methods outlined above are the main techniques for measuring the phase noise of oscillators. There are some other subordinate techniques that refer to those certain methods. Zhang et al. [10] proposed a two-oscillator technique based on injection locking for synchronizing the oscillators, whose process is simpler than the PLL. Nick et al. [11] presented a method again based on the two-oscillator technique, by using inter-injection locking of two similar oscillators. Rubiola et al. [12], [13] used a photonic delay line and cross-correlation technique in the single-oscillator category, which is suitable for electronic and photonic oscillators in a wide range of frequency. In this method, the amount of delay can be increased without a considerable increase in the loss of the delay line. III. MEASUREMENT SETUP AND PROCEDURE The block diagram of a conventional frequency discriminator method is shown in Fig. 1. The delay line can be replaced by a high- resonator (or cavity). Since a more wideband phase-noise measurement system can be obtained with the delay-line discriminator, we developed our theory and equations for the system with a delay line. In the conventional method, the phase shifter is used to provide phase quadrature at the phase detector inputs. This is generally done by manual tuning of a variable phase shifter. When the dc voltage of the phase detector output is set to zero by tuning of the phase shifter, the phase quadrature has been achieved. The major advantage of the phase-shifterless technique over the conventional one is elimination of the phase shifter. In the proposed method, a 90 hybrid, another channel containing a phase detector, and an LNA are added (Fig. 2). A dualchannel synchronized sampling system is needed to sample the detected signals and perform the necessary processing. In other words, it can be said that, an in-phase/quadrature (I/Q) phasenoise detection is developed. In the following, we introduce how to obtain the phase noise of the oscillator under test. For the phase-noise analysis, it is usual to assume the phase noise as two narrowband FM sidebands at a certain offset around

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(7) where and represent the sensitivity and phase shift of the phase detector at carrier frequency . The sensitivity of a double-balanced mixer as a phase detector is a function of its and the frequency of operation. Thus, two input levels in this setup, its output voltage is related to level of the oscillator under test, loss of the power dividers, loss of the delay line, loss of the 90 hybrid, and loss of the interconnecting cables. Using triangular relations, we get (8) (9) Fig. 2. Proposed phase-noise measurement setup [6].

is substituted by and by in which for the sake of simplicity. By expanding (8) and (9), we obtain the carrier. Thus, neglecting AM noise, we can consider the source under test to be a modulated FM sinusoid (10)

(2) We can write the equations representing the signals at each node in Fig. 2. For the indicated signal with condition , . the ratio of the sideband FM level to carrier level is At nodes 5 and 6, the voltages become

(11) Using small argument approximation for simplify (10) and (11) to

, we can

(3)

(12)

where and represent the loss of the delay line and timedelay value. For nodes 7 and 8,

(13)

(4) (5) and represent the hybrid’s loss and phase shift where relative to the main branch at carrier frequency . The path lengths between power divider #2 and the mixers and also the path lengths between the hybrid outputs and the mixers should be equal. This is a critical point because we need the mixers to be fed from power divider #2 in phase and from the hybrid with quadratic phase. The mixers and all the components following them to the dual-channel FFT analyzer should have the same characteristics. Therefore, at the outputs of the mixers, we obtain

It is considered from (12) and (13) that there are two terms at each phase detector output. One term represents the dc component and the other represents the ac or the interested FM component. As can be seen, the ac component depends on the constant is set to phase . In the conventional delay-line technique, by using a phase shifter. In the proposed method, the phase shifter does not exist. Therefore, for getting rid of , the dc components of the phase detectors’ outputs are measured by dc volt meters. If the dc value of (12) and (13) are called A and can be calculated by solving and B, then parameters triangular equations according to (14) and (15) as follows: (14) (15) where the function

(6)

is defined as

GHEIDI AND BANAI: PHASE-NOISE MEASUREMENT OF MICROWAVE OSCILLATORS USING PHASE-SHIFTERLESS DELAY-LINE DISCRIMINATOR

We added the second term in (14) in order to correctly deterwith regard to dc value signs. mine the triangular region of It is obvious that if one of the channels has zero dc voltage, the will be equal to the dc voltage of the other channel. value of Since the level of phase detector output (ac component) for the interested signal is very low, it is necessary to be amplified. After eliminating dc components and low-noise amplification, the detected signals will be applied to a two-channel synchronized sampling system. If we perform a calculation as follows according to (16) on the sampled data, the constant phase will be eliminated:

IV. ERROR SOURCES IN THE MEASUREMENT SETUP Up to this point, we have assumed that everything in the proposed system is ideal and the components of the two channels are exactly the same, but in an actual setup, the behavior of similar components may be a little different. Such factors can result in error on the measurement result. In what follows, we study the effect of these imperfections on the phase-noise measurement results. A. Mismatch of the Phase Detectors In this section, we assume that the sensitivity factors of the two phase detectors are different as (19) (20)

(16) where represents the LNA voltage gain. With regard to (16), it is concluded that the calculated voltage becomes zero at fre. This effect is comquency offsets equal to multiples of pletely similar to the behavior of the conventional delay-line technique. If the measurement for the offsets that satisfy the is desirable, then the function can be condition approximated by 1 without any considerable error. For example if the delay is 125 ns, a maximum phase-noise measurement error of 0.22 dB is incurred up to 1-MHz offset. The calculated voltage can thus be simplified to (17) It is necessary to apply a conversion factor to the calculated as follows: voltage to reach the sideband voltage of (18) It can be seen from (18) that for the measurement at an offset , one needs to know , , and . Fortunately, and of are constant parameters and do not change with changes in the carrier frequency and the level of the oscillator under test. Thus, it is sufficient to measure the LNA gain and the delay of delay line once, and use the measured values for all other measurements. Therefore, the only parameter that is needed for the . In each measurement, may have a difmeasurement is ferent value based on the level and the frequency of the oscilis calculated according to (15) from dc components lator. of two channels. Thus, there is no need to perform a separate calibration procedure. In the conventional delay-line technique, the dc value of the phase detector output is set to 0. Therefore, phase detector sensitivity should be measured in each measurement or the whole setup should be calibrated by applying a narrowband FM signal at its input. Thus, another important advantage of the phaseshifterless method over the conventional delay-line technique is that it is a self-calibrated method. In other words, the calibration procedure is inherently a part of the measurement process. We have discussed this advantage, in the self-calibration property part of Section V in more detail.

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Therefore, at the output of phase detectors with regard to (12) and (13), we obtain (21) (22) Using (16), we obtain

(23) Since the dc components of the channels have changed due and to the mismatch of the phase detectors, the parameters , which are calculated according to (14) and (15) and are used in the conversion factor, also change. Thus, a new value for the conversion factor is calculated using (15). Using triangular re, which is used in the conversion lations, the real value for , is obtained factor and is called (24) By applying the conversion factor of (18) with substitution , the sideband level will be calculated according to of (25) as follows: (25) Thus, the relative error is calculated

in measuring the noise sideband

real value ideal value ideal value (26) The measurement error (in decibels) versus the relative difference of phase detector sensitivities is depicted for different in Fig. 3. It can be investigated that the curves for values of from 0 to 360 lie between the curves all possible values of and . of Assuming a 10% mismatch between the sensitivities of phase detectors, the maximum error of 1 dB can be created.

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Fig. 3. Phase-noise measurement error caused by value of .



K

difference for different

B. Difference of Phase Detectors’ Phase Shifts In (6) and (7), we have assumed the phase shift of the two phase are equal, but they may have some discrepancies. detectors Thus, this phenomenon degrades the phase quadratic feeding of the phase detectors, and consequently results in error on the measurement results. For the analysis of this effect, we assume there is a phase difference between the phase shifts of the two phase detectors. Thus, at the outputs of the phase detectors, after approximations and simplifications on (12) and (13), we get

Fig. 4. Phase-noise measurement error caused by different phase shifts of the two phase detectors.

#2 or difference between the lengths of the cables results in unequal levels of the signals at the inputs of the phase detectors, and consequently, different sensitivity factors. These effects can be considered as the effect of phase detector mismatch. Any phase imbalance at the inputs of the phase detectors, which can be originated from phase imbalances of the 90 hybrid or Power Divider #2, also prevents the complete phase quadrature feeding of the phase detectors and ultimately causes error on the measurement results according to (32). C. DC Offsets of the Mixers

(27) (28) Using (16), we obtain (29) For calculating the sideband level, we need to apply the conversion factor of (18) to the calculated voltage. Again the dc values of channels have changed due to the different phase shifts. Thus, we apply instead of in the conversion factor. Using triangular relations, is obtained (30) By applying the conversion factor of (18) with band level will be calculated

Double-balanced mixers usually are low offset mixers. However, practical mixers due to some imperfections such as mismatch of diodes or transformer asymmetry generate dc offset at the IF port. DC offset of a mixer depends on the LO drive level and LO to IF isolation [15]. Thus, at the outputs of the phase detectors, the signals can be represented as (33) (34) in which and are the dc offsets of two channels. The dc values of the channels have changed due to dc offsets. Therefore, the calibration factor also changes. The equations for calculation of parameters and become (35) (36)

, the side(31)

By solving the equations for

and

, we get (37)

The relative error caused by this phase difference is (32) The graph of the relative error versus the different between the phase shifts of the two phase detectors for some values of is depicted in Fig. 4. It can be seen in this figure that a phase difference of approximately 10 can cause a maximum error of about 1.4 dB. Any amplitude imbalance prior to the phase detectors such as imbalances of the outputs of the 90 hybrid or Power Divider

(38)

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Using (16), we obtain

(39) Now it is necessary to apply the conversion factor to the calculated voltage

Fig. 5. Phase-noise measurement error caused by the dc offsets of the mixers.

(40) Therefore, at the output of the LNAs, we have Thus, the relative error happened due to the dc offsets of the phase detectors is (41)

For simplicity, we define After simplifying (41), we obtain

and

(45) (46) Again using (16), we obtain

. (47) (42)

For calculating the relative error, it is necessary to know the and dc offsets of the phase detectors and the parameters at the frequency and power of the oscillator under test. Considering to be a constant, the relative error is a function of two independent variables. To plot the error versus dc offset, we . As we will perform a test at the need to know the value of frequency of 2.8 GHz, we study the effect of dc offsets of the mixers as an example at that frequency. At this frequency, the sensitivity of the M85C mixer from M/A-COM, San Jose, CA, which is used in the setup of Fig. 2, for the input signal with , the rel13-dBm power is about 0.23 V/rad. By knowing ative error can now be calculated from (42). The graph of the error (in decibels) versus the dc offset of the mixers for some is depicted in Fig. 5. In this figure, equal dc offsets values of is assumed. We calculated the error numerically for all possible values of and dc offsets between 30 and 30 mV. The maximum error in phase-noise measurement is 1.77 dB. D. Gain Difference of LNAs For the analysis of the gain difference of the two LNAs, we suppose two different gains for the LNAs as follows: (43) (44)

Since the dc values of the channels have not changed due and are calculated to this gain difference, parameters correctly for the conversion factor. By applying the conversion factor of (18), the sideband level can be found through (48) The relative error caused by the relative difference of the LNAs’ gains becomes (49) The measurement error versus the gain difference of LNAs is depicted for some values of , as shown in Fig. 6. Considering (49), the relative error depends on the value of , but its maximum value occurs when . Thus, the maximum relative error is (50) It means that any difference in the gain of LNAs directly translates to the error in the worst case at the measurement result. This dictates that wedesign the LNAs as similar to each other as possible. Up to now, we have studied the effect of discrepancies in the two channels separately, but in practical situations, all sources of error may exist simultaneously. If the calculation of the error with considering all sources of error is of interest, the aroused complications would not give us intuitive insight to the effect

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Fig. 6. Phase-noise measurement error caused by gain difference of LNAs.

of each source of error. Besides, the factors that cause error are usually independent so we can use statistical rules to calculate the total error. On the other hand, we are not willing to measure all differences in the setup and then apply the measurement process because this task is very time consuming and superfluous. Fortunately, none of the calculated errors is related to frequency offset. Thus, for each measurement case, a constant error may be occurred over the offset range due to the sources of error explained earlier. We will show in Section V that, by performing calibration, we can compensate the effect of the error sources. V. EXPERIMENTAL VERIFICATION A. System Description To evaluate the validity and accuracy of the proposed method, we designed and implemented two setups according to the conventional and phase-shifterless block diagrams shown in Figs. 1 and 2, respectively. The components and devices were selected in a such way that operate properly in the frequency range of 2–18 GHz. To have a better sensitivity, it is necessary for the delay line to have the minimum possible loss. We used 100-ft low-loss (EZ250-WP) coaxial cable from the EZform Company, Hamden, CT. This length of cable provides a time delay of about 125 ns. The power dividers (42100) used in the setup are from Anaren Inc., East Syracuse, NY, and have sufficient amplitude and phase balance. A broadband (2–18 GHz) 90 hybrid was designed and fabricated using offset parallel-coupled and tapered striplines. Measurement of hybrid scattering parameters showed that the amplitude imbalance was less than 1.2 dB and the phase imbalance was less than 5 over the full frequency range. Two (M85C) double-balanced mixers from M/A-COM were used as phase detectors. A low-pass filter with 1-MHz cutoff frequency was used in each channel for both cancelling the additional mixing products and limiting the bandwidth to prevent the aliasing problem. The dc components of the two phase detectors are selected with two relays, and sampled by an analog to digital converter (AD1674). To amplify low-level detected signals, we used ultra-low noise op-amps (AD797) from Analog Devices, Norwood, MA, in two stages with a total gain of 61 dB. A dual channel 14-bit analog to digital converter (AD9248)

Fig. 7. Photograph of the constructed setup for evaluating the proposed method.

evaluation board from Analog Devices was used for sampling and recording the data. The clock rate of the sampling system was set to 4.096 MHz. A photograph of the implemented setup is shown in Fig. 7. B. System Calibration To consider all the factors that affect the measurement results such as the delay time, phase detectors’ sensitivity, LNAs’ gain, amplitude and phase response of power dividers and hybrid, and any component that exists in the measurement setup from the RF section to input of ADCs, it is necessary to perform a calibration on the setup. A straightforward calibration procedure, which is usually used in phase-noise measurement systems, applies a narrowband FM signal with a specific sideband level relative to the carrier to the measurement setup. This signal, which is usually generated by a signal generator, should have the same power and frequency of the oscillator under test. A similar sideband level after data gathering and processing according to (16) and performing (18) should be measured at the offset of the modulating signal in the measurement setup. Thus, it may be necessary to add a constant (in decibels) to the processed data. This constant is called the calibration factor. Since and the response of the filter and LNA are flat over the desired range of frequency offsets, it is sufficient to calibrate the system only at one offset frequency. In other words, the calibration factor is constant over the frequency offset range. Thus, the steps of phase-noise measurement in the phaseshifterless method can be summarized as follows. Step 1) Measuring parameters and only once for all the measurements and saving their values in the measurement software. Step 2) Connecting the oscillator to the input port, measuring the dc voltages of the two channels, and calculating and . Step 3) Using (16) on the sampled data of two channels to calculate the sideband noise voltage.

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Step 4) Applying the conversion factor found through (18) to the noise voltage calculated in Step 3). Step 5) Using the FFT algorithm on the noise voltage calculated in Step 4) to obtain power spectral density of phase noise. Step 6) Calibrating the system according to the procedure discussed in Section V-B and applying the calibration factor. C. Phase-Noise Floor Measurement It is important to determine the range for which the measurement is valid and acceptable. The sensitivity in a phase-noise measurement system means the minimum phase-noise level that can be measured by the system. In the proposed method, the noise of the active devices including LNAs and mixers prior to the digital section limits the sensitivity of the measurement system. The phase-shifterless method is a kind of frequency discriminator method in which the frequency noise is detected. The power spectral density of phase noise is calculated from the power spectral density of frequency noise from (51) The presence of in the denominator of the conversion factor in (18) represents the frequency to the phase conversion effect. Thus, the phase-shifterless method, like the conventional slope from the point of sensitivity one, suffers from a view. The procedure of determining the noise floor of the system is as follows. First, we calibrate the system according to the instruction stated before and obtain the calibration factor. After the calibration, we substitute the delay line by an attenuator with the same attenuation at that frequency. In this case, the system is no longer a frequency discriminator since the amount of delay is near zero. Thus, the voltages detected in the outputs of the phase detectors represent the inherent noise of phase detectors in the same measurement condition. It means the phase detectors are excited at the same frequency and level of the main measurement. By performing (16) and then the conversion factor on the sampled data, we obtain the noise floor of the system. D. Evaluating the Measurement Results For preparing an oscillator, we designed a PLO at a frequency of 2.8 GHz. We used a synthesizer IC (PE3336) from Peregrine Inc., San Diego, CA, a voltage-controlled oscillator (VCO) (ROS-3000V) from Mini-Circuits Inc., Brooklyn, NY, and a 20-MHz reference TCXO with 0.9-ppm stability (CFPT-125TS) from C-Mac Micro Technology, Amersham, U.K., to achieve a relatively low phase-noise PLO operating at 2.8 GHz. We measured phase noise of the PLO by three methods, which are: 1) the phase-shifterless method [according to the above-mentionted Steps 1)–6)], the conventional delay-line technique, and the phase detector method (using E5052A instrument from Agilent Technologies Inc. [16]) and then compared the results. For each measurement with the phase-shifterless method and the conventional delay-line method, we performed

Fig. 8. Results of phase-noise measurement of a 2.8-GHz PLO with three different methods and the measured phase-noise floor.

an average of over 100 measurements in order to reduce spectrum fluctuations. After averaging, we performed a smoothing function over the averaged data to obtain a smoother curve. The results of these measurements are plotted in Fig. 8. As shown in Fig. 8, there is a good correspondence between the three measurement results. For close-to-carrier offsets, some differences are observed. It is expected that all frequency discriminator methods suffer from measuring near-carrier offfactor in the denominator of sets due to the presence of an the conversion factor. The intersection between the phase-noise floor and the phase-shifterless curves is about 500 Hz. Therefore, for the offsets less than 500 Hz, the measurement is limited to the setup noise floor. Another comparison for verifying the accuracy of the proposed setup was arranged at 4.9 GHz. We used a synthesizer integrated circuit (IC) (ADF4106) from Analog Devices, a lownoise VCO (CRO2527A) from ZCOMM Inc., San Diego, CA, and the same reference TCXO with 0.9-ppm stability. The design of the PLL was based on the lowest phase noise achievable at the output of the synthesizer and the frequency of the PLL was 2.45 GHz. By using a frequency doubler (HMC188) from Hittite Inc., Colorado Springs, CO, we then generated the 4.9-GHz carrier frequency. We also used a low- and high-pass filter at the output to eliminate extra harmonics. The measurement procedure and setup was similar to the first test. We measured the phase-noise floor of the setup at the same frequency and amplitude of the synthesizer according to technique explained in Section V-C. The result is shown in Fig. 9. Again there is a very good correspondence between the results of the three different measurement methods. It can be seen that for the offsets less than approximately 400 Hz, the phaseshifterless curve is separated from that of E5052A. As can be seen from the noise floor curve in Fig. 9, for the offset frequency of 400 Hz and lower, the measurement is limited to the inherent phase-noise floor of the setup. If we are willing to compare the phase-shifterless method with the conventional delay-line method from the accuracy point of view, we can say that there is no serious difference between them. It seems that the conventional delay-line technique

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Fig. 9. Results of phase-noise measurement of 4.9-GHz PLO with three different methods and the measured phase-noise floor.

Fig. 10. Calibration factor measured by a 13-dBm swept narrowband FM signal in phase-shifterless setup.

is a bit more accurate, especially in near-carrier offsets. We can explain the reason with regard to received signal strength to the phase detectors. In conventional method, the signals received to the phase detector have a higher level. This translates to higher phase detector sensitivity and ultimately higher accuracy. On the other hand, if we do not perform the calibration procedure to the phase-shifterless method due to the self-calibration property, it may add some errors to the measurement result because a few imperfections unavoidably exist in the setup. E. Self-Calibration Property In the conventional delay-line technique, the dc component of the phase detector output is set to zero and no information can be extracted from the dc value. In this technique, should be separately measured at the same condition of the oscillator under test (with regard to the frequency and level of the oscillator and setup behavior) or the whole setup should be calibrated effect should be considered using an FM signal and then the in the calibration factor. The former method for measuring for each oscillator is tedious and time consuming. In a practical situation, the latter method is usually used in order to both eliminate the need for a separate measurement of and consider all factors that affect the measurement results. efIn this case (in which the calibration factor includes the fect), the calibration factor changes due to varying the signal is calculevel, but in the proposed method, the parameter lated each time during the measurement process and used in calculating the conversion factor using (18). Thus, we expect that in the phase-shifterless technique, the calibration factor (which effect) does not considerably changes does not include the with changes in frequency and the level of the oscillator under test. To prove this claim, we arranged a test for measuring the calibration factor. We used an N5181A MXG signal generator from Agilent Technologies Inc. to provide a frequency-modulated signal with variable power and carrier frequency. The frequency of the modulating signal was 50 kHz. We set the output level to 13 dBm and swept the frequency of the signal generator over the range of 2–6 GHz with 50-MHz steps, applied it to the

Fig. 11. Calibration factor measured by sweeping the power of narrowband FM signal at 2.8- and 4.9-GHz frequencies.

measurement setup, and then measured the calibration factor. The result is shown in Fig. 10. It is seen in Fig. 10 that the average value over the frequency range is nearly zero and the maximum deviation from zero is about 2 dB. This difference, as explained in Section IV, is related to the imperfect behavior of the elements, and discrepancies of the two channels exist in the system. We arranged another test to investigate the effect of the signal level on the calibration factor. In this test, the frequency was fixed and the power was swept. It is obvious that by decreasing the signal power, the phase detector sensitivity is decreased due to lower receiving power to its ports. Thus, the phase-noise floor of the measurement system is increased. We have run the above-mentioned test at two different frequencies of the oscillators. We swept the power from 16 to 2 dBm in 1-dB decreasing steps. The results are depicted on Fig. 11. It is seen that at the frequency of 2.8 GHz, by reducing power to 5 dBm, the calibration factor does not change much, but below 5 dBm, the total calibration factor starts to change considerably. For the frequency of 4.9 GHz, the variations of the

GHEIDI AND BANAI: PHASE-NOISE MEASUREMENT OF MICROWAVE OSCILLATORS USING PHASE-SHIFTERLESS DELAY-LINE DISCRIMINATOR

calibration factor below 5 dBm is much smaller than for the frequency of 2.8 GHz in the same range. However, with regard to signal strength at the phase detector output, we conclude that, for the signal power below nearly 7 dBm, the phase-noise floor of the system increases by a large factor. For higher power levels of oscillator, the calibration factor is approximately constant. These two tests confirm the self-calibration property of the phase-shifterless method. This means that if we prepare a setup with proper elements and the discrepancies of the two channels are low enough, the calibration factor will approach zero. In other words, if only the first five steps of the measurement procedure is done without the calibration step, the error caused due to the above nonidealities is dispensable. VI. CONCLUSION In this paper, we have introduced a new technique for phase-noise measurement of microwave oscillators. The proposed method has the same quality as the conventional frequency discriminator method from the sensitivity point of view, but it has the advantage of automatic phase-noise measurement due to eliminating the need for manual tuning of the phase shifter. By increasing the delay value of the delay line, the sensitivity of the measurement in lower offset frequencies improves. With regard to the measurement process explained, if the LNAs’ gain and the delay quantity are measured once, the phase detector sensitivity, and as a result, the conversion factor, can be calculated during the measurement process from the dc components of two channels. The sensitivity of the proposed setup to different nonidealities in the setup has been analyzed. It has also been shown that the introduced method is a self-calibrated method and the calibration procedure is done only for compensating for the lack of complete similarity in two channels, while in the conventional delay-line technique, the calibration process should be done for each measurement. Overall, the phase-shifterless method has lower sensitivity in comparison with the PLL method; however, the complexity and implementation cost of this method is lower. This method can also be easily used for measuring phase noise of free-running oscillators. The possibility of using this method for a wide range of frequency is the other advantage of the phase-shifterless technique.

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[3] D. B. Leeson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE, vol. 54, no. 2, pp. 329–330, Feb. 1966. [4] A. Hajimiri and T. Lee, “A general theory of phase noise in electrical oscillators,” IEEE J. Solid-State Circuits, vol. 33, no. 2, pp. 179–194, Feb. 1998. [5] A. Demir and A. M. 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. [6] H. Gheidi and A. Banai, “A new phase shifter-less delay line method for phase noise measurement of microwave oscillators,” in Proc. 38th Eur. Microw. Conf., Amsterdam, The Netherlands, Oct. 2008, pp. 325–328. [7] A. L. Lance, W. D. Seal, and F. Labaar, Phase Noise and AM Noise Measurements in the Frequency Domain. New York: Academic, 1984, vol. 11, Infrared Millim. Waves, pp. 239–289. [8] D. Owen, “Good practice guide to phase noise measurement,” Nat. Phys. Lab., Middlesex, U.K., Tech. Note, May 2004. [Online]. Available: http://www.npl.co.uk [9] W. F. Walls, “Cross-correlation phase noise measurements,” in Proc. IEEE Freq. Control Symp., 1992, pp. 257–261. [10] X. Zhang, B. J. Rizzi, and J. Kramer, “A new measurement approach for phase noise at close-in offset frequencies of free-running oscillators,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 2711–2717, Dec. 1996. [11] M. Nick, A. Banai, and F. Farzaneh, “Phase-noise measurement using two inter-injection-locked microwave oscillators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 7, pp. 2993–3000, Jul. 2006. [12] E. Rubiola, E. Salik, S. Huang, N. Yu, and L. Maleki, “Photonic-delay line for phase-noise measurement of microwave oscillators,” J. Opt. Soc. Amer., vol. 22, no. 5, pp. 987–997, May 2005. [13] E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay line cross correlation method for phase noise measurement,” in Proc. IEEE Freq. Contr. Symp., 2004, pp. 303–306. [14] “Understanding and Measuring Phase Noise in the Frequency Domain, AN-207,” Hewlett-Packard, Palo Alto, CA, 1967., Part #59528708. [15] S. R. Kurtz, “Mixers as phase detectors,” Watkins-Johnson Company, Palo Alto, CA, Tech. Note, 1978, vol. 5, no. 1. [16] “E 5052A signal source analyzer datasheet,” Agilent Technol. Inc., Santa Clara, CA, 2007. [Online]. Available: http://www.agilent.com

Hamed Gheidi (S’08) was born in Tehran, Iran, in 1979. He received the B.S. and M.S. degrees in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2001, and 2004, respectively, and is currently working toward the Ph.D. degree at the Sharif University of Technology. His doctoral dissertation concerns phase-noise measurement systems for microwave oscillators. His research interests include linear and nonlinear microwave circuits, especially RF synthesizers. He is experienced in the design of RF and microwave systems and circuits such as transceivers, filters, LNAs, power amplifiers, and frequency synthesizers.

ACKNOWLEDGMENT The authors wish to thank the Iran Telecommunication Research Center (ITRC), Tehran, Iran, for their support. The authors also would like to express their appreciation to Dr. S. Mohammadi, Georgia Institute of Technology, Atlanta, for his useful comments. REFERENCES [1] B. Razavi, RF Microelectronics. Upper Saddle River, NJ: PrenticeHall, 1998, ch. 7. [2] M. L. Skolnik, Introduction to Radar Systems. New York: McGrawHill, 2001, ch. 3.

Ali Banai (M’01) was born in Mashhad, Iran, in 1968. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 1991, 1994, and 1999, respectively. Since 1999, he has been as a member of the faculty with the Department of Electrical Engineering, Sharif University of Technology. His main research interests are nonlinear microwave circuits, synchronization of coupled oscillators, and numerical techniques in passive microwave circuits. Dr. Banai was the corecipient of the Maxwell Premium Award presented at the 2001 IEE Microwave, Antennas, and Propagation Proceedings.

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Capacitive RF MEMS Switches Fabricated in Standard 0.35-m CMOS Technology Siamak Fouladi, Student Member, IEEE, and Raafat R. Mansour, Fellow, IEEE

Abstract—The objective of this paper is to investigate the integration of capacitive type RF microelectromechanical systems (MEMS) switches in a standard CMOS technology. A maskless monolithic integration process dedicated to electrostatically actuated capacitive type RF MEMS switches is developed and optimized. The fabricated switches consist of composite metal-dielectric warped membranes. The warped-plate structure is used to increase the capacitance ratio of the switch. The switches are fabricated using the interconnect metal and dielectric layers available in a standard 0.35- m CMOS process. Measurement results for the first switch show an insertion loss less than 0.98 dB, a return loss below 13 dB up to 20 GHz in the up-state, and a down-state isolation of 12.4–17.9 dB from 10 to 20 GHz. The capacitance ratio is enhanced up to 91:1 using the warped-plate structure. A second cascaded switch consisting of two shunt capacitive switches and a slow-wave high-impedance transmission line section is designed and fabricated for high-isolation applications. The measured insertion loss for this switch is less than 1.41 dB up to 20 GHz, the return loss is below 19 dB, and the isolation is 19–40 dB across the frequency band from 10 to 20 GHz. The proposed RF MEMS switches can be used in millimeter-wave CMOS RF front-ends where multiband functionality and reconfigurability is required. Index Terms—Capacitive switches, CMOS microelectromechanical systems (MEMS) integration, millimeter-wave CMOS, RF MEMS switches, silicon monolithic integrated circuits.

I. INTRODUCTION HE silicon-based standard CMOS technologies have always been of great interest for the implementation of wireless communication systems due to their mature fabrication process, higher levels of integration, and also lower manufacturing cost. During the past few years, the need for a wider frequency bandwidth has been a main reason to extend the applicability of silicon-based CMOS technologies for microwave and millimeter-wave applications. Millimeter-wave CMOS circuits with superior RF performance such as CMOS oscillators [1], mixers [2], amplifiers [3], and microwave passive components [4], [5] have been previously demonstrated. In addition to a higher frequency of operation, another key requirement in the current wireless communication industry is the multiband functionality enabling the integration of several

T

Manuscript received May 04, 2009; revised August 21, 2009. First published January 19, 2010; current version published February 12, 2010. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and COM DEV Ltd. The authors are with the Center for Integrated RF Engineering, Electrical and Computer Engineering Department, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2009.2038446

wireless standards into a single RF front-end that can operate in different frequency bands. Most recent solutions for the implementation of these multiband RF front-ends employ RF microelectromechanical systems (MEMS) switches [6]–[9]. RF MEMS switches offer an excellent RF performance, low dc power consumption, light weight, better linearity, and low intermodulation products at millimeter-wave frequencies [10]. However, the MEMS-based multiband RF front-ends incorporate off-chip MEMS switches and have not led to a fully integrated silicon solution using a mainstream CMOS process. An integrated monolithic CMOS implementation of the RF MEMS switches will result in low-cost single-chip RF multiband systems with enhanced performance and functionality by eliminating the packaging parasitics present in the hybrid integration approaches. Monolithic integration of RF MEMS switches with active CMOS circuitry based on a CMOS-compatible MEMS fabrication process was reported in [11] where the RF MEMS switches were stacked on a CMOS chip and controlled by the underlying CMOS control circuitry. The fabrication of the proposed monolithically integrated RF MEMS switch requires developC) MEMS fabrication ment of a low-temperature ( process that does not damage the underlying CMOS active circuits. An alternative CMOS-MEMS integration approach was pioneered by Fedder et al. [12], [13] to create electrostatically actuated microstructures with high aspect-ratio composite beam structures. RF MEMS devices like tunable capacitors [14] and micromachined inductors [15] using this post-CMOS maskless micromachining process have been developed. A capacitive series-type RF MEMS switch using the same integration approach was reported in [16]. The switch is thermally actuated and has a comb-finger structure for the capacitive coupling between the input/output RF ports. The maximum reported capacitance ratio of the switch is limited to 15:1. Moreover, thermal actuators consume high dc power for actuation; therefore, they require latching mechanisms adding to the complexity of the RF MEMS switch design and increasing the chip real state. In this paper, novel CMOS-MEMS capacitive shunt-type switches for microwave and millimeter-wave applications are demonstrated. The switches are based on a warped-plate structure increasing the capacitance ratio. Electrostatic actuation is utilized to reduce the dc power consumption. The switch is implemented using the standard 0.35- m CMOS process and a three-step maskless post-CMOS processing developed for the fabrication of parallel-plate electrostatically actuated microstructures at the University of Waterloo, Waterloo, ON, Canada. A capacitance ratio of 91:1 is achieved for the fabricated switches. An insertion loss better than 1.41 dB and an

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FOULADI AND MANSOUR: CAPACITIVE RF MEMS SWITCHES FABRICATED IN STANDARD 0.35- m CMOS TECHNOLOGY

Fig. 1. (a) Top view, (b) cross-sectional view, and (c) equivalent-circuit model of the shunt capacitive CMOS RF MEMS switch.

isolation of 19–40 dB from 10 to 20 GHz is demonstrated. The proposed switches can be used in reconfigurable CMOS RF front-ends. II. SWITCH DESIGN Fig. 1 shows the top view and the cross-sectional view of the shunt capacitive RF MEMS switch implemented using the standard 0.35- m CMOS process. The switch consists of a coplanar waveguide (CPW) transmission line section and two warped plates anchored on the center conductor and suspended on top of the ground conductors of the CPW line. As shown in the cross-sectional view of Fig. 1(b), the warped plates consist of a composite Al SiO layer. The warping of the plates after releasing the MEMS switch is due to the difference in the residual stress of the constituent metal and dielectric layers. The warped plates form an RF capacitance between signal and ground: when the plates are up and when the plates are pulled down on the ground conductors. The warped plate structure is used in order to decrease the up-state capacitance while enhancing the down-state capacitance. This will increase the capacitance ratio (1) The actuation electrodes are placed inside the gap between the CPW signal and ground conductors and separated from the

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RF ports. To actuate the switch, a dc-bias voltage, , is applied between the actuation electrodes and warped plates. The bias voltage is provided through high-resistivity poly-silicon lines. The air-gap between the actuation electrodes and the warped plates is maintained as small as possible to decrease the actuation voltage, . A second lower dc-bias voltage, , is applied between the signal and ground conductors and through the RF ports to bring the switch to the down-state position. The switch also includes a 65- m air trench in the silicon substrate and under the signal conductor. This trench will improve the RF performance and the insertion loss of the switch by removing the parasitic effects of the low-resistivity (8–12 cm) Si substrate commonly used in standard CMOS processes. The substrate loss is mainly due to the the eddy currents present at high frequencies inside the Si substrate. 275 m warped The switch consists of two 210 m plates suspended over a CPW line with dimensions of m and a characteristic impedance . As shown in the equivalent-circuit model of Fig. 1(c), the warped plates are presented by a series capacitor–inductor–resistor (CLR) model terminated by two sections , where m of transmission line with a length of is the distance from the edge of the warped plates to the referm is the width of the warped plates at ence lines and the anchor point. For the up-state, the impedance of the switch is approximated by the small shunt capacitance of the switch . The characteristic impedance of the loaded CPW line in the up-state position of the switch is close to 50 . When the switch is actuated, the shunt capacitance is increased to , creating an RF short between the signal and ground. The equivalent-circuit model parameters can be obtained using the electromagnetic (EM) simulations and also by fitting measured -parameters of the switch using the modeling approach presented in [17], and will be discussed in a later section. III. FABRICATION CMOS RF MEMS switches are fabricated using the standard 2P4M 0.35- m CMOS process from TSMC, Taipei, Taiwan, and then post-processed by optimizing the technique previously reported by the authors for the fabrication of RF MEMS variable capacitors [18], [19]. Fig. 2 presents the schematic view of the post-CMOS processing steps required to manufacture the integrated CMOS RF MEMS switches. The cross section of the CMOS die after standard CMOS processing is shown in Fig. 2(a). First the CMOS dielectric layer is removed using reactive ion etching (RIE) of oxide [see Fig. 2(b)]. This is performed using a CF H plasma etch recipe presented in Table I. The generated RIE polymer was subsequently removed using the post-RIE polymer remover EKC265 (EKC Technology, Hayward, CA). As shown in the scanning electron microscopy (SEM) image of Fig. 3, after this step both the sacrificial metal layer and silicon substrate around the MEMS devices will be exposed for subsequent etching. Next a time controlled isotropic RIE of silicon in an SF O plasma is used to create the 60- m trench under the signal lines, as presented in Fig. 2(c). An SEM image of the MEMS device after this step is presented in Fig. 4. During the oxide and silicon RIE steps, which are similar to the ones used in [12] and [13] to

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Fig. 3. SEM image of the switch after the CMOS dielectric RIE.

Fig. 4. SEM image of the switch after the isotropic RIE of the Si substrate.

Fig. 2. Post-CMOS processing steps. (a) CMOS die after standard CMOS processing. (b) Anisotropic RIE of CMOS dielectric layer. (c) Isotropic RIE of Si substrate. (d) Wet etching of the sacrificial metal layers. (e) Second RIE of the oxide layer on top of the pads and the warped plates.

TABLE I RIE ETCH PARAMETERS FOR THE PROPOSED POST-CMOS PROCESSING

(PAN) etch and 60% diluted potassium hydroxide (KOH) at 40 C for 15 min and 30% H O at 60 C for 30 min were applied. The KOH solution is used in order to remove the remaining piles of silicon inside the trench, which are left after the RIE of silicon. The oxide layer surrounding the top was also slightly etched during this structural metal layer stage. The measured thickness of the surrounding dielectric m. After the wet etching step, layer is found to be the CMOS dies were placed in a CO critical point dryer (CPD) system to avoid stiction. The final post-processing step is the second RIE of the oxide layer on top of the pads for electrical contact and also on top of the warped plates to increase the amount of warpage [see Fig. 2(e)]. The same oxide RIE recipe as in Table I was used for this step. Fig. 5 shows an SEM image of the final fabricated CMOS RF MEMS switch after all the post-CMOS processing steps. IV. SIMULATION RESULTS

create lateral CMOS-MEMS microstructures, the uppermost is used as an etch mask. CMOS interconnect metal layer Following the RIE steps, the warped plates of the switches are [see released by wet etching of the sacrificial metal layer Fig. 2(d)]. During this step the masking metal layer is also removed. Release holes on the warped plates are required to facilitate the wet etching of the sacrificial aluminum layer. For the wet etching, solutions of (16:1:1) phosphoric–acetic–nitric

Residual stresses present in the constituent metal and dielectric layers of the CMOS process that are induced by thermal mismatch cause warping of the plates of the proposed RF MEMS switch. This property is used to increase the capacitance ratio of the switch. To illustrate this concept, finite-element analysis with CoventorWare was performed to simulate the warpage of the switch’s top plates. The RF performance of the switch was also simulated using Ansoft High Frequency Structure Simulator (HFSS) software.

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Fig. 7. SEM image of the cantilever beams used as test structures for stress analysis. Fig. 5. SEM image of the fabricated CMOS RF MEMS switches.

Fig. 6. (a) Top view and (b) cross section of the composite Al=SiO cantilever beams used to extract residual stress components of each layer.

A. Mechanical Analysis As shown in the cross-sectional view of the composite metaldielectric layer in Fig. 6, the bilayer warped plates of the switch are subjected to residual stresses generated from the fabrication process. The biaxial residual stress in the top Al layer is assumed to be tensile while that in the bottom oxide layer is compressive throughout the thickness of the oxide layer. The accurate characterization and control of the stress-induced warpage is essential for the design and implementation of the proposed switch. The residual stress values of each layer is determined by conducting experiments on the stress-induced bending of bilayer cantilever beams. Fig. 7 shows the SEM image of an array of released cantilever beams with lengths from 100 to 200 m used as test structures for stress analysis. The curvature-based approach presented in [20]–[22] is used to derive the residual stress values present in the oxide and aluminum layers of the CMOS process. The warped plates of the proposed CMOS-MEMS switch consist of the same composite Al SiO layer as the cantilever beams shown in Fig. 7. The bending curvature of this bilayer structure is related to the residual stress values by [20] (2) is the modwhere denotes Young’s modulus, is the thickness ratio, and ulus ratio, represents the difference in the residual stress values for the aluminum and oxide layers.

Fig. 8. Measured deflection profile of the bilayer cantilever beam and FEM simulation result for  : MPa.

= 144 74

The measured deflection profile of a 156- m-long and 30- m-wide Al SiO cantilever beam using an optical interferometer WYKO is shown in Fig. 8. The measured deflection profile is then decomposed into tilt and curl components induced from the mean and stress gradient components, respectively [22], (3) where is the position along the beam, represents the angular tilt, and is the bending curvature that are determined by curve fitting of the measured deflection profile. The stress gradient obtained from different cantilevers is averaged to be MPa and the standard deviation is calculated to be 2.1 MPa. As illustrated in Fig. 8, the measured deflection profile agrees with the simulation results using CoventorWare and the determined residual stress gradient in the finite-element method (FEM) model. Fig. 9 shows the final FEM simulation result for the warpage of the proposed CMOS-MEMS switch. The maximum simulated tip deflection of the warped plates is 59 m. By comparison between the maximum deflection of the top plate using the FEM simulation result and the measured maximum deflection of 66 m, as shown in the SEM image of Fig. 5, we can see that by using the extracted residual stress values present in the oxide

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Fig. 9. FEM simulation result for the fabricated CMOS-MEMS switch with warped plates using the determined residual stress values, the maximum deflection of the top plate is simulated to be 59 m.

and aluminum layers we are able to closely predict the warpage of the fabricated device. Coupled-field electromechanical simulation was also performed with CoventorWare to evaluate the actuation voltage of the switch. In order to actuate the switch first, a dc-bias voltage, , is applied between the warped plates and actuation electrodes. The simulated pull-down voltage between the warped V. As plates and actuation electrodes is predicted to be shown in Fig. 10(a), after the warped plate comes into contact with the actuation electrode, the air gap between the warped plate and the ground plane is significantly reduced. This will , result in lowering the second required actuation voltage, applied to the RF port and between the signal and ground plane. pulls down the The second electrostatic force produced by warped plate into complete contact with the ground plane in a rolling motion. As shown in Fig. 10(b), the switch is actuated V and V. The to the down-state position with simulated hold-down voltage is obtained to be 12 V. B. EM Simulations EM simulations of the proposed switch are performed using Ansoft HFSS tools. The deformed mesh structure obtained from the FEM stress analysis is transferred from CoventorWare to HFSS to simulate the RF response of the switch in the up-state. Fig. 11(a) shows the simulated -parameters of the switch from 1 to 20 GHz for the up-state. The maximum insertion loss at 20 GHz is simulated to be 0.81 dB and the return loss is better than 15 dB for the frequency range up to 20 GHz. The equivalent-circuit model parameters of the switch shown in Fig. 1(c) are extracted from the simulated -parameters. The switch is fF predicted to demonstrate an up-state capacitance of between the signal and ground. For the up-state position, since the impedance of the shunt capacitive switch is mainly deterand resistance are not fitted. mined by , the inductance The simulated return loss and isolation for the down-state position are presented in Fig. 11(b). The maximum isolation in this state is simulated to be 12.9 dB at 10 GHz and 20.2 dB at 20 GHz. The switch down-state capacitance , inductance , are determined from fitting the -parameters and resistance to the equivalent CLR model in Fig. 1(c). The down-state capF resulting in a downpacitance is simulated to be

Fig. 10. FEM simulation results for the actuation voltage of the switch: (a) when the first bias voltage V is applied between the signal and actuation electrode and (b) when the warped plates are pulled down by applying the second bias voltage V between signal and ground conductors.

state/up-state capacitance ratio of 108:1. The equivalent inpH is mainly associated to the width of ductance m, as shown in the warped plates over the CPW gap Fig. 1. The series resistance does not have any significant effect on the -parameters below the self-resonance frequency GHz and it can only be fitted of the series CLR circuit around this frequency. The equivalent series resistance is deter. mined to be V. MEASUREMENT RESULTS The RF performance of the switch is measured using twoport on-wafer measurements up to 20 GHz using an HP8722ES vector network analyzer. The measured -parameters of the switch for the up-state are presented in Fig. 11(a) along with the simulation results. The maximum insertion loss at 20 GHz is measured to be 0.98 dB and the return loss is better than 18 dB at 10 GHz and 13 dB at 20 GHz. There is a good agreement between the simulation and measurement results as shown in this figure. Using the same procedure as explained earlier for the EM simulation results, the value of the up-state capacitance

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Fig. 12. Switching time measurement results of the fabricated switch for: (a) up-to-down state and (b) down-to-up state transitions.

Fig. 11. Simulated and measured S -parameters of the fabricated capacitive switch for: (a) up-state and (b) down-state positions.

is extracted to be fF from the measured results. The switch is actuated to the down-state position by applying the V on the actuation electrodes and actuation voltages V applied to the RF port through a bias-tee connected to the ports of the network analyzer. The measured -parameters of the switch in the down-state position are presented in Fig. 11(b). The maximum isolation in this state is obtained to be 12.4 dB at 10 GHz and 17.9 dB at 20 GHz. The measured pF, resulting down-state capacitance is extracted to be of 91:1. The reduction in the in a measured capacitance ratio down-state capacitance compared to the simulation result is attributed to the surface roughness of the oxide dielectric layer between the warped plates and ground plane. Assuming a perand fectly flat oxide layer with a dielectric constant of a thickness of m for the simulations, a capacitance degradation of 19% occurs due to the surface roughness. The dynamic response of the fabricated switch is also evaluated by switching time measurement results as shown in Fig. 12. The dynamic transient response is measured with a square wave signal used to actuate the switch. The switch is actuated at a rate of 1 kHz with a 0–85-V unipolar voltage and 25 dBm of input RF power at 10 GHz. A high-speed RF power detector is used at the output port to record the transmitted RF power through the switch. Fig. 12(a) shows both the actuation voltage and output signal of the power detector when the switch changes its state from the up-state to down-state. The switching time is estimated

Fig. 13. Equivalent-circuit diagram of the cascaded switch with  -match circuit.

to be 96 s for the up-to-down state transition. The squeeze film damping coefficient plays an important role for this transition. The measured switching time for the down-to-up state transition is 49 s, as shown in Fig. 12(b). VI. CASCADED SWITCH The maximum isolation and return-loss performance of the capacitive type RF MEMS switches are limited by the capacitance ratio of the switch. The maximum achievable capacitance ratio itself is set by the limitations of the fabrication process. By using cascaded switch structures, one can achieve a higher isolation and better return loss compared to a single element switch with limited capacitance ratio [23], [24]. A second capacitive type shunt RF MEMS switch integrated in CMOS technology and with higher isolation and better return-loss performance is designed and fabricated. The cascaded switch consists of a -match circuit, as shown in the equivalent-circuit diagram of Fig. 13, where a transmission line secis used between tion with a high characteristic impedance of two shunt capacitive MEMS switches with a maximum measured capacitance ratio of 91:1. The extracted CLR model of the

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W = 30  G = 60  S = 10  W =

Fig. 14. Top view and the cross-sectional view of the CPW slow-wave structure with geometric parameters m, m, m, m, and m.

5

W = 1:4 

Fig. 16. Optical micrograph of the cascaded switch with improved isolation and return loss.

Fig. 15. (a) Attenuation constant and (b) effective propagation constant of three different CPW transmission lines on CMOS Si substrate.

single switch is used to design the cascaded switch. The charand the length of the transmission line acteristic impedance section is determined following the design procedure in [23]. The switch is optimized for an isolation better than 20 dB at 10 GHz. Since the CMOS silicon substrate has a very low resistivity 8 cm , it is not suitable for microwave applications. Hence, a deep trench in the silicon substrate and under the signal path of the transmission line section is crucial in order to eliminate the parasitic effects of the lossy silicon substrate and obtain a reasonable RF performance for the fabricated switch. Although the air trench improves the RF performance, it also results in a for the suspended very low effective propagation constant transmission line, increasing the total required footprint of the fabricated switch on the CMOS chip. Therefore, a slow-wave structure, such as the one shown in Fig. 14, is utilized to reduce the length of the CPW transmission line and size of the fabricated switch. The proposed slow-wave structure consists of multiple ground fingers attached to the signal line through an oxide bridge. The 1.4- m-wide oxide layer is used to increase the capacitive loading on the signal line and to increase its effective propagation constant. It also mechanically connects the fingers to the signal line and prevents them from warping due to the residual stress after release from the silicon substrate. Fig. 15 shows the attenuation constant and the effective propagation constant of the proposed slow-wave suspended CPW transmission line compared to a standard CPW line on a lossy Si substrate and also a conventional suspended CPW line with an air trench. The slow-wave suspended transmission line section used for the cascaded switch design has a characteristic impedance , an effective propagation constant of , of



S

Fig. 17. Measured -parameters of the fabricated cascaded switch with -match circuit integrated in CMOS technology for: (a) up-state and (b) down-state.

and an attenuation constant of 0.83 dB/cm at 10 GHz. An optical micrograph of the fabricated cascaded switch is presented in Fig. 16. Fig. 17 shows the measured -parameters of the cascaded capacitive shunt RF MEMS switch with -match circuit. The measured return loss is obtained to be better than 19 dB across the frequency band from 1 up to 20 GHz. The insertion loss is measured to be 0.58 dB at 10 GHz and 1.41 dB at 20 GHz. The isolation of the switch is significantly improved compared

FOULADI AND MANSOUR: CAPACITIVE RF MEMS SWITCHES FABRICATED IN STANDARD 0.35- m CMOS TECHNOLOGY

to the single switch. Using the -match circuit, the isolation is obtained to be higher than 19 dB for the frequency band from 10 to 20 GHz. VII. CONCLUSIONS For the first time, capacitive shunt-type RF MEMS switches implemented using a standard CMOS process without any metal deposition or patterning steps have been presented. The switches have been fabricated using the 2P4M TSMC 0.35- m CMOS process and by employing the available dielectric and interconnect metal layers of the CMOS process. The capacitance ratio has been improved by using a warped-plate structure. A capacitance ratio of 91:1 has been achieved for the fabricated switches. The first switch shows an insertion loss better than 0.98 dB, a return loss of 13 dB, and an isolation of 17.9 dB at 20 GHz. A second cascaded switch with improved return loss and isolation performance has been designed and fabricated using the -match circuit method. The switch demonstrated an insertion loss less than 1.41 dB, a return loss better than 19 dB, and an isolation of more than 19 dB all over the frequency band from 10 to 20 GHz. The proposed integrated capacitive RF MEMS switches can be used to implement multiband and reconfigurable RF front-ends. The fabrication of the proposed RF MEMS switches in a standard CMOS process enables the fully integrated silicon solution for these RF front-ends. ACKNOWLEDGMENT The authors would like to thank the Canadian Microelectronics Corporation (CMC), Kingston, ON, Canada, for providing CMOS fabrication services. The authors gratefully acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada and COM DEV Ltd., Cambridge, ON, Canada, for their financial support of this study. REFERENCES [1] Y.-H. Chen, H.-H. Hsieh, and L.-H. Lu, “A 24-GHz receiver frontend with an LO signal generator in 0.18-m CMOS,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 5, pp. 1043–1051, May 2008. [2] R. M. Kodkani and L. E. Larson, “A 24-GHz CMOS passive subharmonic mixer/downconverter for zero-IF applications,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 5, pp. 1247–1256, May 2008. [3] 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. [4] M. K. Chirala and C. Nguyen, “Multilayer design techniques for extremely miniaturized CMOS microwave and millimeter-wave distributed passive circuits,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4218–4224, Dec. 2006. [5] T. O. Dikson, M.-A. LaCroix, S. Boret, D. Gloria, R. Beerkens, and S. P. Voinigescu, “30–100-GHz inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 123–133, Jan. 2005. [6] D. Qiao, R. Molfino, S. M. Lardizabal, B. Pillans, P. M. Asbeck, and G. Gerinic, “An intelligently controlled RF power amplifier with a reconfigurable MEMS-varactor tuner,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 3, pp. 1089–1095, Mar. 2005. [7] M. Kim, W. B. Hacker, R. E. Mihailovich, and J. F. DeNatale, “A monolithic MEMS switched dual-path power amplifier,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 7, pp. 285–286, Jul. 2001. [8] M. Liu, M. Libois, M. Kuijk, A. Barel, J. Craninckx, and B. Come, “MEMS-enabled dual-band 1.8 and 5–6 GHz receiver RF front-end,” in IEEE Radio Wireless Symp. Dig., Long Beach, CA, Jan. 2007, pp. 547–550.

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[9] A. Fukuda, T. Furuta, H. Okazaki, and S. Narahashi, “A 0.9–5-GHz wide-range 1 W-class reconfigurable power amplifier employing RF-MEMS switches,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 2006, pp. 1859–1862. [10] E. R. Brown, “RF-MEMS switches for reconfigurable integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 11, pp. 1868–1880, Nov. 1998. [11] K. Kuwabara, N. Sato, T. Shimamura, H. Morimura, J. Kodate, T. Sakata, S. Shigematsu, K. Kudou, K. Machida, M. Nakanishi, and H. Ishii, “RF CMOS-MEMS switch with low-voltage operation for singlechip RF LSIs,” in IEEE Electron Devices Meeting, San Fransisco, CA, Dec. 2006, pp. 1–4. [12] G. K. Fedder, S. Santhanam, M. L. Reed, S. C. Eagle, D. F. Guillou, M. S.-C. Lu, and L. R. Carley, “Laminated high-aspect ratio microstructures in a conventional CMOS process,” Sens. Actuators A, Phys., vol. 57, no. 2, pp. 103–110, Nov. 1996. [13] H. Xie, L. Erdmann, X. Zhu, K. J. Gabriel, and G. K. Fedder, “PostCMOS processing for high-aspect-ratio integrated silicon microstructures,” J. Microelectromech. Syst., vol. 11, no. 2, pp. 93–101, Apr. 2002. [14] A. Oz and G. K. Fedder, “RF CMOS-MEMS capacitor having large tuning range,” in Proc. IEEE Transducers, Solid-State Sens., Actuator, Microsyst., Boston, MA, Jun. 2003, pp. 851–854. [15] H. Lakdawala, X. Zhu, H. Luo, S. Santhanam, L. R. Carley, and G. K. Fedder, “Micromachined high-Q inductors in a 0.18-m copper interconnect low-K dielectric CMOS process,” IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 394–403, Mar. 2002. [16] S. Zhang, W. Su, M. Zaghloul, and B. Thibeault, “Wideband CMOS compatible capacitive MEMS switch for RF applications,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 9, pp. 599–601, Sep. 2008. [17] J. B. Muldavin and G. M. Rebeiz, “High-isolation CPW MEMS shunt switches—Part 1: Modeling,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 6, pp. 1045–1052, Jun. 2000. [18] M. Bakri-Kassem, S. Fouladi, and R. R. Mansour, “Novel high-Q MEMS curled-plate variable capacitors fabricated in 0.35-m CMOS technology,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 530–541, Feb. 2008. [19] S. Fouladi, M. Bakri-Kassem, and R. R. Mansour, “An integrated tunable band-pass filter using MEMS parallel-plate variable capacitors implemented with 0.35 m CMOS technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, Jun. 2007, pp. 505–508. [20] S. Huang and X. Zhang, “Study of gradient stress in bimaterial cantilever structures for infrared applications,” J. Micromech. Microeng., vol. 17, no. 7, pp. 1211–1219, Jul. 2007. [21] S. Huang and X. Zhang, “Gradient residual stress induced elastic deformation of multilayer MEMS structures,” Sens. Actuators A, Phys., vol. 134, no. 1, pp. 177–185, Feb. 2007. [22] W. Fang and J. A. Wickert, “Determining mean and gradient residual stresses in thin films using micromachined cantilevers,” J. Micromech. Microeng., vol. 6, no. 3, pp. 301–309, Sep. 1996. [23] J. B. Muldavin and G. M. Rebeiz, “High-isolation CPW MEMS shunt switches—Part 2: Design,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 6, pp. 1053–1056, Jun. 2000. [24] G. M. Rebeiz, RF MEMS Theory, Design, and Technology. Hoboken, NJ: Wiley, 2003, pp. 230–231.

Siamak Fouladi (S’03) received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 2002, the M.Sc. degree in electrical engineering from Concordia University, Montreal, QC, Canada, in 2005, and is currently working toward the Ph.D. degree in electrical and computer engineering at the University of Waterloo, Waterloo, ON, Canada. In May 2005 he joined the Center for Integrated RF Engineering (CIRFE), Electrical and Computer Engineering Department, University of Waterloo, as a Research Assistant. His research interests include RF MEMS device fabrication and characterization and integrated millimeter-wave circuits. Mr. Fouladi was the recipient of the Natural Sciences and Engineering Research Council of Canada (NSERC) Scholarship.

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Raafat R. Mansour (S’84–M’86–SM’90–F’01) was born in Cairo, Egypt, on March 31, 1955. He received the B.Sc (with honors) and M.Sc degrees from Ain Shams University, Cairo, Egypt, in 1977 and 1981, respectively, and the Ph.D. degree from the University of Waterloo, Waterloo, ON, Canada, in 1986, all in electrical engineering. In 1981, he was a Research Fellow with the Laboratoire d’Electromagnetisme, Institut National Polytechnique, Grenoble, France. From 1983 to 1986, he was a Research and Teaching Assistant with the Department of Electrical Engineering, University of Waterloo. In 1986, he joined COM DEV Ltd., Cambridge, ON, Canada, where he held several technical and management positions with the Corporate Research and Development Depart-

ment. In 1998, he became a Scientist. In January 2000, he joined the University of Waterloo, as a Professor with the Electrical and Computer Engineering Department. He holds a Natural Sciences and Engineering Research Council of Canada (NSERC) Industrial Research Chair in RF Engineering with the University of Waterloo. He is the Founding Director of the Center for Integrated RF Engineering (CIRFE), University of Waterloo. He has authored or coauthored numerous publications in the areas of filters and multiplexers, high-temperature superconductivity and MEMS. He coauthored Microwave Filters for Communication Systems (Wiley, 2007). He holds several patents related to the areas of dielectric resonator filters, superconductivity, and MEMS devices. His current research interests include MEMS technology and miniature tunable RF filters for wireless and satellite applications. Dr. Mansour is a Fellow of the Engineering Institute of Canada (EIC).

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S. Islam M. Ito K. Itoh T. Itoh Y. Itoh A. Ittipiboon F. Ivanek D. Iverson M. Iwamoto D. Jablonski D. Jachowski C. Jackson D. Jackson R. Jackson A. Jacob K. Jacobs S. Jacobsen D. Jaeger J. Jaeger S. Jagannathan N. Jain G. James M. Janezic S. Jang M. Jankovic D. Jansen L. Jansson H. Jantunen H. Jardon-Aguilar J. Jargon N. Jarosik B. Jarry P. Jarry A. Jastrzebski B. Jemison W. Jemison S. Jeng A. Jenkins S. Jeon D. Jeong J. Jeong Y. Jeong A. Jerng T. Jerse T. Jiang X. Jiang G. Jianjun D. Jiao J. Jin J. M. Jin J. Joe T. Johnson B. Jokanovic U. Jordan K. Joshin J. Joubert S. Jung T. Kaho S. Kanamaluru K. Kanaya S. Kang P. Kangaslahti B. Kapilevich I. Karanasiou M. Karim T. Kataoka A. Katz R. Kaul R. Kaunisto T. Kawai S. Kawasaki M. Kazimierczuk L. Kempel P. Kenington P. Kennedy A. Kerr D. Kettle A. Khalil W. Khalil S. Khang A. Khanifar A. Khanna R. Khazaka J. Khoja S. Kiaei J. Kiang B. Kim C. Kim D. Kim H. Kim I. Kim J. Kim S. Kim T. Kim W. Kim N. Kinayman R. King N. Kinzie S. Kirchoefer A. Kirilenko M. Kishihara T. Kitazawa J. Kitchen T. Klapwijk E. Klumperink D. Klymyshyn L. Knockaert R. Knoechel M. Koch K. Koh N. Kolias J. Komiak A. Komijani G. Kompa A. Konanur A. Konczykowska H. Kondoh B. Kopp B. Kormanyos J. Korvink P. Kosmas Y. Kotsuka S. Koziel A. Kozyrev V. Krishnamurthy H. Krishnaswamy C. Krowne J. Krupka D. Kryger H. Ku H. Kubo A. Kucar

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