OCTOBER 2010 IEEE MTT-V058-I10 (2010-10) [58, 10 ed.]

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OCTOBER 2010

VOLUME 58

NUMBER 10

IETMAB

(ISSN 0018-9480)

PAPERS

Smart Antennas, Phased Arrays, and Radars A Low-Power Shoe-Embedded Radar for Aiding Pedestrian Inertial Navigation ........ ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ...... C. Zhou, J. Downey, D. Stancil, and T. Mukherjee Active Circuits, Semiconductor Devices, and ICs A 5.5-mW 9.4-dBm IIP3 1.8-dB NF CMOS LNA Employing Multiple Gated Transistors With Capacitance Desensitization ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... . T. H. Jin and T. W. Kim A Jitter-Optimized Differential 40-Gbit/s Transimpedance Amplifier in SiGe BiCMOS ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ C. Knochenhauer, S. Hauptmann, J. C. Scheytt, and F. Ellinger 2-D Electrical Interferometer: A Novel High-Speed Quantizer .. ......... ........ ......... ...... Y. M. Tousi and E. Afshari Optimized Design of a Highly Efficient Three-Stage Doherty PA Using Gate Adaptation ....... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... I. Kim, J. Moon, S. Jee, and B. Kim A Compact 0.1–14-GHz Ultra-Wideband Low-Noise Amplifier in 0.13- m CMOS .... ... P.-Y. Chang and S. S. H. Hsu Optimization of a Photonically Controlled Microwave Switch and Attenuator .. ......... .. J. R. Flemish and R. L. Haupt Wireless Communication Systems Theoretical and Experimental Investigation of the Modulated Scattering Antenna Array for Mobile Terminal Applications ... ......... ........ ......... . ........ ........ ......... .... M. He, L. Wang, Q. Chen, Q. Yuan, and K. Sawaya A Multimode/Multiband Power Amplifier With a Boosted Supply Modulator .. ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... . D. Kang, D. Kim, J. Choi, J. Kim, Y. Cho, and B. Kim Field Analysis and Guided Waves Space-Charge Plane-Wave Interaction at Semiconductor Substrate Boundary .. ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ........ I. A. Elabyad, M. S. Eldessouki, and H. M. El-Hennawy Full-Space Scanning Periodic Phase-Reversal Leaky-Wave Antenna .... ........ ......... ... N. Yang, C. Caloz, and K. Wu

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(Contents Continued from Front Cover) CAD Algorithms and Numerical Techniques Eliminating the Low-Frequency Breakdown Problem in 3-D Full-Wave Finite-Element-Based Analysis of Integrated Circuits ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ...... J. Zhu and D. Jiao A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship ..... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... Z. Szabó, G.-H. Park, R. Hedge, and E.-P. Li Filters and Multiplexers A Substrate-Integrated Evanescent-Mode Waveguide Filter With Nonresonating Node in Low-Temperature Co-Fired Ceramic ........ ......... ........ ...... .... ......... ........ ......... L.-S. Wu, X.-L. Zhou, W.-Y. Yin, L. Zhou, and J.-F. Mao Instrumentation and Measurement Techniques De-Embedding Method Using an Electromagnetic Simulator for Characterization of Transistors in the Millimeter-Wave Band ... ......... ......... ......... ......... ......... ........ .. T. Hirano, H. Nakano, Y. Hirachi, J. Hirokawa, and M. Ando Temperature Dependence of Resonances in Metamaterials ...... ......... ........ ......... ......... . V. V. Varadan and L. Ji Whispering Gallery Mode Hemisphere Dielectric Resonators With Impedance Plane .. ......... ........ ......... ......... .. .. ........ ...... A. A. Barannik, S. A. Bunyaev, N. T. Cherpak, Y. V. Prokopenko, A. A. Kharchenko, and S. A. Vitusevich

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MEMS and Acoustic Wave Components High-Reliability RF-MEMS Switched Capacitors With Digital and Analog Tuning Characteristics .... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... . A. Grichener and G. M. Rebeiz

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Biological, Imaging, and Medical Applications Considerations for Developing an RF Exposure System: A Review for in vitro Biological Experiments ........ ......... .. .. ........ ......... ......... ..... A. Paffi, F. Apollonio, G. A. Lovisolo, C. Marino, R. Pinto, M. Repacholi, and M. Liberti

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

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CALLS FOR PAPERS

Special Issue on RF Nanoelectronics ..... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .

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Digital Object Identifier 10.1109/TMTT.2010.2084896

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

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A Low-Power Shoe-Embedded Radar for Aiding Pedestrian Inertial Navigation Chenming Zhou, Member, IEEE, James Downey, Student Member, IEEE, Daniel Stancil, Fellow, IEEE, and Tamal Mukherjee, Member, IEEE

Abstract—Navigation in global positioning system (GPS)-denied or GPS-inhibited environments such as urban canyons, mountain areas, and indoors is often accomplished with an inertial measurement unit (IMU). For portable navigation, miniaturized IMUs suffer from poor accuracy due to bias, bias drift, and noise. We propose to use a low-power shoe-embedded radar as an aiding sensor to identify zero velocity periods during which the individual IMU sensor biases can be observed. The proposed radar sensor can also be used to detect the vertical position and velocity of the IMU relative to the ground in real time, which provides additional independent information for sensor fusion. The impacts of the noise and interference on the system performance have been analyzed analytically. A prototype sensor has been constructed to demonstrate the concept, and experimental results show that the proposed sensor is promising for position and velocity sensing. Index Terms—Direct conversion, inertial navigation, position and velocity sensor, zero velocity update (ZUPT).

I. INTRODUCTION

HILE THE global positioning system (GPS) is typically used in current navigation systems for pedestrians, alternative techniques still need to be developed for environments such as indoors, underground, urban canyons, and mountain areas where GPS signals are degraded or unavailable. Pedestrian tracking in GPS-denied environments is often accomplished with inertial navigation sensors since they operate independently of external assets and without prior knowledge of the environment. Recent improvements in microelectromechanical systems (MEMS) have made possible low-power shoe-mounted inertial sensors for pedestrian tracking [1]–[3]. However, an inertial measurement unit (IMU) equipped only with accelerometers and gyroscopes does not provide acceptable accuracy owing to accumulated integration errors from unknown sensor biases [4].

W

Manuscript received December 23, 2009, revised May 15, 2010; accepted June 03, 2010. Date of publication September 07, 2010; date of current version October 13, 2010. This work was supported by the Air Force Research Laboratory (AFRL) and by the Defense Advanced Research Projects Agency (DARPA) under Agreement FA8650-08-1-7824. C. Zhou, J. Downey, and T. Mukherjee are with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: [email protected]; [email protected]; [email protected]). D. Stancil was with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA. He is now with the Electrical and Computer Engineering Department, North Carolina State University, Raleigh, NC 27695 USA. 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.2010.2063810

A technique known as zero velocity update (ZUPT) has been applied to reduce the accumulated error [1]. ZUPTing systems require a mechanism to measure when the velocity of the IMU is zero. While estimating zero velocity from the IMU data itself provides some improvement, an independent means for directly determining the time interval over which the ZUPT can take place is preferred. To address this challenge, we propose to use a compact shoeembedded radar—terrain relative velocity (TRV) radar—as an aiding sensor to improve the accuracy of a MEMS-based inertial navigation system [5]. In addition to estimating ZUPTs, the proposed TRV sensor may also be used for accurately detecting the position and velocity of the IMU relative to the ground in the vertical direction in real time, adding independent information for sensor fusion. The principle of the proposed TRV sensor is based on continuous wave (CW) radar that compares the RF source phase with the ground reflected wave phase. The phase difference is proportional to distance. We have implemented this concept using connectorized modular commercial off-the-shelf (COTS) components. The preliminary results show that the proposed RF motion sensor is promising for identifying the timing and duration of a stance phase, independent of an IMU. A design constraint of this sensor is that it must be small enough to be embedded into a shoe. Low power consumption is also a desirable feature since it will be powered by a battery. RF sensing of zero velocity is chosen over other sensing mechanisms such as optical and acoustic waves because of its relative insensitivity to the external environment. A similar mechanism has been used for remote monitoring of vital signs [6]. II. SYSTEM WORKING PRINCIPLE AND PERFORMANCE ANALYSIS A. Working Principle The system block diagram of the proposed TRV sensor is shown in Fig. 1. A single signal source provides both the RF output and local oscillator (LO) signals, through a two way-0 power splitter (the 1:2 block shown in Fig. 1). The LO signal split from the source is further divided into two branches with a phase difference of 90 . These two orthogonal LO signals then mix with RF signals from the receive antenna and produce two IF signals (here at zero frequency). A power amplifier (PA) and a low-noise amplifier (LNA) are added to the system to increase the signal-to-noise ratio (SNR). A direct conversion scheme has been employed due to the following reasons: • low complexity and low power consumption;

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The dc component output from the channel in-phase/quadrature (I/Q) of the sensor is

(4) , and where is the gain of the mixer and . and Therefore, given measured voltages of the path length can be reconstructed from

Fig. 1. Shoe-embedded radar: system block diagram.

. Here, , an estimate

(5) where is the estimated path length and is an integer to compensate for the phase ambiguity caused by the inverse tangent operation. If the sensor always starts with a stance phase in with a known initial path length , the unknown phase (5) can be removed

Fig. 2. Distance illustration of a shoe-embedded radar sensor.

• small size; • elimination of image-rejection issue; • reduced requirement on the phase noise of the VCO since a single oscillator is used to measure the distance. However, it is known that a direct conversion receiver suffers from dc offsets caused by interfering signals that are in-band to the receiver [7], [8]. DC offset and its impacts on the system performance will be addressed in Section II-C. denote the single-tone signal generated by the Let signal source, where is the angular frequency. The LO signal for the in-phase channel mixer can be represented as (1) where and are the amplitude and phase of the LO signal, respectively. The RF signal before the mixer can be written as

(6) It should be noted that phase unwrapping should be considered . The velocity can then be obtained by in (6) if differentiating the path length with respect to time (7) The vertical velocity relative to ground is calculated by (8) At large distances where , we have , and . The inconvenience of transforming to can be avoided by replacing the two antennas in Fig. 1 with a single antenna. Transmit signals and receive signals could share the same antenna through a directional coupler or a circulator. in this case, so that and . However, isolation we have between the transmitter and receiver could be more challenging. B. System Noise Analysis

(2) where is the amplitude of the RF signal, is the speed of is a constant phase delay. Here, represents half light, and of the path length that a signal travels when it is emitted from the transmit antenna, reflected by the ground, and finally detected by the receive antenna. The two antennas (RX and TX) are mounted on the same antenna plate with a separation dis, as shown in Fig. 2. Let denote the distance betance of tween the antenna plate and ground plane, given by (3) For the RF motion sensor proposed in this paper, the antenna plate will be embedded in the heel of the shoe and gives the elevation of the heel.

Equation (6) assumes an ideal system where noise is absent. However, for a practical system, noise disturbances must be taken into account [9]. In this section, we will investigate how noise presented in the system affects the distance and velocity reconstructions. The received noise-corrupted RF signal can be represented , where with a vector notation as and denote the signal and noise vectors, respectively. In the I/Q plane shown in Fig. 3, the random noise vector is added onto the signal vector with a uniformly distributed based on a probrandom phase , and a random amplitude ability distribution. As a result from the noise vector, the amplitude and phase of , the corrupted signal randomly change over time. Let denote the phase reconstruction error due and to the noise disturbance. Given a fixed and signal vector ,

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Fig. 3. Impact of SNR on the distance reconstruction.

the phase estimation error varies with . The noise vector forms a circle in the I/Q plane, as shown in Fig. 3, as randomly changes. It is apparent that reaches its maximum value when is tangential to the circle of with a maximum value of (9)

Fig. 4. Impact of SIR on the distance reconstruction.

can be greatly decreased by reIt should be noted that ducing the bandwidth of the system until . C. Impact of Interference on the System Performance

Considering additive Gaussian noise with a zero mean and a standard deviation of , it is known that the possibility for is 95.4%. Let . The corresponding maximum distance estimation error (with 95.4% confidence) is (10) For high SNR, we have the approximation (11) It is shown by simulation that the above approximation only introduces 1% position error with an SNR of 15 dB. Therefore, the above approximation is valid for most practical TRV sensor analyses. According to (11), the system positioning accuracy only depends on two factors: operating frequency and system SNR. An increase of SNR and/or results in better positioning accuracy. Another application of (11) is to estimate the required minimum SNR to meet a target position resolution, assuming a noise-limited system. As an example, for our system with an GHz, a positioning resolution of operating frequency 1 mm requires the system SNR to be greater than 14 dB. If the velocity is sufficiently low such that the distance of a is less than sensor moved within two samples separated by , the system cannot the above minimum distance error give a reliable velocity estimation. Therefore, the position accuracy in (11) also sets a lower limit for the velocity that can be detected by the sensor. This minimum detectable velocity is simply determined by

Besides the desired RF signal, which is reflected by the ground, sometimes other undesirable in-band RF signals are present at the receiver. It should be noted that this interference could be from the RF source of the radar (coherent interference) or independent sources (noncoherent interference). Usually the power of noncoherent interference is much lower compared to coherent interference, depending on the system operating frequency. In this paper, we will focus on coherent interference and analyze its impact on the system performance. These interfering signals will enter into the mixer and mix with the LO signal, resulting in dc offsets at the output of the sensor. DC offset is one of the major issues caused by a direct conversion design and will have a significant impact on the system performance if there is no compensation for it. Several interference sources may contribute to the dc offset, including • multiple reflections between the antenna plate and ground, time variant, depending on the distance between the ground and antenna plate; • feed through due to poor isolation between Tx and Rx antennas [10], [11], time invariant; • insufficient LO-RF isolation [8], time invariant. We follow a similar procedure as in Section II-B and replace with a interference vector . To simplify the noise vector the problem, we assume the noise power in this scenario is very low compared to interference and can be ignored. The received and the signal-toRF signal is then written as . Note interference ratio (SIR) is defined by that the interference has a phase of , which is not randomly changing. Considering the triangle formed by the three vectors and applying the law of sines, we have (13)

(12) where

is the wavelength. For example, considering Hz, dB, and ms, a minimum detectable velocity of 5.08 mm/s can be obtained based on (12).

where is the estimation error caused by interference . According to Fig. 4, we have and . Therefore, (14)

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GHz, the maximum distance error caused considering dB is about 1.2 mm. by an interference with The reconstructed velocity is obtained by directly differentiating (16) with respect to time , yielding (20) where . It is apparent that is time variant even when the sensor is moving at a constant velocity. denote the velocity estimation error, then Let we have

Fig. 5. Distance comparison between the simulated result and the closed-form result.

Substituting (14) into (13) and solving for

yields (15)

Recalling be expressed as

, the distance estimation error

can

(21) increases with the velocity . In other According to (21), words, an uncalibrated interference could introduce a large velocity estimation error when the sensor is moving at high speed. for , implying interOn the other hand, we have ference has little impact on zero velocity sensing. Additionally, repeats itself as the sensor moves every it can be found that half wavelength distance. This phenomena has been observed in our experimental results in Sections IV-A and IV-C. D. System With Both Interference and Noise

(16) We thus establish the relationship between the SIR and distance error in a closed form. Fig. 5 illustrates how the distance changes with respect to the distance reconstruction error in wavelength. The closed-form results and the simulated results are calculated using (16) and (6), respectively, with a frequency of 6.7 GHz. As shown in Fig. 5, the closed-form results agree well with the simulated results, implying our derivation in (16) is correct. varies periodically with Another observation in Fig. 5 is that . The magnitude of the variation distance with a period of increases as the value of the SIR decreases from 10 to 4 in is dB. The relationship between the SIR and the maximum given below. occur when In (16), vertices of (17) with a maximum value of (18) If the SIR is large, (18) can be simplified by the small angle approximation as (19) Equation (19) gives an estimate of how the distance accuracy is affected by an uncalibrated interference. As a quick example,

When both interferences and noise are present in the system, the distance estimation error is the summation of the individual errors caused by noise and the interference (22)

III. SYSTEM PROTOTYPING To prove the concept, a TRV sensor prototype has been built using COTS components, as shown in Fig. 6. A Mini-Circuits ZX95-6740C voltage-controlled oscillator (VCO) is used as the signal source. A potentiometer is added into the system to provide a tuning voltage for the VCO according to the antenna resonant frequency. A high system frequency is desirable since higher frequencies allow the design of smaller antennas and also provides better position resolution. The working frequency of 6.7 GHz chosen in our prototype is a balance between the antenna size and commercially available components. The two mixers, quadrature hybrid, and 0 power splitter shown in Fig. 1 are integrated and implemented with a single-chip Hittite monolithic microwave integrated circuit (MMIC) I/Q mixer module (HMC520LC4) (labeled “mixers” in Fig. 6). All the components are mounted in an 8.7 6.3 2 in aluminum box. Power consumption of this TRV prototype is about 1 W. The antenna design is a critical part of the shoe-based RF motion sensor. This application requires the antennas to be both small and have low mutual coupling between transmit and receive antennas. This mutual coupling will contribute to the dc offset during direct conversion and is thus undesirable. To make

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Fig. 6. RF motion sensor based on COTS components.

Fig. 8. RF motion sensor characterization: experimental setup.

Fig. 7. Measured S -parameters of the circularly polarized patch antenna.

the antenna small in size and embeddable in a shoe, a patch antenna topology was chosen with both transmit and receive antennas on the same substrate. This patch topology presents a challenge in that the substrate can allow surface waves to propagate between antennas increasing mutual coupling. To mitigate this effect, circularly polarized square patch antennas were used with opposing circular polarizations. In theory, this should cancel all mutual coupling of the antennas, only allowing the receive antenna to detect radiation reflected off the ground. The circularly polarized patch antenna for the TRV sensor was fabricated using an FR4 1.6-mm substrate with a size of 7.1 3.1 cm. The measured -parameters of the antenna in Fig. 7 show that it resonates at the design frequency of 6.7 GHz and has 38.6 dB of isolation between the antennas. IV. PERFORMANCE EVALUATION A. Motion Test With Stepper Motor The experimental setup used to evaluate the TRV sensor prototype is shown in Fig. 8. A stepper motor is used to control the motion of the sensor. The position and velocity of the sensor can be computed based on the motion commands sent to the stepper motor, providing a “ground truth” reference for the performance of the sensor. The antenna plate is mounted on the carriage of the stepper motor. Two long (7 ft) RF cables are used to connect

the Tx/Rx antennas with the TRV box. An op-amp is used to amplify the dc signals output from the TRV box. The data is sampled and collected by a National Instruments data acquisition (DAQ) system (NI-USB-6009) with a resolution of 14 bits. Both the DAQ and stepper motor are controlled by a laptop through Labview. For the measurements reported in this section, motion of the stepper motor was programmed in the following way: 1) stationary (1 s); 2) constant velocity forward 0.1016 m (4 in); 3) stationary (400 ms); 4) constant velocity forward 0.1016 m (4 in); 5) stationary (400 ms); 6) constant velocity forward 0.0127 m (0.5 in); 7) stationary (10 s); 8) constant velocity backward 0.0127 m (0.5 in); 9) stationary (400 ms); 10) constant velocity backward 0.1016 m (4 in); 11) stationary (400 ms); 12) constant velocity backward 0.1016 m (4 in); 13) stationary (1 s). The velocity of the stepper motor was set as 0.03175 m/s in/s . The (1.25 in/s) and the acceleration was 0.0508 m/s initial position of the sensor was measured as m m. and the antenna separation was The dc voltages collected from the I and Q channels are have been reshown in Fig. 9. The major dc offsets in moved by prior calibration. Fig. 9(a) shows the overall for the whole motion process given in Section IV-A. To better observe the waveform shape, voltages corresponding to the first 4 s of motion are shown in Fig. 9(b) on an expanded scale. vary with a sinusoidal From Fig. 9(b), it is apparent that pattern when the sensor is moving and are constant when the sensor is static. The distance between the antenna plate and the “ground” can through (6) and be reconstructed based on the measured (3). The position ground truth is computed based on the motion commands given in Section IV-A. As shown in Fig. 10, the reconstructed distance curve agrees well with the computed ground truth. The maximum disagreement between the reconstructed position and the ground truth is about 1 mm. The major . It cause for this disagreement is the residual dc offset in is found in our experiment that dc offsets in the two channels

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Fig. 11. Reconstructed velocity and detected zero velocity periods.

B. Stability Test Fig. 9. V output from the TRV sensor. (a) Overall V during the motion given in Section IV-A. (b) Zoomed-in version of the two voltage waveforms for the first 4 s.

Fig. 10. Reconstructed position based on V

given in Fig. 9.

change slightly with the distance . In other words, the dc offsets cannot be completely removed by prior calibration. Fig. 11 shows the reconstructed velocity and detected zero velocity periods. Velocities are reconstructed based on the distances shown in Fig. 10 by (7) and (8). To remove the short-term variations caused by the electronic noise in the system, a simple arithmetic average (over 20 samples taken at a 1-kHz rate) has been applied. Ground truth for the velocity is obtained by directly differentiating the computed position ground truth with respect to time. As shown in Fig. 11, the reconstructed velocity curve agrees well with the computed ground truth, except on the part where the sensor is moving at a constant velocity. The reconstructed velocity curve shows a variation with an amplitude of about 20 mm/s when the sensor is moving at a constant velocity. This variation is caused by the residual dc offset after the calibration, as addressed in Section II-C. Zero velocity periods are identified by monitoring the change of the reconstructed distances.

With the same experimental setup given in Section IV-A, a stability test where antennas are set close to the reflector and remain static for 1 h was conducted. The motivation for the stability test is twofold: 1) to measure the distance sensing error due to electronic drifts over a long time period and 2) to characterize the system performance when the antenna is very close to the reflector, simulating a scenario when shoes are in contact with the ground. For the stability test, the velocity of the stepper motor was set to 25.4 mm/s (1 in/s) and the acceleration was in/s . The initial position of the sensor was 5.04 mm/s m. The motion of the stepper motor measured as was programmed in the following way: 1) stationary (1 s); 2) constant velocity forward 0.0762 m (3 in); 3) stationary (3600 s); 4) constant velocity backward 0.0762 m (3 in); 5) stationary (1 s). The dc voltages (with offset calibrated) collected from the I and Q channels over 1 h are shown in Fig. 12(a). The reis shown in Fig. 12(b). The constructed distance based on ground truth distance computed based on the motion commands sent to the stepper motor is also provided as a reference. As shown in Fig. 12(b), the reconstructed distance curve agrees well with the computed ground truth, implying our system still performs well when antennas are close to a concrete reflector. Fig. 12(c) gives a zoomed in version of Fig. 12(b). It can be observed from Fig. 12(c) that the distance drift caused by longtime operation over 1 h is less than 1 mm. C. Walking Test A preliminary walking-in-place test was conducted to demonstrate the functionality of the TRV sensor. Antennas were embedded in the heel of a boot, as shown in Fig. 13. Except antennas, the other components in Fig. 13 were placed on a nearby table. Again, two RF cables were used to connect the antenna and TRV box. For the experimental results reported here, the walking area was restricted by the limited length of the two cables and the motion of the foot is up and down only. The reflection interface is a typical flat concrete floor.

ZHOU et al.: LOW-POWER SHOE-EMBEDDED RADAR

Fig. 12. Long-term (1) position accuracy characterization of a TRV sensor. output from the TRV sensor. (b) Reconstructed distance based on mea(a) V in (a). (c) Zoomed-in version of (b). sured V

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Fig. 14. Experimental results of a walking test with a TRV sensor embedded output from the TRV sensor. (b) Reconstructed distance into the heel. (a) V relative to the ground. (c) Reconstructed velocity with respect to time as well as the detected zero velocity periods of the shoe. ZUPT = 1=0 represents zero velocity true/false.

V. CONCLUSION

Fig. 13. Experimental setup for walking test.

A novel concept to use a compact low-power radar to improve the accuracy of pedestrian inertial navigation was proposed and implemented. This paper has described the design, prototyping, and performance evaluation of the proposed radar. The experimental results show that the proposed radar is promising for sensing ZUPT and position, as well as velocity. Further hardware development includes reducing size and power by integrating all the components in the TRV box onto a small single circuit board. ACKNOWLEDGMENT

Fig. 14 shows the experimental results for the first three steps of a total of 100 steps. Fig. 14(a) shows the collected dc voltages during the walking, with dc offsets removed by prior calibration. Fig. 14(b) shows the reconstructed distance between the heel and ground. It can be clearly observed from Fig. 14(b) that the foot starts from a stationary phase with a zero distance and then experiences a motion phase where distance first increases and then decreases. The distance goes back to zero when the foot touches the ground and one step is accomplished. Again, the velocity estimation of the motion can be obtained based on detected distance by applying (8), and zero velocity periods can be identified by monitoring the variation of the reconstructed distance. The detected zero velocity periods and velocity are corresponds shown in Fig. 14(c). In Fig. 14(c), to zero velocity true/false.

The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory (AFRL), the Defense Advanced Research Projects Agency (DARPA) or the U.S. Government. This paper is approved for public release, distribution unlimited. REFERENCES [1] E. Foxlin, “Pedestrian tracking with shoe-mounted inertial sensors,” IEEE Comput. Graph. Appl., vol. 25, no. 6, pp. 38–46, Dec. 2005. [2] L. Ojeda and J. Borenstein, “Non-GPS navigation for security personnel and first responders,” J. Navigat., vol. 60, no. 3, pp. 391–407, Sep. 2007.

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[3] R. Stirling, “Development of a pedestrian navigation system using shoe mounted sensors,” Master’s thesis, Dept. Mech. Eng., Univ. Alberta, Edmonton, AB, Canada, 2003. [4] C. Fischer, K. Muthukrishnan, M. Hazas, and H. Gellersen, “Ultrasound-aided pedestrian dead reckoning for indoor navigation,” in Proc. 1st ACM Int. Mobile Entity Localization and Tracking in GPS-Less Environments Workshop, New York, NY, 2008, pp. 31–36. [5] C. Zhou, J. Downey, D. Stancil, and T. Mukherjee, “A compact positioning and velocity RF sensor for improved inertial navigation,” in IEEE MTT-S Int. Microw. Symp., Boston, MA, Jun. 2009, pp. 1421–1424. [6] C. Li, J. Cummings, J. Lam, E. Graves, and W. Wu, “Radar remote monitoring of vital signs,” IEEE Microw. Mag., vol. 10, no. 1, pp. 47–56, Jan. 2009. [7] A. Mashhour, W. Domino, and N. Beamish, “On the direct conversion receiver-A tutorial,” Microw. J., vol. 44, no. 6, pp. 114–128, Jun. 2001. [8] B. Razavi, “Design considerations for direct conversion receivers,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44, no. 6, pp. 428–435, Jun. 1997. [9] C. Zhou, J. Downey, D. Stancil, and T. Mukherjee, “Compact short range RF motion sensor for improved inertial navigation,” in Government Microcircuits Appl. Crit. Technol., Orlando, FL, Mar. 2009, pp. 53–56. [10] I. Gupta and A. Ksienski, “Effect of mutual coupling on the performance of adaptive arrays,” IEEE Trans. Antennas Propag., vol. AP-31, no. 5, pp. 785–791, Sep. 1983. [11] M. Skolnik, Introduction to Radar Systems. New York: McGrawHill, 1980.

Chenming Zhou (S’05–M’08) was born in Jiangxi, China, in 1979. He received the B.S. degree in physics from the Changsha University of Science and Technology, Changsha, China, in 2000, the M.S. degree in optics from the Beijing University of Technology, Beijing, China, in 2003, and the Ph.D degree in electrical engineering from Tennessee Technological University, Cookeville, in 2008. He is currently a Project Research Scientist with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA. His general research interests include wireless communications, signal processing, and RF system design.

James Downey (S’02) received the B.S.E.E degree from The University of Toledo, Toledo, OH, in 2005, the M.S. degree in electrical and computer engineering from Carnegie Mellon University, Pittsburgh, PA, in 2008, and is currently working toward the Ph.D. degree at Carnegie Mellon University. Mr. Downey is in the National Aeronautics and Space Administration (NASA) Co-Op Program and has been involved with optical measurements/diagnostics and extra-vehicular activity (EVA) navigation with the Langley Research Center and Glenn Research Center, respectively. His research interests include wireless communications, antennas, navigation, radar, and optical measurements.

Daniel Stancil (S’75–M’81–SM’91–F’04) received the B.S. degree in electrical engineering from Tennessee Technological University, Cookeville, in 1976, and the S.M., E.E., and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, in 1978, 1979, and 1981, respectively. In 2009, he returned to North Carolina State University, Raleigh, as Head of the Electrical and Computer Engineering Department, where he is also currently the Alcoa Distinguished Professor. From 1981 to 1986, he was an Assistant Professor of electrical and computer engineering with North Carolina State University. From 1986 to 2009, he was an Associate Professor and then Professor of electrical and computer engineering with Carnegie Mellon University. His research interests include wireless communications and applied electrodynamics. Dr. Stancil is a past president of the IEEE Magnetics Society.

Tamal Mukherjee (S’89–M’95) received the B.S., M.S., and Ph.D. degrees in electrical and computer engineering from Carnegie Mellon University, Pittsburgh, PA, in 1987, 1990, and 1995, respectively. His research interests include design techniques and methodologies at the boundary of analog, RF, MEMS, and microfluidic systems. He is currently a Professor with the Electrical and Computer Engineering Department, Carnegie Mellon University. His current research is focused on RF MEMS passive components and their insertion into RF circuits for both enhanced performance and to achieve frequency reconfigurability. He is also involved in the integration of MEMS inertial sensors with RF sensors for localization applications in GPS-denied environments.

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A 5.5-mW +9.4-dBm IIP3 1.8-dB NF CMOS LNA Employing Multiple Gated Transistors With Capacitance Desensitization Tae Hwan Jin and Tae Wook Kim, Senior Member, IEEE

Abstract—A capacitance desensitization technique is proposed for a multiple gated transistors amplifier with source degeneration to relax second-order distortion contribution to a third-order intermodulation distortion (IMD3), as well as an induced-gate noise contribution to noise figure. An extra capacitance, which is added between gate and source nodes of input transistors in a parallel manner, can desensitize the contribution of second-order harmonic feedback to IMD3. The capacitance is useful for optimizing noise figure, as well by controlling the input matching network quality factor ( ), which can desensitize the induced-gate noise contribution to noise figure. The low-noise amplifier is implemented with the proposed technique using 1P6M 0.18- m CMOS technology for 900-MHz code division multiple access (CDMA) receivers. It shows a third-order intercept point of 9.4 dBm and noise figure of 1.8 dB while consuming 5.5 mW at 1.5 V.

+

Index Terms—Harmonic feedback, linearity, low-noise amplifier (LNA), multiple gated transistors (MGTRs), third-order intercept point (IIP3).

I. INTRODUCTION

T

HE MAJOR parameters for RF circuits are noise figure and linearity [i.e., the third-order intercept point (IIP3)]. As CMOS scales, noise figure performance of the low-noise am(the equivalent noise plifier (LNA) improves with scaling of resistance of the LNA) [1]. However, linearity does not enjoy the benefit of scaling [1]. Thus, linearity optimization continues to be one of the major issues in deep-submicrometer CMOS RF circuit design. Several approaches have been proposed to enhance the linearity of CMOS amplifiers. The nonlinearity compensation method of transconductance is one of the most effective ways to improve linearity in practical applications [2]–[11]. Multiple gated transistors (MGTRs) uses an auxiliary transistor (AT), which is properly sized and biased to compensate for the third-order nonlinearity ( , the second derivative of transconductance) of transconductance of the main transistor (MT) [4], as shown in Fig. 1(a). Fig. 1(b) shows the cancellation Manuscript received October 07, 2009; revised June 07, 2010; accepted June 30, 2010. Date of publication September 02, 2010; date of current version October 13, 2010. This work was supported by the Mid-career Researcher Program through a National Research Foundation (NRF) Grant funded by the Ministry of Education, Science and Technology (MEST) (2010-0012315). The authors are with the School of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea (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.2010.2063790

Fig. 1. (a) Schematic diagram of MGTR. (b) Illustration of g cancellation using MGTR. (c) g of MT, AT, and composite transistor, The composite transistor has a higher and wider g than that of either the MT or AT.

process of the MGTR; a negative peak of of the MT can be linin a strong inversion region earized with the positive peak of the AT, the bias of which is mV toward a weak inversion region shifted by . The threshold voltage for both tranhas sistors is 0.52 V. Thus, the composite transistor

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a negligible value of in the range of 600–700 mV of . -linearized MGTR amplifier still suffers from However, the a second-order distortion combined with harmonic feedback, which limits IIP3 enhancement. , Although the MGTR amplifier effectively eliminates (the first derivative of it has a higher and wider value of transconductance) than that of the MT or AT, as shown in of both the strong and weak inversion Fig. 1(c). Since regions is positive, the composite transistor has a significant in the cancelled region of . value of When we apply a two-tone signal at an LNA input, by virtue of the second-order distortion, second-order intermodulation distortion (IMD2) appears at the output node and is then fed back to the input through feedback paths. That feedback component and one of the input signals again experience the and generate second-order distortion of transconductance third-order intermodulation distortion (IMD3) [2], [6]. The second-order interaction with feedback components occurs from two feedback paths in a common source (CS) topology. One is from gate-to-drain capacitance and the other is from gate-to-source capacitance. The gate-to-drain feedback is relaxed by employing a cascode topology, which improves isolation between the gate and drain node, as discussed in [2]. The gate-to-source feedback is compensated using properly chosen multiple inductors, which are implemented by an on-chip tapped inductor [6]. The multiple inductors are used to provide multiple source degeneration impedances. The multiple source degeneration inductances generate IMD3s with their own phases and magnitudes from their second-order interactions with the corresponding feedback components depending on the inductance values. The vector sum of the IMD3s from the second-order nonlinearity is then used to compensate the vector sum of the IMD3s from the third-order nonlinearity. The cascode topology applied in [2] tries to minimize the second-order contribution to IMD3 by reducing gate–drain feedback. In contrast, the multiple source degeneration method [6] tries to completely eliminate both the second- and third-order contributions to IMD3 using cancellation. However, the tapped inductor cannot be implemented with a bond-wire inductor, which is one of the convenient ways to provide source degeneration inductance without area and noise penalties. Source degeneration using bond-wire inductor is employed in many practical applications in academia as well as industry. The elimination of the IMD3 generated by the third-order distortion contribution with another properly designed second-order distortion contribution also makes the cancellation range narrow. There exist two cancellations in that technique: one is transconductance cancellation and the other is inductor cancellation. Thus, it is hard to maintain all cancellation conditions wide enough. As a result, the wide cancellation characteristic shown in [2] no longer exists in [6]. A more convenient method is proposed to relax the harmonic feedback effect in an MGTR amplifier by desensitizing the second-order contribution to IMD3 with the addition of an extra gate–source capacitance in parallel with the intrinsic gate–source capacitance (first presented in [12]), as shown in Fig. 2. The addition of an extra gate–source capacitance was originally proposed to desensitize noise and input matching

Fig. 2. Schematic of the proposed LNA.

issues from the input transistor size in a low-power LNA [13], [14]. There are other benefits to the extra gate–source capacitance, when it is combined with the MGTR. The gate–source capacitance converts second-order feedback current from source degeneration impedance to a corresponding voltage. Thus, the addition of extra gate–source capacitance can reduce the converted voltage of the second-order feedback component by reducing the gate–source impedance. Thus, it can relax the second-order distortion contribution to IMD3. The extra gate–source capacitance along with MGTR can relax not only second-order distortion contributions to IMD3, but also induced-gate noise influence, which aggravates noise performance in a MGTR amplifier. Reference [6] shows that a transistor in a weak inversion region generates greater induced-gate noise than a transistor in a strong inversion region because the induced-gate noise is inversely proportional to the drain current in a weak inversion region. The AT in the MGTR operates in a weak inversion region so the noise figure of the MGTR is higher than the conventional one. When we employ the extra gate–source capacitance, we can relax the induced-gate noise contribution to the noise figure by bringing down the input is expressed as follows [13] matching quality factor ( ). is replaced by the inductor for input power matching: when

(1)

where

(2) Thus, the extra gate–source capacitance effectively relaxes the second-order distortion contribution to IMD3, as well as the induced-gate noise contribution to the noise figure. The proposed technique is especially useful for a low-power LNA design in which a small size transistor is preferred to bring down current. The induced-gate noise issue is aggravated when the input transistor is small because it inevitably increases the input matching network [13].

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This paper is organized as follows. Following the introduction in Section I, Section II provides the linearity analysis of the extra capacitance with the MGTR. In Section III, a noise issue of the proposed method is analyzed. In Section IV, measurement results are presented. A conclusion follows in Section V. II. LINEARITY ANALYSIS In a high-frequency region, the IMD3 of a CS amplifier is composed of two parts: one from the third-order nonlinearity of and the other from a second-order intransconductance teraction combined with harmonic feedback. By applying the MGTR technique, we can minimize the third-order distortion contribution to IMD3, and then the second-order distortion contribution dominates IMD3 [2], [6]. Volterra series analysis provides good understanding of those behaviors. The drain current of the CS amplifier shown in Fig. 3 can be expressed as the following Volterra series:

(3) and (3a)–(3f), shown at the bottom of this page, where is the th-order complex coefficient with magnitude and phase in is the Laplace variable. is an Volterra expansion, and applied input voltage. The operator “ ” denotes “multiply the by the magnitude amplitude of each frequency component in of the corresponding coefficient and ” [6], shift its phase by the phase of [15]–[17]. with the fundamental response at The IIP3 at with a two-tone excitement is given by [6], [16]

(4) Thus, the term, denominator of (4), explains how IMD3 is generated by the CS amplifier.

Fig. 3. (a) Equivalent circuit of proposed LNA. (b) Visual explanation of second-order interaction with harmonic feedback.

The first term of the right-hand side in (3c) relates to the third-order distortion of transconductance, as you can see in (3c). The in the second term of the right-hand side in (3c) relates to a second-order interaction with harmonic feedback. In order to have more insight on the second-order contribution, we put the two-tone signal in . Note that the two signals . are close As shown in (3e), the second-order interaction mainly comes (in this case, ) and . The from of transconductance generates second-order nonlinearity and components. Those terms harmonic components are then applied in , which is explained by the and terms in (3e) and interact with one of the input signals by the second-order nonlinearity of transconductance. However,

(3a) (3b) (3c) (3d) (3e) (3f)

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terms that contain in (3e) have a trivial effect on IMD3 be. Thus, (3e) can be approximately rewritten as cause (5)

(5) Fig. 3(b) offers a visual explanation of the above process. This process can be summarized as follows. 1) The applied two-tone signal experiences a second-order and nonlinearity of transconductance and generates components at the drain output current. and components are fed back to the 2) The gate–source capacitance by voltage–current feedback. component is shorted to ground with its low Here, the . impedance of 3) The feedback component, , and one of the applied signals, , again experience the second-order nonlinearity of transconductance and generate IMD3 at the drain output current. to relax the Thus, it is important to bring down second-order distortion contribution to IMD3 [6]. One way to is to add an extra capacitance in parallel with reduce the gate–source capacitance. The denominator in (3d) contains term. Thus, if we add extra capacitance to the intrinsic a can be gate–source capacitance, as shown in Fig. 2, reduced. The extra capacitor, , is implemented using a metal–insulator–metal (MIM) capacitor. The IIP3 of the CS amplifier can be calculated from (4), and is is the intrinsic capacitance of and given by (6), where is the extra capacitor in parallel with [6]. Equation (6) also explains the effect of third- and second-order distortion of the denominator of (6) is neglicontribution to IMD3. cancellation in the MGTR, thus the second gible because of term, which contains of the denominator of (6) dominates is divided by the denominator of (6). The term containing term. Thus, the influence of to IIP3 is relaxed by the term. Thus, can relax the second-order distortion the contribution to IMD3

Fig. 4. IIP3 calculation and simulation result versus C and AT-off cases.

for both AT-on and

6

Fig. 5. IIP3 simulation result over bond-wire inductance variation ( 5% variation is assumed).

chosen for values in consideration of linearity, as well as noise figure, which we discuss in Section III. The proposed technique is insensitive to a bond-wire variation because the desensitizes linearity dependence on the bond-wire. Comparing with , it shows that the latter has much greater dominates (6). Thus, admittance than the former so the linearity is less sensitive to the variation of bond-wire inductance. Fig. 5 shows a simulation result of IIP3 dependence on bond-wire inductance. It shows that IIP3 is insensitive to the bond-wire variation. In our design, the bond-wire inductance is chosen to be 1 nH and the variation range is assumed to be 5%. III. NOISE ANALYSIS

(6) Fig. 4 shows a calculated IIP3 for various values, as well as a simulation result. For comparative purposes, both AT-on and AT-off cases are shown. As you can see in Fig. 4, when we , it will decrease the input matching network , and add then the voltage boosting from the input matching network will also also be decreased, which results in IIP3 improvement. of 2 pF, helps the MGTR to improve IIP3. When we add we can obtain as large as 10-dB IIP3 improvement. As expected values increases. 2 pF is from (6), IIP3 increases as the

A source degeneration LNA shows excellent noise-figure performance compared to other topologies such as common in Fig. 3 gate and resistive feedback [13]. The impedance can be replaced by the inductor for input power matching. The schematic for noise-figure analysis is given in Fig. 6. The input matching of Fig. 6 is shown in (1). The high- input matching network can effectively reduce channel thermal noise by amplifying input signals. However, high- matching network can also enhance induced-gate noise [13]. Thus, the optimization of an input matching network is important in LNA design. The optimization is especially difficult for a low-power LNA, which requires small input transistor. Since a small transistor has small gate–source capaci-

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where

(11)

Since the MT is biased in strong inversion, , the correlated portion can be ignored for simplicity for a noise-figure calculation [13]. Also, we can ignore the drain current noise of the AT and the induced-gate noise of MT because [13]. is obtained at resonance The noise figure

Fig. 6. Equivalent circuit of the LNA for noise-figure analysis.

tance, it then requires a high- input matching network. The high- input matching network allows the induced-gate noise to dominate the entire LNA noise. The extra capacitance can decouple the transistor size and input matching network [13], [14]. Thus, the extra capacitance is useful for a low-power LNA design. A transistor in the weak inversion region shows higher induced-gate noise than a strong inversion region transistor [6]. The MGTR amplifier employs a transistor in the weak inversion region as an AT to cancel the third-order nonlinearity of the main amplifier, which is biased in the strong inversion region. Thus, the input matching network should be lower than that of conventional LNA design. The extra capacitance introduced in Section II has another benefit to noise-figure optimization. It can relax the effect of enhanced induced-gate noise of the transistor in the weak inversion region by lowering the of the input matching network. The thermal noise of the drain current and an inducedare expressed with the following equations: gate noise

(12) where

(13) (14) and (12) can be re-expressed as follows:

(15) where

(7) (8) where is the Boltzmann’s constant, is the absolute temperais the ture, and are the bias-dependent noise coefficients, is the gate–oxide drain–source conductance at is the channel width, and is capacitance per unit area, the channel length. The induced-gate noise in a weak inversion region is expressed with the following equation:

(15a) (15b) (15c)

(9) (15d) is the drain saturation current and is the thermal voltage . Equation (9) shows that the induced-gate noise is inversely proportional to drain current and it aggravates noisefigure performance in the MGTR LNA. The uncorrelated portion of induced-gate noise from the drain current noise of the MT is given by [6]

(10)

Here,

due to

is the bulk is saturation velocity. and are the charge factor and bias-dependent noise coefficients for a short-channel field-effect transistor (FET). The long-channel values for in (7) and in (8) are 2/3 and 4/15, respectively [13], [18]. In short-channel cases, however, the values of and should be adjusted for a possible increase of our assumption due to short-channel effects.

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TABLE I PARAMETERS AND VALUES IN NOISE-FIGURE CALCULATION

Fig. 8. Noise figure and IIP3 versus input matching network

Fig. 7. Noise-figure calculation versus input matching network

Q.

The values of and are calculated from (15a)–(15c) and are given in Table I [19], [20]. In the noise-figure calculation, noise contribution from output resistance is neglected for simplicity. As expected, the higher input matching we use, the higher induced-gate noise is introduced, while higher decreases drain thermal noise with higher gain, as you can see in (15). Thus, the extra capacitance increases drain thermal noise contribution to noise figure and reduces gain by lowering , but it decreases induced-gated noise contribution to the noise figure. In the MGTR amplifier, input matching network should have a lower than that of a conventional amplifier because the induced-gate noise contribution is greater than that of the conventional amplifier. Fig. 7 shows the noise-figure calculation result. It shows the noise figure from the contribution of induced-gate noise only and noise figure from that of thermal noise only, as well as total noise figure. The BSIM3 model do not provide an induced-gate noise model. Thus, we try to optimize the noise figure using (15). The values of coefficients in the noise-figure calculation are shown in Table I. Even though the values are not obtained from direct measurement of 0.18- m CMOS technology, it is enough to give an optimization guideline for noise-figure design. Fig. 7 shows the noise-figure calculation result over the input matching network . The noise figure, which only increases, while considers induced-gate noise, increases as the noise figure that only considers drain thermal noise decreases as increases, thus there exists optimum , as shown has the lowest in the total noise figure. It shows that noise figure. In a conventional LNA design, the input matching

Q.

Fig. 9. Microphotograph of the proposed LNA.

network is selected around three for low-noise application in order to desensitize [13]. In this design, we choose the influence of induced-gate noise on the total noise perforin the MGTR amplifier, mance. It is plausible to select which has higher induced-gate noise contribution than that of brings the a conventional LNA. In our design, 2 pF of down to around 1 as shown in Fig. 4. Fig. 8 shows the noise is a good choice for figure and IIP3 versus . It shows both the IIP3 and noise figure. IV. DESIGN AND MEASUREMENT RESULTS The LNA is implemented with a 1P6M 0.18- m CMOS process. Fig. 9 shows a microphotograph of the LNA, which occupies a silicon area of 220 330 m excluding pads. It occupies a small silicon area because the source degeneration inductor is implemented with wire-bonding. External components are used for input and output matching, as shown in Fig. 2. A current-mirror-based bias circuit is employed to reduce the influence of process, voltage, and temperature (PVT) variation to IIP3 [2]. The MT operates in a strong inversion region, and the AT operates in a weak inversion region. The widths are 185 and 100 m, respectively. For comparative purposes, the AT can be turned off by applying zero voltage at the gate of the AT. Fig. 10(a) and (b) shows the measured IIP3 at maximum IMD3 reduction and that of AT-off LNA, respectively. IIP3 is measured by a two-tone test whose input frequencies are 900 and 901 MHz. The proposed LNA shows an IIP3 of 9.4 dBm while the AT-off LNA shows an IIP3 of 3.5 dBm. Fig. 11 shows IIP3 measurement versus AT bias, while MT bias is

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Fig. 12. IIP3 and gain measurement result versus frequency.

Fig. 10. IIP3 measurement result of the: (a) proposed LNA and (b) AT-off LNA. Fig. 13.

Fig. 11. IIP3 Measurement of the proposed amplifier versus AT bias.

fixed at 0.61 V. It shows maximum 6-dB IIP3 improvement over the AT bias. Fig. 12 shows IIP3 and gain over frequency at maximum IMD3 reduction. The discrepancy between the maximum IIP3 obtained in the simulation result in Fig. 4 and that of the measurement in modeling, Fig. 10(a) possibly originates from imperfect as discussed in [21]. Fig. 13 shows noise-figure measurement

S 11 and noise-figure measurement result of the proposed amplifier.

results, as well as input matching. The noise figure is 1.8 dB at 900 MHz and input matching is below 10 dB. The AT-off LNA shows similar noise figure (1.85 dB), which indicates that induced-gate noise contribution from the AT is quite relaxed. The reason why the AT-off LNA has a slightly worse noise figure is that the gain of the AT-off LNA is smaller than that of the AT-on LNA so noise from output resistance, which was neglected in our calculation, affects noise figure. Thus, even though the AT generates higher induced-gate noise, the AT-off LNA has a slightly worse noise figure. This also shows that effectively relaxes the contribution of induced-gate noise from the AT. There exists a slight discrepancy between our calculation and measurement result since the parameters used in the calculation such as and are not exact ones. Those values are not obtained from measurement, also layout parasitics such as interconnection loss and external components loss are not considered in the calculation. The performance summary of the proposed LNA and comparisons with other low-power LNAs are shown in Table II. Among the many LNAs, those having below about 20-mW power consumption are selected for comparison, and our result shows the highest figure of merit (F.O.M) among many low-power LNAs. F.O.M is defined by (16) where output third-order intercept

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low-power high-linearity LNA design, which needs a small size input transistor. Measurement results shows an IIP3 of 9.4 dBm, noise figure of 1.8 dB, and gain of 14.9 dB while consuming 5.5 mW at 1.5-V supply voltage.

TABLE II MEASUREMENT SUMMARY AND COMPARISON OF PROPOSED LNA WITH OTHER LOW-POWER LNAs

ACKNOWLEDGMENT The authors would like to thank H. G. Han, Yonsei University, Seoul, Korea, for useful discussions. REFERENCES [1] K.-R. Lee, I.-K. Nam, I.-J. Kwon, J.-H. Gil, K.-S. Han, S.-C. Park, and B.-I. Seo, “The impact of semiconductor technology scaling on CMOS RF and digital circuits for wireless application,” IEEE Trans. Electron. Devices, vol. 52, no. 7, pp. 1415–1422, Jul. 2005. [2] T. W. Kim, B.-K. Kim, and K.-R. Lee, “Highly linear receiver front-end adopting MOSFET transconductance linearization by multiple gated transistors,” IEEE J. Solid-State Circuits, vol. 39, no. 1, pp. 223–229, Jan. 2004. [3] D. Webster, J. Scott, and D. Haigh, “Control of circuit distortion by the derivative superposition method,” IEEE Microw. Guided Wave Lett., vol. 6, no. 3, pp. 123–125, Mar. 1996. [4] B. Kim, J. Ko, and K. Lee, “A new linearization technique for MOSFET RF amplifier using multiple gated transistors,” IEEE Microw. Guided Wave Lett., vol. 10, no. 9, pp. 371–373, Sep. 2000. [5] Y. Ding and R. Harjani, “A 18 dBm IIP3 LNA in 0.35 um CMOS,” in IEEE Int. Solid-State Circuits Conf., 2001, pp. 162–163. [6] V. Aparin and L. E. Larson, “Modified derivative superposition method for linearizing FET low-noise amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 2, pp. 571–581, Feb. 2005. [7] N.-S. Kim, V. Aparin, K. Barnett, and C. Persico, “A cellular-band CDMA 0.25-m CMOS LNA linearized using active post-distortion,” IEEE J. Solid-State Circuits, vol. 41, no. 7, pp. 1530–1534, Jul. 2006. [8] S. Lou, Howard, and C. Luong, “A linearization technique for RF receiver front-end using second-order-intermodulation injection,” IEEE J. Solid-State Circuits, vol. 43, no. 11, pp. 2404–2412, Nov. 2008. [9] T.-S. Kim, S.-K. Kim, J.-S. Park, and B.-S. Kim, “Post-linearization of differential CMOS low noise amplifier using cross-coupled FETs,” J. Semicond. Technol. Sci., vol. 8, no. 4, pp. 283–287, Dec. 2008. [10] K. Kwon, H.-T. Kim, and K. Lee, “A 50–300-MHz highly linear and low-noise CMOS Gm-C filter adopting multiple gated transistors for digital TV tuner ICs,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 2, pp. 306–313, Feb. 2009. [11] T. W. Kim and B.-K. Kim, “A 13-dB IIP3 improved low-power CMOS RF programmable gain amplifier using differential circuit transconductance linearization for various terrestrial mobile D-TV applications,” IEEE J. Solid-State Circuits, vol. 41, no. 4, pp. 945–953, Apr. 2006. [12] T.-H. Jin and T.-W. Kim, “A highly linear LNA employing transconductance non-linearity cancellation with the desensitization technique of harmonic feedback effect,” in 9th Int. Electron., Inform., Commun. Conf., Tashkent, Uzbekistan, Jun. 2008, pp. 464–467. [13] P. Andreani and H. Sjoland, “Noise optimization of an inductively degenerated CMOS low noise amplifier,” IEEE Trans. Circuits Syst. II, Analog, Digit. Signal Process., vol. 48, no. 9, pp. 835–841, Sep. 2001. [14] T. W. Kim and K.-R. Lee, “A simple and analytical design approach for input power matched on-chip CMOS LNA,” J. Semicond. Technol. Sci., vol. 2, no. 1, pp. 19–29, Mar. 2002. [15] H. Dogan and R. G. Meyer, “Intermodulation distortion in CMOS attenuators and switches,” IEEE J. Solid-State Circuits, vol. 42, no. 3, pp. 529–539, Mar. 2007. [16] S. A. Maas, Nonlinear Microwaves and RF Circuits, 2nd ed. Norwood, MA: Artech House, 1997, ch. 4, pp. 235–264. [17] T. W. Kim, “A common-gate amplifier with transconductance nonlinearity cancellation and its high-frequency analysis using the Volterra series,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 6, pp. 1461–1469, Jun. 2009. [18] A. van der Ziel, Noise in Solid State Devices and Circuits. New York: Wiley, 1986. [19] M. J. Deen, C.-H. Chen, S. Asgaran, G. A. Rezvani, J. Tao, and Y. Kiyota, “High-frequency noise of modern MOSFETs: Compact modeling and measurement issues,” IEEE Trans. Electron. Devices, vol. 53, no. 9, pp. 2062–2081, Sep. 2006. [20] Z. Li, J. Ma, Y. Ye, and M. Yu, “Compact channel noise models for deep-submicron MOSFETs,” IEEE Trans. Electron. Devices, vol. 56, no. 6, pp. 1300–1308, Jun. 2009.

+

point (OIP3) is the output-referred IIP3, is the power consumption and

is the noise figure,

mW mW

(16)

CDMA requirements for single-tone desensitization demand greater higher than 8 dBm of IIP3 for LNA [6], [7]. Our result of 9.4 dBm is enough for CDMA application. Our design target is to minimize the power consumption and noise figure, while maintaining the required IIP3. As shown in Table II, our result yields the lowest power consumption with a good noise figure while achieving the CDMA IIP3 requirement. V. CONCLUSION The capacitance desensitization technique is useful to relax a second-order distortion contribution to IMD3, as well as an induced-gate noise to noise figure in the source-degenerated MGTR amplifier. Volterra series analysis shows that extra capacitance in parallel with the intrinsic gate–source capacitance can reduce the second-order amplification of the second-order . Thus, it can maintain harmonic feedback component high linearity. Also, increased induced-gate noise in the MGTR amplifier because of AT in the weak inversion region is properly with controlled by controlling the input matching network the extra capacitance. The technique is especially useful for

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9.4-dBm IIP3 1.8-dB NF CMOS LNA

[21] I. Kwon and K. Lee, “An accurate behavioral model for RF MOSFET linearity analysis,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 12, pp. 897–899, Dec. 2007. [22] H.-J. Song, H.-J. Kim, K.-C. Han, J.-S. Choi, C.-J. Park, and B.-M. Kim, “A sub-2 dB NF dual-band CMOS LNA for CDMA/WCDMA applications,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 212–214, Mar. 2008. [23] G. Gramegna, A. Magazzù, C. Sclafani, M. Paparo, and P. Erratico, “A 9 mW, 900-MHz CMOS LNA with 1.05 dB-noise-figure,” in Proc. 26th Eur. Solid-State Circuits Conf., Stockholm, Sweden, Sep. 2000, pp. 73–76. [24] T.-S. Kim and B.-S. Kim, “Post-linearization of cascode CMOS low noise amplifier using folded PMOS IMD sinker,” IEEE Mircow. Wireless Compon. Lett., vol. 16, no. 4, pp. 182–184, Apr. 2006. [25] G. Gramegna, M. Paparo, P. G. Erratico, and P. De Vita, “A sub-1-dB NF 2.3-kV ESD-protected 900-MHz CMOS LNA,” IEEE J. SolidState Circuits, vol. 36, no. 7, pp. 1010–1017, Jul. 2001. [26] T. K. Nguyen, C.-H. Kim, G.-J. Ihm, M.-S. Yang, and S.-G. Lee, “CMOS low noise amplifier design optimization techniques,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 5, pp. 1433–1442, May 2004. [27] H. Darabi and A. A. Abidi, “A 4.5-mW 900-MHz CMOS receiver for wireless paging,” IEEE J. Solid-State Circuits, vol. 35, no. 8, pp. 1085–1096, Aug. 2000. [28] J.-S. Goo, H.-T. Ahn, D. J. Ladwing, Y. Zhiping, T.-H. Lee, and R. W. Dutton, “A noise optimization technique for integrated low-noise amplifiers,” IEEE J. Solid-State Circuits, vol. 37, no. 8, pp. 994–1002, Aug. 2002. [29] S.-H. Woo, W.-Y. Kim, C.-H. Lee, K.-T. Lim, and J. Laskar, “A 3.6 mW differential common-gate CMOS LNA with positive-negative feedback,” in IEEE Int. Solid-State Circuits Conf., Feb. 2009, pp. 218–220. [30] J. Borremans, P. Wambacq, C. Soens, Y. Rolain, and M. Kuijk, “Low-area active-feedback low-noise amplifier design in scaled digital CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 11, pp. 2422–2433, Nov. 2008.

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[31] W. H. Chen, G. Liu, B. Zdravko, and A. M. Niknejad, “A highly linear broadband CMOS LNA employing noise and distortion cancellation,” IEEE J. Solid-State Circuits, vol. 43, no. 5, pp. 1164–1176, May 2008.

Tae Hwan Jin was born in Seoul, Korea, in 1983. He received the B.S. degree in electronic engineering from Kwangwoon University, Seoul, Korea, in 2008, and is currently working toward the Ph.D. degree at Yonsei University, Seoul, Korea. His research interests are RF/analog circuits and systems for wireless application.

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Tae Wook Kim (S’02–M’06–SM’10) was born in Seoul, Korea, in 1974. He received the B.S. degree in electrical engineering from Yonsei University, Seoul, Korea, in 2000, and the M.S. and Ph.D. degrees from the Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, in 2002 and 2005, respectively. From July 2002 to December 2005, he was with Integrant Technology Inc. (now Analog Device), where he developed CDMA/PCS mixers and LNA and CMOS mobile TV tuner integrated circuits (ICs). From January 2006 to July 2007, he was with Qualcomm Inc., Austin, TX, where he was involved with DVB-H and Media forward link only (FLO) chip design. Since September 2007, he has been with the School of Electrical and Electronic Engineering, Yonsei University, where he is currently an Assistant Professor. His research interests are in microwave, RF, analog and mixed-signal ICs, and systems for wireless applications.

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A Jitter-Optimized Differential 40-Gbit/s Transimpedance Amplifier in SiGe BiCMOS Christian Knochenhauer, Stefan Hauptmann, J. Christoph Scheytt, and Frank Ellinger, Senior Member, IEEE

Abstract—This paper studies the jitter performance at the input of the transimpedance amplifier (TIA) in a communication system based on multimode optical fibers. A method is shown to analyze and effectively reduce data-dependent jitter by proper choice of the TIA input resistance and the use of multiple feedback techniques. A 40-Gbit/s TIA in 0.25- m BiCMOS with T of up to 180 GHz is presented to demonstrate the efficiency of the jitter analysis. It shows 6 k (75.5 dB ) transimpedance gain, 37.6-GHz bandwidth, open eyes, and less than 0.6-ps root mean square jitter at 40 Gbit/s, as well as best-in-class power consumption and noise performance.





Index Terms—BiCMOS, deterministic jitter (DJ), opto-electronic integrated circuit, transimpedance amplifier (TIA).

Fig. 1. First-order model of TIA input node.

communications, however, signal levels are comparably high, and fiber dispersion is considerable, so that timing jitter becomes, next to noise, crucial for the bit error rate (BER) of the system. II. JITTER ANALYSIS AT THE TIA INPUT NODE

I. INTRODUCTION N LONG-HAUL fiber-optic communications, 40-Gbit/s systems are already introduced in the markets. Such systems use single-mode optical fibers to minimize dispersion, data-dependent jitter (DDJ), and inter-symbol interference (ISI). In addition, these fibers have a small diameter allowing for high package density and compact optical elements such as diodes with small electric parasitic capacitances. With multigigabit communications pushing into mass markets and short-range applications, cost reasons imply the use of multimode optical fibers at 850-nm wavelength for such communication systems. The main drawback of these multimode fibers is modal dispersion, which leads to timing jitter and ISI. Another consequence is that photodiodes need to be bigger, as the fiber diameter is typically ten times larger than in singlemode applications, leading to high parasitic capacitances. Both effects limit the speed of these communication systems. In traditional system dimensioning, the input impedance of the transimpedance amplifier (TIA) is chosen according to the photodiode capacitance so that the small-signal bandwidth -constant at the input node of (BW) corresponding to the the amplifier equals 70% of the bit frequency [1]. This is mainly the result of an ISI versus receiver noise tradeoff. In short-range

I

Manuscript received December 11, 2009; revised July 09, 2010; accepted July 14, 2010. Date of publication September 02, 2010; date of current version October 13, 2010. This work was supported in part by Deutsche Telekom Stiftung. C. Knochenhauer, S. Hauptmann, and F. Ellinger are with the Chair for Circuit Design and Network Theory, Technical University of Dresden, 01062 Dresden, Germany (e-mail: [email protected]; [email protected]; [email protected]). J. C. Scheytt is with the Circuit Design Department, IHP Technologies, 15236 Frankfurt (Oder), 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.2010.2063792

In this section, the analysis methodology is shown applying it to a simplistic first-order model of the TIA input node. Although not suitable for high-frequency optimization of the circuit, the analysis clearly shows that the conventional dimensioning fails as it yields to high jitter in the input current when the photodiode capacitance is high and the packaging is taken into account. This analysis methodology will be applied for high-frequency optimization of the TIA input in Section III. A. Packaging Model In order to minimize noise at the receiver input in an optical communication system, the photodiode is best directly connected to the TIA input. Regardless of the mounting technique, the connection always inserts a parasitic inductance into the circuit. For wire bonding, the bonding inductance can be estimated using the well-known and well-studied rule-of-thumb to be nH/mm

(1)

Together with the photodiode capacitance and the input , a first-order model of the input capacitance of the TIA denotes the sum of all can be created as shown in Fig. 1. capacitances at the input node, it is, however, mostly dominated by the parasitic pad capacitance. The effective TIA input current input is the part of the current going into the active part of the . It can be calculated TIA, modeled by the input resistance using from the photodiode current

(2) B. Calculation of DDJ A method of calculating the DDJ for arbitrary linear systems has been shown in [2]. It is based on calculating the time-domain

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response duration response

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of the system when excited by a single bit of the . It can be expressed in terms of the step as (3)

The step response is obtained by an inverse Laplace transfor, yielding mation of (2) multiplied by

(4) where denotes the roots of the expression in in the denominator of (2). The deterministic jitter at the output of the system, i.e., the jitter of the effective TIA input current, is determined by the perturbation method to be

Fig. 2. Dependence of jitter at TIA input on input resistance and photodiode capacitance. The arrows indicate the R value necessary for an input current BW of 27 GHz.

(5)

where

denotes the smallest positive value of that satisfies (6)

Although the method theoretically delivers an explicit solution for the DDJ, (6) can only be solved numerically for in most practical cases. Also, the expression for in (4) is bulky and does not deliver much practical insight. Therefore, to demonstrate the general jitter effects seen at the input of the TIA, (5) has been analyzed numerically using standard values for the parasitic packaging elements pH fF

(7)

Although actual values may vary from those values, they will be close to (7), as they are dependent on parasitics that do not depend on the IC technology used. Also, it can be shown that the general effect is not very sensitive to these values. C. Jitter Optimization for Varied Photodiode Capacitances The results of a DDJ calculation for different values of the TIA input resistance and the photodiode capacitance are shown in Fig. 2. It is evident that there is a that minimizes the input current jitter DDJ. This value is significantly different from the value that would follow out of a conventional BW-noise tradeoff, marked with the arrows in Fig. 2. Therefore, the two values need to be looked at separately in the following. Note that this optimum value regarding jitter cannot be calculated explicitly . It is also already visible either, as in (4) depends on that there is a considerable difference between the curves for low photodiode capacitance and that for high capacitance. The former are very flat, i.e., the jitter is very low within a broad range around the resistance value obtained using the conventional BW-noise tradeoff. For higher capacitances, DDJ

Fig. 3. Comparison of the input resistance optimizing jitter (solid line) and the input resistance yielding to the 27-GHz BW resulting from the conventional ISI-noise tradeoff (dashed line) depending on the photodiode capacitance.

rises rapidly if deviates from its jitter-optimum value underlining the importance of jitter optimization in these cases. A detailed comparison of these values is shown in Fig. 3. It reveals the principal difference between low-capacitance (single-mode) and high-capacitance (multimode) photodiodes. For single-mode diodes, the input resistance optimizing jitter is always below the one resulting in the 27-GHz BW from the conventional ISI-noise tradeoff, whereas for multimode diodes, the jitter optimum is above the conventional optimum. The question arising now is: which value to choose for the ? The classic tradeoff is between input TIA input resistance BW and noise—a low input impedance for a feedback amplifier increases BW, but also increases noise and possibly creates stability problems. The input impedance would always be chosen as low as necessary, but as high as possible. A comparison of the DDJ when the input resistance is chosen to yield to a BW of 27 GHz and the BW at the jitter optimum in Fig. 4 reveals that the classic approach is only valid for small input capacitances, i.e., single-mode photodiodes. The jitter at the ISI-noise tradeoff input resistance is then at acceptably low values around 1 ps. For high-capacitance multimode photodiodes, the jitter at the conventional ISI-noise tradeoff BW is very high, and in addition, very sensitive to capacitance variations. In contrast, the BW at the jitter optimum is lower than the classic 27 GHz for 40 Gbit/s. This translates in a higher signal rise time, which can be compensated for in later stages of the TIA, as will be shown

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Fig. 4. TIA input current jitter at the value for R required by the conventional ISI-noise tradeoff (solid line) and input current BW at the jitter-optimal value for R . The grey dashed line marks the BW resulting of the ISI-noise tradeoff for 40 Gbit/s.

in Section VI. Equalizing DDJ, however, requires considerable effort and power [3]. The preceding calculations for a very simple input node model have shown that the input resistance has to be chosen higher as suggested by the conventional ISI-noise tradeoff when a high-capacitance photodiode is used. This optimization yields to a smaller BW and less noise. In Section III, it will be shown how the frequency-dependent input impedance of a TIA can be optimized for minimal jitter and high BW by means of feedback. III. JITTER OPTIMIZATION OF THE TIA INPUT STAGE A. Input Stage Feedback The input stage of a TIA is typically composed of an amplifying part with a current output (such as a simple bipolar or field-effect transistors (FETs), as well as more complex configurations such as cascodes), resistive shunt feedback, and a load resistance, as shown in Fig. 5(a). With this topology, very few degrees of freedom remain for the circuit designer. The operating point of the input transistor of the transistor. is chosen to maximize the transit frequency mainly determines the transimpedance gain The resistance of the stage. It is practically fixed when the operating current is chosen by the requirement of the dc level at the input of the following stage. The only free value remaining is that of the . Lowering reduces the stage’s input feedback resistance impedance, and therefore enhances the BW at the input node. On the other hand, high gain and low noise require high values as is, together with the parasitic base resistance of the transistor, the main noise source in such a circuit. This tradeoff in the topology of Fig. 5(a) leaves no degree of freedom for jitter optimization. One approach to overcome this is the simultaneous use of multiple feedback principles. An evident option is series feedand back with a degenerated emitter resistance consisting of in parallel, as depicted in Fig. 5(b). These elements add a zero to the transfer function with [1] (8)

Fig. 5. (a) (left) Conventional shunt feedback TIA with (right) simple sample realization. (b) Proposed combined shunt and series feedback, (c) Generic second-order model of the input stage. The base–emitter resistance r is only significant for the input resistance.

Classically, the zero is set to cancel out the first pole of the transfer function, thus enhancing BW. It is also possible to use the zero for optimizing the transfer function for minimal jitter, as will be shown in the following. For this purpose, the amplifier in Fig. 5(b) is replaced by a generic model of input capacitance, and output current source, and parasitic path resistances . In addition, the capacitive load formed by the following stage is included, yielding to the equivalent circuit depicted in Fig. 5(c). It can be shown that this is the minimal model showing the principal BW and jitter behavior of stages composed of realistic transistors. As the TIA is implemented in BiCMOS, the notation of the model elements and the following calculations are based on a bipolar transistors. However, the simplicity of the model implies that all results are also valid for FET implementations, including CMOS and more complex structures like the TIA presented in Section V. Emitter degeneration also significantly influences the input impedance of the circuit. Using the small-signal equivalent of

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the input stage depicted in Fig. 5(b), its input impedance can be and a current gain by approximated for (9) with (10) where is the base–emitter resistance, and and are the base and emitter parasitic resistances, respectively. The for practical values of the other varivalue of (9) rises with ables. would Applying the traditional reasoning, a higher therefore shift the pole at the input created by the input resistance together with the input (and pad) capacitance to lower frequencies, limiting BW. This consideration, however, is not valid when the parasitic elements between the photodiode and TIA are taken into account. The external photodiode and pad and , the bondwire inductance , and capacitances and create four the internal load and emitter capacitance poles and one zero in the complex transimpedance function. The location of the zero can be well approximated by (8), but the four poles cannot be assigned to single nodes or elements, nor does their analytical expression deliver practical insight. Numerical calculations show three dominant poles, whose (when position in the complex -plane for different values of const.) is depicted in Fig. 6. It is clearly keeping , the complex pole pair is dominating, visible that, for creating an overshoot in the frequency domain. For rising, but , the complex pole pair then moves further away from low the origin, leading to higher BW. This effect is, in turn, partially compensated by the real pole that simultaneously moves , the real pole dominates toward lower frequencies. For high and limits the BW of the system considerably. The existence of an optimum is evident. This pole-shifting explains why emitter degeneration in a TIA input stage does not—in contrast to the intuitive estimation and traditional reasoning—necessarily limit the BW of the system, when all input-bound parasitic effects are taken into account. In and are well chosen, transimpedance BW can fact, if constant. Emitter degeneration be enhanced while keeping also significantly reduces the output jitter, as will be shown in the following. B. Jitter Analysis for Second-Order Transistor Model Given that the TIA input impedance is frequency dependent, the questions arise, whether calculation of the optimal input resistance value in Section II still holds, and if so, how to realize that input impedance. For the performance of high-speed integrated circuits, parasitic elements are the main limiting factor. In this case, the and are undebase and emitter parasitic resistances actually separates the internal sired and crucial for jitter. base node from the point of application of the feedback resis-constant at the internal base node can therefore tance. The introduces an undesired series not be decreased as desired. feedback, preventing the zero in the transfer function to be posicontains all collector-bound tioned exactly according to (8).

Fig. 6. Location of the three dominant poles in the transfer function of the stage in Fig. 5(c) connected to the parasitic network of Fig. 1 for different values of R (R kept constant at 600 ). The dots indicate the positions for R = f0; 5; 10; 15g , respectively.

parasitic capacitances of the transistor, as well as the input capacitance of the following stage. It is transferred to the input by as well, and therefore significantly influences jitter. If the circuit of Fig. 1 is connected to the input stage, the small-signal transimpedance of the stage can be determined by classical methods. With this expression, the output jitter can be calculated numerically using the method of Section II. Fig. 7(a) shows a contour plot of the output jitter as a function of and . The region with minimal jitter is well visible. For comand parison, the dashed line marks all combinations of that result in the optimal input resistance calculated in Section II (see Fig. 3). This line is very close to local minima of the output jitter indicating that the results of the calculation in Section II are still valid for real input stages. Also, it becomes evident that -axis, i.e., inthe global jitter minimum is not located on the and in the circuit does effectively reduce jitter troducing at the output. and , the BW of the stage remains one When choosing of the key targets. It also is a result of a small-signal analysis of the circuit in Fig. 5(c). The solid line in Fig. 7(a) connects pairs realizing a transimpedance BW of 27 GHz. all has been chosen so Along this curve, the emitter capacitance that corner frequency corresponding to the zero of (8) is always at 27 GHz. Due to the pole-shifting effect depicted in Fig. 6, can be kept nearly constant when increasing . The only is a slightly lower gain of the stage. drawback of increasing The output voltage DDJ can now be optimized along this line of constant output BW. The jitter along this line is shown in . Fig. 7(b). It shows a clear minimum at moderate values for For comparison, the total DDJ for a complete transistor model as

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Fig. 8. TIA transimpedance for different values of R . C is always adjusted parallel to R in order to keep the zero frequency constant. Inserting R does not change the transimpedance BW significantly, the effect of jitter reduction shown in Fig. 7 is therefore only due to the frequency-behavior of the TIA input impedance.

on

Fig. 7. Output jitter of the first TIA stage dependent on the feedback resistances. (a) Jitter contour plot, darker filling representing higher jitter. The thick R pairs resulting in an output voltage BW of solid line connects all R 27 GHz. The dashed line indicates pairs resulting in the optimal input resistance calculated in Section II (see Fig. 3). The dot marks the optimum used for the calculation in Section IV. (b) Output jitter for optimal input resistance. The simplified model is the one in Fig. 5(c), the complete model is that furnished with the technology design kit.

0

, or better a lower limit on ; noise and stability. As is together with , the main noise source in the circuit, it should be kept as high as possible. A noise analysis of the input too stage is given in Section IV. Furthermore, decreasing much can make the circuit unstable, which is to be absolutely avoided. The practical design approach would therefore be to determine the optimal input resistance first, then to choose and by solving (9) according to the tradeoff between jitter, noise, and stability. A complete optimization has to include all elements causing jitter and/or reduced rise times in the signal path. In addition to the already mentioned parasitic effects of the photodiode–TIA interconnection, the optical fiber and the electrooptical effects in the photodiode need to be modeled exactly. The equation equivalent to (4) then needs to be solved numerically. It is also possible to simulate the circuit with a complete pseudorandom 1 sequence in a transient simulabit sequence (PRBS) 2 tion. This may require less simulation time than the explicit approach. Experience shows that results obtained with both methods match very well, as shown in Fig. 7(b).

IV. NOISE ANALYSIS OF THE TIA INPUT STAGE furnished with the design kit is also drawn. While the absolute jitter values calculated using the two models differ, the optimum matches very well. value for The efficiency of the method is underlined by an analysis of the first stages transimpedance plotted in Fig. 8. The change is negligible, also in transimpedance BW when inserting the stage exhibits moderate overshoot for all values. The main effect of jitter compensation therefore is the optimization of the input impedance seen into the TIA for the given photodiode and input connection parasitics. This shows the validity of the calculation in Section II and that employing shunt and series feedback simultaneously in a TIA input stage can reduce DDJ significantly without impeding BW or noise, as will be shown in Section IV. C. Other Tradeoffs and Practical Design Approach Naturally, there are other design goals beside jitter for a TIA input stage. Two of those design goals impose an upper limit

A. Noise Model The TIA is designed to have a flat frequency characteristic up to its corner frequency. That is why a static noise model, as depicted in Fig. 9(a), predicts the TIA’s noise behavior accurately nearly up to the corner frequency. About this frequency, the gain drops, which leads to a higher input-referred noise level. The increased noise level can be accounted for by an efficient noise higher than the 3-dB BW [1]. BW being roughly a factor The noise model in Fig. 9(a) comprises the transistor internal , , , and , which model the noise sources , the base and thermal noise of the parasitic base resistor collector shot noise, as well as the thermal noise of the emitter . This resistor includes the parasitic emitter resistor resistor and the intentionally added resistor . The thermal noise and the resistor in the collector of the feedback resistor branch is modeled through the sources and .

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This corresponds to an equivalent circuit, as depicted in Fig. 9(c). The TIA is in practical application driven by a photodiode, which can be approximated as a current source. is without effect; only In this case, the voltage source superimposes a noise signal. Equations (11)–(15) give the transfer functions for every noise source in the circuit to an equivalent noise source at the input. If these transfer functions are arranged in a row vector

(16) the spectral noise power density of the equivalent input current can be calculated by [5] noise source

(17)

Fig. 9. Transformation of noise sources. (a) Noise model of the input stage. (b) Intermediate transformation step. (c) All sources transformed to the input.

The individual noise sources can be shifted through the network to form two equivalent noise sources at the input and the output, respectively, as depicted in Fig. 9(b), where

where the star denotes the complex conjugate of the vector entries and is the transpose operator. In general, the noise sources and are correlated. With operating frequencies approaching several 10% of the transition frequency, the influence of this correlation grows. However, most of the current circuit simulators and process design kits do not account for correlated base and collector noise. Since the TIA’s corner , the correlation will be frequency is significantly below neglected here too. Thus, only the main diagonal of the noise spectra matrix is different from zero. B. Calculation of the Transfer Function Vector

(11) (12) (13)

(14) In the final step, the two sources from the output can be transformed to the input by multiplication with the chain matrix [4]

(15)

Equation (17) allows to calculate the spectral noise power density of the equivalent input current noise source . This and of the TIA to be requires the chain matrix entries known. Since the circuit has two feedback loops, one current and one voltage feedback over , the equafeedback over tions for and become quite complex so that rather rough approximations are commonly done in early stages of the calculation. In the case discussed here, such approximations are not valid. This can be demonstrated by calculating the portion of that stems from . With (12)–(17), it can be written as

(18)

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The relative error differential of (18)

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

of

follows from the total

TABLE I CONTRIBUTION OF INDIVIDUAL NOISE SOURCES TO THE TOTAL EQUIVALENT INPUT CURRENT NOISE

(19)

For the given component values this correspond to

(20) An error of only 15% in would result in 70% error in . and have to be used Therefore, the exact solutions of to obtain representative results

(21) with

(22) With (12)–(15), (21), and (22), the transfer function vector can be written

mS mS mS (23) C. Influence of Table I summarizes the individual noise sources’ contributions to the total equivalent input current noise for and . This corresponds to the jitter optimum with a transimpedance BW of 27 GHz, as depicted in Fig. 7(a). The dissipated power heats the transistor and its surrounding compoK. It is remarkable that the feedback resistor nents to is the most significant noise contributor. itself only has a minor effect on the total noise level; however, it can be seen from (23) that it also influences the transfer function vector leading to different input-referred noise values. Furthermore, as , the BW must be discussed in Section III-B, when changing kept above 27 GHz by adjusting and at the same time. values in terms of noise To study the effect of different and for a conperformance, the dependence between stant BW of 27 GHz, as depicted in Fig. 7(a), has been apis proximated by a third-order polynomial. Furthermore,

Fig. 10. Contribution of individual noise sources to the total equivalent input current noise.

adjusted according to (8). The resulting noise contributions of the individual noise sources to the total input-referred noise are depicted in Fig. 10. From this graph, it becomes obvious that and decreasing accordingly to preserve the increasing BW increases noise levels slightly, which is mainly due to the reduced transimpedance. The total input-referred noise current A Hz to 4.8 10 A Hz density increases from 4.6 10 or only 3% when is changed from 0 to 5 . In the discussed example, the noise deterioration is therefore negligible, but in general, one has to keep in mind that changes of the feedback network can have a significant effect on the circuits noise behavior. V. TIA IMPLEMENTATION A TIA for 40-Gbit/s optical communication systems was designed in order to demonstrate the efficiency of the above methods. The schematic is shown in Fig. 11. The input stage is that depicted in Fig. 5(b), where the amplifier is composed of , , and in order to enhance the BW three transistors and reduces of the stage. The cascode configuration of the Miller effect of ’s base–collector capacitance. acts as emitter follower and reduces the effective capacitance at ’s collector node. The feedback resistance is connected the and the emitter of in order to between the base of minimize its dc current.

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Fig. 11. TIA schematic.

Despite the two additional transistors, the results of the caland do not conculation in Section III remain valid, as tribute to the gain of the stage due to their configuration. They mainly reduce the effect of parasitic capacitances, a posteriori justifying the approximations done in Section III. is very large and is only shifting the dc The transistor level of the input stage up in order to leave sufficient voltage headroom for the following stage’s current sources. The feeda TIA so back resistor between collector and base makes that the dc voltage at the emitter of the input transistor , and thus its operating current, can be conveniently adjusted by the . All other diodes are realized as transistor diodes current and used to lower the collector–emitter voltages of the transistors acting as current sources. The dc level for the single-ended to differential conversion is obtained using a dummy stage identical to the input stage, but an adjustable current source is connected to its input. This current source can then be used to compensate input dc (photo) currents and adjust crossing point at the output of the TIA. The dummy stage is laid out identically to the input stage and positioned right next to it. Although this dummy stage consumes considerable power, this solution does not degrade the BW and enables a good output symmetry with advantages regarding process and temperature variations. Cascode configurations were used instead of differential pairs in order to decrease the negative effects of the collector–base capacitances on the BW. Inductive peaking was used in the last two stages for enhancing BW. Peaking in the output stage has been reduced to a minimum as higher peaking also deteriorates high-frequency output matching. The complete design was optimized for a system implementation. 3-D electromagnetic (EM) models were created for the direct bonding connection to the photodiode at the input, as well as for the output connection including bondwires. The input stage was designed based on the method described in Section II. The output stage was optimized for BW and output matching at the

Fig. 12. TIA chip micrograph.

housing connectors. Testing was done on-wafer in order to evaluate the circuit performance isolated from packaging influences. VI. MEASUREMENT RESULTS The circuit was fabricated in a 0.25- m SiGe BiCMOS technology with of 180 GHz. A chip micrograph is depicted in Fig. 12. The chips size is only 0.5 mm 1 mm, including all pads. A. Small Signal As a three-port system with two ports forming a differential output, the most suitable small-signal description of the TIA are mixed-mode -parameters [6]. They are calculated of the measured three-port parameters applying the method of [7] by

(24)

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Fig. 14. Measured total equivalent input referred noise current and spectral density. The dashed gray line marks the value calculated for the input stage in Section IV.

Fig. 13. On-wafer small-signal measurement results compared to simulation. (a) S -parameters. (b) Transimpedance gain and group delay. Simulations include an external capacitor for the input level shifting, which will be inserted in the application. Note that measured phase shift is below 2 at frequencies below 1 GHz so that group-delay measurements are very inaccurate at frequencies V .

50

(

)

(48) where, similar to the detection part, the factor of 2 comes from double sampling. The power required to drive the 16 16 lattice at all four sides for the 50-mV input amplitude is mW

(49)

The total detection power is the sum of the detector and the lattice power mA

Fig. 17. Time-domain simulation. Input sinusoid at 1.7 GHz (blue in online version) and the digital output (red in online version). All other parameters are the same as the constant input simulations we performed before.

the detector circuit. The corresponding spectrum of the digital output is plotted in Fig. 18.

V

(50)

Table I compares the proposed quantizer with other reported designs. The comparison is performed both with and without taking into account the analog memory. The reason is that the memory is not the essential part for the detection, and as soon as the output is quantized, the data can be stored in many ways. For example, time interleaving can be used to design a memory with a considerably lower sampling rate and power consumption. It is noteworthy that we do not have measurement results of this structure and the comparison might not be fair. As a result, we do not draw any conclusions beyond the fact that this structure shows great potential as a high-speed power-efficient quantizer. E. Effect of Noise and Phase Mismatch

D. Design Summary and Comparison We showed that with a 16 16 tapered lattice we can achieve at least 4 bits of linear quantization. The detector circuit’s response time combined with the lattice delay from (46) achieves

The main effects that can degrade the performance of the interferometric quantizer are thermal noise and phase mismatch between input sources. Thermal noise is caused by the source impedance and also the detector circuit, while phase mismatch

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TABLE I PERFORMANCE COMPARISON OF STATE-OF-THE-ART ADCs

between the inputs happen randomly mostly due to process variation across the substrate. To capture both of these effects, we model the th input source as

(51) where is the additive white Gaussian noise and is a random phase. For , we assume a Gaussian distribution with zero mean and variance of . From our analysis in Section II-C, the voltage of any node inside the 2-D lattice is a superposition of four input sources that are in the same column and row as that node. This is assuming that the phase mismatch between sources on one edge of the lattice is not large, and hence, the direction of the wave is not significantly changed. By applying the nonideal sources of (51) to (24), we can write the voltage of each node as

Fig. 19. Noise and mismatch limits for different values of SNDR. The lattice parameters are as specified in Section IV-D. The input V is assumed to be a sinusoid with an amplitude of 150 mV.

(52) where we have given indices to the independent noise and misrepresents the phase shift due to the match sources and and wave propagating along the lattice. Assuming that , we can simplify the superposition of the four nodes from (52) to

sources. We replace noise terms with noise power of mismatch terms with to get

and

(55) The SNDR can be calculated from (55) by taking into account the signal and noise powers (56) (53) The first term in (53) is the desired amplitude coming from (27), while the next two term are the effect of noise and phase mismatch, respectively. We now substitute (53) into (34) and , follow the same approximation to get the quantizer output shown in (54), at the bottom of this page. In order to find the signal to noise plus distortion ratio (SNDR), we calculate the output power by assuming independent noise and mismatch

Form (56), one can find the requirement on noise and phase mismatch for a particular SNDR. Fig. 19 shows the relation between these two noise sources for achieving a desired SNDR based on our analysis. V. CONCLUSION 2-D electrical lattices have been used in signal generation and processing. By engineering the lattice and changing its properties with an analog input, we can form various interference pat-

(54)

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terns that can be exploited for high-speed signal quantization. We described the theory of interference in 2-D lattices, pattern formation, and the effect of lattice tapering. Next, we designed and simulated a 4-bit 20-GS/s quantizer in a 65-nm CMOS technology. This is the first proposed quantizer in CMOS at this sampling rate without time interleaving. It also has a remarkably low power consumption as compared to conventional structures and shows potential in low power detection of very high-speed signals.

ACKNOWLEDGMENT The authors would like to thank O. Momeni, G. Li, W. Lee, M. Adnan, and R. K. Dokania, all with Cornell University, Ithaca, NY, for helpful discussions regarding various aspects of this work, and M. Azarmnia, for her support. The authors are also thankful to the TSMC University Shuttle Program for providing the device models.

REFERENCES [1] M. L. Psiaki, S. P. powell, H. Jung, and P. M. Kintner, “Design and practical implementation of multifrequancy RF front ends using direct RF sampling,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 10, pp. 3082–3089, Oct. 2005. [2] D. S. K. Pok, C. H. Chen, J. J. Schamus, C. T. Montgomery, and J. B. Y. Tsui, “Chip design for monobit receiver,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 12, pp. 2283–2295, Dec. 1997. [3] P. Schvan, J. Bach, C. Falt, P. Flemke, R. Gibbins, Y. Greshishchev, N. Ben-Hamida, D. Pollex, J. Sitch, S. Wang, and J. Wolczanski, “A 24 GS/s 6 b ADC in 90 nm CMOS,” Int. Solid-State Circuits Conf. Tech. Dig., pp. 544–545, Feb. 2008. [4] K. Poulton, R. Neff, B. Setterberg, B. Wuppermann, T. Kopley, R. Jewett, J. Pernillo, C. Tan, and A. Montijo, “A 20 GS/s 8 b ADC with 1 MB memory in 0.18 m CMOS,” Int. Solid-State Circuits Conf. Tech. Dig., pp. 318–319, Feb. 2003. [5] L. Y. Nathawad, R. Urata, B. A. Wooley, and D. A. B. Miller, “A 20 GHz bandwidth, 4 b photoconductive-sampling time-interleaved CMOS ADC,” Int. Solid-State Circuits Conf. Tech. Dig., pp. 320–496, Feb. 2003. [6] S. Shahramian, S. P. Voinigescu, and A. C. Carusone, “A 35-GS/s, 4-bit flash ADC with active data and clock distribution trees,” IEEE J. Solid-State Circuits, vol. 44, no. 6, pp. 1709–1720, Jun. 2009. [7] R. A. Kertis, J. S. Humble, M. A. Daun-Lindberg, R. A. Philpott, K. E. Fritz, D. J. Schwab, J. F. Prairie, B. K. Gilbert, and E. S. Daniel, “A 20 GS/s 5-bit BiCMOS dual-nyquist flash ADC with sampling capability up to 35 GS/s featuring offset corrected exclusive-or comparators,” IEEE J. Solid-State Circuits, vol. 44, no. 9, pp. 1709–1720, Sep. 2009. [8] J. Lee, P. Roux, T. koc, U. link, T. Link, Y. Baeyens, and Y. Chen, “A 5-b 10 G-sample/s A/D converter for 10-Gb/s optical receivers,” IEEE J. Solid-State Circuits, vol. 39, no. 10, pp. 1671–1679, Oct. 2009. [9] S. Krishnan, D. Scott, Z. Griffith, M. Urteaga, Y. Wei, N. Parthasarathy, and M. Rodwell, “An 8-GHz continous-time 6–1 analog–digital converter in an InP-based HBT technology,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 12, pp. 2555–2561, Dec. 2003. [10] F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time streach and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 7, pp. 1309–1314, Jul. 1999. [11] P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 10, pp. 1840–1852, Oct. 2001. [12] M. Jarrahi, R. Fabian, D. A. B. Miller, and T. Lee, “Optical spatial quantization for higher performance analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 9, pp. 2143–2150, Sep. 2008.

[13] Y. M. Tousi, G. Lee, A. Hassibi, and E. Afshari, “A 1 mW 4 b 1 GS/s delay-line based analog-to-digital converter,” Int. Circuits Syst. Soc. Tech. Dig., pp. 1121–1124, May 2009. [14] G. Li, Y. M. Tousi, A. Hassibi, and E. Afshari, “Delay-line based analog-to-digital converters,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 6, pp. 464–468, Jun. 2009. [15] P. B. Johns, “The solution of inhomogeneous waveguide problems using a trnasmission-line matrix,” IEEE Trans. Microw. Theory Tech., vol. MTT-22, no. 3, pp. 209–215, Mar. 1974. [16] W. J. R. Hoefer, “The transmission-line matrix method theory and applications,” IEEE Trans. Microw. Theory Tech., vol. MTT-33, no. 10, pp. 882–893, Oct. 1985. [17] H. S. Bhat and E. Afshari, “Nonlinear constructive interference in electrical lattices,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 77, no. 6, 2008, Art. ID 066602. [18] E. Afshari and A. Hajimiri, “Nonlinear transmission lines for pulse shaping in silicon,” IEEE J. Solid-State Circuits, vol. 40, no. 3, pp. 744–752, Mar. 2005. [19] E. Afshari, H. Bhat, X. Li, and A. Hajimiri, “Electrical funnel: A broadband signal combining method,” Int. Solid-State Circuits Conf. Tech. Dig., pp. 751–760, Feb. 2006. [20] E. Afshari, H. S. Bhat, A. Hajimiri, and J. E. Marsden, “Extremely wideband signal shaping using one- and two-dimentional nonuniform nonlinear transmisison lines,” J. Appl. Phys., vol. 99, no. 5, 2006, Art. ID 054901. [21] D. Sievenpiper, J. Schaffner, J. J. Lee, and S. Livingston, “A steerable leaky-wave antenna using a tunable impedance ground plane,” IEEE Antennas Wireless Propag. Lett., vol. 1, no. 1, pp. 179–182, 2002. [22] G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L–C loaded transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2702–2712, Dec. 2002. [23] G. V. Eleftheriades and O. F. Siddiqui, “Negative refraction and focusing in hyperbolic transmission-line periodic grids,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 396–403, Jan. 2005. [24] A. A. Houck, J. B. Brock, and I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s Law,” Phys. Rev. Lett., vol. 90, no. 13, pp. 137401–137404, Apr. 2003. [25] A. Sanada, C. Caloz, and T. Itoh, “Planar distributed structures with negative refractive index,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1252–1263, Apr. 2004. [26] E. Afshari, H. S. Bhat, and A. Hajimiri, “Ultrafast analog fourirer tranform using 2-D LC lattice,” IEEE Trans. Circuits Syst., vol. 55, pp. 2332–2343, Sep. 2008. [27] O. Momeni and E. Afshari, “Electrical prism: A high quality factor filter for millimeter-wave and terahertz frequancies,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 11, pp. 2790–2799, Nov. 2009. [28] T. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1998. [29] Y. Taur and T. H. Ning, Fundumentals of Modern VLSI Devices, 1st ed. Cambridge, U.K.: Cambridge Univ. Press, 1998. [30] J. G. Proakis, Digital Communications, 4th ed. New York: McGrawHill. [31] “Cadence Design Manual” Cadence, San Jose, CA, 2010. [Online]. Available: http://www.cadence.com/us/pages/default.aspx

Yahya M. Tousi (S’07) received the B.S. and M.S. degrees in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2004 and 2006, respectively, and is currently working toward the Ph.D. degree in electrical engineering at Cornell University, Ithaca, NY. His M.S. project concerned the design of a high-accuracy delta–sigma modulator. In 2007 he joined the Department of Electrical and Computer Engineering, Cornell University. During Summer 2010, he was with the Situne Corporation, where he was involved with RF front-ends for TV tuners. His research interests are RF design and high-speed mixed-signal circuits for applications in communication. Mr. Tousi was the recipient of a 2009 Jacob Fellowship.

TOUSI AND AFSHARI: 2-D ELECTRICAL INTERFEROMETER

Ehsan Afshari (S’98–M’07) was born in 1979. He received the B.Sc. degree in electronics engineering from the Sharif University of Technology, Tehran, Iran, in 2001, and the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, in 2003, and 2006, respectively. In August 2006, he joined the faculty of the Department of Electrical and Computer Engineering, Cornell University, Ithaca, NY. His research interests are high-speed and low-noise integrated circuits for applications in communication systems, sensing, and biomedical devices. Prof. Afshari was the chair of the IEEE Ithaca section and chair of Cornell Highly Integrated Physical Systems (CHIPS). He is a member of the Analog

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Signal Processing Technical Committee, IEEE Circuits and Systems Society. He was the recipient of the 2010 National Science Foundation CAREER Award, the 2010 Cornell College of Engineering Michael Tien Excellence in Teaching Award, the 2008 Defense Advanced Research Projects Agency (DARPA) Young Faculty Award, and Iran’s 2001 Best Engineering Student Award presented by the President of Iran. He was also the recipient of the Best Paper Award of the 2003 Custom Integrated Circuits Conference (CICC), and First Place at the 2005 Stanford–Berkeley–California Institute of Technology Inventors Challenge, the 1999 Best Undergraduate Paper Award in Iranian Conference on Electrical Engineering. He was also the recipient of the Silver Medal of the 1997 Physics Olympiad and the 2004 Award of Excellence in Engineering Education from the Association of Professors and Scholars of Iranian Heritage (APSIH).

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Optimized Design of a Highly Efficient Three-Stage Doherty PA Using Gate Adaptation Ildu Kim, Junghwan Moon, Seunghoon Jee, and Bumman Kim, Fellow, IEEE

Abstract—We demonstrate an optimized design of a highly efficient three-stage Doherty power amplifier (PA) for the 802.16e mobile world interoperability for microwave access (WiMAX) application at 2.655 GHz. The “three-stage” Doherty PA is the most efficient architecture among the various Doherty PAs for achieving a high peak to average power ratio (PAPR) signal. However, it has a problem in that the carrier PA has to maintain a saturated state with constant output power when the other peaking PAs are turned on. We solved the problem using a gate envelope tracking (ET) technique. For the proper load modulation, the gate biases of the peaking PAs were adaptively controlled, and the peak power and maximum efficiency characteristics along the backed-off output power region were successfully achieved. Using Agilent’s Advanced Design System and MATLAB simulations, the overall behavior of the three-stage Doherty PA with the ET technique employed was fully analyzed, and the optimum design procedure is suggested. For the WiMAX signal with a 7.8-dB PAPR, the measured drain efficiency of the proposed three-stage Doherty PA is 55.4% at an average output power of 42.54 dBm, which is an 8-dB backed-off output power. Digital predistortion was used to linearize the proposed PA. After linearization, a 33.15 dB relative constellation error performance was achieved, satisfying the system specifications. This is the best performance of any 2.655-GHz WiMAX application ever reported, and it clearly shows that the proposed three-stage Doherty PA is suitable as a highly efficient and linear transmitter. Index Terms—Efficiency, envelope tracking (ET), GaN, HEMT, linearity, peak to average power ratio (PAPR), power amplifier (PA), RF transmitter, three-stage Doherty PA, world interoperability for microwave access (WiMAX).

I. INTRODUCTION OR A modulation signal with a high peak to average power ratio (PAPR), the transmitter has to be operated in a backed-off average output power region to achieve an acceptable linearity and it has a low efficiency due to the backed-off operation. To achieve a high efficiency and high

F

Manuscript received February 12, 2010; revised June 22, 2010; accepted June 22, 2010. Date of publication August 30, 2010; date of current version October 13, 2010. This work was supported by The Ministry of Knowledge Economy (MKE), Korea, under the Information Technology Research Center (ITRC) support program supervised by the National IT Industry Promotion Agency (NIPA) (NIPA-2009-C1090-0902-0037) and World Class University (WCU) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (Project R31-2008-000-10100-0) and by the Brain Korea 21 Project in 2010. The authors are with the Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Gyeongbuk 790-784, Korea (e-mail: [email protected]; [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.2010.2063831

linearity at the same time, an architecture with efficiency enhancement and linearization techniques should be utilized. As a linearization technique, digital predistortion (DPD) is a powerful and reliable solution and is the most favored method for the linearization of base-station power amplifiers (PAs) [1]. As an efficiency enhancement technique, the hybrid envelope elimination and restoration/envelope tracking technique (H-EER/ET) and Doherty technique can be considered [2]–[8]. Theoretically, the H-EER/ET transmitter has an excellent efficiency and linearity along with a high output power capability. However, its performance is limited due to the difficulties in building a bias modulator with a high efficiency and a wide bandwidth. On the other hand, the Doherty technique is not an optimum architecture for the efficient amplification of a high PAPR signal because the nonoptimum efficiency region exists due to the unsaturated operation of the peaking PA [3], [10]. In spite of this imperfection, the Doherty PA delivers the highest efficiency because of the well-developed simple circuit method. Accordingly, the Doherty PA market has experienced a rapid growth in recent years [11]. Among the various Doherty PAs, the three-stage Doherty PA has a superior efficiency characteristic because it has three maximum efficiency points along the output power level. To implement the three-stage Doherty PA, the size ratio between each PA has to be properly chosen. Furthermore, the saturated operation of the carrier PA with a constant output power is essential for the proper load modulation, and the gallium–nitride high electron-mobility transistor (GaN HEMT) device is difficult to use for the implementation because of the Shottky turn-on problem [12]–[14]. Therefore, the three-stage Doherty PA that utilizes a GaN HEMT device has to employ a complex input power management circuit along the power level [13], and most three-stage Doherty PAs have been designed using LDMOSFET devices [14], [16]. Moreover, it is hard to implement the three-stage Doherty PA, which can simultaneously provide a uniform gain and a proper uneven power combining [13]. Recently, a new three-stage Doherty architecture with no saturated operation of carrier PA has been reported by the NXP Corporation, Nijmegen, The Netherlands [16]. This architecture utilizes a different output combining circuit while delivering the three maximum efficiency points compared to the previously reported three-stage Doherty PA. Since the output power of the carrier PA is increased along with the input power with no hard saturated operation of the carrier PA, the new three-stage Doherty PA can be designed using the GaN HEMT power device. A flat gain response can also be achieved due to the load modulation characteristic of the carrier PA. However, it still has poor load modulation because of the low gate biases of the peaking PAs.

0018-9480/$26.00 © 2010 IEEE

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TABLE I BACK-OFF LEVEL FOR PEAK EFFICIENCY POINT AND AVERAGE EFFICIENCY OF THE “ -WAY” AND THREE-STAGE DOHERTY PA FOR THE 802.16e MOBILE WiMAX SIGNAL WITH 8.5-dB PAPR

N

Fig. 1. Efficiency characteristics of various Doherty PAs versus the normalized output power.

For efficient operation at the backed-off output power region while maintaining peak power, we employed the envelope tracking (ET) technique to adaptively control the gate biases of the peaking PAs [14], which was demonstrated at the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) [15]. In this paper, we will analyze the detailed operation principles of the new three-stage Doherty PA and suggest the optimum design method for the 802.16e mobile WiMAX application with the gate-bias adaptation technique including the linearization of the PA. II. COMPARISON OF -WAY VERSUS PREVIOUS THREE-STAGE DOHERTY PA In Fig. 1, the efficiency curves versus the normalized output power of four types of three-stage Doherty PAs and two types of -way Doherty PAs are illustrated. As reported in many papers [3], [17], the “ -way” Doherty PA has two maximum efficiency points at the backed-off output power and peak power levels, respectively. The backed-off level with the first maximum effi1 [dB], is determined by selecting the size ciency, 20 of the peaking PA. On the other hand, the three-stage Doherty PA has three maximum efficiency points along the output power level [12]. The back-off levels with the two maximum efficiencies are determined by the size ratio of the two peaking PAs compared to the carrier PA, which is derived in the reference paper [13]. and are the input power back-off points on the normalized input voltage magnitude. To evaluate the average efficiency of each Doherty PA, a 802.16e mobile WiMAX signal with a 8.5-dB PAPR was used. The average drain efficiency can be calculated as follows [18]: (1) is the probability of occurrences of for the modulated input signal. In this equation, the overall DE is determined by the ratio of the product of the probability distribution and the power generation terms over that of the distribution and the dc power . The numerator of the above function (probability power) is called the power generation distri-

Fig. 2. Previous “1:2:2” three-stage Doherty PA. (a) Fundamental currents of each PA. (b) Output combining circuit.

bution (PGD) of the Doherty PA [6]. The distribution indicates the important power generation region of the Doherty operation, and the operation at that region determines the average efficiency. In Fig. 1, the PGD is also depicted, and the three-stage Doherty PA broadly maintains the high-efficiency characteristic at the important power generation region, whereas the -way Doherty PAs do not. In Table I, the calculated back-off levels for the peak efficiency points and average efficiencies of each Doherty PA for the WiMAX signal are presented. The three-stage Doherty PA has an improved efficiency of about 10% compared to the -way Doherty PA, showing that the three-stage Doherty PA is the most efficient architecture for amplification of a signal with a high PAPR. Fig. 2 shows the fundamental current profiles and the output combining circuit topology of the previously reported three-stage Doherty PA with a 1:2:2 size ratio between

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Fig. 3. Architecture of the proposed ET three-stage Doherty PA.

each PA [12], [13]. The topology is a parallel combination of one Doherty PA as a carrier PA with one additional peaking PA, and it is hard to implement the three-stage Doherty PA, which can provide a uniform gain and proper uneven power combining simultaneously. To maintain the flat gain profile versus the output power level, the high gain of the carrier PA due to the load modulation has to compensate for the input dividing loss. (In the case of the three-stage Doherty PA with a 1:2:2 size ratio, the load impedance of the carrier PA has to be modulated from to to compensate the input dividing loss.) However, 5 the three-stage Doherty PA cannot provide the proper load modulation for the carrier PA [13]. Accordingly, the gain at the low output power region where only the carrier PA is operating is lower than that of the Doherty PA at the peak output power. Moreover, as shown in Fig. 2(a), the carrier PA has to maintain the saturated state with the constant output power along 0.6 1 of the normalized input power level for the proper load modulation. This operation can cause the Shottky turn-on problem for the GaN HEMT device. Since the GaN HEMT power device is the favored device due to its high efficiency and power density, this problem is a serious limitation for the previously reported three-stage Doherty PA architecture. The NXP corporation has reported a new three-stage Doherty PA architecture [16], which is a parallel combination of one carrier PA and one Doherty PA used as a peaking PA. This architecture solves the problem of the saturated operation of the carrier PA. Accordingly, the GaN HEMT device can be used for the new three-stage Doherty PA. In addition, by using the uniform unit PA, a flat gain response becomes achievable because the high gain of the carrier PA is enough to compensate for the to input dividing circuit through proper load modulation ( 3 ). The load modulation of the new three-stage Doherty PA is analyzed in Section III. The remaining problem for the realization of the Doherty PA is the proper load modulation issue. The peaking PAs of the three-stage Doherty architecture are turned on one after another. Thus, the gate bias of the PA is much lower than that of the -way Doherty architecture, and the load modulation at the peak power region becomes very poor. In this situation, we can design for two cases. The first case is that of a

peak power and flat gain response (linear AM–AM) with a poor efficiency in the backed-off output power region. The other case involves a high efficiency in the backed-off output power level with insufficient peak power and gain flatness. However, neither of the options are optimum designs. To overcome this problem, we can employ the uneven input power drive technique [19], but it reduces the linear gain and is not enough to achieve high efficiency at the backed-off output power level and peak power at the same time. One other method is that a differently modulated signal is applied to each PA while the combined output can recover the original signal [13]. In this case, we need to regenerate the new input signal appropriate for the Doherty operation with three upconverters. The other alternative is a gate-bias adaptation of the peaking PAs [20], [21]. In this paper, we analyzed the operation principle of the optimized design using the gate-bias control of the peaking PA of the new three-stage Doherty PA for the efficiency improvement at the backed-off output power level and peak power at the same time[22]. The architecture of the proposed three-stage Doherty PA is shown in Fig. 3. III. ANALYSIS OF THE NEW THREE-STAGE DOHERTY PA A. Load Modulation Behavior at the Backed-Off Output Power Level In Fig. 4(a), the fundamental current profiles of the new three-stage Doherty PA are presented. The Doherty PA consists of symmetric unit cells, and all PAs are saturated at the maximum input power at the same time. To find the back-off levels with the maximum efficiency, the maximum output power and backed-off output power of the three-stage Doherty PA are derived as follows [13]: (2) (3) (4)

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TABLE II CALCULATED  AND  VERSUS THE INPUT POWER LEVEL

quarter-wave transformers in the circuit can be derived. The fundamental drain current ratios between the carrier and peaking PAs are defined as

(8)

(9) We assume that is the final output load impedance, and is the impedance transforming ratio of the three-stage the Doherty PA. If the characteristic impedances of each quarter, , and are assigned as , wave transformer, , and , respectively, the load impedances of each PA are derived as follows: (10)

Fig. 4. (a) Fundamental currents of each PA. (b) Output combiner of the new three-stage Doherty PA.

(11) where

(12) (13) In Table II, and are calculated based on the fundamental and of 0.5 and current profiles shown in Fig. 4(a) using 0.33, respectively. Thus, the load impedance variations of each PA at the backed-off output power can be determined as follows:

The backed-off output power can be written as (5) (6) Using (3)–(6),

and

(14)

are obtained as or

(7)

The three-stage Doherty PA can have two or three maximum efficiency points depending on the biases of the peaking PAs. It is selected that the three-stage Doherty PA has the maximum efficiency at the 9.54- and 6-dB backed-off output power and maximum peak power using the different biases of peaking PAs. In Fig. 4(b), the output combiner topology of the new three-stage Doherty PA is presented [13]. Using the active load–pull principle [10], the characteristic impedances of

(15)

(16)

If all of the PAs are matched to at the 1 of equations can be obtained from (14)–(16), and

, three and are

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ulation. For the exact modeling of the peaking PA operation, we used the fundamental and dc current components derived from the conduction angle versus the input voltage magnitude. The RF current waveform can be defined as [10], [14]

(20) is a quiescent bias current, and is the magnitude of the drain current of a given PA. For simplicity, we assume versus input voltage. The that all of the PAs have a constant final conduction angle versus input voltage magnitude can be derived as [14], [23]

where

(21) is an absolute amplitude of the drain current for , and it is proportional to the input the given input voltage, voltage. Therefore, the fundamental and dc currents of the carrier and two peaking PAs based on each conduction angle can be defined as follows:

(22)

(23) Fig. 5. Load-lines of the three-stage Doherty PA according to the input power levels. (a) Carrier PA. (b) Peaking PA 1. (c) Peaking PA 2.

calculated as a function of the parameter. Accordingly, each characteristic impedances can be summarized as follows:

(24) and

(17) (18) (19) The load modulation ratios of the carrier PA are , and the load modulation ratios of the peaking and , respectively, PA 1 and 2 are with increasing input power. In Fig. 5, the load-lines of each PA are dynamically presented.

(25)

B. Conduction Angle of Each PA Versus Input Voltage Magnitude To analyze the operation of the three-stage Doherty PA before and after the gate-bias adaptation, we conducted a MATLAB sim-

(26)

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(27) where

C. Efficiency of the Three-Stage Doherty PA axis, only the carrier In the region of 0 0.33 on the PA is operated, and the carrier and one peaking PA are operated in the region of 0.33 0.5. All of the PAs are turned on in the region of 0.5 1 on the axis. The ideal current source expression of the three-stage Doherty PA in the region of 0 0.33 is shown in Fig. 6(a). The load impedance at the carrier PA’s current source can be written as (28) The drain efficiency below the second back-off region can be calculated using the RF power and dc power as

Fig. 6. Ideal current source expression of the three-stage Doherty PA. (a) Second back-off region. (b) First back-off region. (c) Full power condition (black: turned on state, gray: turned off state).

(29) where

where

In Fig. 6(b), which shows the region of 0.33 0.5, the carrier PA and one peaking PA supply the fundamental currents to the load. The load impedances at the each current source can be calculated using the active load–pull principle [10]

(31)

In Fig. 6(c), which shows the region of 0.5 1, all of the current sources of the PAs supply the fundamental current to the load. The load impedances at each node can also be calculated in the same way

In the same way, the drain efficiency below the first back-off region can be calculated

(33)

(30)

(34) (35) (32)

(36)

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Fig. 7. Optimum gate-bias shapes for the peaking PAs versus the normalized input voltage.

The drain efficiency up to the full power state can be calculated using the RF power and dc power as

(37) where

D. MATLAB Simulation Results of the Three-Stage Doherty PA With and Without the Gate ET Operation For the simulation, the conduction angle of the carrier PA at , and those of the full power state was set to 180 the peaking PAs were set to 151.05 and to turn on the PAs above and 141.06 , respectively [14], to deliver the maximum efficiency of the carrier and peaking PA 1. The drain dc bias applied was 30 V. In Fig. 7, the optimum gate-bias shapes versus the normalized input voltage magnitude are illustrated, and the biases were increased from the class C mode to enhance the output power of each peaking PA as the input power level was increased. Fig. 8 illustrates the simulation results of the three-stage Doherty PA with and without the gate adaptation to the peaking PAs. Fig. 8(a) shows the simulated fundamental drain current increment of each PA [24]. Without the gate-bias adaptation, the fundamental drain currents of the peaking PA 1 and 2 did not reached 1 A (which is the maximum drain current of each PA) due to the low gate biases. Fig. 8(b) shows the fundamental drain voltage variation versus the normalized input voltage. As

Fig. 8. Simulation results of the “1:1:1” three-stage Doherty PA with and without the gate-bias adaptation (GA). (a) Fundamental drain currents. (b) Fundamental drain voltages. (c) Fundamental load impedances at the each current source. (d) Calculated  and  .

expected from Fig. 8(a), the drain voltage of the two peaking PAs do not reach 30 V. In particular, the fundamental current and voltage of the peaking PA 2 show significantly insufficient load modulation. The load impedance variation at each current source is presented in Fig. 8(c) and Table III. None of the PAs

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TABLE III LOAD IMPEDANCE VARIATIONS OF THE THREE-STAGE DOHERTY PA WITH AND WITHOUT THE GATE-BIAS ADAPTATION VERSUS THE INPUT POWER LEVEL

reached the required load impedances after 0.33 of the normalized input power level. The fundamental drain current ratios, and , had to be increased from 0 to 2 and from 0 to 1, respectively. The variations of and are shown in Fig. 8(d). The optimum gate biases help the fundamental current expansion of each peaking PA and are generated by monitoring the fundamental drain voltage and load impedance of each peaking PA because these parameters determine the efficiency and output power (or gain flatness) characteristic versus input 0.5 voltage level of the Doherty PA. In the region of 0.33 on the normalized input voltage axis, only the gate bias of the peaking PA 1 is increased. As the gate bias is increased, the fundamental drain voltage of the PA reaches 30 V, and the of the load impedance load impedance converges to 4 in Fig. 8(a) and (b). In the region of 0.5 1, both of the gate biases of the peaking PAs have to be adapted. After applying the gate-bias adaptation, all of the fundamental drain currents of the PAs reach the maximum magnitude, and the fundamental drain voltage of the carrier PA and peaking PA 1 remain near 30 V. The load impedances of all PAs also converge the 50 , and the proper load modulation behavior is clearly achieved within the overall input power level. and are also enhanced to 2 and 1, respectively. In Fig. 9(a), the simulated load-lines of each PA are illusof 30 V, for simplicity. trated, with only the left-side at a As shown in the figure, without the gate control, the peaking PAs do not reach the knee region because the fundamental drain voltages of the two peaking PAs do not reach 30 V. This operation causes a serious efficiency degradation of the two peaking PAs, and the overall efficiency of the Doherty PA is decreased at the backed-off output power region, as shown in Fig. 9(b). Therefore, the optimum gate bias have to be properly shaped such that the fundamental drain voltage of the carrier PA and peaking PA 1 remain at 30-V magnitude. In this simulation, for simplicity, the gate bias of the peaking PA 1 is determined such that the fundamental drain current of the PA is linearly increased. The gate bias of the peaking PA 2 is then optimally shaped based on the above criteria for the maximum efficiency of the Doherty PA. The improper load modulation reduces the peak power by about 3.54 dB. The simulated gain flatness versus output power level is depicted in Fig. 9(c). The calculated gain flatness is improved from 3.8 to 1 dB after applying the gate-bias control technique, indicating the more linear AM–AM response of the proposed PA. In Fig. 10, the calculated dc and RF powers of each PA and the overall three-stage Doherty PA are illustrated. By applying the gate-bias control technique, the RF power generation of the two peaking PAs is significantly enhanced, and the three-stage Doherty PA delivers the full power to the load. In Table IV, the

Fig. 9. Simulated: (a) fundamental load-line behavior, (b) efficiency characteristic, and (c) gain characteristic of the “1:1:1” three-stage Doherty PA with and without the gate-bias adaptation.

calculated performances of the three-stage Doherty PA with and without the gate-bias control technique are summarized for the WiMAX signal with 8.5-dB PAPR. The proposed Doherty PA shows enhanced efficiency together with an improved average output level. These simulation results clearly show the limitation on the load modulation behavior of the normal three-stage Doherty PA, and that this limitation can be removed by the gate-bias control technique. E. Output Impedance Consideration of the Peaking PAs A high output impedance of the peaking PA in the off state is essential; otherwise, the output power of the carrier PA can leak to the peaking PA, reducing the output power and efficiency [25]. For the new three-stage Doherty PA, the peaking PAs are connected to the output power combining node through

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Fig. 10. Simulated dc and RF power of each PA: (a) without and (b) with the gate-bias adaptation.

TABLE IV CALCULATED PERFORMANCE OF THE THREE-STAGE DOHERTY PA WITH AND WITHOUT THE GATE-BIAS ADAPTATION FOR THE 802.16e MOBILE WiMAX SIGNAL WITH 8.5-dB PAPR

the two quarter-wave transformers, as shown in Fig. 11(a). In at the output node is fact, the final output impedance determined by and as follows: (38) Thus, as the parameter becomes smaller, the final output becomes higher, and the leakage through the impedance peaking PA can be minimized. If the matching impedance of the peaking PA at the maximum output power is not matched to 50 , the final output impedance becomes: 50 , but to (39) Consequently, the final output impedance at the is inversely proportional to the two paramoutput node eters of and . However, if the matching impedance of the peaking PA is decreased, the output impedance of the peaking

Fig. 11. (a) Output circuit topology of the new three-stage Doherty PA. (b) Output impedance (R ) at the output combining node (V o) versus Y and  .

PA is also reduced because the characteristic impedance of the offset-line is also decreased. Therefore, a large reduction is not recommended. In this analysis, we assume that in 50 , which does the value ranges from 0.8 to 1 40 not affect the output impedance of the peaking PA . expansion from The simulated final output impedance is shown in Fig. 11(b). As shown in the figure, if the parameter up to all of the PAs are matched to 50 , a 0.75 causes the final output impedance to decrease, and it can disturb the proper load modulation. On the other hand, the selection of a small value can cause the linewidth problem of the quarter-wave transformer ( ) due to the high characteristic impedance. Therefore, the value has to be selected by considering the output impedance of the peaking PA and the linewidth of the quarter-wave transformer for a given substrate. In Table V, the implemented output combiner substrate is summarized. using TACONIC’s TLY-5 IV. IMPLEMENTATION AND MEASURED RESULTS As a unit cell of the Doherty PA, a class AB mode PA was designed at 2.655-GHz using Cree’s CGH40045 GaN HEMT device [22]. The quiescent bias current of the carrier PA is 55 mA, and the PA delivers 64.6% of the drain efficiency at an output power of 46.4 dBm. Under the quiescent bias point at the

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TABLE V OUTPUT COMBINING CIRCUIT DESIGN OF THE THREE-STAGE DOHERTY PA USING THE TLY-5 SUBSTRATE

deep class C mode, the offset-line length of the implemented PA was determined to achieve the proper Doherty operation. The measured phase offset was 72 , and the transformed output impedance was 1.4 k . A. Uneven Input Power Drive Method If the three-way input power dividing circuit, which has an equal dividing ratio, is used, the input power of each PA is 1/3 decreased about 4.77 dB than the total input power. Since the load of the carrier PA is initially 3 50 in the region of 0 0.33, the overall gain of the three-stage Doherty PA can be maintained the same with the unit PA under a 50- load impedance. However, the load of the carrier PA can be completely modulated and cause a serious gain degradation similarly to the three-way Doherty PA. To minimize the gain degradation, the input power dividing circuit has to be changed, more input power should be applied to the carrier PA than to the other PAs, and the carrier PA should reach its full power early under the 3 50 load condition. This input dividing method does not significantly affect the overall efficiency of the three-stage Doherty PA along the output power when the gate-bias adaptation is also used. In Fig. 12(a), the uneven input dividing circuit topology is shown. To adjust the input dividing ratio, a pi-attenuator was used. The attenuation level has to be selected by simultaneously monitoring the peak power of the three-stage Doherty PA and the gate current of the carrier PA, and the selected attenuation level was 1.7 dB. Here, we could employ an elaborate power divider without the lossy components. Fig. 12(b) shows the 1.5-dB gain improvement of the implemented three-stage Doherty PA with the input driving method. B. Measured Results of the Continuous Wave (CW) Signal Fig. 13 shows the measured optimum gate-bias control shapes versus input power level. A constant gate bias was applied to the carrier PA. The gate biases of the other PAs were initially maintained at deep class C modes for the turned-off operation. To minimize the gate voltage swing, which is relative to the size of the gate-bias modulator, the initial gate biases of the two peaking PAs were fixed to 6.7 and 9.5 V, respectively, along the output power level. Above each backed-off average output power level, the gate biases of the PAs were increased to the class AB mode to accelerate the load modulation. The measured results versus the output power level for a one-tone signal are summarized in Fig. 14. Fig. 14(a) shows the dc current profiles of each PA. By using the gate-bias adaptation, the peaking PA was properly turned on at the backed-off output power. Furthermore, the Shottky turn-on problem of the carrier PA was clearly eliminated. The measured efficiency performances are illustrated in Fig. 14(b). Above the second backed-off output

Fig. 12. (a) Uneven input power drive circuit. (b) Measured gain profiles of the proposed three-stage Doherty PA with even and uneven input power drive circuits for a one-tone signal.

power region, the proposed PA maintained an efficiency of 55% with 1.6 dB of gain flatness. The gain of the implemented three-stage Doherty PA could be increased by optimizing the unit PA for the gain under the modulated load impedance. In this experiment, the carrier PA was optimized to obtain a high efficiency under a 3 50 load impedance. C. Measured Results for the Modulation Signal Using the gate-bias shaping functions shown in Fig. 13, the ET signals for each peaking PA were generated by the MATLAB simulator. Agilent’s ESG4438C was used as a signal source and delivered the signals to the gate driver circuit, which was implemented as a noninverting type of gain amplifier using the TI’s THS3001 OP-Amp. To investigate the efficiency of the proposed three-stage Doherty PA versus the average output power, an 802.16e Mobile WiMAX signal with a 7.8-dB PAPR and a 10-MHz signal bandwidth was used. Fig. 15(a) shows the measured efficiencies of the ET three-stage Doherty PA with and without the gate-bias adaptation. As expected from the MATLAB simulation, the efficiency and gain of the three-stage Doherty PA with gate-bias adaptation were significantly improved at the backed-off average output power level. The implemented three-stage Doherty PA with gate-bias adaptation delivered a 56.9% drain efficiency at an average output power of 42.58 dBm, which was a 7.9-dB backed-off output power from the peak power level. The MATLAB simulation in Table IV did not consider the knee voltage of the PA, output matching, and combining loss. Furthermore, the carrier PA in the simulation was assumed to be a class B mode PA, which has a maximum

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Fig. 13. Gate-bias shapes versus input voltages used in the experiment.

Fig. 15. Measured performances of a three-stage Doherty PA with and without the gate-bias adaptation. (a) DE, gain, and PAE characteristics. (b) Upper and lower ACLRs.

Fig. 14. Measured CW characteristics of three-stage Doherty PA. (a) DC current profiles. (b) DE, power-added efficiency (PAE), and gain performances of the proposed three-stage Doherty PA. Fig. 16. Measured output spectra of the ET three-stage Doherty PA before and after the linearization.

efficiency of 78.5%. Thus, the simulated efficiency was higher than the measured efficiency. Fig. 15(b) presents the linearity of the proposed three-stage Doherty PA at 6.05- and 10.6-MHz offsets. Since the gate-bias control was optimized for the load modulation behavior to achieve maximum efficiency and peak power and not for the linearity, the adjacent channel leakage

ratios (ACLRs) are not good. Accordingly, the DPD technique is essential for the linearity specification. The measured relative constellation error (RCE) was 17.06 dB before linearization. To linearize the three-stage Doherty PA, the digital feedback

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Fig. 18. Measured signal constellation diagrams of the ET three-stage Doherty PA, (left) before and (right) after linearization.

successfully satisfying the system specifications. The performances of the 3GPP WCDMA and mobile WiMAX transmitter using GaN technology are summarized in Table VI, and the efficiency of our work is the state-of-the-art performance for the WiMAX application at 2.655 GHz. The constellation diagrams before and after the linearization are also presented in Fig. 18. These experimental results clearly show that the proposed three-stage Doherty PA with the ET technique has a superior efficiency with a high peak power, and it is suitable for use as a linear transmitter. V. CONCLUSIONS

Fig. 17. Measured AM–AM and AM–PM characteristics of the three-stage Doherty PA before and after linearization. (a) AM–AM. (b) AM–PM.

TABLE VI PERFORMANCE COMPARISON OF THE 3GPP WCDMA AND MOBILE WiMAX TRANSMITTER USING GaN TECHNOLOGY

predistortion (DFBPD) was applied to the RF input signal and the gate bias [1] to maximize the linearization. The measured output spectra before and after the linearization are presented in Fig. 16. By employing the DFBPD algorithm, the ACLR at the 6.05-MHz offset was linearized to 40 dBc. The measured AM–AM and AM–PM responses before and after the linearization are shown in Fig. 17, and a linear AM–AM and AM–PM response was successfully achieved. After the linearization, an efficiency of 55.45% was obtained at an average output power of 42.54 dBm, an 8-dB backed off output power from the peak power level, while maintaining a gain similar to that before linearization. The RCE was also enhanced to 33.15 dB,

In this paper, we have analyzed a new three-stage Doherty PA. It was verified through MATLAB simulation that the three-stage Doherty PA has the highest efficiency versus output power level among the various Doherty architectures, and its operation principles and optimum design method were clearly described. Furthermore, we have found that the three-stage Doherty PA has a serious improper load modulation problem, and by applying the gate-bias control technique, a proper load modulation can be achieved. The unit PA was designed using Cree’s CGH40045 GaN HEMT device at 2.655 GHz. In the experiment, the gate bias was adapted to achieve the maximally efficient Doherty operation. To enhance the gain along the output power, the uneven input dividing circuit was employed. After linearization, the proposed three-stage Doherty PA had an excellent efficiency of 55.4% at an average output power of 42.54 dBm, an 8-dB backed-off from the peak output power level. The RCE was 37.23 dB, satisfying the system specification. These results clearly show that the ET three-stage Doherty PA is a very powerful architecture for achieving a high efficiency, and the proposed gate-bias control method employing the ET technique is essential for obtaining the proper load modulation behavior. REFERENCES [1] Y. Woo, J. Kim, J. Yi, S. Hong, I. Kim, J. Moon, and B. Kim, “Adaptive digital feedback predistortion technique for linearizing power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 932–940, May 2007. [2] W. H. Doherty, “A new high efficiency power amplifier for modulated waves,” Proc. IRE, vol. 24, no. 9, pp. 1163–1182, Sep. 1936. [3] F. H. Raab, “Efficiency of Doherty RF power-amplifier systems,” IEEE Trans. Broadcast., vol. BC-33, no. 3, pp. 77–83, Sep. 1987. [4] I. Kim, J. Cha, S. Hong, J. Kim, Y. Yun, C. Park, and B. Kim, “Highly linear three-way Doherty amplifier with uneven power drive for repeater system,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 4, pp. 176–178, Apr. 2006.

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[5] F. Wang, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. Lie, P. M. Asbeck, and L. E. Larson, “An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4086–4099, Dec. 2006. [6] I. Kim, Y. Y. Woo, J. Kim, J. Moon, J. Kim, and B. Kim, “High-efficiency hybrid EER transmitter using optimized power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2582–2593, Nov. 2008. [7] D. F. Kimball, J. Jeong, C. Hsia, P. Draxler, S. Lanfranco, W. Nagy, K. Linthicum, L. E. Larson, and P. M. Asbeck, “High-efficiency envelopetracking W-CDMA base-station amplifier using GaN HFETs,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 11, pp. 3848–3856, Nov. 2006. [8] I. Kim, J. Kim, J. Moon, and B. Kim, “Optimized envelope shaping for hybrid EER transmitter of mobile WiMAX—Optimized ET operation,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 5, pp. 335–337, May 2009. [9] J. Choi, D. Kang, D. Kim, J. Park, and B. Kim, “Power amplifiers and transmitters for next generation mobile handset,” J. Semiconduct. Technol. Sci., vol. 9, no. 4, pp. 249–256, Dec. 2009. [10] S. C. Cripps, RF Power Amplifiers for Wireless Communications. Norwood, MA: Artech House, 2006. [11] H. Deguchi, N. Ui, K. Ebihara, K. Inoue, N. Yoshimura, and H. Takahashi, “A 33 W GaN HEMT Doherty amplifier with 55% drain efficiency for 2.6 GHz base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp. 1273–1276. [12] W. C. E. Neo, J. Qureshi, M. J. Pelk, J. R. Gajadharsing, and L. C. N. de Vreede, “A mixed-signal approach towards linear and efficient -way Doherty amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 866–879, May 2007. [13] M. J. Pelk, W. C. E. Neo, J. R. Gajadharsing, R. S. Pengelly, and L. C. N. de Vreede, “A high-efficiency 100-W GaN three-way Doherty amplifier for base-station applications,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 7, pp. 1582–1591, Jul. 2008. [14] I. Kim, J. Moon, S. Jee, J. Son, and B. Kim, “Highly efficient 3-stage Doherty power amplifier using gate bias adaption,” Int. J. Microw. Wireless Technol., unpublished. [15] I. Kim and B. Kim, “A 2.655 GHz 3-stage Doherty power amplifier using envelope tracking technique,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 1496–1499. [16] J. Gajadharsing, “Recent advances in Doherty amplifiers for wireless infrastructure,” in IEEE MTT-S Int. Microw. Symp. Workshop, Jun. 2009, WSC-2. [17] Y. Yang, J. Cha, B. Shin, and B. Kim, “A fully matched -way Doherty amplifier with optimized linearity,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 986–993, Mar. 2003. [18] G. Hanington, P.-F. Chen, P. M. Asbeck, and L. E. Larson, “Highefficiency power amplifier using dynamic power-supply voltage for CDMA applications,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 8, pp. 1471–1476, Aug. 1999. [19] J. Kim, J. Cha, I. Kim, and B. Kim, “Optimum operation of asymmetrical-cells-based linear Doherty power amplifiers-uneven power drive and power matching,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1802–1809, May 2005. [20] Y. Yang, J. Cha, B. Shin, and B. Kim, “A microwave Doherty amplifier employing envelope tracking technique for high efficiency and linearity,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 9, pp. 370–372, Sep. 2003. [21] J. Moon, J. Kim, I. Kim, J. Kim, and B. Kim, “A wideband envelope tracking Doherty amplifier for WiMAX systems,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 1, pp. 49–51, Jan. 2008. [22] B. Kim, I. Kim, and J. Kim, “Advanced Doherty architecture,” IEEE Microw. Mag., vol. 11, no. 5, pp. 72–86, Aug. 2010. [23] P. Colantonio, F. Giannini, R. Giofre, and L. Piazzon, “Theory and experimental results of a class F AB–C Doherty power amplifier,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 8, pp. 1936–1947, Aug. 2009. [24] K. J. I. Smith, K. W. Eccleston, P. T. Gough, and S. I. Mann, “The effect of FET soft turn-on on a Doherty amplifier,” Microw. Opt. Technol. Dig., vol. 50, no. 7, pp. 1861–1864, Jul. 2008. [25] Y. Yang, J. Yi, Y. Y. Woo, and B. Kim, “Optimum design for linearity and efficiency of microwave Doherty amplifier using a new load matching technique,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 20–36, Dec. 2001.

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Ildu Kim received the B.S. degree in electronics and information engineering from Chon-nam National University, Kwangju, Korea, in 2004, and the Ph.D. degree from the Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2010. His current research interests include highly linear and efficient RF PA design, linear power amplifier (LPA) system design, and highly linear and efficient RF transmitter architectures.

Junghwan Moon received the B.S. degree in electrical and computer engineering from the University of Seoul, Seoul, Korea, in 2006, and is currently working toward the Ph.D. degree at the Pohang University of Science and Technology (POSTECH), Pohang, Korea. His current research interests include highly linear and efficient RF PA design, memory-effect compensation techniques, DPD techniques, and wideband RF PA design. Mr. Moon was the recipient of the Highest Efficiency Award of the Student High-Efficiency Power Amplifier Design Competition, 2008 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS).

Seounghoon Jee received the B.S. degree in electronic and electrical engineering from Kyungpook National University, Daegu, Korea, in 2009, and is currently working toward the Ph.D. degree at the Pohang University of Science and Technology (POSTECH), Pohang, Korea. His current research interests include highly linear and efficient RF PA design.

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Bumman Kim (M’78–SM’97–F’07) received the Ph.D. degree in electrical engineering from Carnegie Mellon University, Pittsburgh, PA, in 1979. From 1978 to 1981, he was engaged in fiber-optic network component research with GTE Laboratories Inc. In 1981, he joined the Central Research Laboratories, Texas Instruments Incorporated, where he was involved in development of GaAs power field-effect transistors (FETs) and monolithic microwave integrated circuits (MMICs). He has developed a large-signal model of a power FET, dual-gate FETs for gain control, high-power distributed amplifiers, and various millimeter-wave MMICs. In 1989, he joined the Pohang University of Science and Technology (POSTECH), Pohang, Gyungbuk, Korea, where he is a POSTECH Fellow and a Namko Professor with the Department of Electrical Engineering, and Director of the Microwave Application Research Center, where he is involved in device and circuit technology for RF integrated circuits (RFICs). He has authored over 300 technical papers. Prof. Kim is a member of the Korean Academy of Science and Technology and the National Academy of Engineering of Korea. He was an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, a Distinguished Lecturer of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), and an Administrative Committee (AdCom) member.

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A Compact 0.1–14-GHz Ultra-Wideband Low-Noise Amplifier in 0.13-m CMOS Po-Yu Chang and Shawn S. H. Hsu, Member, IEEE

Abstract—A compact ultra-wideband low-noise amplifier (LNA) with a 12.4-dB maximum gain, a 2.7-dB minimum noise figure (NF), and a bandwidth over 0.1–14 GHz is realized in a 0.13- m CMOS technology. The circuit is basically an inductorless configuration using the resistive-feedback and current-reuse techniques for wideband and high-gain characteristics. It was found that a small inductor of only 0.4 nH can greatly improve the circuit performance, which enhances the bandwidth by 23%, and reduces the NF by 0.94 dB (at 10.6 GHz), while only consuming an additional area of 80 80 m2 . The LNA only occupies a core area of 0.031 mm2 , and consumes 14.4 mW from a 1.8-V supply. Index Terms—CMOS, current reuse, inductorless, low-noise amplifier (LNA), resistive feedback, ultra-wideband (UWB).

I. INTRODUCTION N RECENT years, for the demand of short-range (within 10 m) and high data-rate (up to 480 Mb/s) wireless communications, the standard of ultra-wideband (UWB) was set up by the Federal Communications Commission (FCC) in 2002. The FCC authorized the unlicensed 7.5-GHz band (3.1–10.6 GHz) for UWB applications. Motivated by implementing the transceivers with low cost and a high integration level, CMOS technology becomes the most attractive candidate. Owing to the rapid progress of CMOS technology, many studies of CMOS RF integrated circuits (RFICs) for UWB applications were published in succession with good results [1]–[6]. In an UWB receiver, the low-noise amplifier (LNA) with a wideband operation capability is critical to the overall receiver performance. The bandwidth of the LNA is ultimately limited by the parasitic capacitances of the devices. Two techniques for extending the bandwidth are commonly used to design UWB LNAs in CMOS technology, namely, the inductive peaking techniques [1]–[3] and the distributed amplifier (DA) topology [5]. LNAs based on the two techniques were both reported with adequate bandwidth for UWB applications. However, one drawback is that the design usually employs many spiral inductors, which occupy a large chip area.

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Recently, inductorless design for wideband LNAs in CMOS technology attracts much attention because of the considerably reduced chip area. Various approaches were proposed for wideband LNA design without using any inductors [7]–[12]. The noise-canceling technique was adopted [7]–[9], which sensed the dominant noise source and canceled it by an auxiliary out-ofphase forward path to lower the noise figure (NF). However, the phase error becomes difficult to predict, and the noise cancellation is not as effective at high frequencies. The resistive-feedback technique was also reported [10]–[12]. With a large enough input transconductance, the resistive-feedback LNA can achieve several gigahertz of bandwidth, over 10-dB gain, and less than 3-dB NF, but usually under a large bias current [10] or with a more advanced technology [12] needed. To lower the power consumption, the current-reuse technique is employed to enhance the input transconductance [11]. In this study, a compact UWB LNA in 0.13- m CMOS technology is proposed. Based on the concept of inductorless design, the amplifier includes a resistive-feedback configuration and a current-reuse input stage. One small inductor of only 0.4 nH is employed at the most critical node, namely, the gate of the input stage of the LNA to enhance the bandwidth and lower the NF simultaneously. Compared with the circuit without the inductor, the bandwidth is increased by 23% and the NF is reduced by 0.94 dB (at 10.6 GHz) with an additional area of only 80 80 m . The proposed LNA achieves a wide enough bandwidth to cover the whole 3.1–10.6-GHz frequency range, a 12.4-dB maximum gain, and a 2.7-dB minimum NF with a 0.031 mm core area under a 14.4-mW power consumption. This paper is organized as follows. Section II analyzes the design techniques in this study including resistive feedback and gate inductive peaking. Section III discusses the amplifier design in detail. Section IV presents the measured results. Finally, Section V concludes this study. II. TECHNIQUES OF UWB LNA DESIGN A. Resistive Feedback

Manuscript received January 21, 2010; revised June 17, 2010; accepted June 17, 2010. Date of publication August 30, 2010; date of current version October 13, 2010. This work was supported in part by National Tsing Hua University (NTHU)–Taiwan Semiconductor Manufacturing Company (TSMC) under a Joint-Development Project and by the National Science Council (NSC) under Contract NSC 96-2221-E-007-168-MY2, Contract NSC 96-2752-E-007-002PAE, and Contract 97-2221-E-007-107-MY3. The authors are with the Department of Electrical Engineering and Institute of Electronics Engineering, National Tsing Hua University, Hsinchu 300, Taiwan (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.2010.2063832

Feedback is a common technique to design wideband amplifiers. Shown in Fig. 1 is the common-source amplifier with a resistive feedback. In this configuration, the NF and input matching are generally a tradeoff [7], [12]. The tradeoff can be alleviated with a voltage buffer inserted in the feedback path, as shown in Fig. 2(a). Theoretically, the NF in this topology can be of the transistor lowered by increasing the transconductance [7], [12], and the matching condition can be maintained by deand the load appropriately. signing the feedback resistor A source follower is commonly used to implement the voltage

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Fig. 3. (a) Common-source amplifier with a gate inductor. (b) Small-signal model of (a). Fig. 1. Common-source amplifier with resistive feedback.

Equation (2) shows that this amplifier can be approximated as a single-pole system. The input impedance can also be calculated as

(3) Fig. 2. Resistive-feedback amplifiers with: (a) an ideal voltage buffer and (b) a source follower buffer in the feedback path.

buffer, as indicated in Fig. 2(b). The voltage gain of the amplifier in Fig. 2(b) can be derived as (1), shown at the bottom of is the transconductance of , is that this page, where for the buffer stage , and represents the equivalent input , and capacitance of the following stage. If and are with similar values, can be simplified as

For wideband applications, the low-frequency input impedance is designed to be ( in most cases) for input matching. As can be seen from (3), the frequency response of contains one zero and two poles. If the parasitic capacitances are small, the poles and zero will locate at high frequencies, and thus a wideband matching is possible. However, good input matching near the 3-dB frequency is not easy to be achieved in practical design [10], [11]. B. Inductive Peaking Fig. 3(a) shows a common-source stage with a gate inductor , and Fig. 3(b) is the corresponding small-signal model. The voltage signal at the gate can be expressed as

(2)

(4)

(1)

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Fig. 4. Resistive-feedback amplifier with a gate inductor connected to the input stage.

Fig. 5. Circuit schematic of the proposed compact UWB LNA.

Therefore, the output current induced by

is (5)

From (5), we obtain the equivalent transconductance of this configuration (6) Equation (6) indicates that increases with frequency when the operation is below the resonance of and . The inputreferred noise sources can be expressed as (7) and

Fig. 6. Simulated: (a) S , (b) S , and (c) NF with different L .

C. Resistive-Feedback LNA With Gate-Inductor Peaking (8)

where is the Boltzmann’s constant, is the absolute temperature, is the noise bandwidth, and is the thermal excess noise factor, which is 2/3 in a saturated long channel device [13]. Note that increases as the channel length scales down. Equation (7) indicates that decreases with frequency, while is not considered. Obtained it is independent of frequency if is identical to that without . As a result, the total from (8), input-referred noise can be suppressed at high frequencies with the gate inductor in a common-source topology.

Fig. 4 shows the resistive-feedback design through a source follower with the gate-inductor peaking [14]. The voltage gain in (2) with the equivalent can be calculated by replacing transconductance , as obtained in (6). Therefore,

(9)

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Fig. 8. Simulated inductance and Q of the gate inductor L .

Fig. 9. Chip micrograph of the proposed LNA.

Fig. 7. Simulated: (a) S , (b) S , and (c) NF with different L .

Since decreases with frequency, the gain reduction due to the pole can be compensated, and thus the bandand NF are width is enhanced. The analytical equations of rather complicated, do not provide intuitive guidance, and are not shown here. For the following analysis, Agilent Technologies’ Advanced Design System (ADS) is employed to provide quantitative explanation and also observe the tradeoffs between different design considerations such as NF, gain, and circuit stability. In practical design, the input impedance for wideband and of . For high matching is mainly determined by gain and low noise design, it is required to have a large input is preferred. However, a transconductance, and thus a large large is associated with large parasitic capacitances, which can degrade the matching and gain characteristics at high frequencies. For example, with a total channel width of 200 m

of 100 mA/V (under a drain (0.13- m NMOS) has a large of 300 fF. Note current of 10 mA), but also with a large that the effective gate–source capacitance would be even larger is too if considering the Miller effect. On the contrary, if small (associated with a small ), a large enough transconducis needed to have a suittance cannot be obtained, and a large able resonant frequency for bandwidth enhancement. It can be estimated that a relatively large peaking inductor of 0.8 nH based on the circuit topology in Fig. 4 is needed for a 60- m for the desired UWB applications. The size selection of plays a critical role in this configuration and more discussion will be carried out with the proposed topology. For noise considerations, the main noise contributor is the . Since an ideal feedback network has first-stage transistor no impact on the circuit noise performance [15], it is expected that the NF has a similar trend with that of the gate peaking design shown in Fig. 3(a), i.e., the inductor can suppress the high-frequency noise, as will be illustrated in Section III. III. DESIGN OF COMPACT UWB LNA A. Circuit Topology Fig. 5 shows the circuit schematic of the proposed compact UWB LNA, which includes a cascode amplifier with a current-reuse input stage, a source follower as the feedback buffer, a feedback resistor, a gate peaking inductor, and another

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Fig. 11. Measured NF.

Fig. 10. Measured S -parameters. (a) S

and S . (b) S

and S . Fig. 12. Measured IIP3 at 6 GHz.

source follower for the output buffer. The cascode amplifier , , and . The two includes three transistors, i.e., (NMOS) and (PMOS) are common-source transistors arranged as a current-reuse topology, and the transistor functions as the common-gate stage of the cascode topology. In the current-reuse design, the overall transconductance is the sum of both transistors. The enhanced transconductance allows high-gain performance under low power consumption. Note is only part of the current of , and that the bias current of is reduced, leading to increased output the voltage drop of headroom. In this configuration, the input transconductance stage ( and ) first converts the input voltage to a current signal, to the load as the output signal. which then flows through The amplified signal is also fed back to the input through the (source follower) and the feedback resistor feedback buffer . As described in Section II, is resonated with the gate and . As a result, the voltage signal at capacitances of , and thus the equivalent transconductance, the gate of both increase rapidly when the operation approaches the resonant frequency. and are critThe transistor size and bias condition of ical for achieving high gain and low noise in this design. For the is more important than since input transconductance, is an NMOS and also with a larger bias current than that of . The total width of transistor is chosen as 96 m to and have sufficient transconductance and low noise. Both

contribute to the gate capacitance of the input stage, and thus affect the resonant frequency for bandwidth extension. With the can not only enhance current-reuse design, the transistor the transconductance, but also provide the flexibility to optimize contributes the input equivalent capacitance. The transistor additional capacitance allowing a small gate peaking inductor while maintaining an appropriate resonant frequency for bandtransistor selected for this design has width extension. The a width of 64 m. B. Design of Gate Inductor The peaking inductor is determined by considering the resonant frequency with the combined input capacitance conand . The input capacitances of and tributed of can be extracted from the foundry provided device model to estimate the required value of . With a desired bandwidth up resonant frequency should be higher than to 10.6 GHz, the can be esthis frequency to ensure stable circuit operation. timated to be in the order of 0.3 0.4 nH to create a resonant 16 GHz. Fig. 6 shows the simulated frequency at about 14 , and NF versus frequency with different . Note that the results shown here are based on electromagnetic (EM) simulated spiral inductors for more precise prediction. The 3-dB circuit bandwidth is enhanced from 11.5 GHz (without any in23 with a gate inductor of 0.4 nH. ductor) to 14.2 GHz An improved input matching can also be obtained. Moreover,

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TABLE I PERFORMANCE SUMMARY AND COMPARISON WITH PRIOR ARTS

the NF is reduced by 0.94 dB at 10.6 GHz. For the proposed resistive-feedback amplifier peaking with a gate inductor, the gain and NF tradeoff can be clearly observed in Fig. 6. As the gate inductance increases, the gain and bandwidth can both be effectively improved. However, a large gate inductor can lead to overpeaking of gain, and hence, circuit instability. As suggested by simulation, the circuit becomes unstable when the gate inductor exceeds 1 nH. It is worth pointing out that the gate inductor peaking is more effective compared with a drain peaking design in the proposed topology. As discussed in Section III-A, a well-designed current-reuse stage only needs a small gate inductor for effective peaking. In addition, since the drain peaking connects the inductor at the load, its impact on the input-referred noise is relatively small. Fig. 7 illustrates this point by simulation. The core circuit is identical to that as shown in Fig. 5, except the is connected in series with the load . peaking inductor Compared with the results in Fig. 6(a), a significantly larger inductance is required for similar bandwidth enhancement, as shown in Fig. 7(a). More importantly, the gate peaking is much more effective in suppressing the high-frequency noise, which can be clearly seen from the difference between Figs. 6(c) and 7(c). Fig. 8 presents the inductance and as a function of frequency for the gate peaking inductor in our design. The top metal (whose thickness is 3.4 m) is used for the inductor, which only occupies an area of 80 80 m . The inductor is 0.4 nH value is 17.8 at in the frequency range of interest and the 10 GHz. IV. MEASUREMENT RESULTS The proposed UWB LNA was fabricated in a standard 0.13- m CMOS process. Fig. 9 shows the chip micrograph. 0.63 mm and the core cirThe overall chip area is 0.58 0.22 mm 0.031 mm . The LNA cuit area is only 0.14 consumes 14.4 mW from a 1.8-V supply. The -parameters measured from 0.1 to 14 GHz by on-wafer coplanar probing are shown in Fig. 10 together with the simulation results. Within 3.1–10.6 GHz, the measured small-signal gain

achieves a maximum value of 12.4 dB at 7.5 GHz, and has a minimum value of 11.1 dB at 9.8 GHz. In this frequency range, is less than 14 dB, the the measured output return loss is less then 7.3 dB, and the measured input return loss is less than 38.9 dB. The simulation measured isolation in general agrees well with the measured results. The relatively can be attributed to the source follower large discrepancy in used for output matching. In measurements, it is difficult to have the actual voltage applied to the circuit exactly the same with that used in simulation. Since the output impedance of the source follower is sensitive to the bias current controlled by (see Fig. 5), a small variation of could cause an obvious , which can be verified by simulation. The difference in stability factor calculated from the measured -parameters is greater than 1 suggesting unconditional stability of the circuit. Note that the 3-dB bandwidth of the gain exceeds the measured frequency range (the gain varies from 9.7 to 12.4 dB within 0.1–14 GHz). Fig. 11 shows both the simulated and measured NF from 3 to 14 GHz with a minimum of 2.7 dB at 7.4 GHz and a maximum of 3.7 dB at 9.6 GHz (within the 3.1–10.6-GHz range). Fig. 12 shows the measured input third-order intermodulation (IIP3) at 6 GHz with a two-tone separation of 5 MHz. An IIP3 of 3.8 dB is obtained by extrapolation. Since this study emphasizes a wideband LNA realized in a compact area, the figure-of-merit (FOM) proposed in [17] is adopted here, which takes the core chip area into consideration

mW

GHz Core Area mm

(10) where is defined as the mean of the minimum and maximum values. Table I summaries the performance of the proposed LNA. The comparison with the prior arts based on 0.13- m CMOS technology is also listed. For the FOM calculation, the 3-dB bandwidth is considered, while the NF is the average value within the range of 3.1–10.6 GHz. If this frequency range cannot be covered [9], the NF within the 3-dB bandwidth is employed to calculate the FOM.

CHANG AND HSU: COMPACT 0.1–14-GHz UWB LNA IN 0.13- m CMOS

V. CONCLUSION A compact UWB LNA with a core area of only 0.031 mm was demonstrated in a standard 0.13- m CMOS technology. Based on the inductorless design considerations, the resistivefeedback and current-reuse techniques were employed. A small inductor of 0.4 nH was added at the gate of the input stage to effectively extend the bandwidth and suppress the increase of the NF at high frequencies. The amplifier achieved a bandwidth more than 13.9 GHz, a minimum NF of 2.7 dB, and a maximum gain of 12.4 dB. The proposed amplifier presented an FOM among the best compared with other published UWB LNAs in 0.13- m CMOS technology. ACKNOWLEDGMENT The authors would like to thank the Chip Implementation Center (CIC), Hsinchu, Taiwan, and the Taiwan Semiconductor Manufacturing Company (TSMC), Hsinchu, Taiwan, for chip fabrication and measurement. 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] Y.-J. Lin, S. S. H. Hsu, J.-D. Jin, and C. Y. Chan, “A 3.1–10.6 GHz ultra-wideband CMOS low noise amplifier with current-reuse technique,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 3, pp. 232–234, Mar. 2007. [3] C.-F. Liao and S.-I. Liu, “A broadband noise-canceling CMOS LNA for 3.1–10.6-GHz UWB receivers,” IEEE J. Solid-State Circuits, vol. 42, no. 2, pp. 329–339, Feb. 2007. [4] M. T. Reiha and J. R. Long, “A 1.2 V reactive-feedback 3.1–10.6 GHz low-noise amplifier in 0.13-m CMOS,” IEEE J. Solid-State Circuits, vol. 42, no. 5, pp. 1023–1033, May 2007. [5] Y.-J. Wang and A. Hajimiri, “A compact low-noise weighted distributed amplifier in CMOS,” IEEE Int. Solid-State Circuits Conf. Tech. Dig., pp. 220–221, 2009. [6] J.-H. Lee, C.-C. Chen, H.-Y. Yang, and Y.-S. Lin, “A 2.5-dB NF 3.1–10.6-GHz CMOS UWB LNA with small group-delay-variation,” in Proc. IEEE RFIC Symp., 2008, pp. 501–504. [7] F. Bruccoleri, E. A. M. Klumperink, and B. Nauta, “Wide-band CMOS low-noise amplifier exploiting thermal noise canceling,” IEEE J. SolidState Circuits, vol. 39, no. 2, pp. 275–282, Feb. 2004. [8] S. C. Blaakmeer, E. A. M. Klumperink, D. M. W. Leenaerts, and B. Nauta, “An inductorless wideband balun-LNA in 65 nm CMOS with balanced output,” in Proc. 33rd Eur. Solid-State Circuits Conf., Munich, Germany, Sep. 2007, pp. 364–367. [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. Microw. Theory Tech, vol. 55, no. 10, pp. 2015–2023, Oct. 2007. [10] J.-H. C. Zhan and S. Taylor, “A 5 GHz resistive-feedback CMOS LNA for low-cost multi-standard application,” IEEE Int. Solid-State Circuits Conf. Tech. Dig., pp. 200–201, 2006.

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[11] B. G. Perumana, J.-H. C. Zhan, S. S. Taylor, B. R. Carlton, and J. Laskar, “Resistive-feedback CMOS low-noise amplifiers for multiband applications,” IEEE Trans. Microw. Theory Tech, vol. 56, no. 5, pp. 1218–1225, May 2008. [12] J. Borremans, P. Wambacq, C. Soens, Y. Rolain, and M. Kuijk, “Low-area active-feedback low-noise amplifier design in scaled digital CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 11, pp. 2422–2433, Nov. 2008. [13] 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. [14] T. Chang, J. Chen, L. A. Rigge, and J. Lin, “ESD-protected wideband CMOS LNAs using modified resistive feedback techniques with chip-on-board packaging,” IEEE Trans. Microw. Theory Tech, vol. 56, no. 5, pp. 1817–1826, Aug. 2008. [15] P. R. Gray, P. Hurst, S. Lewis, and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th ed. New York: Wiley, 2001. [16] H. Zhang, X. Fan, and E. S. Sinencio, “A low-power linearized ultrawideband LNA design technique,” IEEE J. Solid-State Circuits, vol. 44, no. 2, pp. 320–330, Feb. 2009. [17] H.-K. Chen, D.-C. Chang, Y.-Z. Juang, and S.-S. Lu, “A compact wideband CMOS low-noise amplifier using shunt resistive-feedback and series inductive-peaking techniques,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 8, pp. 616–618, Aug. 2007. Po-Yu Chang was born in Changhua, Taiwan, in 1983. He received the B.S. degrees in engineering and system science and electrical engineering (double major) and M.S. degree in electrical engineering from National Tsing Hua University, Hsinchu, Taiwan, in 2006 and 2009, respectively. He is currently serving as a Corporal in the R.O.C. Army. His research included CMOS RF and analog integrated circuits design.

Shawn S. H. Hsu (M’04) was born in Tainan, Taiwan. He received the B.S. degree from National Tsing Hua University, Hsinchu, Taiwan, in 1992, and the M.S. degree in electrical engineering and computer science and Ph.D. degree from The University of Michigan at Ann Arbor, in 1997 and 2003, respectively. In 1997, he joined the III–V Integrated Devices and Circuits Group, The University of Michigan at Ann Arbor, as a Research Assistant. He is currently an Associate Professor with the Institute of Electronics Engineering, National Tsing Hua University. His current research interests include the design of monolithic microwave integrated circuits (MMICs) and RFICs using Si/III–V-based devices for low-noise, high-linearity, and high-efficiency system-on-chip (SOC) applications. He is also involved with the design and modeling of high-frequency transistors and interconnects. Prof. Hsu has served as a Technical Program Committee member of the SSDM (2008-present) and A-SSCC (2008-present). He was the recipient of the Junior Faculty Research Award of National Tsing Hua University in 2007 and the Outstanding Young Electrical Engineer Award of the Chinese Institute of Electrical Engineering in 2009.

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Optimization of a Photonically Controlled Microwave Switch and Attenuator Joseph R. Flemish, Member, IEEE, and Randy L. Haupt, Fellow, IEEE

Abstract—A silicon-based photoconductive switch and attenuator for microwave signals has been demonstrated and optimized for low insertion loss and high attenuation response upon illumination from a standard infrared LED. This device is fabricated within a coplanar waveguide for easy integration into a planar antenna for photonic control of an array. A general tradeoff exists between the goals of low insertion loss and high attenuation range. However, design and process enhancements are found to improve the device performance. A device that offers up to 20-dB attenuation with insertion loss of only 0.6 dB at 2.0 GHz is demonstrated. These devices show a frequency range where the insertion phase shift upon attenuation is significantly less than 1 dB. Index Terms—Microwave attenuator, photoconductive, RF switch, silicon.

I. INTRODUCTION

O

PTICAL control of microwave transmission is attractive in part because of the advantage of high isolation between the controlling electronics and the microwave circuit. Photoconductive switches have traditionally utilized metal–semiconductor–metal (MSM) structures on materials such as gallium arsenide to enable high-speed switching or the conversion of light signals to electrical signals at radio, microwave, or millimeterwave frequencies [1]. Additionally, silicon-based photoconductive attenuators and switches have been fabricated from coplanar waveguides (CPWs) in structures whereby the device can be in either a normally on or a normally off state in the absence of illumination. The former configuration was demonstrated in [2]–[4] by utilizing a simple CPW metal structure on a high-resistivity semiconductor so that signal attenuation was achieved by illuminating the gap between the conducting lines using a focused laser. Alternatively, in a normally off configuration, reported in [5], a conductive state was achieved using a laser to illuminate a slab of high-resistivity silicon which bridged a gap in the center conductor of a CPW. Owing to the longer carrier lifetimes in silicon compared to gallium arsenide, these silicon devices offer greater dynamic range for controlling signal intensity, albeit at the expense of proportionately longer switching times. Manuscript received May 28, 2010; revised June 22, 2010; accepted July 20, 2010. Date of publication September 13, 2010; date of current version October 13, 2010. This work was supported by the U.S. Army under Contract N00024-02-D-6604 DO-295. J. R. Flemish is with the Applied Research Laboratory and the Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA (e-mail: [email protected]). R. L. Haupt is with the Applied Research Laboratory, Pennsylvania State University, University Park, PA 16802 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.2010.2065350

Since there are many possible embodiments of photoconductive switches, their application will dictate the choice of material and the device configuration. For example, for applications requiring very fast switching, GaAs MSM structures with submicrometer metal gap spacings have turn-on and turn-off times on the order of nanoseconds [6]. However, to achieve low on-resistance in these devices, high-power illumination from a focused laser source is necessary. In sharp contrast, the motivation behind our work was to develop a device that has inherently low insertion loss and offers a wide range of controllable attenuation upon low-power optical illumination. The intended application for this device is an adaptive antenna array where reconfiguration time of less than 100 s is required. In this case, the optical source is a light-emitting diode (LED) that can be easily integrated into the antenna structure or component package. Recently, we reported on a preliminary device design, which showed a remarkably enhanced range of signal attenuation at a lower optical power density than other structures that have been previously reported [7]. This device showed insertion loss of less than 3 dB over the range of 0.1–6.0 GHz and a switched attenuation of more than 20 dB above 1.0 GHz upon low-power illumination from a single infrared LED. This paper reports on the simulation-based optimization, fabrication, and characterization of this type of device, which can function as a switch or attenuator with low insertion loss. In particular, we address its performance in light of design tradeoffs, regimes in which it can function with nearly constant insertion phase, and its integration into an antenna element, which has been employed in an optically controlled adaptive array. II. DEVICE MODEL A. Device Concept The general layout of the optically controlled attenuator is shown in Fig. 1. The device is fabricated on a high-resistivity silicon substrate and has distributed inductive, capacitive, and resistive elements, which can be loaded through a photoconductive effect. The circuit elements arise from the meandering path of the center signal trace, which traverses the gap between the outer conductors. In this design, the capacitance can be adjusted by varying the gap distance and the length of the trace in proximity to the ground. Likewise the inductance and resistance can be adjusted by varying the traverse distance and the trace width . A simplified equivalent circuit for this device in its dark state, shown in Fig. 2, resembles that of a low-pass filter. In the illuminated state, the shunt capacitors become lossy and can be effectively replaced by resistors in this circuit model. Under dark operation, this device is in a normally on quiescent state with low insertion loss. Signal attenuation occurs by

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be extremely useful in comparing device designs and predicting general trends in device performance. In the absence of reflection of the IR illumination and assuming a quantum conversion efficiency near unity for this (in siemens square) wavelength, the sheet conductivity during illumination is proportional to the optical power density and effective carrier recombination lifetime according to (1) Fig. 1. Layout and design parameters used for device optimization within a CPW structure from [5].

Fig. 2. Simplified equivalent circuit of the device in its dark state where n for our designs.

=6

illuminating the device using an infrared LED. Like the illuminated CPW reported in [9], conduction in the silicon adds a resistive shunt from the center conductor to ground. By increasing the silicon conductivity in the region in proximity to the meandering trace, signal attenuation occurs due to a combination of ohmic losses in the silicon and to reflection caused by the resulting impedance mismatch. Therefore, one can control the impedance characteristics of this device in both dark and illuminated states by adjusting the parameters , , , and . In our devices, the CPW inner conductor (not shown) is 2-mm wide and tapers to the meandering linewidth . We employed electromagnetic (EM) simulations to optimize the design for the desirable characteristics of minimum insertion loss under dark operation and maximum signal attenuation upon illumination. B. Model for Photoconductivity The performance of this device was optimized in two ways. The first involved maximizing the range of conductivity that is achievable in the active semiconductor regions through the best choices of substrate material, fabrication methods, and the use of passivation and antireflection layers. The second way utilized simulations to evaluate and optimize structures for best exploiting moderate changes in conductivity for RF attenuation. The -parameters of various designs were compared through EM simulation using CST Microwave Studio software with simplifying approximations made to compare their relative performance. For example, we assume the metal traces are lossy metal with a conductivity of 4 10 S/m consistent with the value for gold. Furthermore, we assume the silicon substrate has a dark S/m, and that the silicon can be made conductivity uniformly conductive up to a given depth. This conductive region is modeled to extend from the surface to a depth of 0.1 mm, which corresponds to optical absorption of approximately 95% nm. Although this simplification igfor a wavelength nores many factors related to the generation, recombination and diffusion of photogenerated electrons and holes, it has proven to

where is the electronic charge, and are the electron and is the photon energy. hole mobilities, and In our models, we restricted the allowable area of illumination to a 0.25-cm -square region and consider an LED having 100-mW peak optical output at nm, corresponding 10 cm s. Using a to an average photon flux of 1.75 plausible effective lifetime of photogenerated carriers of s [10] results in a calculated conductivity of approximately 10 S/m. Therefore, we expect that conductivity ranging from 0.005 S/m in the dark state to approximately 20 S/m under illumination is a reasonable estimate of what may be achievable from an LED source and was the range assumed during our simulation-based design. C. Semiconductor Contact Considerations Our simplified EM model does not consider how photogenerated electrons and holes behave at the interface between the silicon and metal features and the effect such behavior has on the effective carrier lifetime. In our earlier paper [6], two approaches were taken toward the structure of the contacts. In one approach, the metals were made to be in ohmic contact with silicon. In another, the metal features were capacitively coupled to the silicon through a 16-nm thermally grown silicon–dioxide layer. The ohmic contacted device had inferior performance by way of higher insertion loss and weaker attenuation response. In comparison, the capacitively coupled device had greater sensitivity to illumination, which we attribute to longer carrier lifetime due to passivation of the silicon surface. Therefore, in this work, we focus on optimization of the capacitively coupled device, but also compare results to those made with ohmic contacts. III. DEVICE FABRICATION AND TESTING Devices were fabricated on single-side-polished 0.525-mmS/m specified thick high-resistivity silicon wafers ms. The to have bulk carrier recombination lifetime wafers were first oxidized in dry oxygen to form a 16-nm-thick silicon–dioxide passivation layer. Metal features were created by sputtering a titanium/tungsten/gold seed layer and then selectively electroplating 2.5 m of gold using a photoresist mask. The excess seed layer was removed by etching and a 100-nm silicon–nitride film was deposited by plasma enhanced chemical vapor deposition to act as an antireflective coating. The silicon nitride was selectively etched to expose the ends of the CPW for soldering of end-launch subminiature A (SMA) connectors. Processing details of the ohmic contacted devices were reported in [7]. A finished device is shown in Fig. 3. -parameters of the devices were measured using an Anritsu 37369D vector network analyzer with short–open–load–thru

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Fig. 3. Photograph of device with SMA connectors assembled for testing.

TABLE I SIMULATED S -PARAMETERS (dB) AT 2.0 GHz

calibration. Measurements were made with and without illumination of the active region from an IR-LED having peak nm and a half angle of 22 [12]. This LED emission at has nominal optical output of 40 mW (60 mW/sr) at a forward current of 100 mA. It has a maximum useful forward current of 250 mA, beyond which the output saturates at approximately 70 mW. Switching speed of the devices was measured by capturing the transient transmission characteristics of a 1-dBm input signal at 2.0 GHz using an Anritsu ML2488A RF power meter. An Agilent 8114A high-power pulse generator was used to drive the IR-LED with 250 mA at a pulsewidth of 100 s. Switching time is defined as the time for the transmitted power to change from 10% to 90% of the difference in final versus initial values measured in decibels. IV. RESULTS The frequency range of 1.8–2.2 GHz is of particular interest to us for optimization of this device for its integration into a controllable antenna element. Table I therefore compares the simulated -parameters at 2.0 GHz. These results show two important trends with respect to the design parameters. First, as the segment length decreases and the trace width increases, the insertion loss in the dark state decreases due to better impedance matching and lower ohmic loss in the metal. This result is understood as a path having a shorter length and a greater width offers lower values of inductance and resistance in the circuit model of Fig. 2. Second, a clear tradeoff exists between maximizing the achievable attenuation ( , LED-ON) and minimizing the insertion loss. One reason is that fewer photons are absorbed when there is greater shadowing from wider metal traces. Another is that there is a larger active area associated with devices having a longer segment length , which increases both the light absorption and total resistive losses. The simulations suggest that reducing the gap improves impedance matching. In practice,

we did not observe this trend, as we limited the gap to a minimum of 0.015 mm due to the risk of incurring electrical shorts at smaller dimensions. To confirm the predicted trends, an initial matrix of designs (Design Set 1) was fabricated with various values of , , and using both styles of contacts: capacitively coupled and ohmic. Measured results at 2.0 GHz are shown in Tables II and III. Some comparisons with the simulations are worth noting. In agreement with the simulations, there is a clear dependence of the insertion loss and attenuation on the trace width . However, a strong effect of the segment length on the attenuation is not immediately discernable. The measured results for the designs having capacitively coupled contacts, listed in Table II, show that attenuation ranging from 20 to 30 dB can be achieved concurrently with insertion loss ranging from 0.9 to 1.8 dB. In these measurements LED-ON corresponds to a forward dc current to the LED of 250 mA. The switching time for these devices, which is governed by the effective carrier lifetime, was independent of the design parameters and had average values for turn-on and turn-off of 64 and 18 s, respectively. In Fig. 4, we compare the measured and simulated results more completely over a wider frequency range for the mm, capacitively coupled device of design “A” ( mm, and mm). In general, the measured attenuation was slightly greater than that modeled using a conductivity of 10 S/m, but the trend of greater attenuation with increasing frequency compares reasonably well. The insertion loss characteristics and trends in this case also agree well with modeled results up to 5 GHz, the upper limit in the simulations. Experimentally this device has an insertion loss of less than 3 dB for frequencies below 7.0 GHz. At approximately 7.5 GHz, a significant decrease in limits the usable bandwidth. The location of these dips in are design dependent. For example, design “B,” which differs only in having a greater trace width mm shows better insertion characteristics at 2.0 GHz, but has an upper frequency limit (3 dB) of only 6.0 GHz. In contrast, results for the ohmic contacted devices are shown in Table III. In all cases, ohmic contacts to the silicon degraded the attenuation characteristics by 10–20 dB. For devices with narrower traces, the insertion loss degraded by approximately 1–2 dB, even when the return loss indicated better impedance matching. These higher losses may be a consequence of ion-implantation doping introduced under the metal regions to facilitate ohmic contact formation. For the cases of thicker metal traces mm , the insertion loss looks comparable to the capacitively coupled devices. On the other hand, switching speed is considerably faster with average turn-on and turn-off times of 12 and 10 s, respectively. These characteristics are consistent with shorter effective lifetimes of photogenerated carriers due to recombination at the metal–semiconductor interface. In a subsequent design set (Design Set 2), a goal was to achieve better impedance matching and lower ohmic loss to minimize the insertion loss while maintaining a maximum attenuation of at least 20 dB. Lower losses were realized through more compact designs and wider traces. To this end, we evaluated design modifications, which included reducing the traverse

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TABLE II MEASURED S -PARAMETERS AT 2.0 GHz FOR CAPACITIVELY COUPLED DEVICES

TABLE III MEASURED S -PARAMETERS AT 2.0 GHz FOR OHMIC-METAL CONTACTED DEVICES

distance from 3.2 to 2.5 mm for reduced inductance and ohmic loss, maintaining a minimum trace width of 0.140 mm in the traverse direction, and reducing the segment length to 0.3 mm. Attempts were also made to increase the attenuation response by allowing more light to enter critical regions of the structure by thinning the traces only where they are in close proximity to the ground plane. The measured maximum attenuation versus dark values of insertion loss are plotted in Fig. 5 for all designs in both design sets. Although a tradeoff of these characteristics is apparent, it is also clear that some designs give good attenuation ( 20 dB) while also showing good impedance matching and insertion loss of less than 1 dB. One of our compact designs, designated in Fig. 5 as design “L,” shows a large improvement in matching relative to the larger design “B.” This compact design shows only a small degradation in the attenuation response, despite a 42%

reduction in footprint. Comparison of the dark and illuminated -parameters for these two designs are shown in Fig. 6. Significantly, the compact design has a measured insertion loss of only 0.6 dB, which includes all losses associated with its CPW feed and attachment to the SMA connectors. The device with the lowest insertion loss of approximately 0.3 dB corresponded to the design with the smallest trace lengths and largest widths. However, this device showed a maximum attenuation of only 17 dB, which was less than the goal of this work. It is worth noting that through further improvements in surface passivation of the silicon, the attenuation response of all devices could likely be significantly enhanced at the expense of switching speed. In certain frequency ranges, these devices work well as variable attenuators with only a small shift in the insertion phase upon attenuation, as shown in Fig. 7, for the larger device. At

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Fig. 4. Comparison of simulated (dashed line) and measured (solid line) values of S indicative of insertion loss (dark) and attenuation (illuminated) characteristics of design “A.” Fig. 7. Measured shift in insertion phase at different states of attenuation for device design “B.”

0

Fig. 5. Measured insertion loss ( S dark) at 2 GHz versus maximum attenuation ( S illuminated) for the design variations evaluated.

0

Fig. 8. Measured group delay in different states of attenuation for the compact device design.

is little shift in the phase upon attenuation. For the larger design, the shift is less than 0.2 dB in the range of 2.9–3.3 GHz. In contrast, our compact design shows similar behavior in the range of approximately 3.8–4.4 GHz. Outside of this range, the insertion phase can vary by as much as 1.5 dB. Although our simulations also predict this type of crossover behavior, we have thus far not been able to accurately predict the frequency at which it occurs for specific designs, perhaps due to the simplifying assumptions made in our models regarding the photoconductive effect. The corresponding group delay for the compact design is shown in Fig. 8 for various states of attenuation. In the unattenuated state, the group delay is constant at 0.24 ns below 2 GHz, but disperses by 0.04 ns/GHz at higher frequency. For attenuation of approximately 8 dB, the dispersion disappears at higher frequency, but now appears below 2 GHz with a value of 0.04 ns/GHz. At higher attenuation, the group delay decreases continuously with frequency. Fig. 6. Comparison of measured transmission and reflection in dark and illuminated states for large design “B” (dashed lines) and compact design “L” (solid lines).

lower frequency, the phase of an attenuated signal lags that of the unattenuated signal, whereas at higher frequency, the phase leads. Within some range of intermediate frequencies, which is design dependent, there is a crossover regime where there

V. DEVICE INTEGRATION WITH AN ANTENNA ELEMENT Our compact design was integrated into an antenna to create an element with controllable gain for an adaptive array [13]. For this application, a tab monopole antenna [14] fabricated on FR4 with a CPW feed provided a targeted bandwidth of 1.8–2.4 GHz upon integration. The attenuator was soldered flip-chip style onto a cut out of the CPW, which feeds the antenna, as shown

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Fig. 9. (a) Front and (b) back views of antenna element integrated with the photoconductive attenuator.

Fig. 11. Attenuation of transmitted signal for various levels of current to the illuminating LED as measured by receiving antenna.

Fig. 10. Measured return loss of the integrated element in the quiescent state and power transmitted to the receiving antenna.

in its front and back views in Fig. 9. A hole though the board allows for LED illumination. This element was evaluated for transmission and reflection characteristics by connecting it to port 1 of a network analyzer and connecting to port 2 a receiving antenna spaced 10 cm away. The receiving antenna was another tab monopole without an integrated attenuator. The meaand ) with sured values of reflected and received signals ( the element in the quiescent state are shown in Fig. 10. The impedance bandwidth extends from 1.75 to 2.45 GHz, and radiation over this bandwidth is confirmed by the received signal. Fig. 11 shows the reduction in the received power as a function of LED current supplied to the transmitting element. Similar to the attenuation characteristics of the discrete device, controllable attenuation of up to 20 dB is possible for the integrated element over this frequency range by LED illumination. It is noted that the response to the LED current is not linear, but instead approaches a saturated state of attenuation in response to the LED optical output power. The phase shift in the received signal at different attenuation levels is shown in Fig. 12. Interestingly, the phase shift observed upon integration is less than that measured in the discrete device. Moreover, the crossover point of phase invariance occurs at a significantly lower frequency (2.45 versus 4.1 GHz) indicating that the reactance of the device is different when coupled with the antenna in the integrated structure. Specifically, at 2.0 GHz, the phase shift is approximately 1.0 dB and decreases to 0.5 dB at 2.2 GHz. We have not evaluated the attenuator designs experimentally for their temperature dependence. We predict however that the

Fig. 12. Phase shift of signal received from integrated element for different states of attenuation.

insertion loss characteristics will degrade slightly at temperature above approximately 70 C at which point the silicon intrinsic carrier concentration will exceed the background doping level. Our simulated results show that at 120 C, the insertion loss is greater by approximately 0.25 dB. Approximately 0.2 dB is attributable to the rise in silicon conductivity and another 0.05 dB to the temperature dependence of the resistance associated with the gold traces. VI. CONCLUSION The design tradeoffs of a new silicon-based photoconductive switch and attenuator for microwave signals has been demonstrated. This device is fabricated within a CPW on high-resistivity silicon and offers a higher magnitude of signal attenuation per optical power input than other optically controlled devices that have been reported, enabling controllable signal attenuation by way of illumination from a standard LED. Modification of the design parameters show that a clear tradeoff exists between the conflicting goals of a low insertion loss and a high attenuation range. For our application of integration into an antenna element having optically controlled gain, we have designed a device that offers up to 20-dB attenuation with an insertion loss of only 0.6 dB at 2.0 GHz, and has less than 3-dB insertion loss up to 5.9 GHz. These devices show a frequency range in which the

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insertion phase associated with attenuation can be significantly less than 1 dB with the specific range being design dependent. ACKNOWLEDGMENT The authors gratefully acknowledge Dr. E. Potenziani, U.S. Army CERDEC, Fort Monmouth, NJ, and Dr. M. Lanagan, Pennsylvania State University, University Park, for useful discussions, and the assistance of H. Kwan, Pennsylvania State University, in device fabrication and testing. The authors acknowledge use of facilities at Materials Research Institute Nanofabrication Laboratory, Pennsylvania State University, University Park, under the National Science Foundation Cooperative Agreement 0335765. REFERENCES [1] D. L. Rogers, “Integrated optical receivers using MSM detectors,” J. Lightw. Technol., vol. 9, no. 12, pp. 1635–1638, Dec. 1991. [2] W. Platte and B. Sauerer, “Optically CW-induced losses in semiconductor coplanar waveguides,” IEEE Trans Microw. Theory Tech., vol. 37, no. 1, pp. 139–148, Jan. 1989. [3] S. E. Saddow and C. H. Lee, “Optical control of microwave-integrated circuits using high-speed GaAs and Si photoconductive switches,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 9, pp. 2414–2420, Sep. 1995. [4] S. Spiegel and A. Madjar, “Impact of light illumination and passivation layer on silicon finite-ground coplanar-waveguide transmissionline properties,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 10, pp. 1673–1679, Oct. 2000. [5] C. J. Panagamuwa, A. Chauraya, and J. C. Vardaxoglou, “Frequency and beam reconfigurable antenna using photoconducting switches,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 449–454, Feb. 2006. [6] A. Karabegovic, R. M. O’Connell, and W. C. Nunnally, “Photoconductive switch design for microwave applications,” IEEE Trans. Dielectr. Electr. Insul., vol. 16, no. 4, pp. 1011–1019, Aug. 2009. [7] J. R. Flemish, H. Kwan, R. L. Haupt, and M. Lanagan, “A new silicon-based photoconductive microwave switch,” Microw. Opt. Technol. Lett., vol. 51, no. 1, pp. 248–252, Jan. 2009. [8] G. Poesen, G. Koers, J. Stiens, G. Carchon, W. De Raedt, and R. Vounckx, “Opto controlled substrate losses in a coplanar waveguide on HR-Si,” in IEEE MTT-S Int. Microw. Symp. Dig., 2005, pp. 1401–1404.

[9] R. Gary, J.-D. Arnould, and A. Vilcot, “Semi-analytical computation and 3D modeling of the microwave photo-induced load in CPW technology,” Microw. Opt. Technol. Lett., vol. 48, no. 9, pp. 1718–1721, Sep. 2006. [10] D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. Electron Devices, vol. 44, no. 1, pp. 160–170, Jan. 1997. [11] M. J. Kerr, P. Campbell, and A. Cuevas, “Lifetime and efficiency limits of crystalline silicon solar cells,” in 29th IEEE Photovolt. Specialists Conf. Rec., 2002, pp. 38–441. [12] “TSFF5400 Data Sheet 81016,” Vishay Semicond., Malvern, PA, 2002. [13] R. L. Haupt, J. Flemish, and D. Aten, “Broadband linear array with photoconductive weights,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1288–1290, 2009. [14] J. M. Johnson and Y. Rahmat-Samii, “Tab monopole,” IEEE Trans. Antennas Propag., vol. 45, no. 1, pp. 187–188, Jan. 1997. Joseph R. Flemish (M’99) received the B.S. degree in chemical engineering, M.S. degree in materials science, and Ph.D. degree in materials science from Pennsylvania State University, University Park, in 1984, 1986, and 1989, respectively. He is currently a Senior Scientist with the Applied Research Laboratory and Professor of materials science and engineering with Pennsylvania State University. From 1996 to 2004, he was a Senior Principal Engineer and Chief Scientist with ANADIGICS Inc., Warren, NJ. From 1989 to 1996, he was a Research Engineer with the U.S. Army Research Laboratory, Ft. Monmouth, NJ. His professional interests are in the area of electronic and opto-electronic materials, devices, and processes.

Randy L. Haupt (M’76–SM’81–F’00) received the B.S.E.E. degree from the USAF Academy, Colorado Springs, CO, in 1978, the M.S. degree in engineering management from Western New England College, Springfield, MA, in 1981, the M.S.E.E. degree from Northeastern University, Boston, MA, in 1983, and the Ph.D. degree in electrical engineering from The University of Michigan at Ann Arbor, in 1987. He is currently a Senior Scientist and Department Head with the Applied Research Laboratory, Pennsylvania State University, University Park. He was a Professor and Department Head of the Electrical and Computer Engineering, Utah State University, Professor and Chair of electrical engineering with the University of Nevada, Reno, and Professor of electrical engineering with the USAF Academy. He was a Project Engineer for the OTH-B radar and a Research Antenna Engineer with the Rome Air Development Center. Dr. Haupt is a Fellow of the Applied Computational Electromagnetics Society (ACES). He is a member of the IEEE Antenna and Propagation Society (AP-S) Administrative Committee (AdCom) and the Antenna Standards Committee. He is an associate editor for the IEEE Antennas and Propagation Magazine and the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS.

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Theoretical and Experimental Investigation of the Modulated Scattering Antenna Array for Mobile Terminal Applications Mang He, Member, IEEE, Lin Wang, Qiang Chen, Member, IEEE, Qiaowei Yuan, and Kunio Sawaya, Senior Member, IEEE

Abstract—The performance of the modulated scattering antenna array (MSAA) for mobile terminals is investigated in this paper. The electromagnetic scattering of the modulated scattering elements (MSEs) loaded with Schottky diode is analyzed by using the Volterra series method in conjunction with the method of moments, which rigorously includes the mutual couplings among the MSAA elements. By virtue of closed-form analytical expression of Volterra analysis, useful physical insights and guidelines are provided to find optimum parameters of the MSEs in order to improve the performance of the MSAA for wireless communications. Parametrical studies are carried out for the purpose of enhancing the scattered power level of the second-order intermodulation caused by the nonlinear load in the MSEs. Both numerical simulations and experiments validate the proposed theoretical analysis. Index Terms—Modulated scattering antenna array (MSAA), modulated scattering element (MSE), nonlinear circuits, method of moments (MoM), Volterra series.

I. INTRODUCTION HE MODULATED scattering technique was firstly presented by Richmond to improve the accuracy of measurement of electric fields [1]. Recently, based on this technique, Yuan et al. proposed a new concept, called the modulated scattering antenna array (MSAA), and utilized it as a receiving antenna array for the mobile terminals in the multiple-input multiple-output (MIMO) communication systems [2]. In this configuration of the MSAA, only one branch of front-end circuits is needed in the normal receiving antenna, and other output signals required in the MIMO channel are realized by using the scattered fields of the second-order mixing product from the modulated scattering elements (MSEs) loaded with nonlinear devices. Therefore, the MSAA is particularly useful for mobile handsets in which compactness of the receiving antennas

T

Manuscript received April 14, 2010; revised July 22, 2010; accepted July 23, 2010. Date of publication September 02, 2010; date of current version October 13, 2010. This work was supported in part by the National Science Foundation of China under Grant 60801008, and in part by the Global COE Program of Tohoku University, Japan. M. He was with the Department of Electrical and Communication Engineering, Tohoku University, Sendai 980-77, Japan. He is now with the Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China (e-mail: [email protected]). L. Wang, Q. Chen, Q. Yuan, and K. Sawaya are with the Department of Electrical and Communication Engineering, Tohoku University, Sendai 980-77, Japan (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.2010.2063850

is of primary importance because the MSAA saves the complex front-end circuits for most receiving antenna elements, although it provides slightly inferior performance compared to the commonly used antenna array in MIMO systems [2]–[4]. The performance degradation of the MSAA is mainly due to the low power level of the modulated scattering field received by the normal receiving antenna to which the front-end circuit is connected [2]. Therefore, how to improve the modulated scattering power level from MSEs is extremely important for the applications of the MSAA to MIMO system and is the major focus of this paper. In the authors’ previous work [2]–[4], the performance of the MSAA in the wireless communication systems has been extensively studied through experiments in terms of the spatial diversity, the channel capacity, and the error vector magnitude (EVM) in Rayleigh fading environments. However, a theoretical analysis method has not been provided yet to systematically investigate and further improve the performance of a MSAA system. In this paper, a rigorous and accurate analysis of the MSAA is presented based on the Volterra-series method and the method of moments (MoM), which aims at optimizing the parameters of the MSAA and further improving its performance. This paper is organized as follows. In Section II, the basic configuration and features of the MSAA are introduced, and the theoretical analysis of a two-element MSAA with diode loads based on the Volterra-series method and MoM are presented. InSection III, both numerical and experimental parametrical studies are carried out, and several effective means to increase the scattered power level of the second-order intermodulation from MSEs are discussed in detail. II. MSAA CONFIGURATION AND ANALYSIS METHOD A. Configuration of the MSAA Fig. 1 shows the configuration of a typical MSAA loaded with diodes. The MSAA consists of two types of elements: one is a normal receiving antenna and the others are MSEs. Only one branch of the RF receiver is connected to the normal antenna element, while the MSEs do not have their own receiving circuits. The MSEs can be seen as antennas or scatterers that are loaded with the nonlinear devices and are fed by local signals . with low-frequency impinges When the incident signal with the frequency the MSAA, the scattered fields with new mixing frequencies will be produced due to the nonlinear loads connected to the MSEs and will be received by the normal receiving antenna that

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Fig. 2. Structure of a two-element MSAA loaded with a Schottky diode.

Fig. 1. Configuration of the MSAA loaded with diodes.

is connected to the RF receiver. Thus, the received signals at the normal receiving antenna have an infinite number of frequencies ( and ) since the local signal frequency for each MSE may be distinct. These received signals can be used for adaptive combination in the RF receiver by tuning the corresponding weight for each receiving signal. In the MSAA, the normal receiving antenna and the MSEs can be of any type, their relative positions are arbitrary, and the nonlinear devices can also be selected with great freedom. In particular applications, all these parameters could be adjusted to optimize the performance of the MSAA. Therefore, the MSAA may be a very flexible and attractive candidate as the receiving antenna array in MIMO systems [4]. More important, only one branch of the RF receiver is needed in the MSAA. This feature makes the MSAA be very appealing when it is used for the mobile terminals in MIMO systems where compactness and energy saving are of primary concerns. B. Analysis Method Based on Volterra Series and MoM In [2]–[4], extensive experiments have been conducted to study the applicability of the MSAA for mobile handsets, where the second-order intermodulation scattering field was used as the modulated signal. It was found that the performance of the MSAA was slightly inferior to that of the normal receiving array antenna whose elements are all half-wavelength dipoles without any nonlinear device. The main reason is that the power level of the modulated scattering from MSEs with the is much lower than that of the signal with the frequency appearing at the normal receiving antenna due frequency to direct incidence. Such power level imbalance apparently degrades the performance of the MSAA [2]. In this section, for the first time, we will investigate the performance of a two-element MSAA from the theoretical point of view. Although the analysis procedure is demonstrated for the two-element array case for brevity, it can be easily extended

Fig. 3. Equivalent circuit of the MSE under incident electromagnetic (EM) wave.

to an MSAA of an arbitrary number of elements in a straightforward manner. The structure of a two-element MSAA loaded and are the dc with Schottky diode is shown Fig. 2. and are the inbias and the local signal voltages, while ternal resistors of the corresponding signal generators, respectively. and are the RF choke inductance and dc block capacitance, respectively. The MSAA resides at the yoz-plane under , and the distance the plane-wave incidence with frequency between two array elements is . The equivalent circuit for the MSE is shown in Fig. 3 by using is the short-circuited curthe similar procedures in [5]–[7]. , and is the input admitrent at the port of the MSE at and are calcutance of the MSE without loading. Both lated in the presence of the normal receiving antenna, therefore the effect of mutual coupling between the MSE and the normal antenna element is included. According to Kirchhoff’s current law (KCL), following equations are established: (1) where

(2)

is the – characteristics of the nonlinear device. For a and typical Schottky diode [8], (3)

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is the reverse saturation current and and depends on the structure of the diode. Replacing (2) into (1), we obtain

(4) Further, the time-domain voltage and current can be decomdue to the exposed into the dc part and the dynamic part istence of dc block capacitance and RF choke inductance. These are expressed as (5) and are dc and time-varying parts of where spectively. Thus, (3) becomes

, re-

(6) Let

(7) and

Fig. 4. DC bias and dynamic sub-circuits of the MSE under the incident EM wave. (a) DC-bias sub-circuit. (b) Dynamic sub-circuit.

Hence, our analysis is based on the small-signal approximation, but it is accurate enough for modeling MSAA application in the wireless communication system. For the analysis of the nonlinear circuit in Fig. 4, there exists a variety of approaches [5]–[7], [9]. The Volterra-series method is employed in this paper due to its closed-form formulation for the final output that could provide clear physical insights of the performance of MSAA, although other purely numerical approaches could produce more accurate results if strong nonlinearities are considered [6], [7]. Another advantage of this choice is that Volterra analysis can be implemented entirely in the frequency domain without the use of the fast Fourier transform (FFT) [5], [9]. Fig. 4(b) is a two-tone excited nonlinear circuit. The shortand the voltage of the local signal are circuited current written in the frequency domain as follows:

(8) Equation (6) then becomes (9) Therefore, (4) can be rewritten as follows. For the dc part,

(12) and

(10) (13) and for the dynamic part, (11) . In (10) and (11), the current and voltage where involving and are neglected since their contributions are much smaller compared to other terms. Therefore, the equivalent circuit of the MSE can also be decoupled into two sub-circuits: one is the dc-bias circuit and the other one is the timevarying circuit, as shown in Fig. 4. It is noted that we have used in (6). the first three terms in the Taylor-series expansion of

where and and are the phasor representations of and , respectively. In (13), the initial is assumed to be zero. phase of Substituting (12) and (13) in (11), we obtain

(14)

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Let

In the derivation of (19a) and (19b), following relations of the transfer functions have been used: (15) (21)

where the superscript “*” denotes the complex conjugate. The excitation signal on the right-hand side of (14) becomes Finally, the frequency-domain output voltages of the circuit and are Fig. 4(b) at (16)

(22) and (23)

According to Volterra analysis [9], [5], the output voltage in Fig. 4(b) can be expressed by a series whose term is the product of the frequency-domain excitation signals and the transfer functions for the nonlinear circuit

(17)

where and and are the first- and second-order transfer functions, respectively. In (17), the negative frequencies are defined as (18) It is noted that only up to second-order responses have been considered in (17) because the modulated scattering signal used in the MSAA is the second-order mixing product with the frecaused by the nonlinear diode [2]–[4]. quency This means that MSAA only utilizes the weak nonlinearities of the nonlinear device. The contributions from the higher can also order nonlinearities to the output at the frequency be included in the analysis, at the expense of computation complexity, but their effects are much smaller compared to the second-order intermodulation. Therefore, (17) could depict the second-order modulated signal without appreciable accuracy limitation in the small-signal wireless communication scenario. The transfer functions are found by exciting the circuit in and , and calculating the Fig. 4(b) at two frequencies, output voltages at the frequencies and . The final results of the first- and second-order transfer functions are (19a) and (19b) where is the linear admittance of the shunt circuit shown in Fig. 4(b) (20)

In summary, the analysis procedures of the Schottky diode loaded two-element MSAA are organized as follows. Step 1) Solve the nonlinear equation (10) to obtain the dc-bias voltage at the terminal of diode. Step 2) According to (3) and (7), obtain the coefficients and . Step 3) At the frequency , calculate the input admittance of the MSE in the presence of the normal receiving antenna using the MoM [10], and then of the circuit compute the shunt admittance Fig. 4(b) using (20). at using the method similar to Step 4) Compute that in Step 3). at by using the same Step 5) Compute method as in Step 3). Step 6) Calculate the short-circuited current of the MSE in the presence of the normal without loading at receiving antenna by using the MoM. Then obtain acthe excitation phasors cording to (15). and Step 7) Calculate the output voltages at the terminal of the MSE by using (22) and (23). Step 8) Finally, calculate the received power by the normal receiving antenna as the summation of the direct incidence and the scattering from the MSE at the frequency , and the recaused by ceived power at from MSE due to the . reradiation of and from In fact, the radiation produced by the MSE will be reflected by the normal receiving antenna again, and these reflected waves will excite new mixing products with and . The multiple reinfinite frequencies including flections between the elements in the MSAA will proceed until the ultimate equilibrium is reached. However, the contributions from these multireflection effects to the final received power and are higher order quantities compared levels at and from the to the first-order reradiation of MSE as calculated in the above procedures. Therefore, they are neglected in Step 8) for efficient and fast computation without much loss of accuracy. C. Discussion As been pointed out before, the performance of the MSAA can be improved by enhancing the received power of the

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modulated scattering signal. Thus, it is important and interesting . According to the analto exploit the approaches to increase ysis presented in Section II-B, this power level is determined by . Replace (19b) and (20) into (23), can be rewritten as

(24) From (24), the following means could be adopted in order to for the fixed internal admittance of increase the level of the local signal generator. and by tuning the dc-bias • Optimize the coefficients voltage to increase level, which means that the circuit should work at an appropriate driving point of the diode. and • Adjust the short-circuited current of the MSE at the input admittance of the MSE without loading at and in the presence of the normal antenna, which can be realized through the following. • Modifying the shape of the MSE for given types of the MSE and the normal receiving antenna (e.g., we can change the length of MSE if it is a metallic thin-wire scatterer). • Loading the diode at different positions in the MSE. • Choosing a suitable frequency of the local signal that can reradiate the second-order modulated signal at more effectively. • Increasing the magnitude of the local signal since is linearly proportional to . However, the effect will be limited to the small-signal regime because the saturation will occur if it is too large. By virtue of the simple expression of (24) resulting from Volterra analysis, the above guidelines give us some useful physical insights to optimize the behavior of the MSAA. However, any parameter in (24) is not independent of others. Therefore, we will investigate the feasibility of the proposed theoretical analysis in Section III through numerical simulations and experimental validations. III. PARAMETRICAL STUDIES In this section, we will carry out the numerical parametrical in the MSAA by study to maximize the receiving power using an in-house MoM code [11] combined with Volterra analysis, as presented in Section II firstly, and then experiments are conducted to validate the numerical simulations. The geometry of the two-element MSAA is shown in Fig. 5, where the normal receiving antenna is a half-wavelength dipole at fre, while the MSE is chosen as a thin-wire scatterer quency loaded with a Schottky diode and relevant circuits. The length of the MSE is and the loading position measured from the center of the thin wire is . The entire structure is within the yoz-plane, and the distance between two elements is with the coordinate origin being the midpoint. A vertically polarized plane wave

Fig. 5. Geometry of the two-element MSAA with a half-wavelength dipole receiving antenna and a thin-wire-like MSE loaded with a Schottky diode.

Fig. 6. Measured and calculated received power diode parameters under different dc-bias voltages.

P

and

P

with various

TABLE I PARAMETERS OF DIODE A AND B

with the frequency is assumed as the excitation signal of the MSAA, where is the -direction. angle of the propagation vector with respect to the The configuration of nonlinear circuit connected to the MSE is shown in Fig. 2. In the simulations, we set the internal resistors and of the signal generators and the input impedance of the RF receiver to be 50 , and both the dipole antenna and MSE having the length-diameter ratio of 74.2. A. Effect of the Driving Point of the DC-Bias Circuit First, we investigate the effect of the different driving point of . the dc-bias circuit on the received power level at and and with two different typFig. 6 shows the calculated ical diodes versus various bias voltages under the front incident plane wave. The parameters of diode A and B are listed in Table I and other parameters used in the simulation is the magnitude of local signal are shown in Fig. 6, where is the wavelength in free space at . voltage and It is found that the scattered signal levels rise rapidly with the increasing , and then fall at a slower speed after reaching its remains almost constant with different diode maximum.

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TABLE II MAXIMUM P AND THE CORRESPONDING BIAS VOLTAGE AND CONSUMED POWER OF DC CIRCUIT FOR VARIOUS DIODE TYPES AND ELEMENT DISTANCE POWER UNIT: DBM, VOLTAGE UNIT: V, DISTANCE UNIT: 

Fig. 8. Simulated received power P frequencies.

Fig. 7. Experiment setup in the anechoic chamber.

parameters and bias voltages, which means that is dominated by direct incidence and the contribution of the reradiation occurs at a from the MSE is small. Moreover, maximum lower bias voltage (about 0.15 V) when the diode is of type A, which has steeper – characteristics (larger ) compared to diode B. For other incidence direction and element distance , a similar phenomenon is also observed. Therefore, a Schottky diode with a larger saturation current is preferred in the MSAA for the purpose of power saving if other parameters of the diode remain fixed. Table II shows the consumed power of the dc-bias occurs by using two circuit at the point where the maximum different types of the diodes and various element distances. It is of the dc-bias circuit with clear that the consumed power diode A is much less than that with diode B and the maximum are almost same in both cases. received To validate the numerical results, an experiment is carried out in the anechoic chamber. In the experimental setup, as shown in Fig. 7, a log-periodic dipole array (LPDA) (electro-Metrics EM6952) is used as the transmitting antenna and is 3.0 m away from the MSAA. At the transmitting frequency 2.5 GHz, this distance is large enough to guarantee that the MSAA is in the far field of the LPDA and that the radiating wave is nearly a local vertically polarized plane wave when it impinges the MSAA. The LPDA is fed by an Agilent E4438C ESG vector signal generator and the input power is set to be 5 dBm. At the receiving end, the MSE is a half-wavelength (at 2.5 GHz) thinwire conductor loaded with a Schottky diode HSC276 from Renesas Ltd., and a two-channel multifunction synthesizer (NF WF 1966) is connected to the MSE as the local signal generator with the frequency of 50 MHz. While the normal receiving antenna is a half-wavelength dipole, followed by a real-time spectrum analyzer (Tektronix RSA3308A) that is used to measure

and P

by using various local signal

the received power levels at (2.45 GHz) and at (2.5 GHz). It is worth mentioning that, in the numerical simulations, at are firstly adjusted to the calculated received power match the first measured power level from the spectrum analyzer (when the bias voltage is 0.1 V in Fig. 6) by simply tuning the to 0.09 V/m in the code magnitude of the incident plane wave since we do not know the exact power density of the incident is then used throughout wave at the MSAA. This value of the following numerical simulations. The above tuning process can be considered as a numerical calibration. The paramof and , which characterize the Schottky diode, are not eters measured in the experiment and two typical values [8] for the Schottky diode type A and B (see Table I) are used in all numerical simulations. It is found that the measured result presented in Fig. 6 shows reasonable agreement with the calculated one for the MSAA loaded with diode A, the relative error of the maxis less than 3%, which means the characteristics of imum the diode HSC276 is close to the typical Schottky diode with A and mV. The measured the parameters bias voltage for maximum is around 0.15 V, which matches well to the numerical prediction (for diode A). B. Effect of Local Signal Frequency Fig. 8 shows the numerical results of the received power level and by tuning the local signal frequency for at the MSE from 10 to 400 MHz under the front incident plane wave with vertical polarization. It is seen that the local signal and remains almost frequency has a minor effect on increases slowly constant. However, the received power is changed from 10 to 150 MHz, and decreases when rapidly when is beyond 150 MHz. The maximum occurs when is 150 MHz. At this frequency, the length of , which the thin-wire MSE is about 0.47 wavelengths at exhibits the strongest reradiation ability of the second-order mixing signal from the diode. A similar phenomenon is also observed when the distance and incident angle are changed to other values.

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Fig. 9. Simulated received power P lengths.

and P

with different thin-wire MSE

Fig. 10. Simulated received power P and P different positions along the thin-wire MSE.

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when the diode is loaded at

C. Effect of the Length of Thin-Wire MSE The effects of the thin-wire MSE length on the received power level are investigated by numerical simulations. An apparent resonance is found in Fig. 9 when the length of the MSE is about 0.5 wavelengths at , which means strong mutual coupling occurs between the elements of MSAA at this length. It is also nois very low if the length of the MSE is ticed that the level of much shorter than a half-wavelength. A second resonance will also happen if we increase to about 1.5 , but the MSE of such a length is of little useful applications in the mobile terminals when compactness is considered in the communication system design. D. Effect of Loading Position in the MSE It is well known that the loading position of the linear or nonlinear device on antenna plays an important role in determining the radiation and scattering properties of the loaded antenna structure. The effect of the loading position of the Schottky diode along the MSE on the received power levels in MSAA system is demonstrated in Fig. 10. For three different element at is reduced monodistances, the received power tonically when the loading point approaches to the end of the is only changed slightly. Clearly, the thin-wire MSE, while center-loaded MSE should be chosen in the MSAA in order to . produce maximum E. Effect of the Magnitude of the Local Signal in MSE As been pointed out in Section II, is linearly proin the small-signal sceportional to the local signal voltage nario. Fig. 11 shows the relation between the received power level and the magnitude of the local signal voltage through both experiments and numerical simulations. It can be seen from Fig. 11 that the numerical results agree well with the measured ones and the maximum error is less than 1.5 dB (the relative error is less than 2.5%) in the small-signal regime ( V). Within this voltage range, is increased by about is doubled, and remains almost unchanged 6 dB when exceeds since it is dominated by direct incidence. When remains almost constant due to the 0.25 V, the measured saturation of the diode. However, the simulated based on

Fig. 11. Measured and simulated received power P local signal voltage of the MSE.

and P

versus various

the present theoretical analysis will increase continuously because of the limitation of Volterra analysis for strong nonlinearities prediction [9]. F. Effect of the Distance Between the MSAA Elements The measured and simulated received power levels of the versus various distances between the eleMSAA at ments, under the vertically polarized incident plane wave from front direction, are shown in Fig. 12. Reasonable agreement of two types of results is observed, and the largest error is less than decreases rapidly 2 dB (the relative error is less than 3.4%). and then changes only slightly when is of intermediate value , indicating complicated interaction between two elements of the MSAA in this distance range, and decreases monotonically again with a large element distance where the mutual coupling becomes weak. Furthermore, Fig. 13 shows the relation of the received power level and the element distance when the plane wave impinges the MSAA from difand curves have ferent directions. It is noticed that changes, which means the perquite different shapes when formance of the MSAA is a strong function of the incident angle. exceeds if is small and the plane More interestingly, wave illuminates the MSAA from the MSE side .

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2) The incident wave to the MSAA is not a perfect plane wave in the experiment, while in numerical simulations, the incident wave is an ideal plane wave. This inconsistence will also cause some errors between two kinds of results. 3) In the experiment, the nonideal free-space environments (cables, supporting foam for the MSAA, etc.) may affect the measured results to some extent. IV. CONCLUSION

Fig. 12. Measured and calculated received power P distances between MSAA elements.

Fig. 13. Simulated received power P and P MSAA elements under various incident angles.

and P

versus various

versus distances between

In such a case, the MSE blocks the incident wave and subsequently reduces the power received by the normal receiving antenna due to direct incidence. Therefore, the distance between the MSE and the normal receiving antenna can be adjusted according to the relative power requirement of two signals in the MSAA system. G. Discussion of Uncertainties As seen from the above theoretical and experimental results, there are small discrepancies between the measured controls and simulated results. We consider that these uncertainties are mainly due to the following factors. 1) Since we cannot find a way to obtain the exact reverse saturation current , the exact value of , and the true – relation of the diode used in the experiment, the parameters and used in numerical simulations are derived using typical values of and and ideal – characteristics of Schottky diodes. The inaccuracy between the estimated and exact diode parameters is one of the main reasons for the discrepancy between the calculated results and measured ones.

In this paper, an accurate and efficient theoretical scheme based on the Volterra analysis and the MoM has been proposed to investigate the performance of the MSAA with potential application to communication terminals in the MIMO systems. Experiments are conducted to validate the proposed theory, and the relative errors between the numerical results are within 5% for most results. The theoretical analysis gives clear relations of the nonlinear component parameters with the received power levels at two distinct frequencies, which may provide very useful guidelines to improve the performance of the MSAA system. More specifically, in order to increase the receiving power level of the second-order mixing product signal caused by the nonlinear diode, we can choose an optimal dc bias voltage to excite the MSE, appropriate local signal frequency and voltage magnitude, suitable length of the MSE, correct loading position to maximize the reradiation of the modulated signal, etc. Although the numerical and experimental results are illustrated only for the plane-wave incidence with fixed incident angles, the performance of the MSAA in realistic MIMO communication channels can also be predicted by using the proposed method in addition to the use of statistical approaches, which will be the focus of the authors’ future work. REFERENCES [1] J. H. Richmond, “A modulated scattering technique for measurement of field distribution,” IRE Trans. Microw. Theory Tech., vol. MTT-3, no. 4, pp. 13–15, Jul. 1955. [2] Q. W. Yuan, M. Ishizu, Q. Chen, and K. Sawaya, “Modulated scattering array antennas for mobile handsets,” IEICE Electron. Exp., vol. 2, no. 20, pp. 519–522, Oct. 2005. [3] Q. Chen, Y. Takeda, Q. W. Yuan, and K. Sawaya, “Diversity performance of modulated scattering array antenna,” IEICE Electron. Exp., vol. 4, no. 7, pp. 216–220, Apr. 2007. [4] Q. Chen, L. Wang, T. Iwaki, Y. Kakinuma, Q. W. Yuan, and K. Sawaya, “Modulated scattering array antenna for MIMO applications,” IEICE Electron. Exp., vol. 4, no. 23, pp. 745–749, Dec. 2007. [5] T. K. Sarkar and D. D. Weiner, “Scattering analysis of nonlinearly loaded antennas,” IEEE Trans. Antennas Propag., vol. AP-24, no. 3, pp. 125–131, Mar. 1976. [6] C. C. Huang and T. H. Chu, “Analysis of wire scatterers with nonlinear or time-harmonic loads in the frequency domain,” IEEE Trans. Antennas Propag., vol. 41, no. 1, pp. 25–30, Jan. 1993. [7] K. Sheshyekani, S. H. H. Sadeghi, and R. Moini, “A combined MoM–AOM approach of nonlinearly loaded antennas in the presence of a lossy ground,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1717–1724, Jun. 2008. [8] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005. [9] S. A. Mass, Nonlinear Microwave and RF Circuits, 2nd ed. Boston, MA: Artech House, 2003. [10] R. F. Harrington, Field Computation by Moment Methods. New York: Wiley, 1993. [11] M. He, “On the characteristics of radome enclosed archimedean spiral antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 7, pp. 1867–1874, Jul. 2008.

HE et al.: THEORETICAL AND EXPERIMENTAL INVESTIGATION OF MSAA FOR MOBILE TERMINAL APPLICATIONS

Mang He (M’09) received the B.S. and Ph.D. degrees in electrical engineering from the Beijing Institute of Technology, Beijing, China, in 1998 and 2003, respectively. From September 1998 to July 2003, he was a Graduate Research Associate with the Antenna and Propagation Laboratory, Beijing Institute of Technology. Since 2006, he has been an Associate Professor with the Beijing Institute of Technology. From September 2003 to September 2004, he was a Research Associate with the Department of Electronic Engineering, City University of Hong Kong. From May 2008 to March 2009, he was with the Department of Electrical and Communication Engineering, Tohoku University, Sendai, Japan, as a Postdoctoral Research Fellow. His research interests include computational electromagnetics, conformal microstrip antennas, and electromagnetic theory.

Lin Wang received the B.E. degree from the Shenyang Institute of Chemical Technology, Shenyang, China, in 2006, the M.E. degree from the Tohoku University, Sendai, Japan, in 2009, and is currently working toward the Ph.D. degree in electrical and communication engineering at Tohoku University. His research interests include diversity, MIMO wireless communications, and antenna measurement.

Qiang Chen (M’97) received the B.E. degree from Xidian University, Xi’an, China, in 1986, and the M.E. and D.E. degrees from Tohoku University, Sendai, Japan, in 1991 and 1994, respectively. He is currently an Associate Professor with the Department of Electrical Communications, Tohoku University. He has been an Associate Editor of the IEICE Transactions on Communications since 2007. His primary research interests include computational electromagnetics, array antennas, and antenna measurement. Dr. Chen is a member of the IEEE and Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the secretary and treasurer of the IEEE Antennas and Propagation Society (IEEE AP-S) Japan Chapter in 1998, the secretary of the Technical Committee on Electromagnetic Compatibility, IEICE from 2004 to 2006, the secretary of the Technical Committee on Antennas and Propagation, IEICE from 2008 to 2010. He was the recipient of the 1993 Young Scientists Award and the 2009 Best Paper Award and 2009 Zen-ichi Kiyasu Award of the IEICE.

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Qiaowei Yuan received the B.E., M.E., and Ph.D. degrees from Xidian University, Xi’an, China, in 1986, 1989 and 1997, respectively. From 1990 to 1991, she was a Special Research Student with Tohoku University, Sendai, Japan. From 1992 to 1995, she was with Sendai Research and Development Laboratories, Matsushita Communication Company, Ltd., where she was engaged in research and design of the compact antennas for second-generation mobile phones. From 1997 to 2002, she was a researcher with the Sendai Research and Development Center, Oi Electric Company Ltd., where she was engaged in the research and design of small antennas for pager communication and the parabolic antenna for 26.5-GHz fixed wireless access (FWA) communication. From 2002 to 2007, she was a Researcher with the Intelligent Cosmos Research Institute, Sendai, Japan, where she was involved in the research and development of adaptive array antennas and RF circuits for mobile communications. From 2007 to 2008, she was an Associate Professor with the Tokyo University of Agriculture and Technology. She is currently an Associate Professor with the Sendai National College of Technology. Dr. Yuan was the recipient of the 2009 Best Paper Award and 2009 Zen-ichi Kiyasu Award of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

Kunio Sawaya (SM’02) received the B.E., M.E., and Ph.D. degrees from Tohoku University, Sendai, Japan, in 1971, 1973 and 1976, respectively. He is currently a Professor with the Department of Electrical and Communication Engineerin, Tohoku University. His areas of interests are antennas in plasma, antennas for mobile communications, theory of scattering and diffraction, antennas for plasma heating, and array antennas. Dr. Sawaya is a Fellow of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He is a member of the Institute of Image Information and Television Engineers of Japan. From 2001 to 2003, he was the chairperson of the Technical Group of Antennas and Propagation, IEICE. He was the chairperson of the Organizing and Steering Committees of the 2004 International Symposium on Antennas and Propagation (ISAP’04) and the president of the Communications Society of IEICE from 2009 to 2010. He was the recipient of the 1981 Young Scientists Award, the 1988 Paper Award, the 2006 Communications Society Excellent Paper Award, and the 2009 Zen-ichi Kiyasu Award of the IEICE.

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A Multimode/Multiband Power Amplifier With a Boosted Supply Modulator Daehyun Kang, Dongsu Kim, Jinsung Choi, Jooseung Kim, Yunsung Cho, and Bumman Kim, Fellow, IEEE

Abstract—A multimode/multiband power amplifier (PA) with a boosted supply modulator is developed for handset applications. A linear broadband class-F amplifier is designed to have a constant fundamental impedance across 1.7–2 GHz and its second and third harmonic impedances are located at the high-efficiency area. To reduce the circuit size for handset application, the harmonic control circuits are merged into the broadband output matching circuit for the fundamental frequency. An envelope-tracking operation delivers high efficiency for the overall power. The linearity is improved by envelope tracking (ET) through intermodulation-distortion sweet-spot tracking at the maximum output power level. The efficiency and bandwidth (BW) are enhanced by a boosted supply modulator. Multimode operation is achieved by an ET technique with a programmable hysteresis control and automatic switching current adaptation of the hybrid supply modulator. For demonstration purpose, the PA and supply modulator are implemented using an InGaP/GaAs heterojunction bipolar transistor and a 65-nm CMOS process. For a long-term evolution signal, the envelope-tracking (ET) PA delivers a power-added efficiency (PAE) and an error vector magnitude of 33.3%–39% and 2.5%–3.5%, respectively, at an average power of 27.8 dBm across 1.7–2 GHz. For a wideband code-division multiple-access signal across 1.7–2 GHz, the ET PA performs a PAE, an ACLR1, 42.5 dBc, and and an ACLR2 of 40%–46.3%, from 39 to 51 to 58 dBc, respectively, at an average output power of 30.1 dBm. The ET PA with an EDGE signal delivers a PAE, an ACPR1, 59.3 dBc, and and an ACPR2 of 37%–42%, from 56.5 to 63.5 to 69.5 dBc, respectively, at an average power of 28 dBm across the 300-MHz BW. These results show that the proposed design achieves highly efficient and linear power amplification for multimode/multiband wireless communication applications.

Index Terms—Efficient, enhanced data rates for GSM evolution (EDGE), envelope tracking (ET), handset, heterojunction bipolar transistors (HBT), linear, long-term evolution (LTE), monolithic microwave integrated circuit (MMIC), power amplifier (PA), supply modulator, wideband code division multiple access (WCDMA).

Manuscript received May 19, 2010; revised July 04, 2010; accepted July 04, 2010. Date of publication September 02, 2010; date of current version October 13, 2010. This work was supported by the World Class University (WCU) Program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (Project R31-2008-000-10100-0), and by The Ministry of Knowledge Economy (MKE), Korea, under the Information Technology Research Center (ITRC) Support Program supervised by the National IT Industry Promotion Agency (NIPA) [NIPA-2010-(C1090-1011-0011)]. D. Kang, D. Kim, J. Kim, Y. Cho, and B. Kim are with the Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk 790-784, Korea (e-mail: [email protected]; [email protected]). J. Choi is with the Samsung Advanced Institute of Technology (SAIT), Yongin-si, Gyeonggi 446-712, Korea. Digital Object Identifier 10.1109/TMTT.2010.2063851

I. INTRODUCTION

P

OWER amplifiers (PAs) for multifunctional smart mobile phones have become a very challenging area because the PA should handle voice, data, and broadcast with global roaming capability. Therefore, the PAs should have a multimode/multiband capability with high efficiency [1]. The input/output matching components of the transmitter are sensitive to frequency, thus preventing multiband operation. Low amplification efficiency leads to a short battery life and heat in mobile handsets. Moreover, as the information content increases, modulation systems need to have wider bandwidths (BWs) and a higher peak-to-average power ratio (PAPR), causing the PA to operate in a less efficient back-off region for linearity. To improve the low efficiency at the back-off power region, many efficiency enhancement techniques have undergone research for a long period of time. The Doherty and the envelope elimination and restoration (EER) techniques have been investigated for high efficiency at the back-off power region. The efficiency at the back-off power region is important for handset applications because of frequent use of lower power levels and the high PAPR of the signals. The Doherty technique modulates the load according to the power level [2]–[5]. The load modulation is often achieved by a quarter-wavelength transformer, and linear operation is accomplished by third-order intermodulation (IM3) cancellation between the main and auxiliary amplifiers. Both of these are sensitive to the frequency of operation. Thus, the Doherty PAs have a limit for broadband operation. The EER technique involves modulating the supply voltage according to the power level of a PA, and enhances efficiency at the back-off power region [6]–[16]. The EER structure comprises the supply modulator and the PA. Only the PA determines the RF operating frequency band. Thus, the EER technique is more advantageous for broadband operation than the Doherty technique. The efficiency of the EER structure is determined by multiplication of the efficiencies of the supply modulator and the PA [12]. A highly efficient EER structure requires that both the supply modulator and PA be efficient. Thus, class-E, class-F, class-D, and class-J PAs can be candidates. The class-E PAs achieve high efficiency by turning on the transistor at the point when the drain–source (collector–emitter) capacitor does not have any charge. The class-F PA controls the voltage waveform to ensure it is square shaped, which increases the magnitude of the fundamental voltage, output power, and efficiency [17], [18]. The class-D PA controls the harmonics in a similar way to the

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KANG et al.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR

class-F PA, using a push–pull structure. The class-J PA utilizes the phase shift between the output current and voltage waveforms to render the second harmonic termination to a purely reactive regime [19]. The broadband approaches for class-E PAs and class-F PAs have been studied in [20] and [21]. However, these concepts are for base-station PAs, and use microstrip lines for matching. The microstrip lines are too bulky to be employed in PAs for handset applications. In [22], we have proposed broadband class-F PAs, which control the second and third harmonic impedances across a broad BW, but linearity is not considered as we intend to use a digital pre-distortion (DPD) technique. Broadband class-J PAs for base-station PAs have been also investigated [19]. The researchers have found the optimum efficiency contour for class-J operation across a broad BW, and matched the load impedance to the contour, thus, a 50% fractional BW with high efficiency is achieved. A gallium–nitride (GaN) device with a high supply voltage has a low for the output impedances due to the small output capacitance, and its gain drops 3 dB per octave frequency (normally it is 6 dB/octave because of its operation at the maximum stable gain (MSG) region). Despite the advantageous characteristics of the GaN device, it is too expensive at the moment to be utilized for handset devices and it requires too high bias voltage. The ideal EER structure would deliver a 100% efficiency using a highly efficient supply modulator, but the limited BW of switching amplifiers and the low efficiency of wideband linear amplifiers for the modulators degrades the ideal efficiency. Some researchers have utilized the advantages of the wide-BW linear amplifier and the high-efficiency switching amplifier [10]–[15]. The switching amplifier does not follow most of the high slew-rate load current, and operates as a quasi-constant current source. The linear amplifier supplies and sinks the current to regulate the load according to the envelope of the signal. This structure is suitable for the envelope signal of modern wireless communication systems, which has the most power in the low-frequency region. In [15], we have proposed a hybrid switching amplifier (HSA) for multistandard applications. Automatic switching current adaption from an HSA and programmable hysteresis control can achieve multimode operation. In this paper, we propose a multimode/multiband PA with a boosted supply modulator for handset applications. For this multiband PA design, the fundamental load is maintained at a consistent level across the BW. Harmonic impedances are searched for highly efficient class-F operation. The harmonic circuits are merged into the broadband matching circuit, thereby reducing their size and increasing the available BW. In contrast to our previous paper [22], the PA matching is modified for linear class-AB bias. An HSA with a boost converter driving the linear stage increases the RF BW due to reduced output capacitance of the RF device at the higher operating voltages provided by the boost converter. The HSA also improves the efficiency due to envelope tracking (ET). Finally the HSA improves linearity due to intermodulation-distortion (IMD) sweetspot tracking. Multimode operation for various wireless applications is accomplished thanks to programmable hysteresis control and automatic switching current adaptation from the HSA.

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Fig. 1. (a) Conventional polar transmitter for multimode/multiband operation. (b) Proposed polar transmitter for multimode/multiband operation.

For demonstration purposes, the PA and supply modulator are implemented using an InGaP/GaAs HBT and a 65-nm CMOS processes, and are operated with signals of long-term evolution (LTE), wideband code division multiple access (WCDMA), and EDGE across frequencies of 1.7–2 GHz. The measured results prove that the proposed design achieves highly efficient and linear power amplification for multimode/multiband applications. II. MULTIMODE/MULTIBAND POLAR TRANSMITTER A conventional polar transmitter for multimode/multiband operation requires a PA and a supply modulator for each wireless communication standard, as shown in Fig. 1(a). For example, if we need transmitters operating for an LTE, a WCDMA, and an EDGE application across a 1.7–2.0-GHz frequency, supply modulators and PAs need to operate at different switching frequencies and operate at different RF frequencies for each standard. The LTE signal has a BW of 10 MHz and a PAPR of 7.5 dB. WCDMA and EDGE signals have BWs of

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3.84 MHz and 384 kHz, respectively, and a PAPR of 3.5 dB. Each supply modulator for each application should be employed for multimode operation. Moreover, if a narrowband PA is used, then every RF band will require the addition of another PA. Therefore, for simplicity and low cost, we propose a multimode/multiband ET polar transmitter using a multimode supply modulator [15] and a broadband class-F PA [22], as illustrated in Fig. 1(b). The broadband class-F PA can cover the frequency band of 1.7–2 GHz while maintaining high efficiency and linearity. This will be revisited in Sections III and IV. The switching frequency and switching currents of the switching stage can be controlled by programmable hysteresis control and automatic switching current adaptation from the hybrid supply modulator according to each communication application. Moreover, by employing the ET technique, the supply voltage provided to the PA follows the envelope of the signal so the dc power that the PA consumes can be significantly reduced, and the power-added efficiency (PAE) can be significantly increased at the average power level, as well as at the peak output power level. III. TECHNIQUES FOR HIGH EFFICIENCY AND BROADBAND A. Class-AB/F PAs A highly efficient class-AB/F PA has been proposed in [25], which enhances the efficiency by controlling the second and third harmonics while maintaining their linearity. By setting the base bias to near class B, it efficiently amplifies phase-only information such as the global system for mobile communications (GSM) signal. With a bias level of class AB, it efficiently and linearly amplifies both the phase and amplitude information including CDMA, LTE, WiMAX, and EDGE signals. The output is set to an intermediate value for mulload impedance timode operation. Class-E, inverse class-F, or class-J PAs can provide an even higher efficiency or a broader BW, but we adopt the efficient and linear class-F PA for ET operation because linearity improvement techniques such as DPD are still a burden for the PAs of handset applications. To employ a class-AB/F PA for an ET polar transmitter V , the fundamental with a boosted supply voltage for a 1-dB compression load impedance is set to be power (P1 dB) of 32 dBm, and a class-AB bias level (98 mA) is chosen. The second and third harmonic impedances are found for high-efficiency operation with a fixed fundamental output load, as shown in Fig. 2. This figure shows that a third harmonic impedance several times larger than the fundamental load impedance delivers high efficiency. This can be easily achieved across the broadband frequency range. The second harmonic impedance is more sensitive to the matching circuit than the third harmonic impedance, but is manageable over a few hundred megahertz BW using a second harmonic control circuit. B. Broadband Matching Techniques There are equations that transform a low-pass filter (LPF) to a bandpass filter (BPF) [26]. The BPF does not allow the impedance transformation required for PA designs. The BPFs

Fig. 2. Simulated load–pull results at a frequency of 1.85 GHz. (a) For third harmonic impedance. The fundamental and second harmonic impedances are fixed at 6+j 1 and 0:5 j 2:5, respectively. (b) For second harmonic impedance. The fundamental and secord harmonic impedances are fixed at 6 + j 1 and 25 + j 200, respectively.

0

shown in Fig. 3(c) and (d) make it possible to transform the impedances and to have bandpass characteristics. To analyze the needs to be recalled. A loaded , deBW, the concept of , is defined by noted by (1) The circuit node

, denoted by

, is defined at each node as (2)

is a transformed resistance from and is larger where . The smaller leads to broader BW, which means than that the same impedance transformation ratio using two-section matching achieves a wider BW. In Fig. 3(c)–(f), to get the lowest with the impedance transformation, the relationship of impedances is given by (3) Fig. 3(e) is a high-pass filter (HPF) type matching circuit, as which comprises two sections, and it has the same

KANG et al.: MULTIMODE/MULTIBAND PA WITH BOOSTED SUPPLY MODULATOR

Fig. 3. Impedance-matching circuits. (a) LPF type. (b) BPF type. (c) and (d) BPF type with impedance transformation. (e) Two-section HPF type. (f) Two-section LPF type.

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is resonated out at the third harmonic frequency capacitance by the inductance at the bias line. The fundamental impedance – type broadband matching. The shunt matching uses has an inductance at the operating frequency, and can be for broadband matching. merged into a bondwire The simulated load impedances including the components’ loss are shown in Fig. 5(a). The load impedances across the 1.7–2.0-GHz frequency are constant with power matching. The second harmonic impedances across the 3.4–4.0-GHz frequency are near zero, which is located at the high-efficiency region in Fig. 2(b). The third harmonic impedances across the 5.1–6.0-GHz frequency are high, which is also located at the high efficiency region in Fig. 2(a). Fig. 5(b) shows the broadband characteristic of the insertion over the frequency rage of 1.7–2.0 GHz. has the loss two nulls at 3.3 and 3.8 GHz, which are produced by with , respectively. With this circuit a short microstrip line and topology, the harmonic control circuits are merged into the fundamental matching elements, realizing a small size for handset applications. D. Boosted Supply Voltage

Fig. 3(c) and (d). The 3-dB BW might be the same, but the BPF types are better because the BPFs maintain more consistent impedance level across lower to upper bands. Moreover, the BPF types shown in Fig. 3(c) and (d) have an advantage of smaller inductance than the HPF of Fig. 3(e) because a series inductance (reactance) is smaller than a shunt inductance (susceptance) where a low impedance is transformed into a high impedance of 50 in the PA designs. The series inductors marked with a star and with a circle in Fig. 3(c) and (d), respectively, are smaller than those marked in Fig. 3(e). Fig. 3(f) is an LPF type matching circuit. Even though the BW is broad, an LPF is a unwelcome circuit for the input and output matching of handset PAs because dc currents from the supplies should be blocked. The BPFs shown in Fig. 3(d) are employed in this broadband class-F PA design because of their broadband characteristics and their small inductor values, which can be easily replaced by bondwires. C. Input, Interstage, and Output Matching As illustrated in Fig. 4, an input capacitance composed of and increased by Miller’s theorem is merged into the se– broadband matching circuit [see ries inductor of the Fig. 3(d)] to maximize the BW. The intermediate impedance is set as 10 to transform the 2 of the input resistance to the 50 of the input terminal. The interstage is matched with two-section HPFs, including the bias line inductance at the collector of the drive stage. The HPFs also have a low-impedance transformation ratio to maximize the BW. The output matching comprises a broadband fundamental impedance matching, the second harmonic short circuits and the third harmonic open cirhas a near zero impedance at the upper band of the cuit. with a short microstrip line has a second harmonic and near-zero impedance at the lower band of the second harmonic. Thus, the voltage waveform of the second harmonic is effecprovides tively reduced across the broadband. The shunt a high impedance at the third harmonic frequency. The output

The supply voltage of the linear stage of the HSA is increased from 3.4 to 5 V by the boost converter depicted in Fig. 4. Since the buffer comprising the linear stage has a voltage drop of 0.5 V, the output voltage swing of the supply modulator is boosted up to 4.5 V. Our previous HSA [15] had a maximum output voltage of only 3 V. Due to the boosted output voltage, the PA can generate more power with the same output load. In other words, the output load impedance can be raised for the same output power as illustrated in Fig. 6, which delivers a higher efficiency and broadband characteristics. The broadband characteristics are explored using the output capacitance variation plot is swept with fundashown in Fig. 7. The supply voltage mental load impedances of 2.5, 3.5, 4.7, and 6 , which deliver the same output power with the maximum supply voltages of 3, 3.5, 4, and 4.5 V, respectively. When ET operation follows the highest efficiency at each supply voltage, the output capacitance trajectory in Fig. 7. The output of the transistor follows the capacitance is calculated by the method shown in [24]. As the supply voltage decreases, the output capacitance increases. At of 2.5 with a an output power of 32 dBm, the PA using supply voltage of 3 V has about a 10% larger output capacitance of 6 with a supply voltage of 4.5 V. If an than that using LTE signal with a 7.5-dB PAPR is applied to the PA, the maximum average power is theoretically 24.5 dBm because the P1 dB of the PA is 32 dBm. In actual operation, however, the PA can achieve an average output power of about 28 dBm because some portion of the peak signal could be saturated while maintaining an acceptable linearity specification. Besides the smaller output has a smaller impedance capacitance, the PA with a 4.5-V transformation ratio, which assists in increasing the operational RF BW. Fig. 8(a) shows a simulated continuous wave (CW) performance for PAE and gain of the supply voltages of 2.6 V with a load of 6 and 2 V with a load of 2.5 for the power stage. The supply voltages are reduced for operation of the LTE average output power of 28 dBm. The PA with 6 has 10% higher PAE and higher gain. Fig. 8(b) shows the insertion loss obtained by a

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Fig. 4. Schematic of the ET transmitter with broadband class-F PA and boosted supply modulator.

large-signal -parameter at an output power of 28 dBm, which shows a broader BW for a supply voltage of 2.6 V because of the smaller output capacitance and the impedance transformation ratio. IV. TECHNIQUES FOR MULTIMODE OPERATION OF HSA An HSA consists of a boost converter, linear stage, hysteretic comparator, and switching stage, as shown in Fig. 4. The boost converter is connected to the linear stage to boost the output voltage swing. The linear stage works as an independent voltage source throughout the feedback network, while the switching stage operates as a dependent current source to provide most of the current to the output. The current sensing circuit detects the current at the output of the linear stage, and controls the state of the switching stage according to the magnitude and polarity of the sensed current. A detailed overview of the HSA operation is explained clearly in [15]. Multistandard signals have different

PAPRs and BW. The adaptation of the switching currents for the various PAPRs are automatically performed by the current sensing circuit and the hysteretic comparator in the HSA. The switching current is proportional to the difference between and , as shown in Fig. 4. The sensed current generates the , which is proportional to the input of the sensed voltage envelope signal. Thus, the square of the switching current is inversely proportional to the PAPR. The adaptation of switching currents for multistandard signals is shown in Fig. 9, which illustrates the probability density function (pdf) and the efficiency of the HSA. For a multimode HSA design, the switching condition is optimized for the wideband signal by determining an inductor value at the output of the switching stage. A narrowband signal whose slew rate is lower than that of the switching amplifier leads to an excessively high switching frequency and poor efficiency of the switching stage. Thus, we utilize a programmable hysteretic comparator, and the which enables us to control the hysteresis voltage

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Fig. 7. Output capacitance as functions of R , V , and output power. With trajectory. an ET operation, the output capacitance of the PA follows the C

Fig. 5. Simulated nents’ loss.

S -parameters of output matching circuit including compo-

Fig. 6. Load line of 2.5 and 6 for 3.4- and 4.5-V operation for the same maximum output power. Load line for 4.5 V gives higher efficiency and broader BW, as well as more linear ET operation at the low-power level.

switching frequency. Efficiency of about 3% is enhanced by controlling the hysteresis voltage for the EDGE signal. The envelope is modified for linear ET operation, as depicted in Fig. 10. The equation for the envelope shaping is given by Envelope

Envelope

Offset (4)

where is a back-off power level from the peak average power. The PA has AM/AM and AM/PM distortions at a low supply voltage because of the increased output capacitance, as shown

Fig. 8. (a) Simulated CW performance of PAE and gain with supply voltages of 2.6 and 2 V for the power stage. The PAs with 2.6- and 2-V V have R of 6 and 2.5 , respectively, to generate the same powers. Ideal LC –CL type broadband matching circuits are employed at the input and the output. (b) Simulated large-signal insertion loss at an output power of 28 dBm.

in Fig. 7, and increased ratio of knee to the . Thus, the minimum of the envelope is set as 0.8 V. As the power level is varied, the slope of the envelope is modified by the equation for the compensation of low gain near the knee region while back-off maintaining the offset voltage. It is noted that or a lower value is applied to the equation for the maximum average output power because PAs often operate in saturation, but is still under the specification. With the envelope-shaping method, the PA always operates at the IMD sweet spot tracked

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Fig. 9. Simulated average switching currents adaptation for LTE, WCDMA, and EDGE signals. The switching currents are normalized as 640 mA. The pdf ). of each signal is also depicted as a function of i (= V =R

Fig. 10. Function of envelope shaping.

by the envelope of signal, and the overall IMD level is lowered significantly [23]. V. EXPERIMENTAL RESULTS The proposed multimode/multiband PA with a boosted supply modulator is fabricated in an InGaP/GaAs HBT 2- m process and a CMOS 65-nm process, respectively. The HBT PA is integrated onto a chip, except for five capacitors at the input and the output. Inductors are replaced by bondwires and slab inductors on the chip to ensure low loss. The second harmonic control circuit is implemented with an off-chip capacitor and a bonding wire, and the third harmonic control is accomplished by on-chip slab inductors and metal–insulator–metal (MIM) capacitors for a high- factor. For the CMOS supply modulator, all the circuit blocks are integrated on the chip, except the large inductor. The two chips are mounted on an FR-4 printed circuit board. The broadband PA is built by comparing the simulated and measured -parameter results. Fig. 11 shows that the simulated and measured results with a shows a flat supply voltage of 3.4 V are well matched and response across the fundamental frequencies (1.7–2 GHz). The quiescent currents are set as 38 and 98 mA for the drive and power stages, respectively. It is interesting to note that with the supply modulator, the 98-mA quiescent current is reduced as the input power decreases, and it becomes 3 mA when

Fig. 11. Measured and simulated S -parameters with a supply voltage of 3.4 V.

Fig. 12. Measured CW performance at 1.85 GHz by sweeping a collector voltage from 1.4 to 4.5 V.

there is no input signal that turns off the switching stage and outputs 0.5 V from the linear stage of the supply modulator. The fabricated PA with a supply voltage of 4.5 V delivers a P1 dB of 31.5 dBm, a gain of 29.5 dB, and a PAE of 49.8% at a frequency of 1.85 GHz, as shown in Fig. 12. The supply voltage is swept from 1.4 to 4.5 V, and the expected PAE for the ET operation follows the measured PAE trajectory. The measured performance of the HSA is summarized in Table I. The supply modulator has a peak efficiency of 90% for a load impedance of 8 , and delivers an output swing of 0.5–4.5 V thanks to the boost converter connected to the linear stage. The switching frequency for an EDGE signal is reduced to 3.4 MHz ) by from the switching frequency of 10.5 MHz (at to 90 mV because the low switching provides increasing a higher efficiency for the EDGE signal, which has a low slew rate due to the narrow BW (384 kHz). The average switching currents are adjusted for the signals’ pdf. For a demonstration of multimode/multiband operation, the ET PA is tested with 10-MHz BW 16 quadrature amplitude modulation (16-QAM) 7.5-dB PAPR LTE, 3.84-MHz BW 3.5-dB PAPR WCDMA, and 384-kHz BW 3.5-dB PAPR EDGE signals. Fig. 13(a) shows the measured performance of the ET PA across a 1.7–2-GHz frequency for the LTE signal. The PA has a PAE and an error vector magnitude (EVM) of 33.3%–39% and 2.5%–3.5%, respectively, at the average

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TABLE I PERFORMANCE OF THE MULTIMODE SUPPLY MODULATOR

Fig. 14. (a) Measured performance of ET PA and standalone PA at the output powers of 27.8 and 25.9 dBm, respectively, across 1.7–2 GHz. (b) Measured spectra.

Fig. 13. (a) Measured performance of ET PA across 1.7–2 GHz for a 10-MHz BW 16-QAM 7.5-dB PAPR LTE signal. (b) Measured performance comparison of ET PA and standalone PA, and the maximum output powers are 27.8 and 25.9 dBm, respectively.

output power of 27.8 dBm. The gain is 26.8–27.8 dB across the BW. ACLR is measured with a 9-MHz resolution BW at both a center frequency and a 10-MHz offset. The ACLR is shown below the LTE ACLR specification of 30 dBc. Fig. 13(b) shows the performance comparison of the ET PA with the boosted supply modulator and the standalone PA with a supply voltage of 3.4 V. The output power is 27.8 dBm for the ET PA and is 25.9 dBm for the standalone PA. The boosted

supply modulator provides the ET PA a dc voltage swing from 0.5 to 4.5 V so larger output power is generated from the ET PA than the standalone PA with a 3.4-V supply voltage with the . The PAE is improved by more than 4% at the peak same average power across the BW, and the PAE is enhanced by up to 7% at the back-off power region. It is worthwhile to note that the linearity of the ET PA is improved at the peak average power level due to the IMD sweet-spot tracking that we proposed in [23]. Fig. 14(a) shows the measured performance of the ET and standalone PAs at power levels of 27.8 and 25.9 dBm, respectively, across the 1.7–2-GHz frequency. It is noted that the gain performance for the ET operation is flatter across the 1.7–2-GHz frequency because of the relatively smaller output capacitance, thanks to the boosted supply modulator. The EVM and ACLR, which indicate the linearity of the PA, are improved by ET operation. Fig. 14(b) is the spectra of the ET PA and the standalone PA at power levels of 27.8 and 25.9 dBm. The ET PA has more margin under the LTE spectrum mask. Fig. 15 is a comparison of measured EVM, and the EVM performance is improved from 3.4% to 2.5% at a frequency of 1.7 GHz due to the sweet-spot tracking [23]. Fig. 16 shows the performance comparison of the ET PA with the boosted supply modulator and the standalone PA with

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Fig. 15. Measured EVM at a frequency of 1.7 GHz. (a) 3.4% EVM at an average power of 25.9 dBm for the 3.4-V standalone PA. (b) 2.5% EVM at an average power of 27.8 dBm for the ET PA with the boosted supply modulator.

Fig. 16. Measured performance of ET PA and standalone PA for a 3.84-MHz BW 3.5-dB PAPR WCDMA signal across 1.7–2 GHz, and the maximum output powers are 30.1 and 28.1 dBm, respectively.

a supply voltage of 3.4 V for a WCDMA signal, which has a BW of 3.84 MHz and a PAPR of 3.5 dB. In comparison with Fig. 13(b), the PAE for the WCDMA signal at the peak average output power shows 1%–2% less improvement than that for the LTE due to the lower PAPR of WCDMA, and the ACLR at the peak average power shows more improvement because the linear stage of the supply modulator has less of a BW burden for the 3.84-MHz WCDMA signal. At a back-off average output

Fig. 17. (a) Measured performance of ET PA and standalone PA for a WCDMA signal at the output powers of 30.1 and 28.1 dBm, respectively, across 1.7–2 GHz. (b) Measured spectra.

power region ( 8 dB), the PAE for the WCDMA has a greater improvement because of the higher efficiency of the supply modulator due to the lower PAPR than that for the LTE signal. ACLR1 and ACLR2 are measured with a 3.84-MHz resolution BW at frequency offsets of 5 and 10 MHz, respectively. ACLR1 and ACLR2 are measured below the WCDMA ACLR specification of 33 and 43 dBc, respectively, for the ET PA. Fig. 17(a) shows the measured performance of the ET PA and standalone PA at the output powers of 30.1 and 28.1 dBm, respectively, across a 1.7–2-GHz frequency. Fig. 17(b) shows the measured spectra of the ET PA and the standalone PA at the output powers of 30.1 and 28.1 dBm, respectively. The ET PA is also performed with an EDGE signal, which has the BW of 384 kHz and the PAPR of 3.5 dB. Fig. 18(a) shows the performance of the ET PA and the standalone PA with a supply voltage of 3.4 V at the average output powers of 28 and 27 dBm, respectively. The PAE of the ET PA is improved by 3%–4% than that of the standalone PA. ACPR1 and ACPR2 are measured with a 30-kHz BW at frequency offset of 400 and is set to 90 mV to reduce 600 kHz. The hysteresis voltage , from 10.7 to 3.4 MHz. The overall the switching frequency PAE is then improved by about 2%. Fig. 18(b) shows the measured spectra. The ACPR around the offset frequency of 400 kHz is improved and the ACPR at the

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56.5 to 59.3 dBc, and 63.5 to 69.5 dBc, respectively, at an average output power of 28 dBm. These results verify that the proposed design achieves highly efficient and linear power amplification for multimode/multiband wireless communication applications. ACKNOWLEDGMENT The authors would like to thank Wireless Power Amplifier Module (WiPAM) Inc., Seongnam, Gyeonggi, Korea, for the advice and the chip fabrication. REFERENCES

Fig. 18. (a) Measured performance of ET PA and standalone PA for an EDGE signal at the output powers of 28 and 27 dBm, respectively, across 1.7–2 GHz. V is set to be 90 mV for f of 3.4 MHz. (b) Measured spectra.

outband is degraded because the ripple currents increase as the switching frequency decreases, but the spectrum is still under the EDGE specification of 60 dBc. VI. CONCLUSIONS A multimode/multiband PA with a boosted supply modulator is developed for handset applications. A linear broadband class-F amplifier is designed to operate across a 1.7–2-GHz frequency. The harmonic control circuits are merged into the broadband output matching circuit for the fundamental frequency. The efficiency and BW are enhanced by the boosted supply modulator. The ET operation delivers high efficiency at the overall power level and improves the linearity at the maximum output power by IMD sweet-spot tracking. Multimode operation for various wireless application is accomplished thanks to programmable hysteresis control and automatic switching current adaptation from the HSA. For an LTE signal, the ET PA delivers a PAE and an EVM of 33.3%–39% and 2.5%–3.5%, respectively, at an average output power of 27.8 dBm across 1.7–2 GHz. For a WCDMA signal across 1.7–2 GHz, the ET PA performs a PAE, an ACLR1, 42.5 dBc, and an ACLR2 of 40%–46.3% from 39 to 58 dBc, respectively, at an average output and 51 to power of 30.1 dBm. The ET PA with an EDGE signal delivers a PAE, an ACPR1, and an ACPR2 of 37%–42%, from

[1] S. C. Cripps, Advanced Techniques in RF Power Amplifier Design. Norwood, MA: Artech House, 2002. [2] W. H. Doherty, “A new high efficiency power amplifier for modulated waves,” Proc. IRE, vol. 24, no. 9, pp. 1163–1182, Sep. 1936. [3] F. H. Raab, “Efficiency of Doherty RF power amplifier systems,” IEEE Trans. Broadcast., vol. BC-33, no. 3, pp. 77–83, Sep. 1987. [4] M. Iwamoto, A. Williams, P. F. Chen, A. G. Metzger, L. E. Larson, and P. M. Asbeck, “An extended Doherty amplifier with high efficiency over a wide power range,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2472–2479, Dec. 2001. [5] D. Kang, J. Choi, D. Kim, and B. Kim, “Design of Doherty power amplifiers for handset applications,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 8, pp. 2134–2142, Aug. 2010. [6] L. Kahn, “Single-sideband transmission by envelope elimination and restoration,” Proc. IRE, vol. 40, no. 7, pp. 803–806, Jul. 1952. [7] D. K. Su and W. J. McFarland, “An IC for linearizing RF power amplifiers using envelope elimination and restoration,” IEEE J. Solid-State Circuits, vol. 33, no. 12, pp. 2252–2258, Dec. 1998. [8] J. Staudinger, B. Gilsdorf, D. Newman, G. Norris, G. Sadowniczak, R. Sherman, and T. Quach, “High efficiency CDMA power amplifier using dynamic envelope tracking technique,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2000, pp. 873–976. [9] P. Raynaert and S. Steyaert, “A 1.75-GHz polar modulated CMOS RF power amplifier for GSM-EDGE,” IEEE J. Solid-State Circuits, vol. 40, no. 12, pp. 2598–2608, Dec. 2005. [10] J. Kitchen, W. Chu, I. Deligoz, S. Kiaei, and B. Bakkaloglu, “Combined linear and -modulated switched-mode PA supply modulator for polar transmitters,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2007, pp. 82–83. [11] T. Kwak, M. Lee, B. Choi, H. Le, and G. Cho, “A 2 W CMOS hybrid switching amplitude modulator for EDGE polar transmitter,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2007, pp. 518–519. [12] F. Wang, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. C. Lie, P. M. Asbeck, and L. E. Larson, “An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 12, pp. 4086–4099, Dec. 2006. [13] F. Wang, D. F. Kimball, D. Y. Lie, P. M. Asbeck, and L. E. Larson, “A monolithic high-efficiency 2.4-GHz 20-dBm SiGe BiCMOS envelopetracking OFDM power amplifier,” IEEE J. Solid-State Circuits, vol. 42, no. 6, pp. 1271–1281, Jun. 2007. [14] W. Chu, B. Bakkaloglu, and S. Kiaei, “A 10 MHz-bandwidth 2 mV-ripple PA-supply regulator for CDMA transmitters,” in IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2008, pp. 448–449. [15] J. Choi, D. Kim, D. Kang, and B. Kim, “A polar transmitter with CMOS programmable hysteretic-controlled hybrid switching supply modulator for multi-standard applications,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 7, pp. 1675–1686, Jul. 2009. [16] J. Choi, D. Kang, D. Kim, J. Park, B. Jin, and B. Kim, “Power amplifiers and transmitters for next generation mobile handset,” J. Semicond. Tech. Sci., vol. 9, no. 4, pp. 249–256, Dec. 2009. [17] Y. Y. Woo, Y. Yang, and B. Kim, “Analysis and experiments for high efficiency class-F and inverse class-F power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 1969–1974, May 2006. [18] P. Colantonio, F. Giannini, G. Leuzzi, and E. Limiti, “On the class-F power amplifier design,” Int. J. RF Microw. Comput.-Aided Eng., vol. 9, no. 2, pp. 129–149, 1999. [19] P. Wright, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “A methodology for realizing high efficiency class-J in a linear and broadband PA,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 3196–3204, Dec. 2009.

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[20] P. Butterworth, S. Gao, S. F. Ool, and A. Sambell, “High-efficiency class-F power amplifier with broadband performance,” Microw. Opt. Technol. Lett., vol. 44, no. 3, pp. 243–247, Feb. 2005. [21] Y. Qin, S. Gao, P. Butterworth, E. Korolkiewicz, and A. Sambell, “Improved design technique of a broadband class-E power amplifier at 2 GHz,” in Proc. Eur. Microw. Conf., Oct. 2005, vol. 1, pp. 453–456. [22] D. Kang, J. Choi, M. Jun, D. Kim, J. Park, B. Jin, D. Yu, K. Min, and B. Kim, “Broadband class-F power amplifiers for handset applications,” in Proc. 39th Eur. Microw. Conf., Sep. 2009, pp. 1547–1550. [23] D. Kim, J. Choi, D. Kang, J. Choi, and B. Kim, “High efficiency and wideband ET PA with sweet spot tracking,” in Proc. IEEE Radio Freq. Integr. Circuits Symp., 2010, pp. 255–258. [24] Y. Zhao, A. Metzger, P. Zampardi, M. Iwamoto, and P. Asbeck, “Linearity improvement of HBT-based Doherty power amplifiers based on a simple analytical model,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4479–4488, Dec. 2006. [25] D. Kang, D. Yu, K. Min, K. Han, J. Choi, B. Jin, D. Kim, M. Jeon, and B. Kim, “A highly efficient and linear class-AB/F power amplifier for multi-mode operation,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 1, pp. 77–87, Jan. 2008. [26] D. M. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 2005. Daehyun Kang received the B.S. degree in electronic and electrical engineering from Kyungpook National University, Daegu, Korea, in 2006, and is currently working toward the Ph.D. degree in electrical engineering at the Pohang University of Science and Technology (POSTECH), Pohang, Korea. His main interests are RF circuits for wireless communications, especially highly efficient and linear RF transmitters and RF PA design.

Dongsu Kim received the B.S. degree in electrical engineering from the Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2007, and is currently working toward the Ph.D. degree in electrical engineering at POSTECH. His research interests are CMOS RF circuits for wireless communications, with a special focus on highly efficient and linear RF transmitter design.

Jinsung Choi received the B.S. and Ph.D. degrees in electrical engineering from the Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2004 and in 2010, respectively. He is currently with the Samsung Advanced Institute of Technology (SAIT), Yongin-si, Korea. His main research interests are analog/RF circuit design in ultra-deep submicrometer CMOS technology, mixed-mode signal-processing integrated-circuit design, and digitally assisted RF transceiver architectures.

Jooseung Kim received the B.S. degree in electrical engineering from the Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2010, and is currently working toward the Ph.D. degree in electrical engineering at POSTECH. His research interests are CMOS RF circuits for wireless communications with a special focus on highly efficient and linear RF transmitter design.

Yunsung Cho received the B.S. degree in electrical engineering from Hanyang University, Ansan, Korea, in 2010, and is currently working toward the Ph.D. degree in electrical engineering at the Pohang University of Science and Technology (POSTECH), Pohang, Korea. His main interests are RF circuits for wireless communications with a special focus on highly efficient and linear RF transmitters and RF PA design.

Bumman Kim (M’78–SM’97–F’07) received the Ph.D. degree in electrical engineering from Carnegie.Mellon University, Pittsburgh, PA, in 1979. From 1978 to 1981, he was engaged in fiber-optic network component research with GTE Laboratories Inc. In 1981, he joined the Central Research Laboratories, Texas Instruments Incorporated, where he was involved in development of GaAs power field-effect transistors (FETs) and monolithic microwave integrated circuits (MMICs). He has developed a large-signal model of a power FET, dual-gate FETs for gain control, high-power distributed amplifiers, and various millimeter-wave MMICs. In 1989, he joined the Pohang University of Science and Technology (POSTECH), Pohang, Gyungbuk, Korea, where he is currently a Namko Professor with the Department of Electrical Engineering, and Director of the Microwave Application Research Center, where he is involved in device and circuit technology for RF integrated circuits (RFICs). In 2001, he was a Visiting Professor of electrical engineering with the California Institute of Technology, Pasadena. He has authored over 200 technical papers. Dr. Kim is a member of the Korean Academy of Science and Technology and the Academy of Engineering of Korea. He was an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and a Distinguished Lecturer of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

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Space-Charge Plane-Wave Interaction at Semiconductor Substrate Boundary Ibrahim A. Elabyad, Mohamed S. Eldessouki, and Hadia M. El-Hennawy, Member, IEEE

Abstract—A theoretical investigation of space-charge planewave interaction at dielectric–semiconductor interfaces is presented. A full-wave and charge transport formulation is applied to the analysis of the fundamental mode of propagation in a semiconductor substrate backed with a ground plane. Closed-form expressions for the field components, charge carrier density, and current density are obtained. The reflection coefficients for both - and -polarized incident waves were then derived from the field solutions. The interaction between the fields and charge carriers causes a charge accumulation at the semiconductor surface in the case of -polarization. The effects of the charge accumulation on the reflection coefficient are accounted for. Results indicate that the space charge exerts a weak effect on the reflection coefficient and a strong screening effect on the normal component of the electric field. The tangential component, however, is mainly governed by energy dissipation effect resulting from the conduction current. Index Terms—Charge accumulation, plane-wave interaction, semiconductor substrate, wave-charge transport model.

I. INTRODUCTION

A

N investigation of space-charge plane-wave interaction at semiconductor substrate backed with a ground plane is performed. In the earlier used approaches, the semiconductor substrates were described by a uniform conductivity and the electrical property of the semiconductor is characterized by conductivity and dielectric constant. When the semiconductor volume contains several junctions such as pn or n n, the uniform conductivity assumption no longer always represents the transverse transport accurately. Diffusion of charge carriers away from the transitional zones between bulk and space-charge depletion regions in the vicinity of a junction causes a change in the field-carrier interaction within a few Debye lengths of each regional interface. Static and dynamic characteristics of the charge transport behavior will be altered and wave propagation behavior will also be changed. These additional considerations

Manuscript received May 17, 2009; revised May 10, 2010; accepted May 10, 2010. Date of publication September 16, 2010; date of current version October 13, 2010. This work was supported by the Thebes Higher Institute of Engineering. I. A. Elabyad is with the Chair of Microwave and Communication Engineering, University of Magdeburg “Otto von Guericke,’’ Magdeburg 39106, Germany (e-mail: [email protected]). M. S. Eldessouki is with the Department of Studies and Designs, Vice Presidency of Projects, King Saud University, Riyadh 11451, Saudi Arabia (e-mail: [email protected]). H. M. El-Hennawy is with the Faculty of Engineering, Department of Electrical and Computer Engineering, Ain Shams University, Cairo, Egypt (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.2010.2065931

are especially important in the process of modeling and developing new microwave and opto-electronic devices. Devices that have very small transverse dimensions, micrometer and submicrometer feature sizes, which are increasingly seen in higher frequency (millimeter wave), higher speed (gigahertz digital and logic pulse), or denser circuits. The full field solution based on the charge transport model gives accurate results compared with the other models because it takes into consideration the dynamics of the charge carriers. Plane-wave interaction with the charge carriers in the semiconductor provides interesting insight into the boundary conditions at the dielectric–semiconductor interface. The field solution in a semiconductor material in terms of its gradient and curl components for biased and unbiased semiconductor half-space based on a drift diffusion model has previously been presented in [1]. When an electromagnetic (EM) wave propagates in a semiconductor, the screening effect of the charge carrier prohibits the EM field from penetrating deep into the semiconductor. In other words, a formula combining the motion equation of carriers and Maxwell’s equations is required in order to include the interaction mechanism between the EM field and the charge carriers in the semiconductor [2]. The merits of a transport-based analysis have been demonstrated by its application to wide microstrips over doped semiconductor layers with either ohmic or Schottky contacts [2]. Previous work on the coupling of the carrier transport equations to Maxwell’s equations has identified the salient features of guided waves in metal–insulator–semiconductor (MIS) structure [3]. The formulation remains, until this day, a computationally intense exercise. It would appear desirable to develop equivalent-circuit representations for canonic structures so that a basis for modeling circuits fabricated on a semiconductor substrate for which distributed and space charge effects may not be ignored could be obtained. In [3], the propagation property of the fundamental mode in a biased parallel-plate MIS waveguide was investigated using a transport-based analysis. A formulation incorporating Maxwell’s equations and the equations of motion of charge carriers was first linearized and then solved using the finite-difference scheme. However, the approach in [3] is applicable only to small-signal analysis due to its linearization of the equations. Investigations on MIS and coplanar waveguides on semiconductor substrate have taken into consideration nonlinear effects [4]. In [4], a very general full-wave frequency-domain-coupled EM formulation including nonlinearity in the motion equations and device level investigations of MIS interconnects was presented. A surface wave in a semiconductor substrate with a ground plane was presented in [5]. A circuit model and a study of surface wave supported by a planar

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semiconductor–dielectric interface to obtain a closed-form solution of the charge and field distribution in small-signal approximation were presented in [6]. A self-consistent full-wave EM and carrier transport model is derived in small-signal conditions [7]. From the EM standpoint, it is generally well known that the presence of high-conductivity layers can strongly affect the microwave propagation characteristics [8], [9]. They also possibly cause slow-wave effects [10], which have obvious implications in the design of long signal lines in RF Si-based integrated circuits (ICs). They also affect the design of opto-electronic traveling-wave structures where synchronous coupling with an optical signal is required. Moreover, simple transmission line quasi-TEM models are known to break down in complex semiconductor structures; for instance, it has been shown that MIS lines exhibit a complex multimodal behavior when operating in high-loss conditions [11]. The reflection and transmission of an EM wave through the active semiconductor nipi-structure are considered in [12]. However, the approach in [12] based on uniform conductivity model and space-charge plane-wave interaction are not considered in the analysis. In [13] and [14], the full field solution in a semiconductor medium based on charge transport considerations to obtain the reflection coefficients for an unbiased n-type semiconductor, when the incident field employed is either of -polarization or of -polarization was presented. In this paper, a full-wave and charge transport formulation is applied to the analysis of the fundamental mode of propagation in a semiconductor substrate backed with a ground plane. By assuming no static field is applied and by considering n-type semiconductor material doped sufficiently with donors to create an electron single carrier transport and neglect the effect of the holes, a closed-form expressions for the field components, charge carrier density, and current density are obtained. The interaction between the fields and charge carriers causes a charge accumulation at the semiconductor surface in the case of -polarization. The effects of the charge accumulation on the reflection coefficient are accounted for. Results indicate that the space charge exerts a weak effect on the reflection coefficient and a strong screening effect on the normal component of the electric field. The tangential component, however, is mainly governed by an energy dissipation effect resulting from the conduction current. The modified wave-charge transport model can be applied to find the field distributions and the charge carrier concentration in multilayer semiconductor and periodic structures to obtain the reflection coefficient. Such a periodic structure can be used for the creation of amplifying and generative devices of millimeter- and optical-wave ranges. II. WAVE-CHARGE TRANSPORT MODEL It is required to provide a quantitative measure on how the charge carriers in a semiconductor medium acts under the influence of the EM fields. Maxwell’s equations macroscopically characterize a semiconductor medium and describe how the semiconductor responses to the EM fields. The field solution in a semiconductor incorporates the full set of Maxwell’s equations and the equation of motion of the charge carriers based on a drift diffusion model. By combining Maxwell’s equations (A1), the charge carrier transport equations (A2), and

the current continuity equations (A3), and under small-signal conditions (A4), one can obtain two sets of coupled equations that describe the EM fields and the charge carrier concentrations in a semiconductor medium. One set for the static parts and another for the dynamic parts. The field distributions and charge carrier concentrations for the fundamental mode of propagation in the semiconductor satisfy the following set of coupled differential equations [3]:

(1a)

(1b)

(1c)

(1d) and are, respectively, the electric and magnetic where and are, refields, is the conduction current density, spectively, the permittivity and permeability of the semiconductor, and are, respectively, the hole and electron density, and are, respectively, the concentrations of donor and acceptor impurities in the semiconductor, and is the electron and are, respectively, the effective carrier mocharge, bility of electrons and holes, and are, respectively, the and are, rediffusion coefficient for electrons and holes, spectively, the average collision times of electrons and holes, and are, respectively, the life times for electrons and holes, and are, respectively, the effective ac mobility and diffusion coefficient of the electrons and holes, reis the semiconductor uniform conductivity, spectively, and [3]. and is given by Equations (1a)–(1d) are the set of coupled differential equations of the EM fields and the space charge carriers. This set of coupled equations along with the appropriate boundary conditions can completely determine the EM fields and the charge carrier concentrations in the semiconductor medium. For simplicity and to obtain a closed-form solution, we assume n-type semiconductor material doped sufficiently with donors to create an electron single carrier transport and neglect the effect of the holes. We also assume there is no static field applied to the semiconductor medium. By applying the previous assumptions in the equations of the wave-charge transport model, (1a) can be written as follows: (2) where

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excitation magnitude. From (A1b), the tangential and normal components of the incident electric fields are given in the form

(5a) (5b)

Fig. 1. Scattering geometry for incident electric–semiconductor interface.

H - or E -polarization fields on a di-

while the reflected magnetic field can be written as (6) Similarly, from (A1b), the tangential and normal components of the reflected electric fields are given in the form

Equations (1c) and (1d) can be written as (3a)

(7a)

(3b)

(7b)

where

where is the magnitude of the reflected wave. The boundary conditions for the variables are taken as follows:

Equation (3a) is a coupled equation of the electric field and the space charge carriers. It is easily seen from (3a) that the total field solution of the electric field in the semiconductor is composed of two parts. The first part is the homogeneous solution of the wave equation and the second part is the gradient part (nonhomogeneous part of wave equation). However, the first part does not depend on the charge accumulation; the second part is mainly charge accumulation dependent. The gradient portion of the electric field depends on the gradient of the ac component of the charge carrier concentration in the semiconductor medium. It is of interest to note that the gradient portion of the is not included in (3b) since is given in electric field , which cancels the gradient portion, and terms of the curl of as a result, the charge accumulation has no contribution to the magnetic field. The set of differential equations was solved analytically to obtain the field, charge, and current density distributions. By using the conventional techniques to solve (2), we can obtain the ac component of the charge carrier distributions, and upon inserting this into (3a), we can find the total electric field distributions in the semiconductor medium. III.

(8a) (8b) (8c) (8d) (8e) Equation (2) can be solved by the separation of variables . The final solution of the method by letting ac component of the majority carrier concentration in the semiconductor medium after applying the boundary condition (8e) can be obtained as (9) is an arbitrary amplitude constant. where For -polarization, the magnetic field has one component in the -direction, and thus, the electric field has no -component. Equation (3b) can be solved by the separation of variables . The final solution of the ac commethod, letting ponent of the magnetic field in the semiconductor after applying the boundary condition (8d) on the tangential component of the electric field at the ground plane can be obtained as

-POLARIZATION (10)

The scattering geometry for incident - or -polarization fields on a dielectric–semiconductor interface is shown in Fig. 1. Assume a uniform plane wave is incident from free-space upon n-type semiconductor substrate backed with a ground plane at , and polarized parallel to the plane of incidence with

is the magnitude of the transmitted wave. where The total field solution in the semiconductor can be obtained by solving (3a) or from (A1b) as follows:

(4)

(11a)

is the wavenumber in vacuum and where is the magnitude of the incident wave, which depends on the

(11b)

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where and are, respectively, the incident, reflected, and transmitted fields. From Snell’s law and after applying the phase matching condition in the incident, reflected, and transmitted fields, we must have

using (13). Upon substituting (12a) and (13) into (12b), it can be found that

and where and are, respectively, the complex refractive index and complex permittivity of the semiconductor material. The importance of the result obtained in (11) is the separation of the electric field in the semiconductor into two parts, one part does not depend on the charge distribution and the second part depends on the charge distribution. Moreover, the modified field solution in (11) takes into account the effect of the charge accumulation at the semiconductor surface. The gradient portion of the electric field in the semiconductor is generated from the charge accumulation at the interface of the semiconductor and the amplitude of the gradient portion is strongly related to the charge accumulation. By applying the boundary conditions (8a) and (8b) in (5)–(11), it can be found that

(12a)

(14) Equation (14) can be written in the form (15) where

and

are, respectively, the free space and semiconductor impedances. Let us present the reflection coefficient as the ratio between the reflected wave amplitude to the amplitude of the incident wave. From (15), the reflection coefficient can be written as (16)

(12b) The standard matching of the tangential electric and magnetic fields at the interface is not sufficient to solve the problem. The normal electric flux must be continuous, or the normal component of the current must be continuous for a pure dielectric interface. In other words, the normal component of the conduction currents must vanish at the dielectric–semiconductor interface. and by applying It is simple to find the relation between the boundary condition (8c) as follows: (13) In (13), the ac component of the charge carrier concentration (i.e., the reflection in the semiconductor depends mainly on ratio (i.e., the angle of incidence). To coefficient) and obtain the solution, it is convenient to eliminate from (12b)

The final from of the modified reflection coefficient for -polarization based on charge transport model is given by (17), shown at the bottom of this page, where

is the new term that represents the effect of the charge transport considerations on the reflection coefficient for -polarization, which is not considered in the earlier approaches, e.g., [1] and [12]. It is expected from the field carrier interaction theory that the additional term has a small effect on the reflection coefficient; this is because the tangential component of the electric field does not couple strongly with the charge carriers. As a result, the charge accumulation part exerts a weak effect on the reflection coefficient so it can be neglected to give the same result of the uniform conductivity in the semiconductor. It is clear , the reflection coefficient from a that as the limit of semiconductor substrate backed with a ground plane satisfies

(17)

ELABYAD et al.: SPACE-CHARGE PLANE-WAVE INTERACTION AT SEMICONDUCTOR SUBSTRATE BOUNDARY

the reflection coefficient from a semiconductor half-space material based on charge transport model [13]. For normal incidence, , and from (20), , thus there is no charge accumulation at the semiconductor interface. Also, the gradient portion of the electric field vanishes due to the lack of the charge accumulation at the interface. In the other extreme of grazing , the reflection coefficient , and incidence, , and consequently, there is no transmitted fields in the semiconductor medium. Thus, the reflected field interferes with the incident field to give a standing wave with a null field solution at the semiconductor surface. In other words, the surface wave does not exist as a possible solution without the introduction of additional modes within the semiconductor, specifically internally generated incident fields, as described in [1]. As a result, there is no charge accumulation at the semiconductor interface for both the normal incidence and the grazing incidence. If the ac components of the carrier densities are dropped form and , the (1c) and (1d) and constant values are used for gradient portion of the electric field vanishes so that the charge accumulation part vanishes and the reflection coefficient of a uniform conductivity in the semiconductor can be rewritten as (18), shown at the bottom of this page. The uniform conductivity model simplified the semiconductor description and resulted in a pure EM problem. Nevertheless, this analytical model provides no knowledge about some important effects caused by field-carrier interactions such as nonlinearity and screening effect of charged carriers. IV.

-POLARIZATION

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of the semiconductor for -polarization. As a result, the gradient portion of the electric field vanishes due to the lack of the charge accumulation. For -polarization, the electric field does not couple with the charge carriers because it has only a -component parallel to the interface; hence, there is no charge accumulation at the dielectric–semiconductor interface, as expected from the field-carrier interaction. The boundary conditions for the variables are taken as follows: (21a) (21b) (21c) Equation (3a) can be solved by the separation of variables method and after applying the boundary condition (21c), the total electric field in the semiconductor can be obtained as (22) From (A1a), the tangent and the normal components of the transmitted magnetic field in the semiconductor can be written as follows: (23a) (23b)

(20a)

By applying the boundary conditions (21a) and (21b) to the incident, reflected, and transmitted fields, the reflection coefficient for -polarization based on the charge transport model can be obtained as (24), shown at the bottom of this page. The reflection coefficient for -polarization does not contain a charge accumulation part because the electric field is parallel to the dielectric–semiconductor interface, as described in [1].

(20b)

V. RESULTS AND DISCUSSION

For an incident plane-wave polarized perpendicular to the plane of incidence with (19) and

The reflected field can be written in the same way as (6) and (7). The normal component of the conduction currents must vanish at the dielectric–semiconductor interface, so by applying and the boundary condition (8c), it can be found that , thus there is no charge accumulation at the interface

An n-type silicon semiconductor was assumed to obtain numerical results for discussion and the following parameters were cm /(V s), specified: cm /(V s), K, s, s, and and were both taken to be 2.5 10 s, where and are, respectively, the permittivity and

(18)

(24)

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Fig. 2. Magnitude of the ac component of the electron concentration n in the cm at 10 GHz. semiconductor with N

= 10

Fig. 3. Magnitude of the normal component of the ac electric field E semiconductor with N cm at 10 GHz.

= 10

in the

permeability in vacuum. The value of , the thickness of the n-type semiconductor, is chosen to be 100 m, which is much larger than the Debye length so that the actual value has little influence on the propagation characteristics. The ac component of the field distributions and the charge carrier concentrations in the semiconductor are dependent on the magnitude of excitation and are assumed to be 1 V/cm. Figs. 2–4 illustrate the magnitude distributions of field components and carrier concentrations of (9) and (11) for the funfor and damental mode against . The normal component of the electric field in the semiconductor is strongly influenced by the screening effect of the dependence against charge carriers, as evidenced by the . Such an observation could not be made if a uniform conductivity was used to characterize the semiconductor. There is a significant difference in the normal components of the elecobtained using the transport-based formulation for tric field

Fig. 4. Magnitude of the tangent component of the ac electric field E cm at 10 GHz. semiconductor with N

= 10

in the

the unbiased case and that given by calculations based on uniform conductivity, as shown in Fig. 3. The screening effect of the charge carriers near the accumulation-depletion layer prevents the normal component of the electric field from penetrating the semiconductor beyond a few Debye lengths. On the other hand, the curve given by a uniform conductivity calculation attains a much lower value throughout the entire region of the semiconductor, as shown in Fig. 3. By comparing Figs. 2 and 3, one may conclude that the ac components of the charge distri, as one would expect from butions are closely related to the screening consideration. The obtained results match that of Han and Wong [3] and Wang et al. [4]. Figs. 2 and 3 are consistent with the published results in ([3, Figs. 6–8]), and ([4, Fig. 3]). Moreover, a few Debye lengths from the boundary (at m), the normal component of the electric field approach that of the uniform conductivity model. It is of interest to note that, with given doping concentration, wave frequency, and for all angle of incidences, the ratio between the charge carriers and the normal component of the electric field is constant cm and GHz, and for all angles, the ratio be[ /(V cm )], as shown in Figs. 2 and tween 3. The latter results are in a close agreement with those of the small- and large-signal analysis, i.e., [3, Figs. 6–8] and [4, Fig. is constant for a 3]. In other words, the ratio between given doping level and at a certain wave frequency. From the field distribution of the normal component of the electric field , we were able to distinguish two mechanisms, one related to the homogeneous solution of the wave equation, and the other is related to the free charge accumulation at the semiconductor surface. The first part does not depend on the charge distribution, while the latter has a significant effect within a few Debye lengths from the semiconductor surface. As the doping level increases, the effect of the charge accumulation part dominates over the homogeneous part and the normal component of the electric field is being screened from penetrating deep into the semiconductor. In the low doping case, the homogeneous part dominates over the charge accumulation part and its effect goes beyond the region in which charge accumulation is present. The

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Fig. 5. Magnitude of the ac component of the electron concentration at the cm . and with N semiconductor surface at x

Fig. 7. Magnitude of the tangent component of the ac electric field E semiconductor at x cm . and with N

Fig. 6. Magnitude of the normal component of the ac electric field E cm . semiconductor at x and with N

Fig. 8. Magnitude of the ac component of the current density J cm at 10 GHz. conductor with N

=0

=0

= 10

= 10

in the

tangential component of the electric field , however, does not couple strongly with the carriers. In all cases, the electric vanishes a few skin depths away from the surface. field The tangential component, however, is mainly governed by an energy dissipation effect resulting from the conduction current. The two formulations obtained using the transport-based formulation and that given by calculations based on uniform conductivity give similar results for the unbiased case, as shown in Fig. 4. Figs. 5–7 illustrate the magnitude distributions of field components and carrier concentrations for the fundamental mode . It shows that against at the semiconductor surface the charge accumulation at normal incidence is zero where the electric field is not coupled to the charge carriers. Furthermore, at grazing incidence, there is no charge accumulation because the field is totally outside the semiconductor surface (i.e., total reflection). The ac component of the charge concentration increases as the concentration of the donor impurity increases and

=0

= 10

= 10

in the

in the semi-

as the frequency decreases. The ac component of the charge carrier concentrations decays exponentially in the semiconductor material so as to have no significant effect away from the interface and vanishes for both the normal and grazing incidence. in the semiThe normal component of the ac electric field conductor is closely related to the charge carriers, it vanishes at the normal incidence and grazing incidence, as shown in Fig. 6. At very high frequencies, and low concentrations of donor impurity, the ac component of the electron concentration is very small because there is no charge accumulation at the semiconductor interface. As a result, the normal component of the electric field is not affected by the charge carriers so it is uniform and the electric field does not penetrate the semiconductor beyond a few Debye lengths. The screening effect of the charge carriers on the normal component of the electric field is observed to be negligible for an intrinsic semiconductor material, but gradually approaching that of a metallic conductor as the doping level reaches 10 cm .

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Fig. 9. Magnitude of the reflection coefficient at 10 GHz. (a) 0 . (b) -polarization 0 .

E

H -polarization

Fig. 8 illustrates the magnitude distributions of the current for the fundamental mode against , for density and . The current density of the wavecharge transport model increases gradually from zero to approach that of the uniform conductivity beyond a few Debye m). In other words, lengths from the boundary (at the normal component of the current is continuous in the modified wave-charge transport model unlike that based on the uniform conductivity model. , it is finite and fixed by the incident field Since behavior from a simple dielectric for a surface normal in the -direction, and since , it may be neglected in order to . The modified term is inversely proportional obtain , and due to the high value of this constant, decreased with to have a weak effect on the reflection coefficient under zero bias. As a result, the reflection coefficient for -polarization obtained using a uniform conductivity description closely matches that obtained using the transport-based formulation under zero

Fig. 10. Magnitude of the reflection coefficient with (a) -polarization0 . (b) -polarization 0 .

H

E

N

= 10

cm

.

bias. Although the modified term in the reflection coefficient in this paper has a weak effect under zero bias, it is expected that for the large-signal model and very high applied field, it will be increased, but in this case, it is impossible to find a closed-form formula of the reflection coefficient and the model will be solved numerically. and of (17) and (24) for Plots of and as a function of , and frequency are shown in Figs. 9 and 10, respectively. When the semiconductor loss is small, i.e., is large, the semiconductor acts like a dielecthe ratio tric. With an intrinsic semiconductor material with cm and cm , the semiconductor acts as a lossless medium so the magnitude of the reflection coefficient for both - and -polarization will equal unity, as shown in Fig. 9. Also, when the semiconductor loss is large, i.e., the ratio is small, the semiconductor acts like a metal. With cm and above, the magnitude of the reflection coefficient will equal unity again because the semiconductor acts as a metal. For

ELABYAD et al.: SPACE-CHARGE PLANE-WAVE INTERACTION AT SEMICONDUCTOR SUBSTRATE BOUNDARY

-polarization, the magnitude of the reflection coefficient decreases with decreasing , but for -polarization, it decreases with increasing , as shown in Fig. 9. The minimum reflection can occur for both - and -polarization for all angles if the cm , concentration of donor impurity is taken as as shown in Fig. 9. The magnitude of the reflection coefficient for -polarization is larger than the magnitude of the reflection coefficient for -polarization at the same angle, as shown in Figs. 9 and 10. For -polarization, the charge accumulation part has a small effect on the reflection coefficient so it can be neglected to give the same result of the uniform conductivity in the semiconductor.

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B. Carrier Transport Equations

(A2a) (A2b) (A2c)

C. Current Continuity Equations

VI. CONCLUSION A full-wave and charge transport formulation has been applied to the analysis of the fundamental mode of propagation in a semiconductor substrate backed with a ground plane. The formulation takes into consideration the dynamics of the charge carriers by coupling their equations of motion to the full set of Maxwell’s equations. The resultant solutions of the dynamic differential equations were used to solve for the plane-wave interaction with the charge carriers at dielectric–semiconductor interfaces. Closed-form expressions for the field components, charge carrier density, and current density are obtained. The reflection coefficients for - and -polarization that are derived based on charge transport take into account the dynamics of the charge carriers and the properties of the semiconductor medium. This paper investigated the idea that, if the incident electric field is parallel to the interface, as in the case of -polarization and normal incidence, then there is no charge accumulation at the dielectric–semiconductor surface. If the electric field is parallel to the plane of incidence, as in the case of -polarization, then there is a charge accumulation at the semiconductor surface. The charge accumulation part has a small effect on the reflection coefficient and gives a close result to the uniform conductivity model. As a result, the reflection coefficient for -polarization obtained using a uniform conductivity description closely matches that obtained using the transport based formulation under zero bias. The normal component of the electric field in the semiconductor is strongly influenced by the screening effect of the charge carriers, whereas the tangent component is governed mainly by energy dissipation arising from the conduction current. APPENDIX A. Maxwell’s Equations

(A1a) (A1b) (A1c) (A1d)

(A3a) (A3b)

D. Small-Signal Analysis For an arbitrary variable

, we my have (A4)

REFERENCES [1] W. A. Davis and C. M. Krowne, “The effects of drift and diffusion in semiconductors on plane wave interaction at interfaces,” IEEE Trans. Antennas Propag., vol. 36, no. 1, pp. 97–103, Jan. 1988. [2] C. M. Krowne and G. B. Tait, “Propagation in layered biased semiconductor structures based on transport analysis,” IEEE Trans. Microw. Theory Tech., vol. MTT-37, no. 4, pp. 711–722, Apr. 1989. [3] K. Han and T. T. Y. Wong, “Space-charge wave considerations in MIS waveguide analysis,” IEEE Trans. Microw. Theory Tech., vol. MTT-39, no. 7, pp. 1126–1132, Jul. 1991. [4] G. Wang, R. W. Dutton, and C. S. Rafferty, “Device-level simulation of wave propagation along metal–insulator–semiconductor interconnects,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 4, pp. 1127–1136, Apr. 2002. [5] M. Eldessouki and T. Wong, “Surface wave in a semiconductor substrate with a ground plane,” in IEEE Wireless Commun. Technol. Top. Conf., Oct. 15–17, 2003, pp. 369–371. [6] T. Wong and M. Eldessouki, “Transport based equivalent circuit models for waveguiding structures on a semiconductor substrate,” in IEEE ICSICT, Oct. 18–23, 2004, pp. 1923–1927. [7] F. Bertazzi, F. Cappelluti, S. D. Guerrieri, F. Bonani, and G. Ghione, “Self-consistent coupled carrier transport full-wave EM analysis of semiconductor traveling-wave devices,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1611–1618, Apr. 2006. [8] E. S. Tony and S. K. Chaudhuri, “Effect of depletion layer on the propagation characteristics of MIS transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp. 1760–1763, Sep. 1999. [9] J. Aguilera, R. Marqués, and M. Horno, “Improved quasi-static spectral domain analysis of microstrip lines on high-conductivity insulator semiconductor substrates,” IEEE Microw. Guided Wave Lett., vol. 9, no. 2, pp. 57–59, Feb. 1999. [10] H. Hasegawa, M. Furukawa, and H. Yanai, “Properties of microstrip line on Si–SiO system,” IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 11, pp. 869–881, Nov. 1971. [11] D. F. Williams, “Metal–insulator–semiconductor transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 2, pp. 176–181, Feb. 1999. [12] A. A. Bulgakov and O. V. Shramkova, “Investigation of reflection and transmission coefficients on active multilayered semiconductor structure,” in IEEE Asia–Pacific Microw. Conf., Dec. 12–15, 2006, pp. 352–355.

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[13] I. El-Abyad, M. Eldessouki, and H. El-Hennawy, “Wave reflection from semiconductor half-space based on charge transport model,” in IEEE ICCCE08, Kuala Lumpor, Malaysia, May 13–15, 2008, pp. 638–642. [14] I. A. El-Abyad, M. S. Eldessouki, El. S. A. El-Badawy, and H. S. El-Hennawy, “Wave reflection from semiconductor substrate with a ground plane based on charge transport analysis,” in WMSCI 2008, Orlando, FL, Jun. 29–July 2, 2008, pp. 7–12.

Mohamed S. Eldessouki received the B.Sc. degree from Alexandria University, Alexandria, Egypt, in 1991, and the Ph.D. degree from the Illinois Institute of Technology, Chicago in 2003. In 2001, he was a Design Engineer with Stratos Lightwave, where he developed 10-Gbit optical transceivers. In 2003, he became an Assistant Professor with the Thebes Higher Institute of Engineering, Cairo, Egypt. In 2008, he joined King Saud University, Riyadh, Saudi Arabia, where he is currently an Assistant Professor with the Vice Presidency for Projects.

Ibrahim A. Elabyad was born in Kalubia, Egypt, on January 1, 1982. He received the M.Sc. degree in electrical engineering, electronics, and communications from Ain Shams University, Cairo, Egypt, in 2009, and is currently working toward the Ph.D. degree in electrical engineering at the Chair of Microwave and Communication Engineering, University of Magdeburg “Otto von Guericke” Magdeburg, Germany. His research interests include EM wave propagation, semiconductor device theory, and microwave circuit design. His current research involves analysis and design of RF coils for MRI applications at high- and ultra-high fields.

Hadia M. El-Hennawy (M’00) received the B.Sc. and M.Sc. degrees from Ain Shams University, Cairo, Egypt, in 1972 and 1976, respectively, and the Doctorate of Engineering (Dr.-Ing.) degree from the Technische Universitat Braunschweig, Braunschweig, Germany, in 1982. Since 1992, she has been a Professor of communication engineering with the Electronics and Communications Engineering Department, Ain Shams University. In 2004, she became a Vice-Dean for graduate study and research. In 2005, she became the Dean of the Faculty of Engineering, Ain Shams Engineering. Her research interests include microwave devices and subsystems, as well as filters and antennas for modern radar and wireless communications applications.

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Full-Space Scanning Periodic Phase-Reversal Leaky-Wave Antenna Ning Yang, Member, IEEE, Christophe Caloz, Fellow, IEEE, and Ke Wu, Fellow, IEEE

Abstract—A novel full-space scanning periodic phase-reversal leaky-wave antenna array is proposed, designed in offset parallel stripline technology, and demonstrated experimentally. This antenna radiates from its small phase-reversing cross-overs, which leads to a small leakage factor and subsequently a large directivity. The operation principle of the antenna is explained from the Brillouin diagram, which shows how single-beam scanning, using the space harmonic, is achieved as a result of the lateral shift of the dispersion curves due to phase reversal. One of the benefits of phase reversal is to permit this radiation performance with relatively small permittivity substrates ( min compared to min for antennas without phase reversal). An unitcell matching technique is applied to avoid reflections, and thereby prevent the presence of an open stopband so as to permit continuous space scanning with efficient broadside radiation. An efficient array synthesis procedure, based on a transmission line modeling of the structure, is utilized for the design of the antenna following specifications in terms of frequency, scanning, directivity, radiation efficiency, and sidelobe level. A uniform-aperture antenna prototype, including a balun-transformer input transition, is presented, featuring experimental beamwidth and gain at the broadside frequency (25 GHz) of 4 and 15.7 dBi, respectively.

= 1

=4

=9

Index Terms—Balanced transmission line, full-space scanning, leaky-wave antenna, millimeter wave, offset parallel stripline (OPS), open stopband, phase reversal, planar antenna.

I. INTRODUCTION RAVELING-WAVE antennas are antennas supporting wave propagation in a unique direction [1], [2]. When the wave has a phase velocity smaller than the speed of light (slow wave), the antenna structure guides the wave along its axis and radiates it from its end. It is a surface-wave antenna and it generally produces endfire radiation [3]. Surface-wave antennas include long wires, dielectric rods, and helixes [3]. In contrast, when the wave has a phase velocity larger than the speed of light (fast wave), the antenna structure progressively radiates the wave from its input to its end. It is a leaky-wave antenna and its beam may be steered to different angles of space by tuning the frequency [4]. Slotted waveguides [5], [6], higher order mode microstrips [7]–[10], and composite right/left-handed structures [11] belong to this family. Leaky-wave antennas, thanks to their high directivity and simple feeding structure, are

T

Manuscript received May 14, 2010; revised July 04, 2010; accepted July 19, 2010. Date of publication September 09, 2010; date of current version October 13, 2010. The authors are with the École Polytechnique de Montréal, Montréal, QC, Canada H3T 1J4 (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.2010.2065890

suitable for various scanning applications, such as radar and multiple-input multiple-output (MIMO) systems. They may also incorporate tunable elements, such as varactors, to provide beam steering at a fixed frequency [12] or active elements for beam shaping [13]. Planar periodic leaky-wave antennas have been intensively investigated due to their low profile, low cost, and ease of fabrication. Most of them are implemented in microstrip technology such as the comb-line array, periodic meandered microstrip array [14], and series-resonant patch array [15]. A fundamental problem of these antennas has been the existence of an open stopband in a narrow frequency region around broadside. This stopband may be understood in terms of coupling between space harmonics, or equivalently, in terms of the constructive interferences from the reflections occurring at the periodic loads. Within the stopband, the radiation efficiency abruptly drops and most of the signal is reflected back to the source [4]. Traditionally, such antennas have been mostly considered as serially fed arrays of individual radiating elements periodically loading the structure [14], [16]. Only recently, they have been investigated theoretically in terms of leaky-wave structures with novel insights and design approaches [17], and the techniques to close the open stopband of a periodic microstrip comb-line leaky-wave antennas for broadside radiation is presented in [18]. This paper presents a full-space scanning leaky-wave antenna using periodic phase-reversal radiating elements interconnected by balanced transmission line sections. The phase-reversal elements have a fourfold function: ensuring the continuity of the transmission line, providing a periodic perturbation to generate space harmonics, radiating, and 180 phase shifting for singlebeam operation. The periodic phase reversal inverses the phase between the two conductors of the structure in each unit cell, and thereby laterally shift the dispersion curves by [19]–[21]. The resulting antenna may be interpreted to operate either in space harmonic or in the space harmonic. the The phase reversal allows single-beam frequency scanning with compared relatively small permittivity substrates ( for antennas without phase reversal). This anto tenna has its radiators directly in the phase reversals, which is in continuity of the balanced transmission line. As a consequence, they induce minima reflections and also lead to small leakage factor and a large directivity. Moreover, these minor discontinuities can be easily matched within each unit cell so as to totally suppress the open stopband, utilizing an unit-cell matching technique, which is similar to that adopted in [18]. The suppression of stopband ensures efficient broadside radiation and continuous beam scanning with frequency. The synthesis procedure

0018-9480/$26.00 © 2010 IEEE

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Fig. 1. Overall configuration of the proposed full-space scanning phase-reversal leaky-wave antenna. For the specific offset parallel stripline (OPS) implementation presented in this paper, the two colors (black and gray) indicate different metal strip layers, which are placed at each side of a thin substrate.

transmission line sections, introducing only minor impedance discontinuities, and because the unit cells will be further internally matched so as to fully suppresses local reflections (Section III), the structure will be seen by the waves as essentially continuous. Therefore, it is de facto a periodic structure with a vanishingly small periodic perturbation, and it therefore exhibits a dispersion diagram whose stopband widths collapse to zero (because of the negligible coupling between the space harmonics due to the negligible discontinuities) and the dispersion curves collapse into a diamond-like dispersion diagram constituted of perfectly linear space harmonic curves [19], as shown in Fig. 2. Applying periodic boundary condition, the phasor waveform along the structure may be written (1) Using Bloch–Floquet’s theorem [19], [22], the wave in a periodic structure consists of the superposition of an infinite number of the of space harmonics waves, and the phase constants th space harmonic is given by (2)

Fig. 2. Dispersion diagram obtained from (2) for the phase-reversal antenna : and p : mm. The structure shown in Fig. 1 for the parameters " shading area represents the fast-wave (radiation) region. The dispersion curve for the corresponding TEM transmission line without phase reversals (red dotted curve in online version) is also shown for reference. The upper abscissa axis represents the case of a rightward (phase delay) shift of the dispersion diagram (convention followed in this paper), corresponding to radiation of the m space harmonic, while the lower abscissa axis represents the case of a leftward (phase advance) shift of the dispersion diagram, corresponding to radiation of space harmonic. the m

= 22

= 41

= 01

=0

of the proposed phase-reversal antenna is presented and an antenna with uniform aperture distribution is designed, fabricated, and measured. II. PRINCIPLE OF OPERATION Fig. 1 shows the overall configuration of the proposed fullspace scanning phase-reversal leaky-wave antenna. The structure is composed of a plurality of balanced transmission line sections periodically interconnected by cross-over conductors with a period of . All the transmission line sections have the and phase constant . The same characteristic impedance cross-overs exchange the relative positions of the two conductors of the balanced transmission line and thereby reverse their polarity. The antenna is fed at one end through a standard balanced transmission line and is terminated at the other end by a load. matched Without the phase-reversal cross-overs, the structure is merely a uniform TEM transmission line, which exhibits a linear dispersion curve, starting from the origin of the dispersion diagram, as shown by the red dotted curve (in online version) in Fig. 2. It is a purely guiding (nonradiative) slow-wave structure. The periodic phase reversals transform the structure into a periodic structure. Since the cross-overs are merely very short

In this relation, it is assumed that so that the positive and negative signs correspond to waves propagating along the positive (forward- ) and negative (backward- ) -directions, respectively, of the selected coordinate system, assuming the time dependence . Fig. 2 shows the complete dispersion diagram for the phasereversal structure of Fig. 1. This diagram differs from that of the most common periodic structures with a vanishingly small periodic perturbation [19], [23]. The phase reversal induced in each unit cell generates an extra frequency-independent phase shift per cell. This results in a horizontal shifting of the entire dispersion diagram by an amount of . Furthermore, due to the small electrical size of the phase-reversing cross-overs (tends to be zero ideally), the sign of the phase shift may be arbitrarily chosen as positive (phase delay) or negative (phase advance). Therefore, all the dispersion curves are shifted, without , either to the right or to the changing their slope left of the dispersion diagram, as illustrated in Fig. 2. In the following, we will follow the convention of Hessel [19], where the phase reversals are considered as phase delays and the dispersion curves are therefore shifted to the right. Consequently, the , specifically the lowest radiating space harmonic is the space harmonic (otherwise, in case of phase forward space harmonic) advance leftward shift, it would be the since it is lowest space harmonic crossing the fast-wave region of the dispersion diagram. Due to phase reversal, the expression for the space harmonics in (2) is transformed into

(3) is the dispersion relation of the original In this relation, transmission line of effective permittivity , which reads (4)

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space harmonic. The space harmonic below A and harmonic below D, are slow and above B, and the therefore do not radiate. According to (5) or (7), the frequencies corresponding to the points A, B, and C are given by (8a) (8b) (8c) while the frequency corresponding to point D is given from (3) and (6) by

m

"

p=

p!= c

(9)

0 ;0 ;0

Fig. 3. Main beam angle of the first space harmonics ( = 1 2 3) = (2 ) (normalized frequency) for difversus the electrical period ferent values of . Single beam radiation is achieved if only one of the space harmonics is presents within the scanning range of the desired space harmonic, which is considered here to be = 1.

m 0

In particular, the forward space harmonic, which is the one of interest for leaky-wave radiation, is related to the transmission line dispersion relation by

The space harmonic radiates backward (due to neg) from A to C and forative phase velocity, ) from C to B, while ward (due to positive phase velocity, space harmonic starts to radiate at backfire at D. Therefore, full-space scanning single beam radiation requires the satisfaction of the condition . Using (8b) and (9), this condition translates into (10)

(5) The angle of radiation of the beam associated with the th space harmonic of the leaky-wave antenna is then given by the , where refers to the classical formula radiating space harmonic [4]. Therefore, with (3), we find that

If the effective permittivity of a transmission line does not satisfy this condition, additional periodic elements may be integrated along the structure to slow down the wave. In this manner, a new larger effective permittivity is seen by the wave ) and (10) (increasing the scanning sensitivity may be satisfied. Without phase reversal, the condition for single-beam full-space scanning [4], (11) is much more constraining, and often difficult to achieve in practice.

(6) III. TRANSMISSION LINE MODELING which shows that all the space harmonics scan space as frequency is varied, despite the linearity of the dispersion curve, shift in (3). Specifically, the scanthanks to the space harmonic reads ning law for the (7) The scanning angle versus frequency for the main beam of the first radiating space harmonics , computed from (6), are plotted in Fig. 3 for different values of . This figure shows that several radiating beams, typically representing spurious grating lobes, may be produced at a given frequency, as a result of the penetration of several space harmonics into the fast-wave region of the dispersion diagram. The points A, B, and C in Fig. 2 indicate the backfire, endfire, and broadside radiation frequencies, respectively, of the space harmonic, while point D indicates the backfire radiation frequency of the

An antenna array consists of a feeding structure and several radiating elements. The proposed phase-reversal antenna (Fig. 1) may be regarded as series-fed antenna array, where the balanced transmission line sections build the series feeding structure and the cross-over conductors constitute the radiating elements. The feeding and radiating parts of the antenna are detailed in Fig. 4. Fig. 4(a) shows the line sections and their currents along the two conductors. Since the two currents flow in opposite directions, they do not contribute to radiation in the far field. Therefore, the line sections play the exclusive role of feeding structures. The radiating elements are the cross-over conductors, shown in Fig. 4(b), in between the transmission line sections. As shown in Fig. 4(c), the longitudinal ( -directed) contributions of these currents cancel out, whereas the transverse contributions added up. Assuming that the two conductors describe an angle of with respect to the transverse direction, the resulting effective radiating current is a purely transverse

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Fig. 5. Transmission line model of the phase-reversal array, where R (n = 1; . . . ; N ) is the normalized radiation resistance of the nth radiator, Q is the power radiated from the radiator R , and P is the remaining power after R . This model shows only the radiation resistances of the cross-overs and assumes ideal transmission line section interconnections. (a) Overall model. (b) Exact unit-cell structure with distributed lossy (radiating) cross-over section and equivalent lumped resistance model for the nth cell, assuming matching to the termination port Z . Fig. 4. Principle of feeding and radiation based on the description of the unit cell. (a) Initial balanced transmission line with its current flow. (b) Corresponding phase-reversal structure with its current distribution. (c) Effective radiating current, obtained by the vectorial summation of the cross-over currents, resulting in an equivalent vertical radiating current of magnitude 2I cos  . (d) OPS implementation of the structure with relevant parameters, the two parallel strips of the TL are shown in black and grey colors, respectively.

current with magnitude , where is the magnitude of the current in each conductor. The proposed structure may be conveniently implemented in coplanar stripline (CPS) technology. In this work, a variation of the CPS configuration is used, which is called the OPS configuration, where the two strips are place on the two sides of a thin substrate. The resulting structure, shown in Fig. 4(d), both avoids air bridges or vias for the cross-overs and allows an easy transition from a microstrip line, while essentially retaining the fundamental features of the CPS configuration. This structure also offers a smooth phase-reversal transition with minimal discontinuity reactance and reduces the fabrication cost. Furthermore, the OPS structure with its two strips on the two layers of a thin substrate offers a large range of characteristic impedance values, where high impedance is easily achieved by increasing the offset between the two strips, while very low impedance achieved by overlapping the two strips. This characteristic facilitates the design of the antenna and the control of its radiated power, which is particularly beneficial in nonuniform structures synthesized for optimal beam shaping. Due to their small electrical size, the radiating currents may be modeled as infinitesimal electric dipoles with the radiation resistance [24] (12) where is the free-space impedance and is the transverse length of the cross-over strips, as shown in Fig. 4(d). This formula does not account for mutual coupling between the radiators in the practical array structure. This aspect will be discussed

in Section V. In this expression, a factor of 2 is added to the conventional formula to account for the contribution of the two strip radiators. The leakage factor [4] of the antenna, , will be proportional to this resistance distributed over the extent of the structure. The overall -cell leaky-wave structure can be modeled by the equivalent circuit shown in Fig. 5. In this circuit, only the radiation resistances are drawn. The reactances of the structure are omitted because they are not essential for the synthesis of the array and because they will later be absorbed in the transmission line sections. The transmission coefficient and reflection coefficient at can be written as a function the th cross-over , where of the normalized radiation resistance is the characteristic impedance of the transmission line sections. th unit cell is matched to , as will be Assuming that the shown in Section IV to be the case as a result of self-matching technique, and are (13a)

(13b) where the approximation holds when , i.e., . is in the order of 1 to 20 and is in the In practice, is in the order of 0.005–0.1, order of 150–250 so that which largely justifies the approximation. The corresponding reflections range from 20 to 40 dB, as confirmed in Fig. 6(a). Though the reflection for a single unit is small, as the number of unit cells increases, the total reflection at the input of the antenna increases at the broadside frequency, where the phase delay of the interconnecting transmission lines is . Suppose unit cells along the the traveling-wave antenna has transmission line, the total reflection coefficient at the input port

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Fig. 7. Dispersion diagrams for the periodic (infinite) antenna structure computed from the circuit model of Fig. 5 with the parameters p =  at 25 GHz, Z = 165 for several values of the radiation resistances R. (The structure is uniform, i.e., R = R; n = 1; 2; . . ..)

Fig. 6. S -parameters: (a) for a one-cell phase-reversal antenna and (b) for a 40-cell phase-reversal antenna simulated from the equivalent transmission line model of Fig. 5 without any unit-cell matching. The radiation resistance R varies in the range from 2 to 18 , which covers the typically required radiation resistances of a traveling-wave antenna. The load and source impedances are of Z = 180 . The length of the transmission line sections between neighboring unit cells are of 180 at the center frequency 25 GHz.

is shown in Fig. 6(b). As the radiation resistance increases from 2 to 18 , the return loss at this frequency decrease from 15 to 4 dB and the insertion loss show a dip. This means that the radiated power drops quickly at this frequency. In contrast, away from this frequency, good impedance matching is maintained because the reflections from the large number of unit cells tend to cancel each other for other than phase shifts. This phenomenon can also be explained from the dispersion diagram of the periodic structure, which is plotted in Fig. 7 , for the case of a uniform array ( ) using the circuit model of Fig. 5. A sharp drop of frethe leakage factor occurs near the broadside quency, where the electric length of the unit cell equals . This point corresponds to a stopband, which opens up in the presence of a periodic discontinuity. In this structure, as mentioned previously, the discontinuity is small, and this is the reason why the stopband is not very wide. Note that in the same frequency region, the phase constant also displays a very small variation where it becomes slightly nonlinear, as a consequence of the small couplings between oppositely directed space har-

monics. This result shows that, independent of the possible reactance discontinuities (not considered yet), small resistance discontinuities produce a stopband, where drops toward zero at , which prevents efficient broadside radiation [18]. In fact, the reactive discontinuities of the structure will next be used to achieve a near-perfect matching of the unit-cell so as to completely close the stopband and thereby achieve efficient broadside radiation. For the synthesis of the array, which consists ofdetermining and which will be the proper values of the set of resistors presented in Section V, a proper relation must be established be, and the power tween the power entering the th unit cell, , i.e., we need to determine . radiated by this cell, Referring to Fig. 5(b), the impedance seen at the input of the th unit cell, assuming that this cell is matched to (as will be ensured later) is (14) The radiation power is due to the radiation related to , will be radiated partly by and partly while the power by the rest of the structure, which is represented by the matched in Fig. 5(b). Consequently, resistance (15)

IV. SUPPRESSION OF THE OPEN STOPBAND FOR BROADSIDE RADIATION The results shown in Fig. 6 show that the proposed periodic phase-reversal antenna cannot radiate efficiently at broadside with radiation resistances only due to the presence of an open stopband. This section will show that addition of proper reactance providing matching of the unit cell leads to complete closure of this stopband, and subsequently, to efficient broadside radiation. A. Unit Cell Impedance Matching unit cells will automatically be A structure composed of matched if all the unit cells are matched, while a very small

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Fig. 9. Dispersion diagram for the periodic (infinite) antenna structure computed from the unit-cell matching circuit of Fig. 8(a) with the same parameters as in Fig. 7 and for several different values of the radiation resistances R. The LC values used are computed from R by (17a) and (17b).

Fig. 8. Principle of unit-cell matching. (a) Equivalent circuit. (b) Smith chart trajectory along the points P to P indicated in (a).

mismatch in the unit cell will be magnified by the factor in the response of the overall structure. Therefore, let us derive now the condition for matching of the unit cell. This is best accomplished with the help of the circuit model shown in Fig. 8(a), where the structure is assumed to be perfectly matched to a port impedance of . The impedance to the right at this input of the unit cell is (16) seen to the This impedance must be equal to the impedance left for matching. This condition yields, after equating the real , and imaginary parts of the relation (17a) (17b)

The impedance-matching procedure following this pair of relations is illustrated by the trajectory drawn in the Smith chart of Fig. 8(b). Since the normalized resistance , representing the radiation of a single cross-over, is very small in practice, the point is very close to the point . Therefore, only the required values for and are very small, and hence, easy to achieve. The dispersion diagram for the circuit of Fig. 8(a) (including the matching reactance and ) is shown in Fig. 9. The phase constant and leakage factor are unaltered compared to the case of Fig. 7 (without the matching reactance) at frequencies away from broadside. In contrast, the abrupt broadside variations observed in Fig. 7 and corresponding to the mismatch shown in Fig. 6(b) have been almost completely suppressed as a result of matching. In particular, the leaky-wave factor does not

drop significantly, which indicates a nearly complete suppression of the open stopband and guarantees a continuous scanning through broadside with an almost constant radiation efficiency, as will be demonstrated experimentally in Section VI. It should also be noted that increasing the radiation resistance not only increases the leakage factor, but also slightly increases the phase constant, as may be easily verified by computing the second-order approximation phase constant of a lossy transmission line. The corresponding matching benefits are seen in Fig. 10(a) and (b). Excellent impedance matching is achieved at all the frequencies, with the lowest return loss at the broadside frequency, where matching was specifically performed. The insertion loss of the corresponding two-port structures is almost constant with frequency, which implies a constant radiation efficiency. Another possible matching technique is shown in Fig. 11. This technique uses antiparallel stubs placed at the center of the transmission line sections. In this configuration, the stubs do not radiate, due to their antiparallel current contributions, and they are thus used exclusively for matching. The small reflections induced from these discontinuities are cancelled out with the reflections from the crossover discontinuities since the distance between them is of at broadside frequency. This approach represents an alternative design technique, which may be used to relax the constrains on the radiating cross-overs in some specific applications. B. Implementation and Results As previously mentioned, the natural reactance discontinuities existing in the practical implementation of the phase-reversal structure in addition to those due to the radiation resistances may be used for the matching procedure just described. Fig. 12 shows the structure proposed for cross-over self-matching, along with the corresponding local characteristic impedance. The impedance steps at the edges of the cross-over are due to the stepped-impedance discontinuities between the low-impedance interconnecting transmission lines and the higher impedance cross-overs, which can be modeled by lumped series inductances [25]. Across the cross-over region,

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Fig. 12. Matched unit-cell cross-over structure and qualitative local characteristic impedance. The impedance just below the overlapping region of the two strips is decreased due to capacitive coupling.

Fig. 10. S -parameters: (a) for a one-cell phase-reversal antenna and (b) for a 40-cell phase-reversal antenna simulated from the equivalent transmission line model of Fig. 5, as in Fig. 6, but with the LCR unit-cell matching depicted in Fig. 8.

Fig. 11. Phase-reversal antenna structure using dummy stubs to suppress the open stopband.

the impedance experiences a decrease followed by an increase, due to the capacitive loading effect of the strip overlapping region. The equivalent circuit of Fig. 8(a) provides a qualitative idea of the proposed self-matching technique. However, its parameters are practically difficult to extract, except for the radiation resistance, which can be estimated by commercial software such as IE3D or the High Frequency Structure Simulator (HFSS). Therefore, the overall cross-over structure is simply designed and optimized by full-wave analysis in practice. This approach also ensures proper account of the effects of mutual coupling between the unit cell. Matching optimization , , and defined in involves tuning of the parameters Fig. 12. Fig. 13 plots the phase constant and leakage factor of the periodic phase-reversal structure extracted from full-wave simof unit cells (1–7). ulation [26], [27], for different number

Fig. 13. Complex propagation constant ( =  + j ) of the matched (Fig. 12) phase-reversal antenna computed by full-wave analysis (method of moments (MoM) IE3D) and then applying Bloch-wave analysis for the parameters " = 2:94, p = 4:1 mm, g = 0:2 mm, l = 0:15 mm, w = 0:3 mm, w = 0:2 mm, and w = 0:3 mm. The number of unit-cells varies from 1 to 7. The extracted leakage factor converged after five units.

. While is stable versus , only converges for This dependence of is due to the mutual coupling existing between the unit cells. The normalized leakage factor varies approximately from 0.01 to 0.02 above 16 GHz, which corresponds to the border frequency of the radiation cone represented in Fig. 2. Below 16 GHz, sharply drops to a value close to zero due to the absence of radiation. Above 16 GHz, in the radiation zone, varies linearly with frequency across broadside decreases and does not experience any significant drop; linearly with frequency and is smooth near broadside. A linindicates a constant leakage over freearly decreasing quency, giving rise to a perfectly equalized radiation efficiency. Since the antenna becomes electrically larger as frequency increases, the correspondingly increasing directivity is naturally expected to result in increasing gain. V. ARRAY SYNTHESIS A. Synthesis of the Radiation Resistance The procedure of synthesizing the attenuation constant of a leaky-wave antennas is well illustrated in [28]. For the proposed phase-reversal antenna, the array synthesis problem conof the sists in determining the resistances structure for a given desired radiation efficiency and given de, which is approximated by distrisired radiation aperture

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bution of radiated powers . Thus, we are as a function of and . seeking an expression for The available powers before and after the cross-over resis, which are denoted and , respectively, in tance Fig. 5, are found to be (18) (19) where the approximation in (18) is justified by the small amount loss occurring in the cross-over of radiation leakage may be then written as sections. The resistance (20) is the sum of the powers radiated by the next where and of the power consumed in elements , i.e., the load, (21) , where is the attenuation In this relation, factor of the transmission lines, which reduces to unity in the limiting case of lossless lines. Combining (20) and (21) yields (22) The radiation efficiency of the antenna is (23) where the approximation transforms into an equality as and where the input power reads

Fig. 14. Radiation resistance R extracted by (29) for a uniform (R = R = const:) phase-reversal antenna with different number of elements N = 1; . . . ; 15. The resistance value converges, indicating suppression of the

edge effects, after seven elements.

are determined by full-wave simulation or measurement. Equation (12) may be used as a first guess for the layout of the crossovers. The design is next performed by iterative full-wave analysis via the scattering parameters. In order to account for mutual coupling between the unit cells, an -cell uniform antenna structure terminated the end by a matched load is made large enough to ensure converis analyzed, where gence of the results, interpreted as the suppression by dilution of the edge effects of the structure. It is assumed that the effects of mutual coupling of nonuniform antenna designs will not depart significantly from those of the uniform extraction model. Since the unit cells are assumed to be well matched, the ratio of the input to the load powers may be obtained by writing the for to ratio of (19) to (18), , and taking the product of all the resulting expressions, which yields (27)

(24)

From the viewpoint of the scattering parameters, this ratio may also be written

Inserting (24) into (23), and next substituting the resulting into (22) leads to the sought synthesis result expression for (25) which reduces to

(28) The resistance

is then obtained by equating these ratios (29)

(26) in the case of transmission lines with negligible loss . Naturally, the achievable set of resistances will be limited by technological constraints, in particular by the achievable range of sizes of the cross-over sections, which sets limitations to the possible designs. B. Cross-Over Realization of the Radiation Resistance The geometric parameters of the cross-overs (Fig. 12) required to implement the radiation resistances prescribed by (26)

Fig. 14 plots the radiation resistance extracted from (29) for phase-reversal antenna with a uniform a different number of elements . Since this procedure is fulfilled by analyzing the antenna as a truncated structure, the extracted radiation resistance only converges after exceeding certain number of cells [29]. As shown in Fig. 14, convergence to the final value of the resistance, taking into account the effects of mutual coupling in a practical structure, is achieved after seven unit cells. Below this number, the dissymmetry of the coupling distribution due to the finiteness of the structure affects the coupling results. Beyond this number, this effect is diluted across

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the structure since the ratio of the number of ports (i.e., two) over the number of coupled cells, becomes negligible. Note that this extraction technique includes tuning of the different geometrical parameters to maintain the matching of the unit cell. The technique provides a fairly accurate model of the unit cell as a basis for the synthesis of the complete -cell structure, which then requires only minor fine-tuning. C. Antenna Design Procedure The proposed phase-reversal antenna is characterized by the following parameters: frequency range of operation, scanning angle , 3-dB beamwidth (directivity), radiation efficiency , and sidelobe level (SLL). Based on the specifications for these parameters, the design procedure may be articulated as follows. 1) Since all the above parameters change with scanning, the design must be performed at a selected angle of radiation. The best approach is to choose the angle located at the middle of the scanning angular range so as to minimize the departure from the specifications as scanning occurs. In typical applications, this angle will be the broadside angle, corresponding to a symmetric scan around the broadside. (e.g., uniform, 2) Determine the aperture distribution Taylor, binomial, etc.) required for the specified value of SLL. 3) Determine, for the chosen substrate (and its effective permittivity ), the period of the structure corresponding to the specified frequency range (Fig. 2). 4) Determine the number of unit cells , corresponding to the , providing the specified value of length for the distribution determined at 2); this, with 2), yields for . the local radiated powers for using (26) for 5) Compute the values of the specified value of . 6) Synthesize (typically by full-wave simulation) the corresponding cross-over geometrical parameters, which are esand ; this requires some minor sentially matching adjustments. 7) Simulate and optimize the overall antenna. D. Example: Uniform-Aperture Antenna As an example, let us design a phase-reversal antenna with the following specifications: center frequency of 25 GHz, symmetric scanning range around broadside, a 3-dB beamwidth of 4 , a radiation efficiency of 80%, and an SLL of at least 13 dB. Following the above design procedure, we have the following. 1) Since a symmetric scanning range around broadside is re. quired, the angle of design will be chosen as dB [24] 2) A uniform aperture, characterized by is sufficient to meet the SLL specification. Thus, over the antenna structure. 3) The specified frequency corresponds to the dispersion dia, leading gram of Fig. 2, which uses a substrate of mm. to a period of 4) According to the corresponding array factor, unit ; correspondcells are required to provide for . ingly,

Fig. 15. Distribution of the normalized radiation resistances for a 41-cell phase-reversal antenna for the efficiencies of 70%, 80%, and 90%. The synthesized resistances for both the uniform distribution (maximum directivity) and the Taylor distribution with SLL = 25 dB (reduced SLL) are shown.

5) For constant

, (26) reduces to (30)

We see that decreases as increases, i.e., as one moves from the source to the load, for a uniform aperture. This is because the fraction of power radiated in each unit cell , to be constant in absolute terms , must compensate for the decay of the available power [see (20)]. This resistance distribution is plotted in Fig. 15, and , as which also shows the cases of well as the case of a Taylor aperture [24], for comparison. This graph shows that, for a given antenna length or directivity, the range of radiation resistances is proportional to the radiation efficiency. This is because a higher efficiency requires a larger amount of radiation per unit length to reduce the amount of power wasted in the load. When the required efficiency exceeds a given limit (e.g., around 90% here), the extreme (most radiating) phase-reversal element become very difficult to realize due to the too large required radiation resistances. 6) In order to follow the requirement of increasing resistances along the structure, the width and length of the cross-overs must be increased along the antenna, while the characteristic impedance of the interconnecting transmission line sections must be kept constant to avoid mismatch. This leads to a tapered structure, as shown in Fig. 16. In this of the transmisstructure, the gap between the strips sion line sections are progressively increased to achieve inof the creasing radiation resistances, while the width lines is also increased to maintain a constant characteristic impedance. To ease the tedious process of full-wave simulating, all of 41 unit cells of the antenna, an interpolation technique, limiting here the number of simulated cells to seven, is used. First, the strip widths are synthesized . for the required (constant) characteristic impedance Second, after designing proper self-matching cross-overs following the technique described in Section III, the correare extracted. Finally, sponding radiation resistances

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Fig. 16. Unit cell design for the phase-reversal antenna tapered so as to produce a uniform effective aperture (broadside case). This figure may be used for design in connection with the synthesis results of Fig. 15. (a) Continuously tapered unit cell. (b) Nonuniform strip with w and resistance R distributions versus the gapwidth g required to maintain a constant characteristic impedance of Z . The results are for a 20-mil Roger 6002 substrate and radiation efficiency  .

165

= 80%

=

as shown in Fig. 16(b), a second-order curve-fitting techand nique is utilized to interpolate the functions (31a) (31b) , , ; , , and , and where is in millimeters. With this interpolation, only a reduced number of unit cells must be synthesized. The above design has assumed a perfectly flat phase distribution across the antenna structure at broadside. However, in practice, the tapering required for a nonuniform resistance distribution also affects the phase distribution since larger resistors require longer strips [see (12)] and larger values of and for self-matching, which exhibit larger phase delays. In a uniform aperture antenna, this will cause the phase to increase along the structure. Fig. 17 shows the phase-error distribution related to this effect. Fig. 17(a) shows phase error occurring in each unit cell with respect to the phase shift across the first cell, and the , showing that the corresponding radiated power ratio phase error is inversely proportional to the radiated power ratio. The phase errors accumulate along the structure and produce the phase distribution shown by the circle curve in Fig. 17(b). In the graph, this curve is fitted by a third-order Taylor approximation, and the corresponding linear, quadratic, and cubic terms are shown separately. According to array theory [24], a linear phase error distribution tends to slightly tilt the main beam by a certain angle. Here, the tilt will be in the forward direction due

Fig. 17. Phase error distribution (at broadside) along a 41-cell uniform-aperture phase-reversal antenna (broadside case) obtained by full-wave simulation. (a) Local error (phase shift across the nth minus phase shift across the first), and corresponding radiated power ratio Q =P . (b) Cumulated error, with corresponding Taylor expansion fitting: linear, quadratic, and cubic.

where

to the increasing delay and the broadside frequency will therefore be shifted to a lower value. The quadratic error term primarily reduces the directivity and symmetrically degrades the SLL, while it leaves symmetric radiation patterns unaffected. The cubic error term introduces asymmetrical shoulders around the main lobe. The SLL of the uniform-aperture antenna ( 13.3 dB) can be decreased by using a Taylor aperture distribution [24]. Fig. 15 also shows the radiation resistance distribution for a 41-element phase-reversal antenna with 25-dB SLL. The upper limit of the resistance range is close to that of the uniform case. In contrast, the lower limit is much lower and close to zero, which can be implemented with very short and strongly overlapping (nonradiating transmission line like region) cross-overs. VI. EXPERIMENTAL DEMONSTRATION A. Antenna Design The overall antenna is designed on a Roger 6002 substrate with a height of 20 mil and permittivity of 2.94. It is simulated with IE3D (MoM) as a two-port structure. The simulation ports are set to 165 , corresponding to the characteristic

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Fig. 20. Phase-reversal antenna prototype.

Fig. 18. Simulated (IE3D MoM) S -parameters for the phase-reversal antenna without input impedance transformer for the geometrical parameters found from Fig. 16(b).

Fig. 21. Measured return loss for the traveling-wave antenna of Fig. 20.

B. Design of Input Balun and Impedance-Transformer Transition

Fig. 19. Three-stage balun and impedance-transformer transition used the excite the phase-reversal antenna. (a) Structure layout and parameters. (b) Simulated S -parameters.

impedance of the transmission lines sections between the cross-overs. Fig. 18 shows the simulated -parameters. Perfect impedance matching is observed, validating the proposed unit-cell matching technique, with a return loss higher than 25 dB at the broadside-radiation frequency, 25 GHz. Thanks to unit-cell matching, the open stopband is completely suppressed. The insertion loss is almost perfectly flat, at a value of around 7.6 dB corresponding to 83% radiation efficiency (very close to the targeted 80% efficiency), immediately after penetration space harmonic into the fast-wave region of the of the dispersion diagram, at 16 GHz (Fig. 2).

The antenna will be terminated by a matched chip resistor. In contrast, a proper feeding mechanism is required at the input. Since the antenna is balanced and the measurement instrumentation is unbalanced, a balun is required at both ends of the structure. Moreover, impedance transformation from the 165impedance of the antenna to 50 of the instruments. A threestage balun and impedance-transformer transition is used for this twofold purpose. Fig. 19(a) shows the transmission line model and layout of the transition. A 50- microstrip line is followed by three sections of high-impedance parallel-strip line at the center frequency sections with the same length of (broadside-radiating frequency). To achieve good matching over the entire scanning bandwidth, an in-band equal-ripple Chebyshev design is performed [30], using the characteristic imped, , and ances of for the three different sections. The simulated -parameters of the transition is shown in Fig. 19(b). The resulting return loss exceeds 20 dB from 11 to 33 GHz. C. Prototype The overall fabricated antenna, including the leaky-wave structure and the input transition, is shown in Fig. 20. A thick-film surface-mount flip-chip resistor (RCD1800302PW1800L) from IMS Inc., Portsmouth, RI, is connected across the parallel-strip line through a vertical via at the end to terminate and match the antenna. The resistance value of the load differs by 15 from the desired 165 and the vias creates additional undesired reactance load, but these imperfections only produce minor reflections at the end. The overall 41-cell

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three-stage Chebyshev transition circuit reduces the return loss by around 10 dB at the upper edge of the leaky-wave radiation band. radiaFig. 22(a) shows the measured co-polarized tion patterns of the antenna in the -plane ( -plane) for a frequency sweep from 16 to 39 GHz. Fig. 22(b) shows the corresponding measured gain and beamwidth. Broadside radiation occurs at 25 GHz. At this point, the measured gain is of 15.7 dBi and the measured 3-dB beamwidth is of 4 . The beamwidth slowly decreases as frequency increases since the antenna aperture increases as the wavelength decreases. However, the beamwidth next saturates and eventually increases as the beam angle approaches endfire, where the effective antenna aperture is reduced. The SLL of the radiation pattern in the plane of beam scanning is of 16.2 dB at broadside frequency, which is 3 dB lower than the expected for an antenna with an exact uniform aperture distribution. The reason for this discrepancy may be the differences due to the curve-fitting design technique used in (31). To better evaluate the results, a rectangular plot of three radiation patterns at 23, 25, and 33 GHz are shown in Fig. 22(c). As expected from the cubic term of the phase-error distribution, the main lobe exhibits a shoulder at certain frequencies. Some of the spurious sidelobes (below 15 dB) are due to re-radiation from the signal reflected from the end chip resistor at mirrored angles with respect to broadside. VII. CONCLUSION

Fig. 22. Measured radiation performance (E ) in H -plane (yz -plane) for the phase-reversal antenna of Fig. 20. (a) Scanned radiation patterns at the frequencies 16, 16.5, 17, 17.5, 18, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25, 27, 29, 31, 33, 35, 37, and 39 GHz. Broadside radiation occurs at 25 GHz. (b) Gain and beamwidth versus frequency. (c) Rectangular plot of the radiation pattern at 23, 25 and 33 GHz, which corresponds to the main beam angle at  = 115 ,  = 90 (broadside), and  = 66 .

antenna including the transitions and connection microstrip line is about 180-mm long. D. Results The antenna follows the design of Section V. Fig. 21 shows the measured of the prototype. The filtering effect of the

A novel full-space scanning periodic phase-reversal space leaky-wave antenna array, radiating in the harmonic, has been proposed, designed in OPS technology, implemented, and measured. In contrast to previously reported antennas of this type, this antenna radiates from its phase-reversing sections as opposed to from the interconnecting transmission line sections or the stubs, which allows for small leakage factor and subsequently large directivities. As a result of phase reversal, singe-beam full-space scanning can be achieved on a relatively low-permittivity substrate. The open stopband, which typically plagues broadside radiation in periodic leaky-wave antennas, is completely suppressed thanks to a special unit-cell matching technique. A millimeter-wave leaky-wave antenna with uniform aperture distribution has been designed using an efficient synthesis procedure. Continuous single-beam full-space frequency scanning has been demonstrated experimentally for this antenna. The measured beamwidth and gain at the broadside frequency of 25 GHz are of 4 and 15.7 dBi, respectively. REFERENCES [1] , R. E. Collin and R. F. Zucker, Eds., Antenna Theory, Part II. New York: McGraw-Hill, 1969. [2] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Peregrinus, 1996. [3] F. J. Zucker, “Surface-wave antennas,” in Antenna Engineering Handbook, J. Volakis, Ed., 4th ed. New York: McGraw-Hill, 2007, ch. 11. [4] A. A. Oliner and D. R. Jackson, “Leaky-wave antennas,” in Antenna Engineering Handbook, J. Volakis, Ed., 4th ed. New York: McGrawHill, 2007, ch. 10. [5] R. S. Elliott, Antenna Theory and Design. New York: Prentice-Hall, 1981.

YANG et al.: FULL-SPACE SCANNING PERIODIC PHASE-REVERSAL LEAKY-WAVE ANTENNA

[6] M. Takahashi, J. Takada, M. Ando, and N. Goto, “A slot design for uniform aperture field distribution in single-layered radial line slot antennas,” IEEE Trans. Antennas Propag., vol. 39, no. 7, pp. 954–959, Jul. 1991. [7] W. Menzel, “A new traveling-wave antenna in microstrip,” Arch. Elektron. Uebertrag. Tech., vol. 33, no. 4, pp. 137–140, Apr. 1979. [8] A. A. Oliner and K. S. Lee, “The nature of the leakage from higher modes on microstrip line,” in IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, Jun. 1986, pp. 57–60. [9] C.-N. Hu and C.-K. C. Tzuang, “Analysis and design of large leakymode array employing the coupled-mode approach,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 4, pp. 629–636, Apr. 2001. [10] K. C. Chen, C. K. C. Tzuang, Y. Qian, and T. Itoh, “Leaky properties of microstrip above a perforated ground plane,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, Jun. 1999, pp. 69–72. [11] C. Caloz, T. Itoh, and A. Rennings, “CRLH metamaterial leaky-wave and resonant antennas,” IEEE Antennas Propag. Mag., vol. 50, no. 5, pp. 25–49, Oct. 2007. [12] S. Lim, C. Caloz, and T. Itoh, “Metamaterial-based electronically controlled transmission line structure as a novel leaky-wave antenna with tunable angle and beamwidth,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 1, pp. 161–173, Jan. 2005. [13] F. P. Casares-Miranda, C. Camacho-Peñalosa, and C. Caloz, “High-gain active composite right/left-handed leaky-wave antenna,” IEEE Trans. Antennas Propag., vol. 54, no. 8, pp. 2292–2300, Aug. 2006. [14] J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and Design. London, U.K.: Peregrinus, 1988. [15] M. Danielsen and R. Jørgensen, “Frequency scanning microstrip antennas,” IEEE Trans. Antennas Propag., vol. AP-27, no. 2, pp. 146–150, Mar. 1979. [16] J. R. James and P. S. Hall, “Microstrip antennas and arrays, part 2: New array-design technique,” Proc. Inst. Elect. Eng.—Microw., Opt., Acoust., vol. 1, pp. 175–181, Sep. 1977. [17] M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antennas Propag., vol. 41, no. 1, pp. 31–37, Jan. 1993. [18] S. Paulotto, P. Baccarelli, F. Frezza, and D. R. Jackson, “A novel technique for open-stopband suppression in 1-D periodic printed leakywave antennas,” IEEE Trans. Antennas Propag., vol. 57, no. 7, pp. 1894–1906, Jul. 2009. [19] A. Hessel, Antenna Theory, Part II, R. E. Collin and R. F. Zucker, Eds. New York: McGraw-Hill, 1969, ch. 19. [20] C. S. Franklin, “Improvements in wireless telegraph and telephone aerials,” British Patent 242.342, Aug. 5, 1924. [21] N. Yang, C. Caloz, and K. Wu, “Fixed-beam frequency-tunable phase reversal coplanar stripline antenna array,” IEEE Trans. Antennas Propag., vol. 57, no. 3, pp. 671–681, Mar. 2009. [22] L. Brillouin, Wave Propagation in Periodic Structures. New York: Dover, 1946. [23] P. Baccarelli, S. Paulotto, D. R. Jackson, and A. A. Oliner, “A new Brillouin dispersion diagram for 1-D periodic printed structures,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 7, pp. 1484–1495, Jul. 2007. [24] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Wiley , 1996. [25] S.-G. Mao, C.-W. Chiu, R.-B. Wu, and C. H. Chen, “Equivalent inductances of coplanar-stripline step discontinuities,” in Proc. Asia–Pacific Microw. Conf., 1997, pp. 613–616. [26] P. Baccarelli, C. D. Nallo, S. Paulotto, and D. R. Jackson, “A full-wave numerical approach for modal analysis of 1-D periodic microstrip structures,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1350–1362, Apr. 2006. [27] L. Zhu, “Guided-wave characteristics of periodic coplanar waveguides with inductive loading unit-length transmission parameters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 10, pp. 2133–2138, Oct. 2003. [28] C. H. Walter, Traveling Wave Antennas. New York: McGraw-Hill, 1965. [29] T. Kokkinos, C. D. Sarris, and G. V. Eleftheriades, “Periodic FDTD analysis of leaky-wave structures and applications to the analysis of negative-refractive-index leaky-wave antennas,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1619–1630, Apr. 2006. [30] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2004.

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Ning Yang (M’03) received the Bachelor’s degree in electric engineering and Ph.D. degree in microwave engineering under a joint-program from Southeast University (SEU), Nanjing, China, and the National University of Singapore (NUS), Singapore, in 2004. In November 2001, he became an Engineer with the Center for Wireless Communications (CWC). In 2003, he became an Associate Scientist with the Institute for Infocomm Research (I R), Singapore. From 2005 to 2006, he was with Motorola Inc., as a Senior RF Engineer, where he was engaged in research and development of emergent RF and antenna technologies for cutting-edge mobile devices. Since October 2006, he has been a Researcher with École Polytechnique de Montréal, Montréal, QC, Canada. He has authored or coauthored over 60 peer-reviewed technical papers. One invention disclosure of his was accepted by Motorola Inc. As one of the key participants, he contributed to the development of V360, V361, V367, and ROKR E8 mobile phones of Motorola Inc. He has been a Reviewer for several transactions, journals, and letters. His current research interests include differentially integrated microwave circuits and antennas/arrays, metamaterials, substrate integrated waveguide (SIW) devices, and integrated active RF subsystems. Dr. Yang was a Technical Program Committee (TPC) member of EuCAP’2009. He was the recipient of the Young Scientist Award of the General Assembly 2008, International Union of Radio Science (URSI) and Best Dissertation Award of 2005 by the Ministry of Education, Jiangsu, China.

Christophe Caloz (S’99–M’03–SM’06–F’10) received the Diplôme d’Ingénieur en électricité and Ph.D. degree from the École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 1995 and 2000, respectively. From 2001 to 2004, he was a Postdoctoral Research Engineer with the Microwave Electronics Laboratory, University of California at Los Angeles (UCLA) In June 2004, he joined the École Polytechnique of Montréal, Montréal, QC, Canada, where he is currently an Associate Professor, a member of the Microwave Research Center Poly-Grames, and the Holder of a Canada Research Chair (CRC). He has authored or coauthored 350 technical conference, letter and journal papers, and ten book and book chapters. He is a member of the Editorial Board of the International Journal of Numerical Modelling (IJNM), International Journal of RF and Microwave Computer-Aided Engineering (RFMiCAE), International Journal of Antennas and Propagation (IJAP), and Metamaterials of the Metamorphose Network of Excellence. He holds several patents. His research interests include all fields of theoretical, computational, and technological electromagnetics engineering with a strong emphasis on emergent and multidisciplinary topics. Dr. Caloz is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Technical Coordinating Committee (TCC) MTT-15. He is a speaker of the MTT-15 Speaker Bureau. He is the chair of the Commission D (Electronics and Photonics) of the Canadian Union de Radio Science Internationale (URSI). He was the recipient of the 2004 UCLA Chancellor’s Award for Post-doctoral Research and the 2007 IEEE MTT-S Outstanding Young Engineer Award.

Ke Wu (M’87–SM’92–F’01) is currently a Professor of electrical engineering, and Tier-I Canada Research Chair in RF and millimeter-wave engineering with the École Polytechnique of Montréal, Montréal, QC, Canada. He 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, FRQNT). He has also held guest and visiting professorship in many universities around the world. He has authored or coauthored over 730 referred papers and a number of books/book chapters. He has served on the Editorial/Review Boards of many technical journals, transactions, and letters, as well as scientific ency-

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clopedias as both an editor and guest editor. He holds numerous patents. His current research interests involve substrate integrated circuits (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 Fellow of the Canadian Academy of Engineering (CAE) and the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He is a member of the Electromagnetics Academy, Sigma Xi, and the URSI. 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. He

will be the general chair of the 2012 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He is currently the chair of the joint IEEE Chapters of MTTS/APS/LEOS, Montréal, QC, Canada. He is an elected IEEE MTT-S Administrative Committee (AdCom) member (2006–2012) and is the chair of the IEEE MTT-S Member and Geographic Activities (MGA) Committee. He is an IEEE MTT-S Distinguished Microwave Lecturer (2009–2011). He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of the IEEE Canada, and the 2009 Thomas W. Eadie Medal of the Royal Society of Canada.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

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Eliminating the Low-Frequency Breakdown Problem in 3-D Full-Wave Finite-Element-Based Analysis of Integrated Circuits Jianfang Zhu, Student Member, IEEE, and Dan Jiao, Senior Member, IEEE

Abstract—An effective method is developed in this work to extend the validity of a full-wave finite-element-based solution down to dc for general 3-D problems. In this method, we accurately decompose the Maxwell’s system at low frequencies into two subsystems in the framework of a full-wave-based solution. One has an analytical frequency dependence, whereas the other can be solved at frequencies as low as dc. Thus, we bypass the numerical difficulty of solving a highly ill-conditioned and even singular system at low frequencies. In addition, we provide a theoretical analysis on the conditioning of the matrices of the original coupled Maxwell’s system and the decomposed system. We show that the decomposed system is well conditioned, and also positive definite at dc. The validity and accuracy of the proposed method have been demonstrated by extraction of state-of-the-art on-chip integrated circuits at frequencies as low as dc. The proposed method bypasses the need for switching basis functions. Furthermore, it avoids stitching static- and full-wave-based solvers. The same system matrix is used across all the frequencies from high to low frequencies. Hence, the proposed method can be incorporated into any existing full-wave finite-element-based computer-aided design tool with great ease to completely remove the low-frequency breakdown problem. Index Terms—Electromagnetic analysis, finite-element methods (FEMs), full-wave analysis, integrated circuits (ICs), low-frequency breakdown.

I. INTRODUCTION

T

HERE EXISTS a wide range of applications in which frequencies ranging from dc to high frequencies are involved. For example, the design of high-speed digital, analog, mixed-signal, and RF integrated circuits (ICs) from dc to tens and hundreds of gigahertz frequencies. In such a broad band of frequencies, static-based modeling and simulation tools have fundamental limits in capturing high-frequency effects accurately. In contrast, full-wave-based modeling and simulation tools can capture high-frequency effects accurately. However, they generally break down at low frequencies [1]–[10]. In

Manuscript received September 19, 2009; revised June 09, 2010; accepted June 28, 2010. Date of publication September 16, 2010; date of current version October 13, 2010. This work was supported by the Intel Corporation under a grant, the National Science Foundation (NSF) under NSF Grant 0747578, and by the Office of Naval Research under Grant N00014-10-1-0482. The authors are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (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.2010.2065930

order to perform circuit design in a broad band of frequencies, a natural solution is to stitch a static-based computer-aided design (CAD) tool with a full-wave-based CAD tool. However, this solution is cumbersome because one has to develop and accommodate both tools and switch between these two when necessary. The other popular solution is to change basis functions. For example, the loop-tree and loop-star basis functions [1], [7] were used to achieve a natural Helmholtz decomposition of the current to overcome the low-frequency breakdown problem in integral-equation-based methods. As another example, the tree–cotree splitting scheme [4], [5] was used to provide an approximate Helmholtz decomposition for edge elements in finite-element-based methods. The edge basis functions were used on the cotree edges, whereas the scalar basis functions were incorporated on the free nodes associated with the tree edges to represent the gradient field. Again, this solution is not convenient since one has to change basis functions to extend the applicability of a full-wave solver to low frequencies. More important, existing tree–cotree splitting based solutions of vector wave equations cannot be used to fundamentally solve the low-frequency breakdown problem. We will soon establish in the sequel that the system matrix resulting from the tree–cotree splitting for solving vector wave equations remains singular at low frequencies, although the tree–cotree splitting scheme was successful in eliminating the null space of the curl operator in magnetostatic analysis [13]. As yet, no results have been reported at frequencies as low as dc for on-chip applications in which the physical dimensions could be less than 1 m. For example, it was shown that a tree–cotree splitting scheme can be used to extend a full-wave finite-element method (FEM)-based solution to 1 MHz for typical on-chip dimensions [5]. However, for frequencies lower than 1 MHz, extrapolation techniques are required. In this work, we consider the following two questions. 1) Whether we switch basis functions or we switch solvers, the system matrix has to be reformulated. The resultant computational overhead is nontrivial. Can we extend the validity of a full-wave FEM-based solver to low frequencies without changing the system matrix? If this can be done, we can, with great ease, fix the low-frequency breakdown problem in existing full-wave FEM-based CAD tools. 2) Can we extend the validity of a full-wave FEM-based solver to frequencies as low as dc? In other words, can we completely eliminate the low-frequency breakdown problem? The answers to these two questions not only can be used to fundamentally overcome the

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low-frequency breakdown problem, but also can be used to develop unconditionally stable time-domain numerical schemes because the use of a large time step suggests that frequencies to be solved are low. In [10], we developed an FEM-based solution that addressed both questions in the framework of a 2.5-D eigenvalue-based FEM method for the broadband modeling of on-chip interconnects. In this paper, we propose an effective solution to eliminate the low-frequency breakdown problem in a 3-D FEM-based solution of vector wave equations. This solution addresses the two questions raised above. It uses the same system matrix across all frequencies. Meanwhile, it is valid at frequencies as low as dc. In addition, we provide a theoretical analysis on the root cause of the low-frequency breakdown problem observed in the solution of vector wave equations, and the reason why this problem is extremely severe in the modeling of very large scale integrated (VLSI) circuits. We show that existing tree–cotree splitting based solutions cannot be used to completely solve the low-frequency breakdown problem for vector wave equations. In addition, a pure mathematics-based matrix scaling technique cannot be used to remove the low-frequency breakdown problem either because physics dictates that the eigenvalue spectrum present in a full-wave FEM-based analysis of ICs is ultra large. We thus develop a method that can bypass the numerical difficulty of solving a highly ill-conditioned system. This method is developed by decomposing the Maxwell’s coupled system into two subsystems at low frequencies in the framework of a full-wave based solution. One system has an analytical frequency dependence, while the other has a well-conditioned matrix down to dc. In addition, the existence of the dc solution in the proposed method is also proved. Our proposed approach constitutes a unified finite-element solution because across all the frequencies, we use the same system matrix. With that, we are able to incorporate the proposed solution into any existing FEM solver to remove the low-frequency problem with great ease. II. LOW-FREQUENCY BREAKDOWN PROBLEM

Fig. 1. Low-frequency breakdown observed in the modeling of on-chip circuits.

a finite-element-based analysis of (1) yields the following matrix equation (3) If the first-order absorbing boundary condition is used to trunand are assembled from cate the computational domain, their elemental counterparts as

(4)

A. 3-D Full-Wave Finite-Element-Based Solution Consider the second-order vector wave equation subject to a certain boundary condition (1) where is relative permeability, is relative permittivity, is conductivity, is angular frequency, is the speed of light, and represents a current source. When discretizing (1), the conducting region in the computational domain is also discretized in order to model fields inside conductors accurately. This is especially important at low frequencies because conductors become transparent to fields due to large skin depth. By expanding the unknown using vector basis function as (2)

In a full-wave analysis, a commonly used vector basis function is edge element [11]. We used edge basis functions in a triangular prism element for all the simulations conducted in this work. It was shown by our numerical experiments that, in general, the solution of (3) breaks down at tens of megahertz in typical on-chip problems, the electric size of which can be smaller than 10 wavelengths. As an example, consider a short single wire of 1- m dimension embedded in an inhomogeneous stack. The is theoretically predicted magnitude of reflection coefficient to be very close to zero at low frequencies. However, as can be obtained from an FEM solution is wrong seen from Fig. 1, at low frequencies. In this example, the conductor loss inside the conducting wire is significant. As another example, which is lossless, consider a 1 m 1 m 1 m parallel-plate structure made of perfect conductors. In Fig. 2(a), we plot the analytical solution of ’s magnitude at each edge in the computational domain at 10 kHz. In Fig. 2(b), we plot ’s magnitude at each

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Fig. 2. Magnitude of the electric field between two parallel plates made of perfect conductors. (a) Analytical result. (b) Numerical result, which breaks down.

edge obtained by numerically solving (3) at 10 kHz. Clearly, the FEM solution breaks down. The low-frequency breakdown problem is analyzed in Section II-B. B. Analysis of Low-Frequency Breakdown Problem Matrix

in (3) can be written as (5)

where

(6) 1) On the Conditioning of the System Matrix: To understand the low-frequency breakdown problem, we first consider a lossless system (7) The eigenvalue distribution of (7) can be analyzed via the following generalized eigenvalue problem (8) Since is symmetric semipositive definite and is symmetric positive definite, the eigenvalues of (8) are nonnegative real numbers. They are located on the real axis, as shown in Fig. 3(a). Among these eigenvalues, some are zero because of the null space of [3]. The remaining eigenvalues correspond to the resonant frequencies of the 3-D structure being simulated. For IC

Fig. 3. Illustration of the eigenvalue distribution. (a) Eigenvalues of (8). (b) Eigenvalue distribution related to S ! T.

0

problems, except for the eigenvalues associated with the dominant gradient-type modes, these eigenvalues are extremely large because the geometrical dimensions of on-chip circuits are very small. , and Denoting the eigenvalues of (8) by , let the corresponding eigenvectors by . Since are orthogonal, we obtain .. .

..

.

.. .

(9)

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which can be used to analyze the condition number of (7). From (9), it can be seen that the eigenspace of (8) is shifted to the left by , as illustrated in Fig. 3(b). All the zero eigenvalues are shifted to the left plane, while the nonzero ones remain in the right plane since the considered here are small, denoting the . The condition number of maximum eigenvalue of (8) by (9) is

where subscripts and denote the quantities associated with a cotree and tree, respectively, and is the same as shown in (6). It has been shown that the null space of is related to the tree edges in a mesh. By arbitrarily setting the value of on the tree edges, (12) is reduced to the following system:

(10)

is symmetric positive definite. Therefore, for magwhere netostatic problems, the tree–cotree splitting successfully converts a singular matrix to a matrix that is solvable. In existing solutions of vector wave equations based on tree–cotree splitting, the edge basis functions are used on the cotree edges. In addition, the scalar basis functions are used on the free nodes associated with tree edges to represent the gradient field. The resultant system matrix is

which is very large since is tens of orders of magnitude larger than . Take a typical IC structure for example, the condition number can be as large as 10 at 1 Hz. Moreover, as the frequency decreases, the condition number increases. As a result, the full-wave-based system (7) becomes highly ill conditioned at low frequencies. At dc, the system even becomes singular. In addition, because of numerical errors, the eigenvalues of (8) due to the null space of are not exactly zeros. Instead, they are clustered around the origin point in the complex plane. The same is true for gradient-type modes that are physical. This problem may not even exist in microwave or millimeter-wave circuits. However, it is very severe in on-chip VLSI circuits because the eigenvalues of (8) spread over a much wider spectrum compared to those in microwave or millimeter-wave circuits. Thus, the eigenvalues, which theoretically should be zero, cannot be obtained as zero numerically. In fact, our numerical experiments show significant values. This is understandable because computers have finite precision. If there exists an eigenvalue that is as large as 10 , it is very difficult to find zero eigenvalues correctly. When frequency is high, the inexact zero is still apeigenvalues do not induce much error because even if is not exactly zero. However, proximately equal to at low frequencies, the error can be very significant. The value can even be overwhelmed by the inaccurate when is of small. As a result, the frequency dependence of the electric field extracted out of (7) can be wrong at low frequencies. Moreover, hits one of the inexact eigenvalues clustered around the if origin point, the system can even become singular. The low-frequency breakdown problem observed in a lossy system shown in (5) can also be understood by a similar analysis. 2) On the Tree–Cotree Splitting Based Solutions of Vector Wave Equations: The tree–cotree splitting has been used to solve the low-frequency breakdown problem in a finite-elementbased solution of vector wave equations. However, in the following, we show that existing techniques based on tree–cotree splitting cannot be used to completely solve the low-frequency breakdown problem, although it has been used to successfully eliminate the null space of the curl operator for magnetostatic applications [13]. Consider a magnetostatic problem (11) a finite-element-based analysis of (11) results in the following matrix system: (12)

(13)

(14) , , , where , , and are the same as those in (6), are different because the gradient basis function is emand ployed on the free nodes. Similar to the magnetostatic case, the is invertible. However, different from the magsub-matrix netostatic case, the system cannot be reduced to a smaller one part. Moreover, when frequency is that only includes the close to zero, only the term involving the curl operator is left while all the other terms vanish because they are all frequency dependent. As a result, even though the tree–cotree gauge is introduced to eliminate the null space of a curl operator, the null portion of the matrix at low frequenspace still exists in the cies. In addition, different from that in magnetostatic cases, the upper left block of the system shown in (14) is now a combinamatrices. Although it will not become ill tion of , , and is solvable now, conditioned at low frequencies because the computed frequency dependence is, in fact, wrong due to the ignorance of the frequency dependent terms resulting from finite machine precision. Therefore, current tree–cotree splitting based methods have not fundamentally solved the low-frequency breakdown problem for vector wave equations. Moreover, the mathematics-based matrix-condition-improving techniques cannot be used to fundamentally solve the low-frequency breakdown problem either. This is because the large spectrum of (8) is due to physical reasons instead of numerical reasons. The physical resonant modes of an IC structure determine the largest eigenvalue of the FEM system, which is very large because of the m- and m-level geometrical dimensions of an on-chip circuit, whereas the null space of or the physical gradient field determines the smallest one, which is theoretically zero. As an example, we employed one of the most advanced scaling techniques [12] and found that it can only extend the full-wave-based solution to a frequency around 1 MHz. In the following, we show an approach that can efficiently and effectively bypass the difficulty of solving an ill-conditioned system at low frequencies. Meanwhile, this approach can make the traditional full-wave FEM-based solution applicable to dc. Applications to on-chip problems of 1- m dimensions have shown a success at frequencies as low as 0 Hz.

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III. PROPOSED METHOD FOR ELIMINATING THE LOW-FREQUENCY BREAKDOWN PROBLEM We first elaborate a solution for problems that do not involve conductor loss, i.e., problems in which conductors are treated as perfect electric conductors. We then show how to handle problems that involve conductor loss, i.e., problems in which fields penetrate into conductors. In fact, when frequency is low, we have to consider the nonideality of conductors because the skin depth can be larger than the conductor dimension. As observed in on-chip VLSI circuits, conductors are transparent to fields. In this section, we also give a detailed analysis on the conditioning of the system matrix resulting from the proposed method. A. Cases Without Conductor Loss When there is no conductor loss, there is no in (5). We consider a system shown in (7). At low frequencies where a full-wave solution breaks down, static solvers have been shown to produce accurate results. This suggests that at these frequencies, and , are very well decoupled. Hence, for a problem that only involves perfect conductors, given a current source excitation (the most commonly used excitation in an FEM-based analysis of circuits), the field satisfies the following two equations:

(15) should scale with frequency From (15), it is clear that as given a constant current source excitation. The . The voltage thereby should scale with frequency as resultant voltage–current relationship suggests that a lossless low-frequency system that has perfect conductors is an effective capacitor, the capacitance of which does not change with frequency. At dc, the entire system that is external to the perfect conductor becomes an open circuit. With the frequency dependence of the field solution analytically derived, we bypass the need for solving a highly ill-conditioned system (7) at low frequencies. Thus, the low-frequency breakdown problem can be readily overcome without the need of any computation. The procedure is as follows. Once the fullwave solution breaks down, we record the field solution at the frequency that is a little bit higher than the breakdown frequency. It is clear that is still valid at this frequency. We call and this frequency the reference frequency. Denoting it by the corresponding by , we can accurately obtain at any by using the following scaling: lower frequency (16) By doing so, we are able to accurately obtain the solution of the full-wave FEM-based system at low frequencies without switching basis functions or switching to static formulations. B. Cases With Conductor Loss The frequency dependence of the electric field in a lossless system has an analytical expression. To take advantage of that, for cases with conductor loss, we order unknowns inside con-

Fig. 4. Circuit representation of an FEM system shown in (5).

ductors and those outside separately, yielding a system matrix as follows: (17) where denotes field unknowns inside conductors, denotes those outside conductors; and is the excitation placed outside conductors. Here, the excitation of is not considered because in a full-wave FEM-based analysis of circuits, a current source excitation is generally launched from the ground to the port that is excited, and hence, excitation only exists in . It is clear that in (17) is a lossless system. Equation (17) constitutes a rigorous discretization of coupled Maxwell’s equations. At low frequencies where a full-wave soare very well decoupled. Therelution breaks down, and fore, in (17), if we set conduction current to be zero, we can solve for only because the source for , which is the conduction current, is set to zero. If we do not enforce the condition that the conduction current is zero, we can solve for . The final solution of (17) can then be obtained by combining and . For clarity, we use a circuit interpretation of (5) to present the proposed solution of (17) at low frequencies. The FEM-based system (5) can be directly mapped to a circuit shown in Fig. 4. The second-order term related to frequency in (5) is associated with capacitance , the first-order term is associated with resistance , whereas the constant term is associated with inductance . In Fig. 4, denotes the conduction current, which can in (17), whereas denotes the displacebe evaluated from ment current. In general, the effective , , and shown in the figure are is frefrequency dependent. However, at low frequencies, quency independent. The proof is given below. From Fig. 4, can be obtained from the resultant voltage–current relationship by setting the conduction current to be zero. Since the conduc, when the conduction current is zero, tion current density is over the conducting region is also zero, and hence, the the dielectric region is subject to an equivalent perfect electric conductor boundary condition. In such a lossless system, based on the analysis given in Section III-A, at low frequencies, since and are decoupled, given a constant current, the electric field, , and hence, the voltage should scale with frequency as as can be seen from (15). The resultant voltage–current relationship dictates a capacitance that does not change with frequency. As a result, by setting conduction current in (17) to be zero, we can solve for given a current, from which the dielectric region external to the conductors, i.e., the network, can be char-

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Fig. 6. Arbitrary

N -port system.

Fig. 5. Illustration of the eigenvalue distribution of the system matrix inside conductors. (a) Eigenvalue distribution of (21). (b) Up-shifted spectrum of (20).

Fig. 7. Mesh with element 1 in the conducting region, and the other three elements in the dielectric region.

acterized. This characterization can be done at one frequency and used throughout the low-frequency range since has no frequency dependence. The detail is given in Section III-B.1. network, On the other hand, if we supply a voltage to the we can solve for , from which the conducting region, i.e., the network, can be characterized. Note that different from , are, in general, frequency dependent due to skin effects. needs to be numerically solved at each frequency. Hence, The detail of this step is given in the following Section III-B.2. subject to is solved, and the subject to a After voltage source excitation is solved, we can combine the resultant and to obtain the -parameters of the entire circuit, the detail of which is described in Section III-B.3. From the aforementioned analysis, it can be seen that the coupled Maxwell’s system involving conductor loss can be decomposed into two subsystems at low frequencies. One is the system outside conductors subject to perfect electric conducting boundary condition. This system has an analytical frequency dependence based on the analysis given in Section III-A. The other in (17). We will is the system inside conductors, which is show that this system is well conditioned even at dc in this section and Section III-C. Thus, we bypass the numerical difficulty of solving the highly ill-conditioned and even singular system (5) at low frequencies. Subject to : To characterize the 1) Solving for system external to conductors, we set conduction current to be . This is because the conduction current zero, and hence, density is nothing but . As a result, (17) is reduced to

Clearly, it is a lossless system. The solution we have developed in Section III-A to solve the low-frequency breakdown problem for lossless cases can be directly used here to solve (18) at any is of inlow frequency. If the circuit parameter instead of terest, once the full-wave solution breaks down, we record the field solution at the frequency that is a little bit higher than , and use the capacitance exthe breakdown frequency, i.e., . tracted therein throughout the frequencies lower than is solved from the first equation in (17) 2) Solving for :

(18)

(19) where serves as a voltage to excite the current inside conductors. Based on the analysis given in [17], such a voltage source excitation can be modeled as a gradient field. A natural and is , i.e., the real part of convenient choice of solved from (17) at the reference frequency . Since at and high frequencies current sources are generally used to peris nothing form a full-wave FEM-based analysis, the but a voltage distribution over the resistance network of the conductors. Hence, it is a gradient field that serves as an effective excitation of (19). Equation (19) can be solved at any low frequency because is a well-conditioned matrix. The proof is given as follows. is formed inside conductors, it has the following Since form: (20) The term associated with is absent because inside conductors, the displacement current can be ignored compared to conduction current.

ZHU AND JIAO: ELIMINATING LOW-FREQUENCY BREAKDOWN PROBLEM IN ANALYSIS OF ICs

Fig. 8. S -parameters of an on-chip interconnect structure simulated by the proposed solution. (Left column: gigahertz); right column: S -parameters at low frequencies (frequency unit: hertz).)

The eigenvalue distribution of (20) can be analyzed by considering the following eigenvalue problem:

(21)

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S -parameters in the entire band (frequency unit:

is symmetric positive definite and is at least semiSince can be made positive definite in the propositive definite ( posed solution, which is to be elaborated upon in Section III-C), the eigenvalues of (21) are nonnegative, as shown in Fig. 5(a). Similar to the analysis given in (9), when considering the system , we superpose by . Therefore, the eigenof

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At low frequencies, the voltage at each port, , is obtained in the same way as (23), where is the used in from . The current at each port, , is the (19), which is combination of the current flowing into the conductor at port and that flowing through the dielectric region, i.e., through a , capacitor. The current flowing into the conductor at port , can be evaluated from an area integral of over the conductor cross section (25) Fig. 9. Geometry of a 3-D spiral inductor (the perfect electric conductor is denoted as PEC).

values are shifted upward by , as shown in Fig. 5(b). As can be seen, only a small shift in Fig. 5 can move the origin out of . In addition, the spectrum rathe eigenspace of smaller than that of (7) for dius of (21) is approximately 10 is proportional to conductivity , good conductors because whereas is proportional to permittivity . For typical on-chip problems, the spectrum radius shown in Fig. 5 can be as small can be solved at low frequencies. as 10 . Hence, the matrix can be made positive In addition, in the proposed solution, definite, and thereby solvable at dc. The detailed explanation is given in Section III-C. 3) -Parameter Extraction: Next we show how to combine and to obtain circuit parameters such as -parameters of a circuit network. Shown in Fig. 6 is a -port system. To extract -parameters, both open- and short-circuit port conditions can be used. In the following, the open-circuit one is used for illustration. With the open-circuit port condition, for a -port system, we have right-hand sides with the FEM system matrix re(the voltage at port ) and maining unchanged. If we know (the current at port ) with for each excitation (right-hand side), we can obtain -parameters of the -port network by solving

Since we need to combine and to make a complete solution, the current that flows through the dielectric region at port , , needs to also be incorporated. can be evaluated from (26) is the capacitance at port . As a result, the total curwhere rent at port is obtained from (27) There are two approaches to obtain the capacitance at each port. The first approach is to use the charge distributed at port divided by , where the charge can be obtained from normal after (18) is solved. The second approach that is more convenient to adopt in the proposed solution is to use the solution of at the reference frequency to extract . We can do this because when the full-wave solution breaks down, the frequency is already low enough that the capacitance does not change with frequency any more. Hence, the capacitance extracted at the reference frequency can be safely used for lower frequencies. With at known, at the nonexcited ports, can be found from

(28) At the excited port,

can be found from

(22) denotes the reference impedance (An industry stanwhere is 50 ). Since there are excitations, there are dard rows of equations in (22), the solution of which is . At high frequencies where the full-wave solution does not can be readily break down, the port voltage obtained from the field outside conductors by evaluating a line integral from the port to the ground (23) is Assuming that the th port is excited, the port current is zero since known from the excitation. At the other ports, other ports are left open, i.e., (24)

(29) where is the excitation current at port at the reference fre, can be evaluated from based on (25), and quency is known from . As can be seen from the proposed procedure, the -parameter extraction approach is the same at high and low frequencies. The only difference is that (for voltage ) and current are generated differently. At high frequencies, is solved directly from (17), and is analytically known. At low frequencies, is solved by comand , and is obtained by combining the current bining flowing into the conducting region and that flowing into the dielectric region. The overall procedure for the cases with conductor loss is summarized as follows.

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Fig. 10. S -parameters of a spiral inductor simulated by the proposed solution. (Left column: S -parameters in the entire band; right column: S -parameters at low frequencies.)

Step 1) When the full-wave solution breaks down, record , which is the field solution at the reference frequency. Use to derive the port capacitance

using (28) and (29), where the and current are evaluated using (23) voltage and (25), respectively.

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Step 2) Use , the real part of the field solution outside conductors at the reference frequency, to evaluate the port voltage at port , , using (23). Step 3) Use as to solve (19). From the solution of (19), evaluate the current flowing into the conductor at port by (25). Evaluate the current flowing through the dielectric region at port by (26) using the port voltage obtained from Step 2) and the capacitance obtained from Step 1). Obtain the total current flowing into port by (27). Step 4) With the port voltage known from Step 2) and port current known from Step 3) at each frequency, extract -parameters using (22). The first two steps can be done once and reused for different . The last low-frequency points since they are only related to two steps are repeated for each frequency point. In other words, at low frequencies, we fix the voltage source excitation applied to the circuit, and extract the frequency-dependent current for each frequency. C. DC Solution of At dc, becomes . In general, the stiffness matrix is only semipositive definite, and hence, has a null space. However, is formed not only by inside conductors, but also here, by an additional matrix. This additional matrix is due to the contribution from the elements outside conductors, which share unknowns with those elements inside conductors. the same Note that the unknowns residing on the conducting surface are shared by interior and exterior regions. , To help better understand the positive definiteness of the we use a 2-D discretization to illustrate the basic concept. Consider a 2-D mesh shown in Fig. 7. Element 1 represents an element in a conducting region, i.e., the region. It is surrounded by the other three elements in the dielectric region, i.e., the region. Using edge bases, a 3 3 matrix can be formed. It can be obtained as follows: (30)

Fig. 11. Illustration of a 4

2 4 on-chip bus.

is not always greater than zero, is semiClearly, since is positive definite, and hence, cannot be inverted. However, not made of only. It has an additional , which is contributed by the exterior elements, which share the edges on the conducting surface with interior elements. Since is positive definite, as shown in (33), the deficiency of matrix is remedied. becomes well conditioned and solvable. In other words, after the null space of the original 3 3 matrix is eliminated, it beitself is comes a full-rank matrix. Therefore, in such cases, is thus solvable even at dc. The above an invertible matrix. proof can also be applied to a 3-D discretization. , it can be seen that reFrom the process of assembling gardless of 2-D or 3-D problems, the dimension of the matrix added upon the original stiffness matrix is equal to the number of edges on the conducting surface, i.e., the boundary between the interior and the exterior domains. At dc, there does not exist skin effect, and hence, current is uniformly distributed over the cross section that is perpendicular to the current flowing direction. Therefore, there is no need to add unknowns interior to is the same as . Since conductors. Hence, the dimension of is positive definite, and is semipositive definite, is also positive definite.

where D. Identifying the Breakdown Frequency

and (31)

denotes the where denotes the length of the th edge, and area of the th element. Given any arbitrary nontrivial vector , the following properties of and can be derived:

(32) (33)

To identify at which frequency the full-wave FEM-based solution breaks down, a natural solution is to execute the program from high to low frequencies. Once the circuit parameters extracted from the field solution, such as -parameters, become physically meaningless, we consider the frequency as the breakdown frequency, at which the low-frequency solution is enabled. However, this procedure relies on physical intuition, which may not be accurate for complicated examples. For instance, consider an interconnect network connected by a lot of vias, given any port of the network, generally, we expect that the diagonal entry of the -parameter matrix, , is close to zero. However, may not be close to zero at all because of the large resistance that is equal to 0.6, for example, of the network. Getting an may not be wrong. We thus developed a rigorous analytical approach for quantitatively determining the breakdown frequency, which was reported in [14].

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Fig. 12. S -parameters of a multiport structure simulated by the proposed solution. (Left column: S -parameters in the entire band; right column: S -parameters at low frequencies.)

IV. NUMERICAL AND EXPERIMENTAL RESULTS

To validate the proposed solution, a number of on-chip interconnect and package inductor structures were simulated.

The first example was a three-metal-layer on-chip interconnect structure fabricated using silicon processing technology on a test chip [15]. The structure was of 300- m width. It involved a 10- m-wide strip in M2 layer, one ground plane in M1 layer, and one ground plane in M3 layer. The distance of this strip to

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the M2 returns at the left- and right-hand sides was 50 m. The strip was 2000- m long. In [16], this structure was simulated successfully by a full-wave-based solver on which our low-frequency solution was built. The full-wave simulation broke down at 10 MHz, at which the low-frequency solution was enabled. The -parameters of this structure were extracted, which are shown in Fig. 8. The figures in the left column depict the -parameters in the entire frequency band in comparison with measured data, while those in the right column show the detail at low frequencies. As can be seen from the left column, the proposed solution agrees very well with the measured data from low frequencies to 50 GHz. Since the measured -parameters were not available below 45 MHz, we compared the low-frequency result with that generated by a static solver, which was validated in [15]. As can be seen clearly from the right column of Fig. 8, the result generated by the proposed solution is in an excellent agreement with the reference data starting from dc. Thus, the accuracy of the proposed solution is validated. In addition, we extracted and parameters from the field solution. At dc, we obtained and pF, which showed an excellent agreement with analytical data. With the proposed solution validated, we next simulated a 3-D spiral inductor residing on a package. The geometry of the spiral inductor is shown in Fig. 9. Its diameter (D) is 1000 m. The wire is 100- m wide, and 15- m thick. The port separation (S) is 50 m. The inductor is backed by two package planes. The backplane is 15- m thick. The conductivity of the metal is 5.8 10 S/m. This structure was simulated successfully by the full-wave-based solver in [16] at high frequencies. The full-wave solution broke down around 1 MHz, at which the low-frequency solution was enabled. Fig. 10 shows the simulated -parameters from dc to 20 GHz. Again, figures in the left column show the -parameters over the entire frequency band, whereas those in the right column depict the detail at low frequencies. Based on the dc resistance of the inductor, the analytof the inductor is 0.999569151 at dc. The generated ical by the proposed solution is 0.9996 at dc, which agrees very well with the analytical data. To demonstrate the capability of the proposed solution in simulating multiport problems. In the third example, a four-port on-chip bus was simulated. Fig. 11 shows the detailed geometry and dielectric material information. The conductivity of the conductors is 5 10 S/m. Port 1 and port 2 are located at the near and far ends of the left wire, whereas the other two ports are located at the right wire. The FEM solution broke down around 10 MHz. With the proposed solution, we were able to successfully simulate the structure at frequencies as low as dc, as can and are 0.25 and be seen from Fig. 12. The analytical and 0.75, respectively at dc. The simulated magnitude of are 0.243 and 0.757, respectively. In addition, the phases of and are zero. Hence, both magnitude and the simulated phase produced by the proposed solution agree well with analytical data. V. CONCLUSION In this paper, we provided a theoretical analysis of the low-frequency breakdown problem observed in the 3-D full-wave FEM-based analysis of VLSI circuits. Based on this

analysis, we develop an effective solution to completely remove the low-frequency breakdown problem. With this solution, we extend the capability of the full-wave FEM-based solver down to dc. In addition, across all the frequencies, the same system matrix is used in the proposed method, and hence, the method can be incorporated into any existing full-wave FEM-based CAD tool with minimal computational overhead. Moreover, from dc to frequency at which a typical full-wave solution breaks down, only the system matrix inside conductors has to be solved, and hence, the problem dimension is reduced greatly. The proposed method has been applied to the modeling of state-of-the-art VLSI circuits starting from dc. Numerical and experimental results have demonstrated its effectiveness in eliminating the low-frequency breakdown problem for full-wave FEM-based solutions. ACKNOWLEDGMENT The authors would like to thank Dr. M. J. Kobrinsky and Dr. S. Chakravarty, both with the Intel Corporation, Hillsboro, OR, for providing measured data. REFERENCES [1] J. Zhao and W. C. Chew, “Integral equation solution of Maxwell’s equations from zero frequency to microwave frequencies,” IEEE Trans. Antennas Propag., vol. 48, no. 10, pp. 1635–1645, Oct. 2000. [2] A. Rong and A. C. Cangellaris, “Electromagnetic modeling of interconnects for mixed-signal integrated circuits from DC to multi-GHz frequencies,” in IEEE MTT-S Int. Microw. Symp. Dig., 2002, pp. 1893–1896. [3] R. Dyczlj-Edllnger, G. Peng, and J. F. Lee, “Efficient finite element solvers for the Maxwell equations in the frequency domain,” Comput. Methods Appl. Mech. Eng., vol. 169, no. 3–4, pp. 297–309, Feb. 1999. [4] S. C. Lee, J. F. Lee, and R. Lee, “Hierarchical vector finite elements for analyzing waveguiding structures,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 8, pp. 1897–1905, Aug. 2003. [5] S. Lee and J. Jin, “Application of the tree–cotree splitting for improving matrix conditioning in the full-wave finite-element analysis of high-speed circuits,” Microw. Opt. Technol. Lett., vol. 50, no. 6, pp. 1476–1481, Jun. 2008. [6] S. Lee, K. Mao, and J. Jin, “A complete finite element analysis of multilayer anisotropic transmission lines from DC to terahertz frequencies,” IEEE Trans. Adv. Packag., vol. 31, no. 2, pp. 326–338, May 2008. [7] Y. Chu and W. C. Chew, “A surface integral equation method for solving complicated electrically small structures,” in IEEE 14th Top. Elect. Perform. Electron. Packag. Meeting, 2003, pp. 341–344. [8] F. P. Andriulli, K. Cools, F. Olyslager, and E. Michielssen, “The Dottrick TDEFIE: A DC stable integral equation for analyzing transient scattering from PEC bodies,” in IEEE Int. AP-S Symp., July 2008, 4 pp. [9] H. Bagci, F. P. Andriulli, F. Vipiana, G. Vecchi, and E. Michielssen, “A well-conditioned integral-equation formulation for transient analysis of low-frequency microelectronic devices,” in IEEE Int. AP-S Symp., Jul. 2008, 4 pp. [10] J. Zhu and D. Jiao, “A unified finite-element solution from zero frequency to microwave frequencies for full-wave modeling of large-scale three-dimensional on-chip interconnect structures,” IEEE Trans. Adv. Packag., vol. 31, no. 4, pp. 873–881, Nov. 2008. [11] J. M. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 2002. [12] D. Ruiz, “A scaling algorithm to equilibrate both row and column norms in matrices,” Rutherford Appleton Lab., Oxon, U.K., Tech. Rep. RAL-TR-2001-034, 2001, also appeared as ENSEEIHT-IRIT Re. RT/APO/01/4. [13] J. B. Manges and Z. J. Cendes, “A generalized tree-cotree gauge for magnetic field computation,” IEEE Trans. Magn., vol. 31, no. 3, pp. 1342–1347, May 1995. [14] J. Zhu and D. Jiao, “A theoretically rigorous full-wave finite-elementbased solution of Maxwell’s equations from DC to high frequencies,” IEEE Trans. Adv. Packag., 2010, to be published.

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[15] M. J. Kobrinsky, S. Chakravarty, D. Jiao, M. C. Harmes, S. List, and M. Mazumder, “Experimental validation of crosstalk simulations for on-chip interconnects using S -parameters,” IEEE Trans. Adv. Packag., vol. 28, no. 1, pp. 57–62, Feb. 2005. [16] D. Jiao, S. Chakravarty, and C. Dai, “A layered finite-element method for high-capacity electromagnetic analysis of high-frequency ICs,” IEEE Trans. Antennas Propag., vol. 55, no. 2, pp. 422–432, Feb. 2007. [17] A. Alonso Rodriguez and A. Valli, “Voltage and current excitation for time–harmonic eddy current problems,” SIAM J. Appl. Math., vol. 68, pp. 1477–1494, 2008. Jianfang Zhu (S’09) received the B.S. degree in electronic engineering and information science from the University of Science and Technology of China, Hefei, China, in 2006, and is currently working toward the Ph.D. degree at Purdue University, West Lafayette, IN. She is currently with the On-Chip Electromagnetics Group, Purdue University, as a Research Assistant. Her current research interest is computational electromagnetics for large-scale high-frequency IC design.

Dan Jiao (S’00–M’02–SM’06) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, in 2001. She then joined the Technology Computer-Aided Design (CAD) Division, Intel Corporation, until September 2005, as a Senior CAD Engineer, Staff Engineer, and Senior Staff Engineer. In September 2005, she joined Purdue University, West Lafayette, IN, as an Assistant Professor with the School of Electrical and Computer Engineering. In 2009, she became a tenured Associate Professor. She has

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authored two book chapters and over 100 papers in refereed journals and international conferences. Her current research interests include computational electromagnetics, high-frequency digital, analog, mixed-signal, and RF IC design and analysis, high-performance very large scale integration (VLSI) CAD, modeling of microscale and nanoscale circuits, applied electromagnetics, fast and high-capacity numerical methods, fast time-domain analysis, scattering and antenna analysis, RF, microwave, and millimeter-wave circuits, wireless communication, and bio-electromagnetics. Dr. Jiao has been a reviewer for many IEEE journals and conferences. She is an associate editor for the IEEE TRANSACTIONS ON ADVANCED PACKAGING. She was the recipient of the 2010 Ruth and Joel Spira Outstanding Teaching Award, the 2008 National Science Foundation (NSF) CAREER Award, the 2006 Jack and Cathie Kozik Faculty Start up Award (which recognizes an outstanding new faculty member of the School of Electrical and Computer Engineering, Purdue University), a 2006 Office of Naval Research (ONR) Award under the Young Investigator Program, the 2004 Best Paper Award presented at the Intel Corporation’s annual corporate-wide technology conference (Design and Test Technology Conference) for her work on generic broadband model of high-speed circuits, the 2003 Intel Corporation Logic Technology Development (LTD) Divisional Achievement Award in recognition of her work on the industry-leading BroadSpice modeling/simulation capability for designing high-speed microprocessors, packages, and circuit boards, the Intel Corporation Technology CAD Divisional Achievement Award for the development of innovative full-wave solvers for high-frequency IC design, the 2002 Intel Corporation Components Research the Intel Hero Award (Intel-wide she was the tenth recipient) for timely and accurate 2-D and 3-D full-wave simulations, the Intel Corporation LTD Team Quality Award for her outstanding contribution to the development of measurement capability and simulation tools for high-frequency on-chip crosstalk, and the 2000 Raj Mittra Outstanding Research Award presented by the University of Illinois at Urbana-Champaign.

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A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship Zsolt Szabó, Gi-Ho Park, Ravi Hedge, and Er-Ping Li, Fellow, IEEE

Abstract—In this paper, an improved algorithm for extracting the effective constitutive parameters of a metamaterial is derived. The procedure invokes the Kramers–Kronig relations to ensure the uniqueness of the solution. The accuracy of the method is demonstrated by retrieving the effective material parameters of a homogeneous slab. This study reveals under which conditions the calculation of the refractive index involves more than one branch of the complex logarithmic function. A metamaterial built up from wires and split-ring resonators is then investigated. The applicability and limits of the presented algorithm are explored by observing how the effective parameters of a metamaterial slab converge as its thickness is increased. Index Terms—Branching problem, effective material parameters, Kramers–Kronig relations, metamaterials.

I. INTRODUCTION LECTROMAGNETIC metamaterial research [1]–[3] has attracted much interest over the last few years. In spite of considerable progress, researchers are still debating the fundamental issues and question the validity of the effective medium concept, which is essential for understanding the electromagnetic behavior of metamaterials (see [1, App. C] or [4]). The usual design of metamaterials requires the computation of transmission-reflection data or -parameters of a unit cell with a full-wave electromagnetic field solver. Electromagnetic material properties such as wave impedance, refractive index, electric permittivity, and magnetic permeability are then obtained by applying the effective medium theory [5], [6]. This theory replaces the electromagnetic response of the complicated metamaterial structure with the electromagnetic response of a homogeneous isotropic or anisotropic slab. The mathematical solution of this problem is generally not unique. To get a unique solution, physically justified constrains must be imposed. The continuity of complex electric permittivity and magnetic permeability with frequency must be enforced. Furthermore, a passive medium cannot have gain or lasing. At this

E

Manuscript received October 25, 2009; revised June 20, 2010; accepted July 23, 2010. Date of publication September 07, 2010; date of current version October 13, 2010. This work was supported by the Agency for Science Technology and Research (A*STAR), Singapore, under Metamaterial Research Program Grant 0821410039. The authors are with the Advanced Photonics and Plasmonics Research Group, Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), 138632 Singapore (e-mail: [email protected]; [email protected]; [email protected]. edu.sg; [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.2010.2065310

point, it should be noted that, in this paper, the time–harmonic is used. Consequently, for passive media convention the imaginary part of the refractive index must be positive. Several effective metamaterial parameter retrieval techniques are found in the literature [7]–[11]. In general, these methods yield a scalar electric permittivity and magnetic permeability, while the electromagnetic behavior of most metamaterial designs is anisotropic, requiring a tensor to properly describe it. Furthermore, a negative refractive index is only possible when the metamaterial is excited by a plane wave with specific polarization direction and angle of incidence. Even when all elements of the full permeability and permittivity tensor are determined [12], [13], the model can predict just the far-field behavior, while the near-field behavior of the metamaterial is lost. For most metamaterial devices, the coupling effects between the metamaterial and surrounding structures cannot be neglected. Hence, a full-wave simulation must be performed to obtain the correct electromagnetic fields. In spite of these limitations, the effective material parameters can be useful in designing optimal metamaterial unit cells with a computer. Due to the high computational cost of the electromagnetic field solution, the metamaterial geometry can be optimized in a first design phase for a specific polarization and angle of incidence. For this purpose, a robust and fast effective metamaterial parameter retrieval procedure is required. A method to retrieve the effective material parameters has been presented in [7]. The advantage of this algorithm is that the wave impedance and the imaginary part of the refractive index can be uniquely determined from the -parameters. However, the retrieval algorithm has two limitations. In order to determine the real part of the refractive index, a cumbersome iterative method based on a Taylor series is required. In addition, when the usual passive material conditions and are imposed, the method cannot find any effective material parameters for some frequency regions. However, as it has been pointed out in [8] and [14] that the magnetic and electric dipoles induced in metamaterials are not independent of each other, and the passivity condition can be fulfilled even when or . Relaxing this condition allows us to calculate effective parameters in regimes where the method in [7] fails. The Kramers–Kronig integrals, which relate the real and imaginary parts of an analytic complex function, are fundamental physical relations based on the principle of causality [15], [16]. They were successfully applied to conventional optical materials [17]; for example, to calculate the refractive index from measured absorption data. In [18], it was shown that the Kramers–Kronig relations are valid for negative index materials as well.

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SZABÓ et al.: UNIQUE EXTRACTION OF METAMATERIAL PARAMETERS BASED ON KRAMERS–KRONIG RELATIONSHIP

The purpose of this paper is to present an enhanced algorithm, which extracts the effective magnetic permeability and electric permittivity of a composite electromagnetic structure from calculated or measured transmission-reflection data. Such an algorithm will be instrumental in designing structures with optimized constitutive parameters. The novelty of our approach lies in employing the Kramers–Kronig relations to estimate the real part of the refractive index in order to ensure the uniqueness of the effective parameters. The procedure of our algorithm is summarized in the following. The wave impedance can be uniquely determined from -parameters. However, the calculation of the refractive index involves the evaluation of a complex logarithm. The complex logarithmic function is a multivalued function [19]. The resulting uncertainty is referred as a branching problem, which affects only the real part of the refractive index. To remove this ambiguity, the Kramers–Kronig relation can be applied to estimate the real part of the refractive index from the imaginary part. The physically realistic values of the refractive index are determined by selecting those branches of the logarithmic function that are closest to those predicted by the Kramers–Kronig relation. The algorithm also enforces the continuity of the refractive index versus frequency. II. EFFECTIVE MATERIAL RETRIEVAL ALGORITHM WITH KRAMERS–KRONIG RELATIONS The input data of the algorithm are the effective thickness and the complex -parameters of the metamaterial slab calculated or measured at distinct frequency points. As was shown in [7] and [8], for metamaterials with symmetrical geometry (in the direction of propagation of the electromagnetic wave), the effective thickness is just the sum of the length of the unit cells it contains. In this paper, metamaterials with symmetric geometries are considered. Therefore, no additional procedure is re. quired to determine One way to generate the -parameters of a metamaterial slab is to model it with a 3-D electromagnetic field solver. As we will show later, this algorithm is well suited to time-domain electromagnetic field solvers because large frequency ranges can be covered in a single run. However, in time-domain solutions, it is more difficult to control modes excited in the structure. When the observation points are placed in the near field of the periodic metamaterial structure, the unwanted higher order modes can be captured, which leads to wrong effective material parameter values. In order to obtain accurate -parameters, the observation points should be positioned far enough from the surface of the metamaterial to sample only the dominant mode. Consequently, the phase delay caused by the additional distance must be compensated to determine the correct phase at the boundaries of the metamaterial. As presented in [7], for a plane wave with normal incidence on a homogeneous slab, the wave impedance and the refractive index are related to the -parameters as follows: (1a) (1b)

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, is the complex where is the complex wave impedance, is the refractive index, is the extincrefractive index, tion coefficient, is the free-space wavenumber, and is the angular frequency. From the previous relations, (2) (3) The sign of the wave impedance (2) is determined by imposing the conditions and , or equivalently, ; for details, see [7] and [11]. The complex refractive index can be calculated as

(4) where is an integer denoting the branch index. Separating the real and imaginary parts of the above expression, the refractive index and the extinction coefficient become (5) (6) where is the refractive index corresponding to the principal branch of the logarithmic function. The parameter extraction procedure takes advantage of the fact that the imaginary part of the refractive index is not affected by the branches of the logarithmic function. Therefore, it can be calculated from (6) without ambiguity. Knowing the imaginary part of the refractive index, we can determine the real part by applying the Kramers–Kronig relation (7)

denotes the principal value of the improper integral where [16]. The limits of the integral are 0 and , therefore the values of the -parameters must be known for the entire frequency range. Since this is not possible, the integral must be truncated, and the Kramers–Kronig relations yield an approximation of the refractive index. For accuracy, the range of the integration should be as large as possible. Since time-domain methods yield the -parameters over a large frequency range in a single run, they are particularly well suited to this algorithm. On the other hand, if the frequency becomes too large, we may reach a point where the concept of effective parameters is no longer meaningful since the guided wavelengths are on the order of the characteristic dimensions of the metamaterial structure. The integration of (7) can be performed numerically by applying the trapezoidal rule of integration. To avoid the singularity of the improper Kramers–Kronig integral, the integration

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is split in two parts (Cauchy method [20]), leading to the following approximation of the Kramers–Kronig relation:

while the magnetic permeability can be described by the Lorentz model

(13) (8) Substituting the refractive index predicted by the can be Kramers–Kronig relation in (5), the branch number expressed as (9) where the function rounds towards the nearest integer. Therefore, the refractive index is calculated such that we select the branch that is closest to the value predicted by the Kramers–Kronig relation. The branch number is substituted in (4), and the exact value of the refractive index is calculated. The algorithm then checks the continuity of the refractive index . A discontinuity close to the limit of the calculation zone may be caused by the truncation error in the Kramers–Kronig integral. If the discontinuity is far from the limits of the covered frequency range and the discontinuity perseveres even when the frequency interval of the simulation is increased, this indicates that the limit of the effective medium theory has been reached. Finally, by inverting the relations (10) the effective magnetic permeability and electric permittivity are calculated as (11) A code written in MATLAB,1 which implements the presented algorithm, is available online.2 III. ORIGIN OF THE BRANCHING PROBLEM AND A TEST OF THE ALGORITHM In this section, the effective material parameters of two homogeneous metamaterial slabs are calculated. Both slabs have the same material parameters, but different thickness, namely, 40 and 200 nm. The electric permittivity of many metamaterials can be represented by the Drude model (12) where is the electric permittivity at high frequencies, is the Drude plasma frequency, and is the collision frequency; 1[Online]. 2[Online].

Available: www.mathworks.com/products/matlab/ Available: http://effmetamatparam.sourceforge.net/

where is the static magnetic permeability, is the magnetic permeability at high frequencies, is the magnetic resonant frequency, and is the magnetic damping factor. The parameters of the investigated homogeneous metamaterial slabs are , rad s, rad s, , , rad s, and rad s. Once the thickness of the homogeneous slab is fixed and the material parameters are known, we can apply the analytical expressions (1a) and (1b) to calculate the -parameters. The effective material parameter extraction algorithm is then employed to calculate the effective magnetic permeability and the effective electric permittivity. We compare the extracted material parameters to the exact values provided by the Lorentz and Drude models. The purpose of this comparison is to demonstrate the applicability of the algorithm and to estimate the accuracy of the extracted effective material parameters. This study also reveals under which conditions the calculations involve more than one branch of the complex logarithmic function. Fig. 1(a) and (b) presents the -parameters of the 40-nm-thick homogeneous slab, and Fig. 1(c) shows the refractive index for this case. In all the figures showing the complex refractive index , the imaginary part is represented with point markers. The Kramers–Kronig approximation is plotted with circle markers. Posof the refractive index for sible branches of the refractive index are plotted as well with upward-pointing triangle, asterisk, downward-pointing triangle, diamond, cross, and bold plus is plotted sign markers. The extracted refractive index with plus sign markers. The slab of 40 nm is thin compared to the wavelengths at which the refractive index is negative. In is continuous in the 180 180 this case, the phase of interval [see Fig. 1(b)]; consequently, no branching problem occurs. The real part of the refractive index calculated with the Kramers–Kronig relation exactly follows the branch corresponding to . The extracted effective electric permittivity and magnetic permeability are presented in Fig. 2. The inset shows the effective parameters in the double-negative frequency region. Fig. 3 shows the -parameters of the 200-nm-thick homogepresents several disneous slab. In this case, the phase of continuities, as can be seen in Fig. 3(b). This fact indicates that the 200-nm slab is thick compared to the wavelengths at which left-handed behavior occurs, and that there are several branches contributing to the physically correct refractive index, as can be seen in Fig. 4(a). Fig. 4(b) shows the branch number as a function of frequency. In case of the thick slab, the branch number can equal 2, 1, 0, and 1. Fig. 4(c) brings into focus the double-negative frequency region to relay the fine details of the negative refractive index and to show how the transitions from one branch to another occur.

SZABÓ et al.: UNIQUE EXTRACTION OF METAMATERIAL PARAMETERS BASED ON KRAMERS–KRONIG RELATIONSHIP

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Fig. 2. Extracted effective electric permittivity and magnetic permeability. The inset shows the effective parameters in the double-negative frequency region. Note that the effective parameters are independent of the thickness of the homogeneous slab.

Fig. 1. S -parameters and the refractive index of the 40-nm-thick homogeneous slab. In (a), the magnitude, and in (b), the phase of the S -parameters are plotted. In (c), the calculated extinction coefficient  , the Kramers–Kronig approximation n , several possible branches of the refractive index for m ; , and the extracted refractive index n are presented. In this case, the refractive index follows the branch with m . Note that pHz GHz.

= [03 3]

=0

1

= 10

Fig. 3. (a) Magnitude and (b) phase of S -parameters for the 200-nm-thick homogeneous slab.

From Figs. 1(c) and 4(a), we can observe that the curves of the Kramers–Kronig approximation and of the refractive index exactly overlap. This fact indicates the accuracy of the approximation given by (8). The extracted electric permittivity and magnetic permeability are independent of the slab thickness. They are the same for both the 40- and 200-nm-thick slabs and equal the exact values given by (12) and (13). This indicates that the extracting procedure accurately reproduces the original values and entered in the model of the metamaterial, and of thus validates the proposed approach. yields useful information on several facts. The phase of If the phase change exceeds 180 , then more than one branch of

the logarithmic function can contribute to the refractive index. In addition, it can also indicate the frequency range in which the refractive index can be negative. Comparison of Fig. 1(b) and (c) or Figs. 3(b) and 4(a) reveals that whenever the refracchanges tive index becomes negative, the slope of the phase does not necessign. However, a sign change in the slope of sarily imply negative refractive index, but it may indicate such an occurrence. This can be explained by the opposite orientation of the group and the phase velocity in the double-negative region [2].

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Fig. 5. Unit cell of the metamaterial slab composed of metallic split-ring resonators and wires separated by dielectric. Note that we consider a plane-wave excitation with perpendicular incidence, and an electric field polarized parallel to the wires.

Fig. 6. Retrieved refractive index, extinction coefficient, the Kramers–Kronig approximation, and several branches of the only one-unit-cell-thick metamaterial slab. The refractive index has a discontinuity in the circled frequency region, but this is a numerical error due to the truncation of the Kramers–Kronig integral and can be removed by increasing the frequency range of the simulation.

Fig. 4. (a) Refractive index of the 200-nm-thick homogeneous slab, (b) the branch number , and (c) a zoom to the double-negative frequency region where more than one branch contributes to the refractive index. (a) presents the calculated extinction coefficient , the Kramers–Kronig approximation , several possible branches of the refractive index for , and . Note that, in this case, the refractive index the extracted refractive index follows different branches of the logarithmic function.

m

n

n



m = [03; 3]

IV. EFFECTIVE MATERIAL PARAMETERS OF A METAMATERIAL SLAB CONSISTING OF WIRES AND SPLIT-RING RESONATORS In order to demonstrate the effective parameter retrieval algorithm for a real metamaterial, a well-studied structure consisting of split-ring resonators and metallic wires is considered (see Fig. 5). The geometry of the unit cell, dimensions, and material parameters are the same as in [8]. In this metamaterial design, the role of the split-ring resonators is to provide the negative magnetic response, while the wires are responsible for producing the negative electric permittivity. This metamaterial design has been extensively discussed in literature, e.g., see [1, Ch. 4] or [21]. In our numerical simulations, the metamaterial is periodic in the direction perpendicular to the propagation of the electromagnetic wave, and the electric field is polarized parallel to the

wires. At the same time, we consider metamaterials with one, three, five, or seven layers of unit cells in the direction of propagation. The aim of the calculation is to determine the effective parameters of this metamaterial in the frequency range from 5 to 20 GHz. Simulations show that this metamaterial presents many resonances outside of this frequency range. Therefore, to get a good estimate for the Kramers–Kronig integral, the simulations cover the 0–30-GHz frequency interval. We found that when this frequency interval is even larger, the accuracy of the Kramers–Kronig approximation does not change noticeably. Note that the calculation of the -parameters presented in this section was performed with the time-domain solver of the commercial software CST Microwave Studio.3 The retrieved refractive indices and extinction coefficients are presented in Figs. 6–9, while Fig. 10 summarizes the effective electric permittivity and magnetic permeability in the frequency region of the first resonance, where the double-negative behavior occurs. As shown in Fig. 6, the metamaterial slab that is only one unit cell thick is thin compared to the wavelength in the considered frequency range. The calculated -parameters are the same as in [8]. The phase of is continuous on the 180 180 interval. Therefore, the refractive index follows the zero branch (see Fig. 6). The discontinuity of the refractive at the end of the covered frequency interval, marked index in Fig. 6 by a circle, is a numerical error due to the truncation 3[Online].

Available: www.cst.com

SZABÓ et al.: UNIQUE EXTRACTION OF METAMATERIAL PARAMETERS BASED ON KRAMERS–KRONIG RELATIONSHIP

Fig. 7. (a) Retrieved refractive index n and extinction coefficient  and (b) the branch number m of the three-unit-cell-thick metamaterial slab. In (a), and several the Kramers–Kronig approximation of the refractive index n branches are plotted as well. The refractive index has discontinuity in the circled frequency regions. Note that the effective medium theory can be applied outside of the gray frequency region of (b).

Fig. 8. (a) Retrieved refractive index n and extinction coefficient  and (b) the branch number m of the five-unit-cell-thick metamaterial slab. In (a), the Kramers–Kronig approximation of the refractive index n and several branches are plotted as well. The refractive index has discontinuity in the circled frequency regions. Note that the effective medium theory can be applied outside of the gray frequency region in (b).

of the Kramers–Kronig integral, and it can be removed by increasing the frequency range of the calculation. Note that in the following graphs presenting the refractive index, the circled regions correspond to frequency regions where a discontinuity of

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Fig. 9. (a) Retrieved refractive index n and extinction coefficient  and (b) the branch number m of the seven-unit-cell-thick metamaterial slab. At low frequencies, the phase of the S -parameters is not well defined, leading to unphysical oscillations in the extracted metamaterial parameters. It is difficult to judge the validity of the effective parameters even in the frequency region between 10–15 GHz.

the refractive index occurs. The extracted effective material parameters are similar to those presented in [8]. The effective refractive index of a metamaterial with a thickness of three unit cells is presented in Fig. 7. This metamaterial is thick compared to the wavelength in the negative refractive index region. The calculations reveal that, in the double negative zone, the refractive index follows branches 0 and 1 [see Fig. 7(a) and (b)]. The refractive index has a first discontinuity GHz; this correspond to the first circled region at in Fig. 7(a), and we found that this discontinuity cannot be removed by extending the frequency range of the simulation. By inspecting the possible branches around the discontinuity point, should be followed henceforth to we note that branch . It should be enforce the continuity of the refractive index noted that the algorithm proposed in [7] also fails in this region. from the discontinuity point until Following the branch the end of the considered frequency region, the imaginary part of the electric permittivity or the imaginary part of the magnetic permeability are alternatively negative. At the discontiand the optical nuity point, the refractive index is wavelength can be calculated as m. The effective thickness is m, which is . Therecomparable to the optical wavelength fore, we interpret this discontinuity as an upper limit of the effective medium theory. The gray areas in Fig. 7(b) represents frequency regions above this upper limit. Fig. 8 refers to a metamaterial consisting of five layers of , we see that the lounit cells. Inspecting the continuity of cation of the first discontinuity shifts to the lower frequency GHz. In this case, the refractive index at the discon. The effective thickness of the metamaterial is tinuity is

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Fig. 10. (a) Electric permittivity and (b) magnetic permeability of one-, three-, and five-unit-cell-thick metamaterial slabs in the first resonant frequency region. Outside of the resonant frequency region, the effective metamaterial parameters are the same for all three cases; however, in the resonant frequency region, they change significantly as a function of the number of layers.

in the resonant frequency reChecking the continuity of GHz. However, begion, we observe a discontinuity at GHz, it is cause the oscillating behavior occurs below difficult to judge the validity of the effective parameters even in the frequency region between 10–15 GHz. The yellow (in online version) and gray areas in Fig. 9(b) represent frequency regions where we cannot extract effective material parameters. The oscillations have a somewhat smaller impact on the imaginary part of the refractive index. Therefore, the refractive index predicted by the Kramers–Kronig relations is relatively smooth in the ripple reand can give an acceptable indication of gion. In addition, there is a range of frequencies where a good overlap can be found between the refractive index predicted by the Kramers–Kronig formula and the exact values calculated from (4). Mesh refinements and smaller time steps of the electromagnetic field solver do not eliminate, but reduce the numerical er; however, this is not practical because rors in the phase of of the resulting increase in the calculation time. This simulation shows the general limitations of the transmission-reflection-based material parameter retrieval techniques. In Fig. 10, the extracted effective electric permittivity and magnetic permeability of metamaterials, which are one-, three-, and five-unit-cell layers thick, are compared in the frequency range of the first resonance, where the double-negative behavior occurs. As can be observed from Fig. 10, outside of the resonant frequency region, the effective metamaterial parameters are the same for all three cases. Consequently, bulk material properties can be meaningful for describing the metamaterial structures in that frequency range. However, in the resonant frequency region, the electric permittivity and magnetic permeability are changing significantly as a function of the number of layers. This fact demonstrates a long-range electromagnetic coupling between the metamaterial unit cells.

V. CONCLUSIONS m and . As in the previous case, this discontinuity can be interpreted as the upper limit of the effective medium theory. In addition, inspecting the trans, we observe that, at low frequencies, the mission parameter are magnitude is small. The small ripples in the phase of exponentially amplified by (3) and lead to large nonphysical os, noticeable in cillations in the values of the refractive index Fig. 8(a). Finally, in Fig. 9, an example is presented for which the retrieval algorithm and the effective medium theory cannot predict properly the electromagnetic material parameters. In this case, the metamaterial design contains seven layers of unit cells. This geometry presents challenges for the time-domain electromagnetic field solver because the magnitude of the transmisis very small outside the resonant frequency sion parameter regions. Consequently, due to numerical errors, the phase of is not well defined, and this leads to very strong ripples, which will influence the retrieved effective material parameters as well. The ripple greatly affects the real part of the re, prohibiting fractive index for the fundamental branch the retrieval of effective material parameters at low frequencies.

We have presented an effective metamaterial parameter retrieval procedure based on Kramers–Kronig relations, demonstrating the applicability, and showing the limits of the algorithm. Our code implementing the presented procedure is published online.2 The results obtained with the Kramers–Kronig relations give a suitable approximation for the real part of the refractive index. When the metamaterial is thick (compared to the wavelength), more than one branch is involved in the final result. As the optical thickness becomes comparable to the wavelength, the effective medium theory cannot be applied anymore. The discontinuity of the refractive index indicates that the limit of the effective medium theory has been reached. When many layers of unit cells are present, the electromagnetic material properties should converge to a bulk value. However, by comparing the retrieved effective metamaterial parameters for different thicknesses, we observe that the effective medium theory breaks down before convergence occurs. This is due to the fact that the geometrical feature sizes are of the order of the wavelength in the frequency range of interest. This

SZABÓ et al.: UNIQUE EXTRACTION OF METAMATERIAL PARAMETERS BASED ON KRAMERS–KRONIG RELATIONSHIP

fact invites many questions about the “real material” nature of metamaterials. ACKNOWLEDGMENT The authors are grateful to Prof. W. Hoefer, Institute of High Performance Computing, Singapore, for useful technical discussions. REFERENCES [1] L. Solymar and E. Shamonina, Waves in Metamaterials. Oxford, U.K.: Oxford Univ. Press, 2009. [2] R. Marqués, F. Martín, and M. Sorolla, Metamaterials With Negative Parameters. New York: Wiley, 2008. [3] C. Krowne and Y. E. Zhang, Physics of Negative Refraction and Negative Index Materials. New York: Springer, 2007. [4] F. Lederer, C. Menzel, and C. Rockstuhl, “Can optical metamaterials be described by effective material parameters?,” in Proc. 3rd Int. Adv. Electromagn. Mater. Microw. Opt. Congr., London, U.K., Aug.–Sep. 30–4, 2009, pp. 11–13. [5] A. M. Nicolson and G. F. 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] G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative index metamaterial at telecommunication wavelength,” Opt. Lett., vol. 31, pp. 1800–1802, Jun. 2006. [7] X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 70, Feb. 2004, Art. ID 016608. [8] D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 71, Mar. 2005, Art. ID 036617. [9] 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. [10] G. Lubkowski, R. Schumann, and T. Weiland, “Extraction of effective material parameters by parameter fitting of dispersive models,” Microw. Opt. Technol. Lett., vol. 49, no. 2, pp. 285–288, Jul. 2007. [11] C. G. Parazzoli, R. B. Greegor, and M. H. Tanielian, “Development of negative index of refraction metamaterials with split ring resonators and wires for RF lens applications,” in Physics of Negative Refraction and Negative Index Materials, C. Krowne and Y. Zhang, Eds. New York: Springer, 2007, ch. 11, pp. 261–329. [12] C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B, Condens. Matter, vol. 77, Apr. 2008, Art. ID 195328. [13] K. Z. Rajab, “Propagation of electromagnetic waves through composite media,” Ph.D. dissertation, Dept. Elect. Eng., Pennsylvania State Univ., University Park, PA, 2008. [14] G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negativeindex metamaterial at 780 nm wavelength,” Opt. Lett., vol. 32, no. 1, pp. 53–55, Jul. 2007. [15] J. N. Hodgson, Optical Absorption and Dispersion in Solids. London, U.K.: Chapman & Hall, 1970. [16] V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers–Kronig Relations in Optical Materials Research. Berlin, Germany: Springer-Verlag, 2005. [17] E. E. Palik, Handbook of Optical Constants of Solids I–IV. New York: Academic, 1985–1998. [18] K. E. Peiponen, V. Lucarini, E. M. Vartiainen, and J. J. Saarinen, “Kramers–Kronig relations and sum rules of negative refractive index media,” Eur. J. Phys. B, vol. 41, pp. 61–65, Sep. 2004. [19] P. K. Chattopadhyay, Mathematical Physics. New York: Wiley, 1990, pp. 23–24. [20] G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers. New York: Dover, 2000. [21] F. J. Rachford, D. L. Smith, and P. F. Loschialpo, “Experiments and simulations of microwave negative refraction in split ring and wire array negative index materials, 2D split-ring resonator and 2D metallic disk photonic crystals,” in Physics of Negative Refraction and Negative Index Materials, C. Krowne and Y. Zhang, Eds. New York: Springer, 2007, ch. 9, pp. 217–250.

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Zsolt Szabó received the Ph.D. degree in electrical engineering from the Budapest University of Technology and Economics (BME), Budapest, Hungary, in 2002. From 2001 to 2004, he was Research Engineer with the Tateyama Laboratory Hungary. From 2004 to 2005, he was a Magyary Zoltán Research Fellow with the Department of Atomic Physics, BME. From 2005 to 2007, he was a Japan Society for Promotion of Science Postdoctoral Fellow with the National Institute for Material Science, Tsukuba, Japan. From 2007 to 2009, he was with the National Institute for Nanotechnology, Edmonton, AB, Canada. Since 2009, he has been with the Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), Singapore, as a Senior Research Engineer. His current research interests include computational electromagnetics, magnetic hysteresis, and composite nanomaterials. Dr. Szabó is a member of the General Assembly of the Hungarian Academy of Science. He was the recipient of the 2000 Pollák–Virág Award of the Hungarian Telecommunication Scientific Society.

Gi-Ho Park received the B.Sc. degree from Hangyang University, Seoul, Korea, in 1994, the M.Eng. degree in telecommunication from the Asian Institute of Technology, Pathumthani, Thailand, in 1998, and the Ph.D. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2006. In 2006, he joined the Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), Singapore, as a Senior Research Engineer. His research interests include computational electromagnetics, metamaterials and photonic crystals.

Ravi Hedge received the B.Eng. degree from the National Institute of Technology, Suratkal, India, in 2001, the M.Sc. degree from the University of Southern California, Los Angeles, in 2002, and the Ph.D. degree from The University of Michigan at Ann Arbor, in 2008, all in electrical engineering. Since 2009, he has been a Research Engineer with the Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), Singapore. His research interests include high-frequency metamaterials, plasmonics, and nonlinear fiber optics.

Er-Ping Li (F’08) received the Ph.D. degree in electrical engineering from Sheffield Hallam University, Sheffield, U.K., in 1992. From 1993 to 1999, he was a Senior Research Fellow, Principal Research Engineer, and the Technical Director with the Singapore Research Institute and Industry. Since 2000, he has been with the Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), Singapore, where he is currently the Principal Scientist and Director of the Advanced Electronic and Photonics Department. He is also a Guest Professor with Zhejiang University, Hangzhou, China, and a Guest Professor with Peking University, Beijing, China. He has authored or coauthored over 200 papers. He holds a number of U.S. patents. His research interests include computational electromagnetics, microscale/nanoscale integrated circuits and electronic packages, and plasmonic technology. Dr Li is a Fellow of the Electromagnetics Academy. He was an associate editor for the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS from 2006 to 2008. He is currently an associate editor for the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY. He was the recipient of the Changjiang Chair Professorship Award of the Ministry of Education in China.

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A Substrate-Integrated Evanescent-Mode Waveguide Filter With Nonresonating Node in Low-Temperature Co-Fired Ceramic Lin-Sheng Wu, Member, IEEE, Xi-Lang Zhou, Wen-Yan Yin, Senior Member, IEEE, Liang Zhou, Member, IEEE, and Jun-Fa Mao, Senior Member, IEEE

Abstract—A cross-coupled substrate-integrated evanescent-mode waveguide filter is proposed with a quasi-elliptic frequency response. It is realized with a coplanar waveguide as a nonresonating node to provide an equivalent negative coupling coefficient. The filter prototype is developed with folded and ridge substrate-integrated waveguides (SIWs) in low-temperature co-fired ceramic. Since evanescent-mode and cross-coupling techniques are used in the design of filters, about 90% area reduction and more than 60% volume reduction are achieved, in comparison with conventional planar cavity-coupled SIW filters. Their unloaded factor is also improved. In particular, the spurious suppression characteristic of the direct-coupled evanescent-mode waveguide filter is kept by the cross-coupled filter with the nonresonating node structure. All these merits are demonstrated numerically, as well as experimentally, with good agreement obtained between the measured and simulated -parameters. Index Terms—Bandpass filter, cross-coupling, evanescent mode, low-temperature co-fired ceramic (LTCC), nonresonating node, spurious suppression, substrate-integrated waveguide (SIW).

I. INTRODUCTION T IS well known that high-performance miniaturized bandpass filters play important roles in various communication systems [1]. Among these, it should be mentioned that the substrate-integrated waveguide (SIW) filter [2]–[8] is one of the most attractive candidates. This is because of its low loss, low cost, small size, high power-handling capability, and easy integration with other planar circuits. Several types of modified SIWs have recently been proposed by researchers. These included ridge [9], folded [10], half-mode [11], dielectric-loaded

I

Manuscript received February 02, 2010; revised July 20, 2010; accepted July 21, 2010. Date of publication September 09, 2010; date of current version October 13, 2010. This work was supported by the National Basic Research Program of China under Grant 2009CB320204 and by the National Natural Science Foundation of China under Grant 60821062. L.-S. Wu, X.-L. Zhou, L. Zhou, and J.-F. Mao are with the Center for Microwave and RF Technologies (CMRFT), Shanghai Jiao Tong University (SJTU), Shanghai 200240, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). W.-Y. Yin was with the Center for Microwave and RF Technologies (CMRFT), Shanghai Jiao Tong University (SJTU), Shanghai 200240, China. He is now with the Center for Optical and EM Research, State Key Laboratory, Modern Optical Instrumentation (MOI), Zhejiang University, Hangzhou 310058, 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.2010.2065290

waveguide filters [12], etc. Their main efforts are devoted to reducing filter size and improving their spurious suppression characteristics. The substrate-integrated evanescent-mode waveguide filter, to the best of our knowledge, is first proposed in [9], where the ridge waveguide is used for width reduction. The evanescent mode means the mode below the cutoff frequency of the waveguide. An evanescent-mode filter usually consists of two types of guiding structures: one works in its propagating mode to provide a capacitive component and the other works in its evanescent mode to provide an inductive component. Therefore, the size of evanescent-mode components is relatively small. In [10], the substrate-integrated folded waveguide resonators are coupled with evanescent-mode sections by inserting -plane shortcircuited septa. Multilayer folded and ridge SIWs have been utilized to further miniaturize the evanescent-mode filter with a multilayer printed circuit board technology [13]. Compared with conventional substrate-integrated cavity-coupled counterparts, they are very compact in size and have good spurious suppression characteristics. In order to improve the frequency selectivity, a cross-coupled evanescent-mode filter is presented in the design of a ridge SIW component [14]. The authors have also developed a quasielliptic substrate-integrated evanescent-mode waveguide filter with an interdigital cross-coupling structure using standard lowtemperature co-fired ceramic (LTCC) technology [15]. However, it can be found that an additional parasitic response arises in these cases due to the introduction of the cross-coupling path. Since the first obvious spurious response is located within an octave band of the central frequency, the spurious suppression performance of these cross-coupled substrate-integrated evanescent-mode waveguide filters is not as good as that of the direct-coupled filters. In this paper, we propose a new cross-coupled quasi-elliptic substrate-integrated evanescent-mode waveguide filter fabricated in LTCC. It is developed using multilayer folded and ridge SIWs, where a nonresonating node is introduced and built up by a coplanar waveguide (CPW) structure. The physical mechanism of two transmission zeros obtained by a nonresonating node is examined. Compared with direct-coupled evanescent-mode filters, the frequency selectivity is improved, while the superior spurious suppression characteristic is kept. By utilizing evanescent-mode waveguide and cross-coupling techniques in our design, more than 60% volume reduction is achieved, in comparison with conventional planar substrate-in-

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Since the resonance is excited in both folded and ridge waveguides, the factor due to conductor loss of the resonator is determined by both of them, i.e., (3) where is the resonant angular frequency, , , and are the stored magnetic energies of the folded part, ridge , , and part, and whole resonator, respectively, are the conductor losses of the folded part, ridge part, and whole resonator, respectively. Set is the ratio of the stored magnetic energy in the folded waveguide to that in the whole resonator, i.e.,

Fig. 1. 3-D view of multilayer folded and ridge SIWs.

(4) tegrated cavity-coupled filters. An unloaded improved.

factor is also

can then be expressed as (5)

II. ANALYSIS AND DESIGN

where and are the factors of folded and cutoff ridge waveguides due to conductor loss, respectively. is calculated by The factor

A. Multilayer Folded and Ridge Substrate Integrated Waveguides

(6)

As demonstrated in [2]–[4], [9], [14], and [15], many SIW components are realized using standard LTCC technologies for high-density integration and packaging. Here, the LTCC techand nology, with the material Ferro A6S of , is used in our design and fabrication. The diameter of m, and the thickmetallic via-holes is chosen to be nesses of each sintered tape and metal plane (silver) are given m and m, respectively. by The multilayer folded and ridge SIWs utilized in the proposed evanescent-mode filter are shown in Fig. 1 with their geometrical parameters also given. There are four metal planes denoted by M1, M2, M3, and M4. The two types of waveguides are equivalent to corresponding metal waveguide prototypes with their via-hole arrays replaced by metallic walls [15]. The thickis set to twice and so as to provide a larger norness malized monomode bandwidth for the folded SIW [13]. The cutoff frequencies of the first three modes in the folded waveguide are 2.45, 5.57, and 9.04 GHz, respectively. The cutoff frequencies of the first two modes in ridge waveguide are 7.03 and 17.95 GHz, respectively. As they are employed in the design of filters, the multilayer folded and ridge SIWs usually work in the propagating and evanescent modes, respectively. The unloaded factor of the resonator can be expressed by

where is the phase constant of the folded waveguide, is its attenuation constant due to conductor loss. and The parameters can be extracted by a full-wave electromagnetic is found to be 204 at 3.45 GHz. (EM) simulation. Generally, the equations for an evanescent mode and equations for a propagating mode differ mainly in the replacement of the attenuation constant of the one case by the phase constant of the other case and conversely [16]. Therefore, the factor is calculated by (7) where is the attenuation constant of the ridge waveguide is the phase constant below the cutoff frequency, and of cutoff ridge waveguide due to conductor loss. The extracted is 280 at 3.45 GHz. value of It is difficult to obtain an accurate value of since the resonator has a relatively complicated configuration, but it is easy to understand that the stored magnetic energy in the folded waveguide is less than that in the ridge waveguide because the folded waveguide mainly provides capacitive component for the resonator. The value of is usually smaller than 0.5. Using can then be estimated within the range from 174 to 197 (1), at 3.45 GHz. On the other hand, if we want to improve the factor, thick substrates are preferred.

(1) B. Internal Direct Coupling and External Coupling are the factors due to the conductor, where , , and dielectric, and leakage losses, respectively. The leakage loss of is given by the structure is very small and negligible. (2)

In our design, the internal direct coupling between adjacent resonant nodes is implemented with evanescent-mode waveguide sections, which are realized by ridge SIWs instead of substrate-integrated rectangular waveguides, to reduce the filter sensitivity to the locating tolerance of via-holes. The structure

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Fig. 3. External Q factor as a function of w

for different values of l .

Fig. 2. Admittance and electrical length of the evanescent-mode coupling section as functions of the: (a) operating frequency and (b) length l of the ridge SIW. Fig. 4. Fields over the cross section of folded SIW. (a) Electric field. (b) Magnetic field.

is represented as a cascade of a -invertor and two transmission lines [13]. Using full-wave EM simulations, the admittance and electrical length of the transmission lines are both obtained and plotted in Fig. 2(a) and (b) as functions of the operating frequency and the length of the ridge SIW. The electrical length increases with increasing the frequency and , while the admittance decreases. Since half-wavelength resonators are built up by the folded SIWs together with the residual transmission lines, the lengths of folded waveguide sections are reduced significantly and are only about 1/9–1/6 of the guided wavelengths. The external coupling is afforded by a tapered stripline [15]. factor is controlled by the length and The external of the tapered structure. Their relationships are the width decreases with increasing plotted in Fig. 3. It is obvious that and . C. CPW Nonresonating Node for Negative Cross-Coupling The electric and magnetic fields on the cross section of the folded SIW are illustrated in Fig. 4(a) and (b), respectively. It is observed that the electric field concentrates mainly between M1 and M3 and reaches the maximum at the edges of M2. Conversely, the magnetic field concentrates mainly between M3 and M4 and reaches the maximum at the shorted sides. In order to obtain a quasi-elliptic frequency response, we can use an interdigital structure on M2 to realize electric coupling between two horizontal folded SIWs [15]. However, an additional obvious spurious response caused by the first even-order

mode, i.e., the mode of the first and last folded SIWs, is introduced. Another method for obtaining a quasi-elliptic frequency response is to introduce negative cross-coupling between two horizontal folded SIWs with a nonresonating node. In our design, the nonresonating node is implemented with a resonator whose resonant frequency is far away from the central frequency. Similar to the case in [17], CPW structures can be utilized for this purpose. An open-ended CPW structure is then integrated on M1, as shown in Fig. 5. The buried holes between the folded waveguides are from M2 to M4. The equivalent normalized coupling coefficient, provided by the nonresonating node, can be calculated by [18] (8) where and are two normalized coupling coefficients between the two resonators and the nonresonating node, is the self-coupling coefficient of the nonresonating node, which is relative to its equivalent reactance and is given by (9) and are the central frequency and fractional where is the bandwidth of the bandpass filter, respectively, and resonant frequency of the nonresonating node structure.

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Fig. 6. Resonant frequency and equivalent coupling coefficient of CPW struc. ture as functions of w

Fig. 5. CPW nonresonating node (NRN) between two folded SIWs. (a) Top and (b) cross-sectional views.

Since the resonant frequency of the CPW structure shown in is a Fig. 5 is much higher than the central frequency, negative number with a large absolute value. On the other hand, since the CPW structure is symmetric and its dominant resonant mode is an odd mode, we have (10) Further, it is obtained that (11) Therefore, the CPW nonresonating node can provide negative cross-coupling between nonadjacent folded waveguides. The coupling between the resonator and nonresonating node is electric here. We would like to point out, though, that the equivalent coupling coefficient is always negative, which is independent of the coupling properties. The coupling coefficients between the nonresonating node and resonators can be de-normalized by [19]

Fig. 7. Extracted coupling coefficient between the nonresonating node and the . resonator as a function of w

where and are the resonant frequencies of the two degenerated modes. As shown in Fig. 6, the resonant frequency of is inthe CPW structure decreases when the end width , creased. The nonresonating node, with a large value of can provide a strong negative cross-coupling. The provided negative coupling coefficient can be controlled within a relatively large tuning range. and are obtained from (9) and (14), Further, respectively, and is calculated by

(12)

(16) The value of

is then given by

(13) where is the sign function. Further, the de-normalized equivalent coupling coefficient of the structure is given by (14) which has the same form as that of general coupling coefficients. Using full-wave EM simulations, the relationships between , , and physical dimensions are determined with given by (15)

(17) As the central frequency and bandwidth of the filter is set to be 3.45 and 0.3 GHz, respectively, the extracted value of is plotted in Fig. 7 as a function of . The coupling coefficient between the nonresonating node and the resonator can be enhanced by using the CPW structure with large patches. D. Transmission Zeros Obtained by Nonresonating Node To have an insight view of the mechanism to generate transmission zeros, the coupling scheme of a fourth-order quasi-elliptic filter with a nonresonating node is shown in Fig. 8. According to the symmetric topology, the normalized coupling ma-

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is usually a very small negative number. Define However, the asymmetricity of transmission zeros as

Fig. 8. Coupling scheme of the quasi-elliptic filter with a nonresonating node.

(25) trix is given by (18), shown at the bottom of this page. The nuis then calculated by merator of transmission coefficient

The pair of transmission zeros are nearly symmetric as the following condition is then satisfied: (26)

(19) where is the normalized angular frequency. The location of the transmission zeros can be obtained from

(20) Set

(21) When

is negative and is positive, we will have . The component has a pair of transmission zeros at real frequencies, which are then derived by (22) Using (11),

can be rewritten as (23)

where is the equivalent negative coupling coefficient between resonators 1 and 4. Obviously, the pair of transmission zeros are not symmetrically located around the passband. Their median, i.e., the offset from central frequency, is (24)

E. Design Procedure The design procedures of the cross-coupled substrate-integrated evanescent-mode waveguide filter with a nonresonating node are given as follows. of SIWs is selected with the predeterStep 1) The width mined dielectric and geometrical parameters of the standard LTCC technology. In our design, the cutoff frequencies of waveguides are mainly determined . In order to build up evanescent-mode resby onators, the cutoff frequencies and of dominant modes in folded and ridge waveguides should be lower and higher than the desired central frequency , respectively. Since an obvious parasitic response will arise near the cutoff frequency of the third TE mode in the folded waveguide, a high is preferred. However, there is an intrinsic relaand . Too large would tionship between reduce , and its corresponded parasitic response would move to the dominant passband. Too small would increase , and the lengths of folded waveguide sections should be increased accordingly to keep the evanescent-mode resonator still working at , which leads to a larger size. Step 2) The dimensions of the CPW structure are selected to afford enough coupling between it and the resonant waveguide sections. The initial value of can then be extracted by (9). Step 3) The normalized coupling matrix is synthesized with and design specifications such as the

(18)

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Step 4)

Step 5)

Step 6)

Step 7)

central frequency, bandwidth, in-band return loss, and locations of transmission zeros. With the synthesized internal direct-coupling coefficients and the curves in Fig. 2, the initial lengths of folded and ridge waveguide sections are determined. The arc-bending technique is applied for the design and the equivalent lengths of bent sections can also be obtained approximately. With the synthesized external coupling coefficient and the curves in Fig. 3, the initial length and width of the excitation structure are obtained. Based on the synthesized coupling coefficients with respect to the nonresonating node and the curves in Figs. 6 and 7, the detailed dimensions of the CPW structure are determined. Although changes with the dimensions, an acceptable filter frequency response can still be achieved if the equivalent cross-coupling coefficient given in (11) is close to its synthesized value. Finally, the whole structure is finely tuned and optimized to meet the specifications by full-wave EM simulators such as Ansoft’s High Frequency Structure Simulator (HFSS).

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Fig. 9. 3-D model of evanescent-mode waveguide filter.

III. RESULTS AND DISCUSSIONS The resonator and coupling structures shown above are used to construct a fourth-order cross-coupled substrate-integrated evanescent-mode waveguide filter, which is built up with the CPW nonresonating node scheme and has a quasi-elliptic frequency response. The standard LTCC technology is utilized to fabricate the filter prototype with the basic technological parameters given in Section II-A. The quasi-elliptic evanescent-mode filter, using a CPW nonresonating node, is designed with the central frequency of 3.45 GHz, bandwidth of 0.3 GHz, in-band return loss of 21 dB, and two additional transmission zeros at the normalized angular frequencies of 2. Its coupling matrix is synthesized to be (27), shown at the bottom of this page, where is determined by the self-resonant frequency of the CPW GHz. The circuit parameters are structure, i.e., then de-normalized as , , , GHz, and . According to (24), the median frequency of two transmission . The de-normalized zeros can be predicted to be

Fig. 10. Photograph of the fabricated filter prototype.

median frequency is 3.438 GHz, only 12 MHz lower than the central frequency. The asymmetricity of transmission zeros is , which means the pair of obtained by (25) to be transmission zeros are nearly symmetrically located around the passband. Its 3-D configuration is shown in Fig. 9. The dimensions are mm, mm, given by mm, mm, and mm. The lengths and angle of the folded and ridge SIW sections are given in Fig. 9. A photograph of prototype is shown in Fig. 10. The main structure of the component has a size of 17.5 14.2 0.8 mm . Its occupied area is only about 10% of the area of conventional planar substrate-integrated cavity-coupled filters. Both the measured and simulated -parameters of this

(27)

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Fig. 11. Measured and simulated S -parameters of the evanescent-mode filter with the CPW nonresonating node. (a) Within a narrow frequency range. (b) Within a wide frequency range.

filter are plotted in Fig. 11. Good agreement is obtained between them, except for a slight frequency shift of approximately 1.0%, which is mainly due to the permittivity deviation of the LTCC substrate. The measured in-band insertion loss is 1.2 dB and the return loss is better than 16.7 dB. Two transmission zeros are located at 3.14 and 3.75 GHz to improve the frequency selectivity. As predicted in Section II-D, their median frequency is a little lower than the central frequency, and then the rejection of the lower stopband is better than that of the higher stopband. If a conventional planar SIW filter is designed on the same m, the unloaded LTCC substrate with its thickness of factor of each resonator is calculated to be only 139 by (28) where is the skin depth of the silver conductor at 3.45 GHz. On the other hand, the effective factor of resonators is about 185 in the cross-coupled substrate-integrated evanescent-mode waveguide filter, which is extracted from the coupled resonator circuit model together with its measured insertion loss. This is just within the predicted range given in Section II-A. In other words, the effective factor is improved by 33% over that of the conventional planar cavity-coupled SIW filter. In particular, a volume reduction of more than 60% can be achieved when compared with the conventional planar SIW filter, with their total thicknesses taken into account.

Fig. 12. Comparison of the measured transmission coefficients between a direct-coupled and two cross-coupled evanescent-mode waveguide filters. (a) Within a narrow frequency range. (b) Within a wide frequency range.

The transmission coefficient of the cross-coupled substrate-integrated evanescent-mode waveguide filter with a nonresonating node is plotted in Fig. 12. The transmission coefficients of a direct-coupled filter and a cross-coupled filter with an interdigital structure [15] are also shown for comparison. The pair of transmission zeros of quasi-elliptic filters help to sharpen their passband slope sides. It is seen that the first spurious response of the evanescent-mode filter with a nonresonating node arises at 6.0 GHz. Its measured maximal magnitude is only 19.8 dB. By inserting a nonresonating node between two resonators, both the resonators and nonresonating node can be designed separately and connected together with minor adjustments [20]. Since more flexibility is introduced into the design of coupling structure by using the nonresonating node, it can be achieved that the original field distributions of resonators are disturbed slightly and more independent dimensions are provided to design the specific coupling coefficients of the desired resonant mode and unwanted harmonic modes. Therefore, the CPW nonresonating node implements a proper negative cross-coupling in our design, while nearly no energy corresponding to the mode of the folded SIWs is coupled through the cross-coupled path. The first obvious parasitic response is then located at 8.2 GHz, about 2.38 times the central frequency. The spurious suppression characteristic of the cross-coupled filter with

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the CPW nonresonating node is similar to that of the direct-coupled filter. It is also better than that of conventional substrate-integrated cavity-coupled filters.

[12] L.-S. Wu, L. Zhou, X.-L. Zhou, and W.-Y. Yin, “Bandpass filter using substrate integrated waveguide cavity loaded with dielectric rod,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 8, pp. 491–493, Aug. 2009. [13] L.-S. Wu, X.-L. Zhou, and W.-Y. Yin, “Evanescent-mode bandpass filters using folded and ridge substrate integrated waveguides (SIWs),” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 3, pp. 161–163, Mar. 2009. [14] J. A. Ruiz-Cruz, M. A. El Sabbagh, K. A. Zaki, J. M. Rebollar, and Y.-C. Zhang, “Canonical ridge waveguide filters in LTCC or metallic resonators,” IEEE Trans. Microw. Theroy Tech., vol. 53, no. 1, pp. 174–182, Jan. 2005. [15] L.-S. Wu, X.-L. Zhou, L. Zhou, and W.-Y. Yin, “Study on cross-coupled substrate integrated evanescent-mode waveguide filter,” in Proc. Asia–Pacific Microw. Conf. Dig., Singapore, Dec. 2009, pp. 167–170. [16] N. Marcuvitz, Waveguide Handbook. London, U.K.: Peregrinus, 1986. [17] W. Shen, X.-W. Sun, W.-Y. Yin, J.-F. Mao, and Q.-F. Wei, “A novel single-cavity dual mode substrate integrated waveguide filter with nonresonating node,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 6, pp. 368–370, Jun. 2009. [18] S. Amari and U. Rosenberg, “Characteristics of cross (bypass) coupling through higher/lower order modes and their applications in elliptic filter design,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 10, pp. 3135–3141, Oct. 2005. [19] G. Macchiarella, “Generalized coupling coefficient for filters with nonresonant nodes,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, pp. 773–775, Dec. 2008. [20] S. Amari and U. Rosenberg, “New building blocks for modular design of elliptic and self-equalized filters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 2, pp. 721–736, Feb. 2004.

IV. CONCLUSION A new method was presented for introducing cross-coupling into substrate-integrated evanescent-mode waveguide filters to obtain quasi-elliptic frequency responses. It uses a CPW nonresonating node structure to insert negative cross-coupling between nonadjacent resonating nodes. We develop a filter prototype based on multilayer folded and ridge SIWs and fabricate it with a standard LTCC technology. A volume reduction of more than 60% is achieved by the cross-coupled filter in comparison with the conventional planar substrate-integrated cavity-coupled counterparts. The unloaded factor is also improved. Further, by using the CPW nonresonating node, the attractive spurious suppression characteristic of the direct-coupled filter is kept by the cross-coupled filter. The superior performance is demonstrated by the simulated and measured -parameters with good agreement obtained between them. It can be expected that our proposed cross-coupled substrate-integrated evanescent-mode waveguide filter will be very useful in the further design of miniaturized microwave and millimeter-wave circuits. REFERENCES [1] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems: Fundamentals, Design, and Applications. Hoboken, NJ: Wiley, 2007. [2] A. Piloto, K. Leahy, B. Flanick, and K. A. Zaki, “Waveguide filters having a layered dielectric structures,” U.S. Patent 5382931, Jan. 17, 1995. [3] T.-M. Shen, C.-F. Chen, T.-Y. Huang, and R.-B. Wu, “Design of vertically stacked waveguide filters in LTCC,” IEEE Trans. Microw. Theroy Tech., vol. 55, no. 8, pp. 1771–1779, Aug. 2007. [4] J.-H. Lee, S. Pinel, J. Laskar, and M. M. Tentzeris, “Design and development of advanced cavity-based dual-mode filters using low-temperature co-fired ceramic technology for V -band gigabit wireless systems,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 9, pp. 1869–1879, Sep. 2007. [5] M. Ito, K. Maruhashi, K. Ikuina, T. Hashiguchi, S. Iwanaga, and K. Ohata, “A 60-GHz-band planar dielectric waveguide filter for flip-chip modules,” IEEE Trans. Microw. Theroy Tech., vol. 49, no. 12, pp. 2431–2436, Dec. 2001. [6] C.-Y. Chang and W.-C. Hsu, “Novel planar, square-shaped, dielectric-waveguide, single-, and dual-mode filters,” IEEE Trans. Microw. Theroy Tech., vol. 50, no. 11, pp. 2527–2536, Nov. 2002. [7] D. Deslandes and K. Wu, “Single-substrate integration technique of planar circuits and waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 2, pp. 593–596, Feb. 2003. [8] X.-P. Chen, K. Wu, and Z.-L. Li, “Dual-band and triple-band substrate integrated waveguide filters with Chebyshev and quasi-elliptic responses,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2569–2578, Dec. 2007. [9] Y. Rong, K. A. Zaki, J. Gipprich, M. Hageman, and D. Stevens, “LTCC wide-band ridge-waveguide bandpass filters,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp. 1836–1840, Sep. 1999. [10] N. Grigoropoulos, B. S. Izquierdo, and P. R. Young, “Substrate integrated folded waveguides (SIFW) and filters,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 829–831, Dec. 2005. [11] Y.-Q. Wang, W. Hong, Y.-D. Dong, B. Liu, H.-J. Tang, J.-X. Chen, X.-X. Yin, and K. Wu, “Half mode substrate integrated waveguide (HMSIW) bandpass filter,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 4, pp. 265–267, Apr. 2007.

Lin-Sheng Wu (S’09–M’10) received the B.S. degree in electronic engineering and the M.S. and Ph.D. degrees in electromagnetic fields and microwave techniques from Shanghai Jiao Tong University (SJTU), Shanghai, China, in 2003, 2006, and 2010, respectively. He is currently a Post Doctor with the Center for Microwave and RF Technologies (CMRFT), Department of Electronic Engineering, SJTU. From August to November 2010, he is also working as a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore (NUS), Singapore. His research interests include novel techniques for microwave integration, microwave and RF components, hybrid electro-thermal problems for system-onpackage (SoP), intelligent information processing, and passive localization.

Xi-Lang Zhou received the B.S. degree in electronic engineering from Shanghai Jiao Tong University (SJTU), Shanghai, China, in 1978. From August 1978 to January 1981, he was a Lecturer with the Applied Mathematics Department, SJTU. He became an Assistant professor, Associate professor, and Professor with the Electronic Engineering Department, SJTU, in 1986, 1992 and 1998, respectively. He has been engaged in and participated in many research programs in the fields of radar, microwave and millimeter-wave techniques, remote sensing, and microstrip antennas. He has authored or coauthored over 100 papers in journals and ten books/book chapters in the areas of EM fields and microwave techniques, microstrip antennas, millimeter-wave techniques, and applications. His research interests include radar signal processing, EM fields and microwave techniques, microwave sensors, microstrip antennas, electromagnetic compatibility (EMC), RF identification (RFID), smart antennas, and multiple-input multiple-output (MIMO) systems.

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Wen-Yan Yin (M’99–SM’01) received the M.Sc. degree in electromagnetic fields and microwave techniques from Xidian University (XU), Shaanxi, China, in 1989, and the Ph.D. degree in electrical engineering from Xi’an Jiaotong University (XJU), Xi’an, China, in 1994. From 1993 to 1996, he was with the Department of Electronic Engineering, Northwestern Polytechnic University (NPU). From 1996 to 1998, he was a Research Fellow with the Department of Electrical Engineering, Duisburg University (under a grant by the Alexander von Humblodt-Stiftung of Germany). Since December 1998, he has been a Research Fellow with the Monolithic Microwave Integrated Circuit (MMIC) Modeling and Packing Laboratory, Department of Electrical Engineering, National University of Singapore (NUS), Singapore. In March 2002, he joined Temasek Laboratories, NUS, as a Research Scientist and the Project Leader of high-power microwave and ultrawideband electromagnetic compatibility (EMC)/electromagnetic interference (EMI). In April 2005, he joined the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University (SJTU), Shanghai, China, as a Chair Professor in EM fields and microwave techniques (until 2007). He is currently the Director of the Center for Microwave and RF Technologies, SJTU. Since 2009, he has been the Qiu Shi Chair Professor with Zhejiang University (ZJU), working with the Center for Optics and Electromagnetic Research, Department of Optical and Electrical Information. As a lead author, he has contributed to over 150 international journal papers including 15 book chapters. One chapter, “Complex Media,” is included in the Encyclopedia of RF and Microwave Engineering (Wiley, 2005). He is a Reviewer of international journals including Radio Science and Proceedings of the IEEE—Part H, Microwave, Antennas, and Propagation. His main research interests are EM characteristics of complex media and their applications in engineering, EMC, EMI, and protection, on-chip passive and active millimeter (RF) integrated circuit (IC) device testing, modeling, and packaging, ultra-wideband interconnects and signal integrity, and nanoelectronics. Prof. Yin is the technical chair of Electrical Design of Advanced Packaging and Systems (EDAPS’06), technically sponsored by the IEEE CPMT Subcommittee. He is a reviewer for six IEEE TRANSACTIONS. He was the recipient of the Best Paper Award of the 2008 APEMC and 19th International Zurich Symposium on EMC, Singapore.

Liang Zhou (M’10) received the B.Sc. degree from Zhongnan University, Changsha, China, in 2001, and the M.Sc. and Ph.D. degrees from the University of York, York, U.K. in 2003 and 2005, respectively. In 2005, he joined Motorola, as a Senior RF Engineer, where he became involved with linear power amplifiers (LPAs) for third-generation basestation transceivers. In 2007, he as a Visiting Scholar with the Massachusetts Institute of Technology (MIT), Cambridge. In 2006, he joined the Center for Microwave and RF Technologies, Shanghai Jiao Tong University, Shanghai, China, as an Assistant Professor. His current research mainly focus on microwave and millimeter-wave active and passive components and devices.

Jun-Fa Mao (M’92–SM’98) was born in 1965. He received the B.S. degree in radiation physics from the University of Science and Technology of National Defense, Changsha, China, in 1985, the M.S. degree in experimental nuclear physics from the Shanghai Institute of Nuclear Research, Shanghai, China, in 1988, and the Ph.D. degree in electronic engineering from Shanghai Jiao Tong University, Shanghai, in 1992. From 1994 to 1995, he was a Visiting Scholar with the Chinese University of Hong Kong, Hong Kong. From 1995 to 1996, he was a Postdoctoral Researcher with the University of California at Berkeley. Since 1992, he has been a Professor with the Center for Microwave and RF Technologies, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University. From 2001 to 2003, he was a Topic Expert of the High-Tech Program of China. From 1999 to 2005, he was an Associate Dean with the School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University. He has authored or coauthored over 200 papers. His current research interests include the interconnect problem of high-speed integrated circuits, microwave components, and circuits. Dr. Mao is a Cheung Kong Scholar of the Ministry of Education, China and an associate director of the Microwave Society of China Institute of Electronics. He was the 2007–2008 chair of the IEEE Shanghai section. He was the recipient of the 2004 National Natural Science Award of China and the 2005 First-Class Natural Science Award of Shanghai.

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De-Embedding Method Using an Electromagnetic Simulator for Characterization of Transistors in the Millimeter-Wave Band Takuichi Hirano, Member, IEEE, Hiroshi Nakano, Yasutake Hirachi, Life Member, IEEE, Jiro Hirokawa, Senior Member, IEEE, and Makoto Ando, Fellow, IEEE

Abstract—A de-embedding method using an electromagnetic (EM) simulator is proposed to extract field-effect transistor (FET) characteristics from FET test-pattern measurements. In the proposed method, the -parameters of the parasitic circuit are analyzed using the EM simulator. Hybrid -parameters, converted from -parameters, are used for the parasitic circuit to express waveguide ports with -parameters and lumped-element ports with -parameters. The proposed method requires a high accuracy of the EM simulator; this method was verified by comparing calculated and measured frequency characteristics of the -parameters of an open/short-pattern. It was shown numerically that the proposed de-embedding method has a better accuracy than the conventional method, which uses the open/short-pattern. For example, the extraction error is below 5% up to 75 GHz for the proposed method and a 5% error is exceeded around 30 GHz for the conventional method. The dominant error factor in the conventional de-embedding method using the open/short-pattern was investigated. It was established that the approximation of the parasitic circuit by an equivalent circuit topology is the cause of the error. The extraction of the FET characteristics by measured data is demonstrated and it is shown that the proposed method can be applied to extract active devices. Index Terms—De-embedding, electromagnetic (EM) simulator, field-effect transistors (FETs), millimeter wave, monolithic microwave integrated circuits (MMICs).

I. INTRODUCTION CCURATE parameter extraction of field-effect transistors (FETs) is necessary for the accurate design of monolithic microwave integrated circuits (MMICs). In the measurement of FET characteristics, the FET is embedded in a parasitic circuit to connect probes and biases, as shown in Fig. 1. The first stage of FET characterization is to de-embed the interconnecting parasitic circuit. The conventional de-embedding method, using an open/short-pattern for obtaining the FET two-port -parameters

A

Manuscript received December 10, 2009; revised July 26, 2010; accepted July 28, 2010. Date of publication September 13, 2010; date of current version October 13, 2010. This work was supported in part by The Ministry of Internal Affairs and Communications, Japan, under the Research and Development Project for Expansion of Radio Spectrum Resources. T. Hirano is with the Department of International Development Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan (e-mail: [email protected]). H. Nakano and Y. Hirachi are with AMMSYS Inc., Kanagawa 248-0002, Japan (e-mail: [email protected]; [email protected]). J. Hirokawa and M. Ando are with the Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2010.2065330

Fig. 1. Measurement arrangement for the FET test-pattern. From [3].

described in [1] is a commonly applied method in the development of MMICs. The accuracy of the conventional de-embedding method has not been discussed well because it was practically sufficient below the microwave band, but many researchers are now facing with a problem of insufficient accuracy in the millimeter-wave band. Due to the insufficient accuracy of the conventional method, especially in the millimeter-wave band, repeated trial manufacture is required to ensure accuracy; this results in increases in costs. It was shown that parasitic couplings between pads, a substrate, and adjacent structures cause degradation in the measurement accuracy [2], but the error factors for the de-embedding method using the open/short-pattern have not been identified. There are a number of uncertainties arising in the conventional de-embedding method, as listed in Table I, which reduce the accuracy of the method. The authors identified the error factors in the conventional de-embedding method in this paper. In order to enhance the accuracy of the de-embedding method, up to the millimeter-wave band, the authors have proposed a de-embedding method to obtain the FET characteristics with the aid of an electromagnetic (EM) simulator [3]. Although a de-embedding method using an EM simulator had been proposed in [4], verification of the accuracy there -parameters for was inadequate. This paper uses hybrid the four-port parasitic circuit with -parameters for the waveguide ports and -parameters for the lumped-element ports [3]; only -parameters were used in [4]. The characteristic impedances for the waveguide ports are not necessary in the -parameter formulation, yet are needed in the -pahybrid rameter formulation. Other features of the method proposed in this paper are listed in Table I. The accuracy of the proposed

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TABLE I FEATURES OF THE PROPOSED METHOD

de-embedding method was investigated and compared with the conventional method. It was found that the proposed de-embedding method has better accuracy than the conventional method, especially in the millimeter-wave band above 30 GHz. II. CONVENTIONAL DE-EMBEDDING METHOD USING OPEN/SHORT-PATTERN The conventional de-embedding method using an open/shortpattern [1] is outlined in this section. 1) Three measurements are made to obtain the FET -parameters shown in Fig. 2(i). The first measurement is done for the interconnect pattern surrounding the FET with the FET part removed (termed “open”), resulting in the open . The second measurement two-port -parameters is done for the interconnect pattern surrounding the FET with the FET part metallized (termed “short”); this re. The third sults in the short two-port -parameters measurement is done for an FET—which also includes the interconnected parasitic circuit—described by the two-port -parameters . 2) The parasitic circuit surrounding the FET is approximated by the equivalent circuit topology shown in Fig. 2(ii). Parand can be determined from asitic elements by comparing with -circuit parameters

Fig. 2. De-embedding method using open/short-pattern. (i) Measurment of two-port S -parameter for open/short patterns and FET test-pattern. (ii) Parasitic circuit of the surrounding parasitic circuit is approximated by equivalent circuit. (iii) Obtain Z ; Z ; and Z . (iv) Extract the FET parameters using two-port circuit theory.

3) Parasitic elements

and

can be removed from . Parasitic elements and can be determined by comparing with into -paramT-circuit parameters after transforming eters

(3) By comparing matrix elements, determined

and

can be

(4)

(1) By comparing matrix elements, determined

and

can be

4) The FET two-port -parameters can be obtained by removing and . Parasitic eland can be removed by subtracting ements from . Parasitic elements and can be removed with the fundamental matrix ( -matrix). Finally, can be removed with the -matrix. III. DE-EMBEDDING METHOD USING THE EM SIMULATOR

(2)

Fig. 3 shows the de-embedding method using the EM simulator; here, the finite-element method (FEM)-based simulator Ansoft HFSS, Version 9 [5] is used throughout. The differences

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Fig. 4. Procedure of de-embedding. (a) Conventional. (b) Proposed.

(5) where Fig. 3. De-embedding method using EM simulator. (i) Analyze S -parameters of four-port parasitic circuit. (ii) Measure S -parameters of the parasitic circuit with FET. (iii) Device characteristics are calculated using S -parameters in (i) and (ii).

of procedures between the conventional and proposed de-embedding methods are shown in Fig. 4. 1) Analyze -parameters of the four-port parasitic circuit by adding the lumped-element ports [termed “lumped ports” in the Ansoft High Frequency Structure Simulator (HFSS)], with arbitrary internal impedances, at and Port4 the terminals of the lumped ports: Port3 . Terminals Port1 and Port2 at the parasitic circuit, which are connected to the vector network analyzer (VNA), are normally treated as waveguide ports. 2) Measure the -parameters of the parasitic circuit with . Conventional calibration the lumped elements algorithms such as short-open-load-thru (SOLT) [6], thru-reflect-line (TRL) [7], [8], impedance standard substrate (ISS), as well as others, can be used to calibrate Port1 and Port2 in the measurement using the VNA. into the hybrid -parameters 3) Transform

and . and are input and output coefficients for the dominant waveguide and are voltage and current at mode at Port . are sub-matrices of , which can be Port . calculated as shown in (6) at the bottom of this page (see the Appendix), where is an identity matrix and is a diagonal matrix, where the diagonal components are the square root of the internal impedances for the lumped ports Port3 and Port4; has the dimension of the -parameters for Port1 and Port2 and has the dimension of the -parameters for Port3 and Port4. Finally, the -parameters for can be obtained the embedded lumped device and the using the terminal condition measured -parameters using the VNA together with (5)

(7) IV. STRUCTURE Fig. 5 shows the structure of the FET test-pattern discussed in this paper. The relative permeability, permittivity, and loss tangent of the substrate are 12.5, 1, and 0.004, respectively, with a thickness of the dielectric substrate of 600 m. One side of the

(6)

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Fig. 5. Structure of the FET test-pattern. From [3]. (a) Cross section at A–A . (b) Top view.

substrate is metalized with gold (Au), 3.8- m thick, with relative permittivity, permeability, and conductivity of 1, 0.99996, and 4.1 10 S/m, respectively. Port1 and Port2 in Fig. 5(b) are coplanar waveguides (CPWs) with a characteristic impedance of 50 . Two FETs with the same characteristics are embedded in the parasitic circuit. Due to the symmetry of the structure and excitation, the model to analyze the Fig. 5 FET test-pattern can be reduced to a half of the whole structure, as suggested in Fig. 6(a) and (b). A magnetic wall, or perfect magnetic conductor (PMC), is assumed at the center of symmetry. The model for the analysis of the 3-D FEM simulator Ansoft HFSS is shown in Fig. 6(c). The terminals of the transmission line are modeled as wave ports, while the terminals for the lumped elements are modeled as the lumped ports, as shown in Fig. 6(c). Port3 is defined as a lumped port between the source and gate electrode. Port4 is also defined to be between the source and drain electrodes. V. VERIFICATION OF THE EM SIMULATOR USING THE OPEN/SHORT-PATTERN In the de-embedding method using the EM simulator, it is necessary to ensure that the simulator is sufficiently accurate; it is also important to ensure that the accuracy of the EM simulator can be determined by comparing the -parameters of the open/ short-pattern of simulations and measurements. Models for the analysis of the open- and short-patterns are shown in Fig. 7. To verify the accuracy of the EM simulator, as well as the material constants, the simulated and measured -parameters were compared. The measurements were performed with an Agilent E8361A network analyzer and probe (67A-GSG-125-P by GGB Industries Inc.) with ISS (CS-5 by GGB Industries Inc.) calibration. Fig. 8 shows the frequency characteristic of the -parameters for the open-pattern with Fig. 9 showing the short-pattern. The simulated values agree well with the measurements; due to this, it may be concluded that the EM simulator and the estimates of the material constants are adequate. at low frequencies suggests good open The (short) conditions of the lumped-circuit element. At higher freis below 0 because of the finite size quencies, the phase of of the pattern.

Fig. 6. Model for the analysis of the FET test-pattern in Fig. 5. From [3]. (a) Cross section at A–A . (b) Top view. (c) HFSS model.

Fig. 7. Models for the analysis of the open- and short-patterns. From [3]. (a) Open-pattern. (b) Short-pattern.

VI. NUMERICAL VERIFICATION OF THE PROPOSED METHOD The proposed de-embedding method using the EM simulator described in Section III is demonstrated fully and numerically in this section; the accuracy of the method is investigated. For numerical verification of the proposed method, the lumped eleand pF are connected in parallel at ments and nH are connected the position of Port3. in parallel at the position of Port4 in the structure, as suggested in Fig. 6. The structure is analyzed using the FEM-based simulator, Ansoft HFSS; the lumped elements to be extracted are , which is implemented by the surmodeled by the lumped face impedance in HFSS. is analyzed by HFSS, which is assumed as The to be the measured value in the algorithm. The parasitic , is determined by the analysis circuit, -parameter using HFSS. The extracted values ( and ) are shown in Fig. 10 as solid lines; they are determined extracted by the proposed method. The pafrom rameters of the lumped devices at Port3 and Port4 were

HIRANO et al.: DE-EMBEDDING METHOD USING EM SIMULATOR FOR CHARACTERIZATION OF TRANSISTORS IN MILLIMETER-WAVE BAND

Fig. 8.

S -parameters of the open-pattern in Fig. 7(a). (a) Amplitude. (b) Phase.

calculated from the extracted

Fig. 9.

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S -parameters of the short-pattern in Fig. 7(b). (a) Amplitude. (b) Phase.

-parameters

. The extracted values, using the conventional de-embedding method with the open/short-pattern, are shown in the figure as broken lines. Both methods give accurate results at lower frequencies and errors become larger as the frequency increases in both methods. The accuracy of the proposed de-embedding method is better in every way than the conventional method. Unfortunately, the error of the proposed de-embedding method using the EM simulator has not been identified yet. Fig. 11 shows the error of the extracted admittance for Port3 and Port4, as defined by the following equation: Fig. 10. Simulated extracted values.

(8) is the extracted admittance for Port and is the where specified admittance at Port . The maximum frequencies of errors of less than 5% are 75 GHz for the proposed method and 30 GHz for the conventional method. It is clear that the accuracy of the proposed method is better than that of the conventional method.

VII. IDENTIFICATION OF ERROR FACTORS IN THE CONVENTIONAL DE-EMBEDDING METHOD A. Errors in the Characteristic of Open/Short-Pattern The conventional de-embedding method employs two approximations using the open/short-pattern [1], which are: 1) the

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Fig. 11. Error in the extracted admittance of Port3 and Port4.

Fig. 13. S -parameters of the short-pattern with the ideal short conditions at Port3 and Port 4. (a) Amplitude. (b) Phase.

the open/short-pattern calculated by the -parameter obtained by the EM simulator of the four-port parasitic circuit was used. yields Solving (7) for (9) The

-parameters of the ideal open-pattern is calculated as because

. The

-pa-

rameters of the ideal short-pattern is calculated as because

Fig. 12. S -parameters of the open-pattern with the ideal open conditions at Port3 and Port 4. (a) Amplitude. (b) Phase.

incompleteness of the open and short pattern and 2) an approximation of a parasitic circuit by an equivalent circuit topology. These approximations introduce ambiguity and nonnegligible errors, especially in the high-frequency range. To identify the error factors in the conventional de-embedding method using the open/short-pattern, the ideal characteristics of

.

The -parameters of the ideal open-pattern are shown with solid lines in Fig. 12 and for the short-pattern in Fig. 13. The results for the open/short-pattern in Fig. 7 are shown here with broken lines. There are small, but negligible, differences in the open-pattern plots, while the agreement is good for the shortpattern. This means that the open and short patterns work as good as open and short elements in a sense of lumped-element circuit theory. B. Errors in the Equivalent Circuit for the Parasitic Circuit The -matrix of the equivalent circuit for the parasitic circuit in Fig. 14 can be calculated as shown in (10) at the bottom of

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Fig. 14. Equivalent circuit for the parasitic circuit in Fig. 2(ii).

Fig. 16. Simulation of extraction for the conventional de-embedding method using the ideal open/short-pattern.

Fig. 15. Frequency characteristic of the Frobenius norm for the matrix S S .S and S are four-port S -matrices obtained by the EM simulator and by the equivalent circuit for the parasitic circuit, respectively.

0

this page, where . The -matrix can be transformed into the -matrix by the following formula: (11) where is a diagonal matrix. is the characteristic impedance of the CPW. and are the internal impedances for the lumped ports Port3 and Port4. The difference between the -matrix obtained by the EM and by the equivalent circuit for the parasitic simulator circuit is considered. Fig. 15 shows the frequency characteristic of the Frobenius norm [9] for the matrix . The Frobenius norm is defined for a matrix with the dimension of as follows: (12)

The equivalent-circuit parameters in Fig. 14 are obtained by using the ideal open/short-pattern for the solid line in Fig. 15. The equivalent-circuit parameters are obtained by using the normal open/short-pattern in Fig. 7 and for the broken line in Fig. 15. The constant value, 0.94, is observed at lower frequencies below 40 GHz and becomes larger at higher frequencies. There are no improvements in the -matrix of the equivalent circuit obtained by using the ideal open/short-pattern. This fact suggests that the approximation of the parasitic circuit by an equivalent-circuit topology is the cause of the dominant error. C. Errors in the De-Embedding Method Using the Open/Short-Pattern A simulation similar to that in Section VI for the conventional de-embedding method, now using the ideal open/shortpattern, was performed. The results, together with the conventional de-embedding method using the ideal open/short-pattern and normal open/short-pattern in Fig. 7, are plotted with solid and broken lines in Fig. 16. The tendencies of the extracted values are very similar, except for the values of . The accuracy is poorer than the proposed de-embedding method using the EM simulator. Fig. 17 shows the difference of errors between the conventional de-embedding method using the ideal open/short-pattern and normal open/short-pattern in Fig. 7, as defined by (8). The error, due to the open/short-pattern, is about 5% at 60 GHz while the error due to the equivalent-circuit approximation of the parasitic circuit is about 10%–20% at 60 GHz from Fig. 11. This suggests that the errors due to the incompleteness of the open/short-pattern do not dominate in the extraction of the lumped-element parameters, thus identifying the dominant error

(10)

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Fig. 17. Error due to the accuracy of the open/short-pattern.

factor for the extraction as the equivalent-circuit approximation of the parasitic circuit. VIII. EXTRACTION OF THE MEASURED FET CHARACTERISTICS The extraction of the FET characteristics, by measuring the FET test-pattern, is demonstrated in this section. Fig. 18 shows the frequency characteristics of the -parameters for the extracted FET with the results of the proposed and conventional methods plotted with solid and broken lines. Fig. 18 shows that the agreement between the proposed and conventional results is good below about 10 GHz, as would also be expected from the results in Section VI. Fig. 19 shows the frequency characteristics of predicted errors for -parameters of the FET. The predicted error is defined as follows:

Fig. 18. Frequency characteristics of (a) Amplitude. (b) Phase.

Y -parameters

for the extracted FET.

(13)

is the extracted -parameter of the FET obtained where by the proposed de-embedding method using the EM simulator. is the extracted -parameter of the FET obtained by is the conventional method using the open/short-pattern. used as a reference value because the true value is unknown. The error in the measurement is expected to be small from Figs. 8 and 9. The maximum error is about 20% at 50 GHz. The similar tendency with Fig. 11 is observed; the error is predicted to be poor accuracy in the conventional de-embedding method using at the low-frequency the open/short-pattern. The error of region, which is normally considered to be small, is relatively large of about 5%–10% in Fig. 19. Similar tendency is observed in Figs. 10 and 11, though the error is smaller, and it is estimated that the conventional de-embedding method is erroneous. IX. CONCLUSION A de-embedding method for the characterization of FETs using an EM simulator is proposed; the method was verified numerically. The proposed method is more accurate than the conventional de-embedding method using an open/short-pattern. It

Fig. 19. Frequency characteristics of predicted errors for Y -parameters of the FET.

was established that the dominant error factor in the conventional de-embedding method is due to the approximation of the parasitic circuit by an equivalent-circuit topology. The extraction of the FET characteristics was demonstrated with measurements of the FET test-pattern, and was shown that the proposed method can be applied to extract active devices.

HIRANO et al.: DE-EMBEDDING METHOD USING EM SIMULATOR FOR CHARACTERIZATION OF TRANSISTORS IN MILLIMETER-WAVE BAND

APPENDIX DERIVATION OF (6) The scattering property of a parasitic circuit is expressed as follows with an -matrix: (A-1) To express Port3 and Port4 with voltage and current paramand into and , (A-2) is eters, or to convert from obtained by expanding (A-1)

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[5] Ansoft HFSS. ver. 9, Ansoft, Pittsburgh, PA, 2004. [Online]. Available: http://www.ansoft.com/products/hf/hfss/ [6] G. F. Engen, “Calibration technique for automated network analyzers with application to adapter evaluation,” IEEE Trans. Microw. Theory Tech., vol. MTT-22, no. 12, pp. 1255–1259, Dec. 1974. [7] G. F. Engen and C. A. Hoer, “‘Thru-reflect-line’: An improved technique for calibrating the dual six-port automatic network analyzer,” IEEE Trans. Microw. Theory Tech., vol. MTT-27, no. 12, pp. 987–993, Dec. 1979. [8] P. Colestock and M. Foley, “A generalized TRL algorithm for S -parameter de-embedding,” Fermi Nat. Accelerator Lab., Batavia, IL, Tech. Memo TM-1781, Apr. 1993, pp. 1–19. [9] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996, pp. 54–59. [10] K. Kurokawa, “Power waves and the scattering matrix,” IEEE Trans. Microw. Theory Tech., vol. MTT-13, no. 3, pp. 194–202, Mar. 1965.

(A-2) The following relations hold for

and

[10]:

(A-3) Substitution of (A-3) into (A-2) yields

(A-4) Solving the second equation of (A-4) for

gives

Takuichi Hirano (A’02–M’09) was born in Tokyo, Japan, on January 28, 1976. He received the B.S. degree in electrical and information engineering from the Nagoya Institute of Technology, Nagoya, Japan, in 1998, and the M.S. and D.E. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 2000 and 2008, respectively. He is currently an Assistant Professor with the Tokyo Institute of Technology. He has been involved with EM theory, numerical analysis for EM problems, and antenna engineering such as slotted waveguide arrays. Dr. Hirano is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan, and the institute of Electrical Engineers of Japan (IEEJ). He was the recipient of the Young Engineer Award of the IEICE and the IEEE Antennas and Propagation Society (AP-S) Japan Chapter Young Engineer Award in 2004.

(A-6)

Hiroshi Nakano was born in Nagano, Japan, on March 13, 1961. He received the B.S. and M.S. degrees in electrical and electric engineering from the Shibaura Institute of Technology, Tokyo, Japan, in 1984 and 1986, respectively. From 1986 to 1998, he was an Engineer with the Olympus Optical Company Ltd., where he was involved with the memory device that used ferroelectric material. From 1998 to 2004, he was with Fujitsu Quantum Devices Ltd., during which time he was engaged in the development of high-frequency RF transmitter and receiver modules. He is currently with AMMSYS Inc., Kanagawa, Japan, where he is engaged in the development of high-frequency MMICs and RF modules.

[1] 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. [2] C. Andre, 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 IEEE Int. Microelectron. Test Structures Conf., Tokyo, Japan, Mar. 2007, pp. 253–256. [3] T. Hirano, J. Hirokawa, M. Ando, H. Nakano, and Y. Hirachi, “De-embedding of lumped-element characteristics with the aid of EM analysis,” in IEEE AP-S Int. Symp. Dig., San Diego, CA, Jul. 5–12, 2008, Session: 436.3. [4] S. Bousnina, C. Falt, P. Mandeville, A. B. Kouki, and F. M. Ghannouchi, “An accurate on-wafer deembedding technique with application to HBT devices characterization,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 2, pp. 420–424, Feb. 2002.

Yasutake Hirachi (M’75–LM’10) was born in Tokyo, Japan, on December 24, 1944. He received the B.S. and M.S. degrees in electrical engineering from the Tokyo University of Agriculture and Technology, Tokyo, Japan, in 1968 and 1970, respectively, and the Ph.D. degree in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1979. Since 1970, he has been engaged in research, development, and business for microwave and millimeter-wave IMPATT diodes, GaAsFETs, HEMTs, and millimeter-wave subsystems. He is currently a Research Fellow with the Tokyo Institute of Technology, and the President of AMMSYS Inc., Kanagawa, Japan. Since 2007, he has been one of the Research Readers of the millimeter-wave project supported by the Ministry of Internal Affairs and Communications. Dr. Hirachi is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan, and the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

(A-5) Substituting (A-5) into the first equation of (A-4), or exby and , leads to the following equation: pressing

A comparison of (A-5) and (A-6) with (5) gives (6). REFERENCES

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Jiro Hirokawa (S’89–M’90–SM’03) was born in Tokyo, Japan, on May 8, 1965. He received the B.S., M.S., and D.E. degrees in electrical and electronic engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1988, 1990, and 1994, respectively. From 1990 to 1996, he was a Research Associate, and is currently an Associate Professor with the Tokyo Institute of Technology. From 1994 to 1995, he was with the Antenna Group , Chalmers University of Technology, Göteborg, Sweden, as a Postdoctoral Fellow. His research area has involved slotted waveguide array antennas. Dr. Hirokawa is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 1991 IEEE Antennas and Propagation Society (AP-S) Tokyo Chapter Young Engineer Award, the 1996 Young Engineer Award of the IEICE, the 2003 Tokyo Institute of Technology Award for Challenging Research, the 2005 Young Scientists’ Prize of the Minister of Education, Cultures, Sports, Science and Technology, Japan, and the 2007 Best Paper Award of the IEICE Communication Society.

Makoto Ando (F’03) received the B.S., M.S., and D.E. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1974, 1976, and 1979, respectively. From 1979 to 1983, he was with Yokosuka ECL, NTT. From 1973 to 1985, he was a Research Associate with the Tokyo Institute of Technology, where he is currently a Professor. Since 2001, he has been a Guest Editor and Guest Editor-in-Chief for seven special issues of Radio Science and the IEICE Transactions. Dr. Ando is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He is a member of the Institution of Electrical Engineers (IEE), U.K. Since 2007, he has been the program officer for the Japan Society for the Promotion of Science (JSPS). He was the chair of ISAP 2007. He was also the technical program co-chair for the 2007 IEEE Antennas and Propagation (AP-S) Symposium. He was the chair of the 2004 URSI EMT Symposium. He was a guest editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. From 2002 to 2005, he was the chair of Commission B of URSI. From 2004 to 2006, he was an Administrative Committee (AdCom) member of the IEEE AP-S. From 2004 to 2007, he was a member of the Scientific Council for the Antenna Centre of Excellence in the European Union (EU) 6th Framework Program. In 2006, he was the president of Electronics Society, IEICE. He was the 2009 president of the IEEE AP-S.

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Temperature Dependence of Resonances in Metamaterials Vasundara V. Varadan, Senior Member, IEEE, and Liming Ji, Student Member, IEEE

Abstract—Metamaterials are increasingly being proposed for many different microwave applications. Metamaterials are highly resonant structures and metamaterial device design is based on the resonance frequency for both civilian and military applications. These applications are often in a high-temperature environment. In this paper, we have performed an experimental study of the shift in resonance frequency of selected metamaterials (split-ring resonators and thin wires) in the 25 C–400 C range using FR4 and low-temperature co-fired ceramic substrates. We have provided a theoretical explanation for the observed shift in resonance frequency by calculating the shift in frequency resulting from the temperature dependence of the substrate permittivity and electrical conductivity of the metal, as well as thermal expansion of the metallo-dielectric structures comprising the metamaterial. The measured downward shift of the resonance frequency with increasing temperature agrees very well with full-wave finite-element simulation. It is found that the change of permittivity of the substrate is the primary effect, while the thermal expansion of the metallic structure is a secondary effect. The reducing resonance strength is due to the decrease in electrical conductivity with rising temperature. This study can be applied to other metamaterial metallo-dielectric structures or other planar microwave resonators printed on dielectric substrates. Index Terms—Electrical resonance, magnetic resonance, metamaterials, resonance, split-ring resonator (SRR), temperature, thin-wire media.

I. INTRODUCTION

S

PLIT-RING resonators (SRRs) and thin wires are ubiquitous in the metamaterials literature. The SRR may be taken as a canonical example of a subwavelength metallo-dielectric structure that exhibits a strong resonance behavior. A time-varying magnetic flux through a very thin electrically small wire loop generates a circulating current that reaches its greatest strength at resonance. The presence of a small gap leads to a high concentration of opposite polarity charges across the gap creating a strong capacitance. Thus, the SRR oscillator as is widely known constitutes a highly resonant from the recent literature. A collection of such SRRs deposited on a dielectric substrate exhibits strong reflection and transmission minima and power absorption when illuminated by Manuscript received January 26, 2010; revised June 12, 2010; accepted June 15, 2010. Date of publication September 07, 2010; date of current version October 13, 2010. The authors are with the Microwave and Optics Laboratory for Imaging and Characterization, Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701 USA (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.2010.2065910

a microwave field. At the resonance frequency of the SRR, the effective medium is described by a highly dispersive magnetic permeability and/or dielectric permittivity [1], [2]. The resonances are deep and narrow. Due to these features, many researchers have developed compact SRR-based designs for transmission line filters [3], [4], backward traveling-wave filters with lumped elements [5], [6], phase shifters [7], radar absorbers [8], and cloaking materials [9]. By cascading filter stages or material layers consisting of different sizes of SRRs, an economy in the size scale can be achieved without sacrificing other performance specifications. Controllable bandwidth can be realized by designing multiresonance structures [4]. The small size of SRRs has also drawn the attention of antenna designers [10]–[12] who have considered metamaterials for realizing electrically small antennas. These designs find both civil and military applications, many of which require device performance under extreme temperature conditions (high and low). Since the bandwidth of metamaterial resonances is narrow (high ), even a small shift in resonance will make a big difference in device performance. For example, an SRR-based antenna usually has a very narrow bandwidth ( 5%), and will have poor radiation efficiency if it is subject to any conditions that shift the resonance frequency. A 3% shift in resonance frequency will be sufficient to filter out the frequency that the antenna is designed for. The resonances are very sensitive to parameters like SRR dimensions and material properties that can be affected by variations in temperature. Therefore, it is necessary to investigate whether metamaterials still perform as designed under different temperature conditions. In addition, metamaterial structures absorb energy at resonance, and a large portion of the absorbed energy will be dissipated as heat. Even if the devices are operating in a stable temperature environment, the dissipated heat may increase the temperature of the devices due to high field localization [13]. The power absorption and heating characteristics of metamaterials have been proposed for use as the sensing element for bolometers [13]. All such applications will require a detailed analysis of the temperature dependence of metamaterial resonances. The purpose of this study is to understand how metamaterial resonances are affected by large fluctuations in temperature, but also giving a guideline in designing metamaterial-based devices and to identify the material and geometric parameters that are most critical in effecting the frequency change. This will be a useful guideline in device/material designs that have to be stable under variable temperature conditions. In this paper, we investigate experimentally for the first time the temperature dependence of metamaterial resonances. Previous experimental and theoretical studies have shown that the SRR resonance depends on the polarization of the exciting electromagnetic field with re-

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TABLE I PERMITTIVITY (AT 10 GHz) OF SUBSTRATES

spect to the orientation in the gap of the SRR [14], [15]. If the gaps of a periodic distribution of SRRs are perpendicular to the exciting electric field, it has been shown that the resonance is magnetic giving rise to a highly dispersive effective magnetic permeability and even negative permeability in the resonance region. If, on the other hand, the gaps are parallel to the electric field, the resonance is electrical in nature and leads to a highly dispersive dielectric permittivity. In this experimental study, we also investigate the temperature dependence of the response to different types of polarization. In [14], it has also been shown that a distribution of randomly oriented SRRs gives rise to both electric and magnetic resonances and near perfect absorption ( 95%) and we study the temperature behavior of such materials also. In this paper, we have also developed a physical model and performed full-wave numerical simulations to explain the observed temperature dependence. Our physical model includes changes in the complex dielectric permittivity of the substrate on which the SRRs are deposited, as well as changes in the electrical conductivity of the copper or silver SRRs and the thermal expansion of the SRRs with temperature. We have measured the temperature dependence of the dielectric permittivity of the substrates—FR4 a commonly used printed circuit board substrate—as well as DuPont 951 that is used in the low-temperature co-fired ceramic (LTCC) process to fabricate 3-D metamaterials. In Table I, we have compared the complex permittivity of FR4 and Dupont 951 with other microwave substrate materials such as Rogers TMM13i series at 10 GHz. While FR4 is slightly more lossy than Rogers materials, it is an order of magnitude less expensive. It may be noted that the stripline method used by Rogers will not yield the same results as the free-space method that we have used. The thermal expansion module in the ANSYS finite-element software was used to obtain the thermal expansion behavior of the SRRs. The temperature dependence of the permittivity, electrical conductivity, and geometrical parameters of the SRR as a function of temperature were input to the Ansoft’s full-wave High Frequency Structure Simulator (HFSS) to obtain the microwave response ( -parameters) as a function of frequency at a specific temperature. The simulation was repeated for different temperatures. The comparison between our experimental measurements and numerical simulation is in good agreement. From a microscopic point of view, metamaterial resonances derive from the oscillations of free electrons in the metal structure. A detailed physical model to explain the observed experimental behavior with rising temperature should include a consideration of changes in free electron motions with temperature.

TABLE II SRR ORIENTATIONS AND DIMENSION FOR FR4-BASED SAMPLES

However, we have considered only macroscopic effects since these provide more useful guidelines for device and material designs using metamaterials.

II. METAMATERIAL SAMPLES Several types of metamaterial samples have been used in the experimental study including periodic and random metamaterials, as well as thin-wire media. The resonant metallo-dielectric structure is chosen to be an SRR since it is a very wellstudied geometry. Our samples are Cu SRRs deposited on an FR4 dielectric substrate using wet etching lithography and Ag SRRs deposited on a DuPont 951 ceramic substrate using screen printing and subsequent sintering at 700 C. In Table I, the thickness and material properties of the substrate materials are listed. The SRRs were designed to have a resonance around 10 GHz ( -band) since this is a commonly studied frequency band and used in many applications. In Table II, the different SRR orientations with respect to the incident electric field and their dimensions are presented. The electrical size of the SRR is small, , the linewidth of the metallization is 250 m, and the spacing between the double split rings is 300 m. The spacing between the split rings is very critical and gives rise to a capacitance that determines the resonance frequency. The split-ring gap of 460 m is important with respect to its orientation and determines the nature of the resonance, but has a smaller influence on the resonance frequency. Since both these parameters , small changes in the values are electrically very small, of these parameters due to thermal expansion may affect the resonance frequency. The FR4 metamaterial sample can be studied in two different arrangements—incident wave vector perpendicular to the plane of the SRR [see Fig. 1(a)] and by cutting the SRR into strips and placing them in a frame with grooves that can support the SRR strips at a fixed lateral spacing [see Fig. 1(b)]. In this case, the incident wave vector is parallel to the plane of the SRR. For this case, we can orient the gap of the SRRs parallel to the -field , gap of the SRRs perpendicular to the -field and randomly oriented SRRs . For the DuPont LTCC substrate, only one sample was studied that consisted of randomly oriented, but periodically distributed SRRs all in a plane [see Fig. 1(c)]. The sample size is 15 cm 15 cm

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Fig. 1. Sample geometries used in study. (a) Incident wave vector perpendicular to the SRR plane. (b) Incident wave vector parallel to the SRR plane. (c) Randomly oriented SRRs on an LTCC substrate.

and the thickness depends on the orientation and placement of the SRRs. III. EXPERIMENTAL SETUP AND VERIFICATION A free-space measurement system, as described in [16] and used in [14] for characterizing metamaterials, is used for the temperature study. Previously, the measurement system was modified to accommodate a furnace between the transmit and receive antennas [17]. This arrangement is shown in Fig. 2(a) and (b). The Tx and Rx antennas are conical horn antennas that are excited by coax-rectangular waveguide–circular waveguide transitions. Back-to-back plano-convex lenses are used to focus the radiation from the antenna into a Gaussian beam with a constant phase front and a focal diameter (3-dB width) of 1 at midband. For -band measurements, the beam width is 3 cm and a sample size of 15 cm 15 cm is sufficient to completely capture the incident beam since the first side lobes are 20 dB down. The focal length of the antenna is 30 cm. Free-space thru-reflect-line (TRL) calibration is implemented to realize a calibration plane on which the amplitude and phase of the incident signal is defined. Time-domain gating is also implemented to remove residual errors and potential multiple reflections between the antennas and furnace windows. A sample holder is placed such that the front surface of a planar

Fig. 2. Experimental setup used in study. (a) Schematic diagram of the setup. (b) Photograph of the measurement setup. (c) Ceramic sample holder in the furnace.

sample is at the calibration plane of the Tx antenna and the Rx antenna is moved back so that the back surface of the sample is at the calibration plane of the Rx antenna. The sample is supported in a picture-frame sample holder, as shown in Fig. 2(d). After performing TRL calibration, a DuPont 951sample with screen-printed SRRs that are randomly oriented and periodically distributed, as shown in Fig. 1(b), is placed in the sample holder and the -parameters are measured. The Nicholson–Ross–Weir method [18] is used to extract the complex permittivity and permeability from the measured complex -parameters. Next the furnace arrangement, shown in Fig. 2(a) and (b), is wheeled into place between the antennas. The furnace has microwave-transparent heat-insulating windows that face the antennas. The furnace has a computer-controlled temperature

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Fig. 3. Verification of measurement data by comparison of measurements with and without the furnace in place at room temperature. (a) S magnitude. (b) S phase.

sensor and the temperature can be varied from 25 C to 1500 C. A ceramic sample holder is used inside the furnace. The first TRL calibration is performed with the furnace in place at room temperature. The SRR sample is first measured at room temperature. In Fig. 3(a) and (b), the -parameters and complex dielectric permittivity of the SRR sample as measured with and without the furnace are compared. We have previously verified the accuracy of the free-space measurements for metamaterial characterization by comparison with HFSS full-wave simulations [19]. We observe that the difmagnitude is less than 0.5 dB and phase differference in ence is less than 3 on average. Since the TRL calibration is performed at room temperature, it is necessary to verify if the calibration parameters drift with temperature. Physically it is not possible to recalibrate after we start heating the furnace. In Fig. 4(a) and (b), we plot the magof the nitude and phase of the transmission coefficient empty furnace as a function of temperature. We plot the transmission at 10 GHz, at the center of the -band frequencies (8–12.4 GHz), since this can give us an idea of the calibration changes only by about drift, if any, with temperature. The 0.2 dB, which is acceptable. The phase varies as small as 3.5 , as can be seen from Fig. 4(b).

Fig. 4. Variation of transmission through an empty furnace at 10 GHz as a function of temperature. (a) Magnitude. (b) Phase.

We may conclude that accurate measurement of the amplitude as a function of frequency and temperature is and phase of possible with the proposed setup and calibration procedure.

IV. HIGH-TEMPERATURE CHARACTERIZATION OF METAMATERIAL SAMPLES Several metamaterial samples, as described in Table II, were characterized in the -band as a function of temperature. For SRRs printed on the FR4 substrate, we had to limit the maximum temperature to 90 C to prevent the FR4 from becoming soft. We heated the Dupont 951 samples to a temperature of strips 420 C. For the FR4 samples, we characterized strips (magnetic resonance), and (electric resonance), (both electric and randomly oriented SRR strips magnetic resonance) for which the -vector is in the plane of the SRRs. The real part of the permeability and/or permittivity, and as appropriate, extracted from the measured complex is plotted in Figs. 5–7. The imaginary part is not presented here. In all three figures, we notice a systematic downward shift of the maxima and minima of and with rising temperature, both in amplitude and frequency. Since the temperature range is only from 30 C to 90 C, the shift is small, but the trend is well defined.

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Fig. 5. Measured real part of permittivity for SRR printed on FR4 substrate at various temperatures.

Fig. 6. Measured real parts of permeability for SRR various temperatures.

Fig. 7. Measured real parts of: (a) permittivity and (b) permeability for the on FR4 substrate at various temperatures. SRR on FR4 substrate at

In Fig. 8, the shift in the resonance frequency is plotted as function of temperature for all three samples. The downward frequency shift is about 0.15 GHz for a temperature change from 30 C to 90 C for all three samples. Although the resonance frequency is slightly different for the three cases, the change is almost the same. We may infer from this that the change is associated with changes in the substrate and electrical conductivity and thermal expansion of the Cu metallization that is the same for all three samples. This will be discussed in Section V. Next, the DuPont 951 sample with randomly oriented SRRs is characterized from room temperature to 420 C. This time we in Fig. 9. The minimum of is present the magnitude of associated with the resonance frequency of the SRRs. The actual definition of the resonance frequency varies; some authors and others as the frequency take this to be the minimum of at which there is maximum power absorption. Again, we observe the systematic downward shift of the maxima and minima amplitude, as well as the resonance frequency with increasing temperature. In Fig. 10, the shift in resonance frequency with temperature is plotted. For the DuPont 951 sample, we observe a frequency shift of 0.35 GHz for a temperature change of almost 400 C.

Fig. 8. Observed change in resonance frequency of FR4-SRR samples versus temperature.

We also performed measurements on a wire sample printed on FR4 using the strip arrangement. It has been shown [20] that a parallel array of very thin wires with the electric field parallel

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Fig. 9. Measured magnitude of S

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of the random SRRs on LTCC substrate.

Fig. 11. Observed change in plasma frequency for a thin-wire medium (printed on FR4).

V. THEORETICAL EXPLANATION OF THE OBSERVED TEMPERATURE BEHAVIOR OF METAMATERIALS

Fig. 10. Observed change in resonance frequency of DuPont 951-SRR sample versus temperature.

to the wires behaves like a plasma medium. The real part of the effective permittivity of such a medium displays the Drude behavior with negative values below a well-defined frequency called the plasma frequency that depends on the radius of the wires and the spacing between the wires. In Fig. 11, we have plotted the real part of the permittivity of an FR4 wire sample extracted from the measured -parameters. We again notice a well-defined, but small downward shift of the plasma frequency from 10.13 GHz at room temperature to 10.03 GHz at 90 C. The per degree shift of frequency for the FR4 sample is 0.021 GHz/ C and the per degree shift of the DuPont 951 sample is 0.0087 GHz/ C, which is much lower. Thus, we may expect that the permittivity of DuPont 951 changes much less with rising temperature than FR4. We also conclude that the per degree shift of the resonance frequency is not dependent on the polarization of the incident wave with respect to the orientation of the SRR gap. The reasons for the decreasing resonance strength and downward shift in the resonance frequency are studied in Section V.

Based on the experimental data, we hypothesize that there are three possible reasons for the decreasing resonance strength and resonance frequency with rising temperature. These are: 1) change in the dielectric permittivity of the substrate with temperature; 2) change in the electrical conductivity of the metal; and 3) thermal expansion of the metal. We next verify our hypotheses by calculating the change in resonance strength and resonance frequency caused by each factor either with experimental data or full-field finite-element simulations. We assume that the three factors are independent and can be calculated separately. We next perform a full-wave finite-element simulation of the transmission and reflection of waves through metamaterial sample inputting the temperaturedependent permittivity, electrical conductivity, and changes in the dimensions of the SRRs due to thermal expansion. This result will be compared with the experimental data to verify if the observed change in resonance frequency agrees with the simulation, thereby verifying our hypotheses.

A. Temperature Dependence of Substrate Permittivity Since the FR4 samples could not be heated to high temperatures, we focused on the temperature behavior of the DuPont 951 substrate. A blank sample of the material of thickness 1.05 mm was fabricated using the LTCC process. The complex dielectric property of the blank LTCC and FR4 samples were measured as a function of temperature and are plotted in Fig. 12. The real part of the permittivity of the LTCC averaged over -band frequencies increases from 7.36 at room temperature to 7.88 at 400 C. The imaginary part of the permittivity increases with temperature. For FR4, the real part of permittivity changes from 4.33 to 4.51 from 20 C to 90 C. It has been shown [21] that lowering the dielectric permittivity of the substrate increases the resonance frequency of metamaterial since this corresponds to a decrease in the electrical size of the structure with increasing wavelength.

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Fig. 13. Temperature dependence of the conductivity of copper and silver calculated using (1).

permeability plots shown in Figs. 5–7. For example, the Lorentz model for the permeability, as given in [1], may be written as

(2)

Fig. 12. Measured temperature dependence of permittivity of DuPont 951 and FR4 averaged over -band frequencies (8.2–12.4 GHz). (a) Real part. (b) Imaginary part.

X

B. Temperature Dependence of the Electrical Conductivity of Cu and Ag

The conductivity of bulk metals has the following dependence on temperature: (1) where is the initial or room temperature at which the conducis known. is the coefficient of thermal expansion tivity of the metal. The decreasing conductivity with rising temperature leads to a lower drift velocity for free electrons. As we know, free electrons in a conductor move randomly if no field is applied. An applied electric field results in an average drift velocity as given by the Drude free electron model. At high temperatures, the free electrons move faster, but randomly, thus the applied electric field cannot accelerate the electrons as effectively, resulting in a lower drift velocity. Therefore, more energy is dissipated in the other terms. We can explain the decreasing resonance strength of the permittivity and/or permeability with increasing temperature by looking at the effect of conductivity on a Lorentz model that describes very well the permittivity and

is the surface resistivity of the metal, is the cawhere pacitance between the inner and outer rings, and is the radius of the ring. The magnitude of and will decrease with increasing resistivity or conversely decreasing electric conductivity. We can thus attribute the small drop in the resonance strength with increasing temperature on the drop in electrical conductivity. In Fig. 13, we present the temperature dependence of the conductivity of Cu (used in the FR4 samples) and Ag (used in the LTCC samples). C. Thermal Expansion of the Substrate The thermal expansion coefficiencts of DuPont 951 and FR4 are very small: 5.8 and 11 ppm, respectively. For example, this will result in a change in thickness for LTCC of only 2.32 m from 20 C to 400 C and for FR4 by 0.5 m from 20 C to 90 C. According to the results in [21], this would lead to a negligible shift in the resonance frequency. D. Thermal Expansion of SRRs The dimensions of the SRRs are quite small, the largest dimension being 2.01 mm and the smallest being 190 m. These dimensions are very critical in determining the resonance frequency of the SRR. As temperature increases and the metal expands, and even small changes in dimensions can shift the resonance frequency. Since the metallization thickness is very small (17 m for Cu and 10 m for Ag) and the thermal expansion of the substrate also plays a role, it is not accurate to estimate the increase in geometrical parameters using a linear thermal expansion model. Instead, we used the thermal expansion simulation

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TABLE III MECHANICAL AND THERMAL PROPERTIES OF SILVER AND DUPONT 951 [22], [23]

Fig. 15. Numerically simulated (using Ansoft HFSS) jS j for random SRRs on an LTCC substrate at 20 C and 400 C. Material and size parameters at 400 C calculated using ANSYS.

Fig. 14. Change in dimensions of an SRR computed using ANSYS due to thermal expansion of silver and the substrate from 20 C to 400 . The unit is millimeters.

TABLE IV SHIFT IN RESONANCE FREQUENCY DUE TO EACH FACTOR (FROM 20 C TO 400 C)

tool in the ANSYS finite-element code for mechanical structures to compute the geometrical size of the SRR on the DuPont 951 substrate at 400 C starting with the known parameters at room temperature. The thermal and mechanical properties of DuPont 951 and Ag are given in Table III. In Fig. 14, we show the room-temperature dimensions of an SRR deposited on DuPont 951 and the dimensions at 400 C calculated using ANSYS. We observe that the parameters increase by approximately 0.33% due to rise in temperature. It is very well known that if the size, and hence, the electrical size of the SRR increases, its resonance frequency will be smaller. Thus, we may conclude that decreasing substrate permittivity and increasing the size of the SRRs leads to a lower resonance frequency as temperature increases. VI. COMPARISON OF FULL-WAVE SIMULATION INCLUDING TEMPERATURE EFFECTS WITH OBSERVED DATA Next we performed a full-wave simulation using Ansoft HFSS and computed the -parameters of the DuPont 951 sample with randomly oriented SRRs. First we included the temperature dependence of each of the three factors we studied separately to understand their relative importance in lowering the resonance frequency. In Table IV, we show the resonance frequencies at 20 C and 400 C, respectively, for: 1) experimental data; 2) including only thermal changes in dielectric permittivity; 3) including thermal changes in electric conductivity only; and 4) effects of thermal expansion only. The

percentage (%) change of resonance frequency is denoted for each case. We observe that the temperature dependence of the dielectric permittivity is the dominant contributor (90% of the observed resonance frequency change) followed by thermal expansion of the SRR (10% of the observed resonance frequency change). The effect of changes in the electrical conductivity is 5%. Finally, all effects were included in a HFSS simulation for the entire -band, and in Fig. 15, we compare the frequency shift for the DuPont 951 sample between 20 C and 400 C obtained from simulation and measurement. It is seen that the comparison is quite good and the HFSS simulation predicts a shift of resonance frequency of 0.35 GHz compared to 0.36 GHz in the experimental data. VII. CONCLUSIONS The shift in the resonance frequency of metamaterials constructed with SRRs with rise in temperature has been measured experimentally. SRRs were chosen since they comprise the canonical elements of a metastructure that can be modeled as an oscillator. Any other shape of a metastructure would simply parameters. The wire structure have different equivalent was included because it is very different in behavior from SRR type metamaterials. The wire sample is a plasma like medium and does not exhibit the classic anomalous dispersion behavior of SRR type resonant samples. Increasingly, wire media are being proposed for invisibility cloaks; hence, it is important to know that plasma frequency shifts with temperature. Our hypotheses regarding the reasons for the downward shift of the resonance frequency with increasing temperature have been substantiated by performing detailed numerical simulations that take into account the change in material properties and thermal expansion of the sample with rising temperature. It is clear that the temperature dependence of the dielectric permittivity is the most critical factor followed by the thermal expansion of the metallized structures of the metamaterial. Thus, in designing metamaterials for RF applications that may be subject to high-temperature conditions, it is necessary to choose substrate materials whose dielectric properties are relatively stable and to use metals with low thermal expansion

VARADAN AND JI: TEMPERATURE DEPENDENCE OF RESONANCES IN METAMATERIALS

coefficients for the resonant structures. In the future, we may also consider thermal tuning of metamaterials to obtain broader bandwidth performance in certain applications.

ACKNOWLEDGMENT The authors wish to thank their colleagues at the University of Arkansas, Fayetteville: H. Wang for his help with the ANSYS simulation and I. K. Kim and M. B. Buscher for their help with the experiments.

REFERENCES [1] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2075–2084, Nov. 1999. [2] S. A. Schelkunoff and H. T. Friis, Antennas: Theory and Practice. New York: Wiley, 1952, pp. 584–585. [3] J. G. Garcia et al., “Microwave filters with improved stopband based on sub-wavelength resonators,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 1997–2006, Jun. 2005. [4] J. Bonache, I. Gil, J. G. Garcia, and F. Martin, “Novel microstrip bandpass fileters based on complementary split-ring resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 265–271, Jan. 2006. [5] G. V. Eleftheriades, A. K. Iyler, and P. C. Kremer, “Planar negative refractive index media using periodically L–C loaded transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2702–2712, Dec. 2002. [6] C. Caloz and T. Itoh, “Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line,” IEEE Trans. Antenn. Propag., vol. 52, no. 5, pp. 1159–1166, May 2004. [7] I. O. Mirza, S. Shi, and D. W. Prather, “Phase modulation using dual split ring resonators,” Opt. Exp., vol. 17, no. 7, pp. 5089–5097, Mar. 2009. [8] F. Bilotti, L. Nucci, and L. Vegni, “An SRR based microwave absorber,” Microw. Opt. Technol. Lett., vol. 48, no. 11, pp. 2171–2175, Nov. 2006. [9] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science, vol. 314, pp. 977–980, Nov. 2006. [10] K. B. Alici and E. Ozbay, “Electrically small split ring resonator antennas,” J. Appl. Phys., vol. 101, Apr. 2007, Art. ID 083104. [11] J. Kim, C. S. Cho, and J. W. Lee, “5.2 GHz notched ultra-wideband antenna using slot-type SRR,” Electron. Lett., vol. 42, no. 6, pp. 315–316, Mar. 2006. [12] R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antenn. Propag., vol. 54, no. 7, pp. 2113–2130, Jul. 2006. [13] N. I. Landy, S. Sajuyijube, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett, vol. 100, May 2008, Art. ID 207402. [14] V. V. Varadan and A. R. Tellakula, “Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation,” J. Appl. Phys., vol. 100, pp. 1–8, Aug. 2006, Art. ID 034910.

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[15] I. K. Kim and V. V. Varadan, “Electric and magnetic resonances in symmetric pairs of split ring resonators,” J. Appl. Phys., vol. 106, Oct. 2009, Art. ID 074504. [16] D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan, “Free-space measurement of complex permittivity and complex permeability of materials at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 39, pp. 387–394, Apr. 1990. [17] V. V. Varadan, R. D. Hollinger, D. K. Ghodgaonkar, and V. K. Varadan, “Free-space, broadband measurements of high-temperature, complex dielectric properties at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 40, pp. 842–846, Oct. 1991. [18] J. B. Jarvis, M. D. Janezic, J. H. Grosvenor, Jr, and R. J. Geyer, “Transmission/reflection and short circuit line methods for measuring permittivity and permeability,” NIST, Boulder, CO, Tech. Note 1335-R, Dec. 1993. [19] V. V. Varadan, Z. Sheng, S. Penumarthy, and S. Puligalla, “Comparison of measurement and simulation of both amplitude and phase of reflected and transmitted fields in resonant omega media,” Microw. Opt. Technol. Lett., vol. 48, no. 8, pp. 1549–1553, Aug. 2006. [20] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett., vol. 76, no. 25, pp. 4773–4776, Jun. 1996. [21] Z. Sheng and V. V. Varadan, “Tuning the effective properties of metamaterials by changing the substrate properties,” J. Appl. Phys, vol. 101, Jan. 2007, Art. ID 014909. [22] I. Yoshihiko, Multilayered Low Temperature Cofired Ceramics (LTCC) Technology. New York: Springer, 2004, pp. 15–15. [23] C. A. Walker, F. Uribe, S. L. Monroe, J. J. Stephens, R. S. Goeke, and V. C. Hodges, “High-temperature joining of low temperature cofired ceramics,” in Proc. 3rd Int. Brazing and Soldering Conf., Apr. 2006, pp. 54–59. Vasundara V. Varadan (M’82–SM’03) received the Ph.D. degree in physics from the University of Illinois at Chicago, in 1974. She has been with Cornell University, The Ohio State University, and Pennsylvania State University. From 2002 to 2004, she was the Division Director of the Electrical and Communications Systems Division, National Science Foundation (NSF). She is currently the Billingsley Chair and Distinguished Professor of Electrical Engineering with the University of Arkansas, Fayetteville. Her research interests are electromagnetic (EM) theory and measurements, metamaterials, electrically small antennas, microwave nondestructive evaluation and imaging, smart materials and devices, numerical simulation of wave problems, and embedded sensor systems. Dr. Varadan is a Fellow of the Acoustical Society of America, the Institute of Physics (U.K.), and The International Society for Optical Engineers (SPIE).

Liming Ji (S’08) was born in Taizhou, Jiangsu, China. He received the B.S. degree in electronic engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1985, and is currently working toward the Ph.D. degree at the University of Arkansas, Fayetteville. His research interests include modeling, characterization, and application of metamaterials.

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Whispering Gallery Mode Hemisphere Dielectric Resonators With Impedance Plane Alexander A. Barannik, Sergey A. Bunyaev, Student Member, IEEE, Nickolay T. Cherpak, Senior Member, IEEE, Yurii V. Prokopenko, Anna A. Kharchenko, Student Member, IEEE, and Svetlana A. Vitusevich

Abstract—The electrodynamic characteristics of a highdielectric whispering gallery mode resonator in the form of a hemisphere positioned on an impedance plane were studied. The analysis of the anisotropic resonator was modeled using Maxwell equations and the impedance Leontovich boundary condition. of the conductor and microwave The interaction coefficient field was determined using a frequency and field distribution of the -type mode in the hemisphere resonator considering a perfect conducting plane. Results of the theoretical study and experimental measurements of the Teflon resonator frequency spectrum and factor are in good agreement. The results obtained are confirmed by calculations using Microwave Studio CST 2008. In the case of the sapphire hemispherical resonator with an impedance plane, comparison of the experimental and simulation results allows us to identify the -type modes in the resonator and their electromagnetic field distribution. In such anisotropic hemisphere resonators, the quasi-TE modes are revealed. The modes are excited together with TE modes inherent to the isotropic resonator and they have an identical distribution of electromagnetic field. Index Terms—Dielectric resonators, electromagnetic fields, frequency, impedance measurement, millimeter-wave measurements, factor.

I. INTRODUCTION

UASI-OPTICAL dielectric resonators excited on whispering gallery modes have found applications in a wide frequency range: from microwave [1] to optical [2] bands. Increased interest in such resonators is related to their high factor and higher operation frequencies due to the larger dimensions of the whispering gallery mode resonator

Q

Manuscript received January 29, 2010; revised June 16, 2010; accepted July 09, 2010. Date of publication September 09, 2010; date of current version October 13, 2010. This work was supported by the Federal Ministry of Education and Research, Germany under BMBF Project UKR 08/008. A. A. Barannik, N. T. Cherpak, Y. V. Prokopenko, and A. A. Kharchenko are with the Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov 61085, Ukraine (e-mail: [email protected]; [email protected]; [email protected]; prokopen@ire. kharkov.ua; [email protected]). S. A. Bunyaev was with the Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov 61085, Ukraine. He is now with the Departamento de Fisica da Faculdade de Ciencias, IFIMUP and IN–Institute of Nanoscience and Nanotechnology, Universidade do Porto, 4169-007 Porto, Portugal (e-mail: [email protected]). S. A. Vitusevich is with the Institute of Bio- und Nanosystems (IBN) and the Jülich-Aachen Research Alliance for Future Information Technology (JARAFIT), 52425 Jülich, 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.2010.2065870

in comparison to dielectric resonators excited on fundamental modes. They are used in the microwave frequency range for the development of high-quality filters [3] and of oscillators with decreased phase noise and high-frequency stabilization [4]–[6], and also for the power combining of several oscillators [7]. They also can be used for the measurement of the complex permittivity of dielectric substances [8], [9], surface impedance of high-temperature superconducting (HTS) films [10]–[12], and studies of semiconductor properties [13], [14]. The increasing sensitivity in the microwave band is important for HTS surface impedance measurements, the development of HTS-based devices, and for a deeper understanding of the nature of unconventional superconductivity phenomena. Obtaining surface impedance data for HTS material is of great significance in a broad temperature range including very low temperatures where the highest sensitivity of microwave loss measurement is required [15]. Resonators excited on whispering gallery modes are usually studied and used in the form of circular cylinders (see, e.g., [16]–[18]). It should be noted that [18] was one of the first papers that compared the matching of theory and experiment in the case of anisotropic dielectric resonators. Recently, it has been shown that these resonators with conducting endplates can be used for measurement of HTS thin-film surface resistance [10], [11], [19]. Such an approach allows enhancing the accu, value measurement due to racy of small surface resistance the increased factor of the resonator, and means there is no need for a calibration procedure of measurement setup. In addition, the possibility of measuring the films with different forms and dimensions is an additional advantage. However, the meais the averaged value of two films. In principle, insured values of conducting endplates can be found by dividual using a so-called “round robin” procedure [20], which requires three thermal cycle measurements of three different pairs of HTS films and is a very time-consuming procedure. Therefore, resonators have recently been developed in a form that allows only one conducting endplate to be studied. In such a resonator, the microwave field has to be localized near the conducting surface. The resonator can be designed in the form of a truncated cone [21] or a hemisphere [22] placed on a conducting plane, i.e., a conducting endplate. It was shown experimentally that, in these resonators, whispering gallery modes can be excited near the surface of the plate, i.e., close to the resonator base [23]. The resonator in the form of a truncated cone was studied in [24]. However, the electrodynamics of hemispherical resonators has not been explored in detail, which substantially hinders their application.

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BARANNIK et al.: WHISPERING GALLERY MODE HEMISPHERE DIELECTRIC RESONATORS WITH IMPEDANCE PLANE

Fig. 1. Hemispherical dielectric resonator with conducting infinite plane.

In this paper, we report on the results of a theoretical and experimental study of hemispherical whispering gallery mode resonators with an impedance plane. Microwave properties of the resonators designed on the basis of isotropic and anisotropic dielectrics were analyzed. The experiment and theory were found to be in good agreement. II. THEORY Hemispherical resonators are very promising for practical applications in a microwave technique. It is evident that the electrodynamics of a spherical whispering gallery modes resonator is a starting point for theoretical studies of a hemispherical resonator with a plane conducting surface. Recently, the authors of [25] and [26] theoretically analyzed the whispering gallery mode resonator in the form of a sphere made of anisotropic dielectric, taking into account that most materials with a small loss are anisotropic. At the same time, analyzing the effect of dielectric anisotropy on the electromagnetic properties of hemispherical whispering gallery mode resonators remains the most important issue of the day. The dependence of hemispherical whispering gallery mode resonator eigenfrequencies and factor on impedance properties of the plane surface have to be studied. A. Hemispherical Dielectric Resonator With Perfect Conducting Plate Electromagnetic fields of the eigen -mode of a hemispherical dielectric resonator with a perfect conducting plane surface (Fig. 1) can be calculated using Maxwell equations

(1) where material equations were taken into account. Here, and , where is the time is the eigen complex frequency of the resonator with and a -mode: , ; and are the tensors of permittivity and permeability of the -medium, counting from the center of the studied resonator taking into account the surrounding environment; is the velocity of light. Tensor components and are complex values and characterize the anisotropic properties of -medium with loss. If the media of the resonator or surrounding environment are isotropic with respect

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to electric or magnetic fields, they are characterized by correor , matrices of which have a diagonal sponding tensors form with the same components. Using such an approach, all expressions obtained by analysis of the case of anisotropic resonator can be transformed easy into those suitable for analysis of the isotropic resonator case. Index consists of three mode . Azimuthal mode index has magniindices, namely, tudes and equals half a number of field vari, where a ations along angle . At the same time, index polar index is determined through the quantity of field variations along the polar angle in a spherical coordinate system: . We used the relation between indices and and quantity of field variations ( with bar accent) along the polar angle taking into account the field distribution on a sphere surface of the resonator [27], which is generally determined by the associated Legendre function. The radial index , which is an ordinal number of the root of the characteristic equation for the studied resonator, corresponds to the quantity of field variations along a radial coordinate . Expressions for electric and magnetic vector components of the -type -mode are used as in [25] and [27]. In the case of isotropic media in the resonator and are surrounding environment, the eigencomplex frequencies determined by solving a corresponding characteristic equation [27]. For the -type mode, we assume or , i.e., eigen TM or TE modes, respectively (and additional quasi-TM or quasi-TE modes for the anisotropic resonator or in the presence of an anisotropic environment). We have found experimentally that additional quasi-TE modes appear in the case of an anisotropic hemisphere. These modes are absent in isotropic resonators. In has hemispherical dielectric resonators, a sum of indices odd numbers for eigen -type modes and even numbers for -type modes [27]. One-mode approach used in solving the electrodynamic problem is justified by the physical background. In the experimental studies, the resonator is excited by some source positioned in the definite point of the space. The source forms monochromatic radiation. As a result of frequency and space selection, as a rule, only one mode is excited in the resonator. A spatial selection is provided by positioning the excitation source in the field maximum of the resonator eigenmode. Therefore, a superposition field of excited modes with the same frequency is formed mainly by the field of the dominant eigenmode in the resonator. This fact exhibits in a theory of stimulated oscillations in the resonator under study, when we solve the electrodynamic problem using a separation of variables. At the same time, we obtain components of the field formed by a superposition of the fields of eigenmodes with the same frequency. The main contribution to the field is introduced by a dominant mode, determined by a spatial selection implemented using the excitation source. Therefore, in a theory of eigenmodes, it is sufficient to study the influence of imperfect conductivity of a plane surface on the field of one (dominant) mode. In addition, in a case of an isotropic resonator with a perfect conducting plane, electrodynamic analysis reduces to a solution of independent differential equations for degenerate TM and TE modes with the same polar indices. The effect of the conducting plane results in the resonator spectrum sparseness, determined by boundary conditions on

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

the conducting surface, and manifested itself in a sum of polar and azimuthal indices. The field distribution pattern of these modes indicates the possibility of their selection using a polar coordinate [27]. Thus, the vector fields with mode indices in (1) describe the resulting electric and magnetic fields whose structure corresponds to the dominant mode in a resonator with a perfectly conducting plane surface. The energy of the electromagnetic field created by the -mode of -type in the resonator with a perfect conducting plane is determined by the expression [28] (2)

of where integration is performed over a total volume and are real magmedium , and tensor components nitudes that characterize the anisotropic properties of the -medium without losses. Here, electric and magnetic fields are represented by resolutions of vectors of identical fields (the -mode of -type) in a resonator in a spherical and coordinate system , where , , and are unit vectors of the corresponding axes. The elementary volume and limits of integration in accordance with the geometry of the resonator are also taken in the spherical coordinate system. Here and below, the symbol “ ” indicates complex conjugation.

is the normal vector directed into the conductor towhere 1 is the surface impedance ward the surface, and —the surface resistance and surface reactance with of a conductor, respectively. Fields and in (4) correspond to their values in the points of the -medium, which are infinitely near, but do not belong to a conductor surface. The relation (4) is an approximation and is feasible in the case of a strong skin effect, when: 1) a field penetration depth in a conductor is much smaller than a wavelength in the -medium and 2) a skin layer thickness is small in comparison to the conductor thickness and radius of curvature of the surface. It should be emphasized that, in (4), both penetration of the electromagnetic field into the conductor and corresponding losses are taken into account. According to [31], the fractional error is related to the influence of the conductor on the electromagnetic field and is , where permittivity and of the order of magnitude correspond to the conductor medium. permeability , After multiplying the set of complex conjugate (3) by , respectively, and the set (1) by complex conjugate magni, , we add them. After integrating the obtained tudes expression over the total space taking into account, the divergence theorem and using the continuity conditions of tangential-field components on the spherical surface of the resonator and also the impedance boundary condition (4) on the plane , we obtain the integral equation in the form

B. Resonator With Impedance Plane Imperfect conductivity of a plane surface has a considerable influence on the spectral and energy characteristics of the resonators (Fig. 1) [29], [30]. They are determined by solutions of the set of homogeneous equations

(3) where and , and is the eigenfrequency of the resonator . It should be noted that both (1) and (3) have to be written for the correct mapping technique for obtaining integral (5). In the opposite case to the perfect conductor, the electromagnetic field in a real conductor penetrates into the depth of the skin layer, the thickness of which is finite and small, especially in the microwave frequency range. In this respect, the perfect conductor in the main reflects the real metal conductor properties [31]. However, Joule heat losses are equal to zero in a perfect conductor, and if it is necessary to take them into account, the idea of a perfect conductor cannot be applied. These losses exist in a real conductor, and their value increases with decreasing skin layer. The case of a real conductor can be considered in an electrodynamic study by taking into account the impedance boundary condition (Leontovich boundary condition) on its surface [31] (4)

(5)

The integration on the left is performed over the total volume of the -medium and on the right over the conducting plane surface contacting with the -medium. It should be noted and , included in (5) on the right, correspond that fields to field magnitudes in the -medium points infinitely near to the conductor surface. The vector is the unit vector of the -axis. and are represented in the eigenmode subThe fields and for a resonator with a perfect conducting setting of surface

(6) where

is the subsetting coefficient.

1It should noted that, in electrodynamics, as a rule, quasi-monochromatic fields are used with time dependence in the form of exp( i!t), which gives a sign “minus” in the expression for surface impedance Z (see, e.g., [32]). In contrast, in microwave superconductivity, the time dependence is used in the form of exp(i!t), which changes the sign before the imaginary part of Z (see, e.g., [15] and [33]).

0

BARANNIK et al.: WHISPERING GALLERY MODE HEMISPHERE DIELECTRIC RESONATORS WITH IMPEDANCE PLANE

By substituting (6) in (5) and taking into account (2), we obtain the infinite in respect of the -modes set of equations

(7) where

the

factor

reflects the energy loss of the electromagnetic field created by the -mode of the -type in the general case of the anisotropic medium in the resonator studied with a perfect conducting plane. The parameter of includes loss in the surface of the plane with finite conductivity and interaction of the modes in the resonator. The condition for the existence of nontrivial solutions of the can be found from the equation when system (7) in regard to the determinant is equal to zero (8) where is the Kronecker symbol. Expression (8) is the of the resequation for determining the eigenfrequencies onator shown in Fig. 1 with finite conducting plates. Equation (8) physically represents the energy conversation law for quasi-monochromatic fields of resonator eigenmodes. In addition, (8) determines the eigenfrequency shift of the resonator studied with a finite conducting plane in respect of the resonator with a perfect conducting plane. at , By neglecting the interaction of modes ( reflecting that surface current in a conducting plane is induced by a dominant mode field in the resonator), (8) can be reduced to the form (9) is the squared where surface current in a resonator conducting plane. This current is the result of the penetration of an eigen -mode electromagnetic and field into the conductor. For the resonator studied . In the general case, (9) also has to be applied for a resonator ). In such a with a perfect conducting surface (i.e., at . Therefore, resonator, the frequencies do not shift and between the electromagnetic energy and its loss in the resonator (Fig. 1) with a perfect conducting plane, the fol, which results lowing relation is fulfilled: in a doubling of the value of the eigen factor of the resonator , the reswith a -type mode. Using (9) and onator eigenfrequency shift as a result of the finite conductivity of the conducting plane can be described as

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The shift of the eigenfrequency of the real part of the resonator is determined, in the main, by the imaginary part of surface . Nondissipative energy stored in impedance (by reactance) the surface layers of the plane wall of the resonator depends deon the magnitude of the reactance. Surface resistance in the termines the power of the Joule losses impedance surface of the studied resonator averaged over the period. Finite conductivity of the surface results in decreasing real parts and increasing imaginary parts of the eigenfrequencies in respect of a resonator with a perfect conducting plane. The effect is caused by the penetration of eigenmode fields into the resonator’ conducting plane, which, in turn, is accompanied by an increase in resonator volume. Assuming identical eigenmode field configurations for two resonators with different conductivity of the plane surface, the resonator with the larger surand surface reactance has a smaller value face resistance of . In principle, (9) allows us to determine the surface impedance of the resonator conducting plane using eigencomplex frequency measured experimentally. C. Interaction Between Microwave Field and Resonator Conducting Plane: Conductor Inclusion Factor In the case of small attenuation of the eigenmode field, i.e., when the decrease in mode amplitude is small and the field can be considered as harmonic within one period, a resonator factor is determined by a ratio of energy , stored in the resonator volume, to the energy , which is lost per period . If the mode amplitude in the resonator is kept constant using an external source, compensating the energy losses, the factor can be calculated by (10)

where is the loss power, which consists of losses in the medium, filling a restricted volume, radiated losses into the surrounding environment, and losses due to the conducting . Therefore, the total losses of elecmedium tromagnetic energy in a resonator with the -type mode are determined by the relation (11) Here, is the resonator factor determined by radiation is determined by the loss and loss in the dielectric, and loss in the conducting surface of the resonator. In the case of strong damping of the mode, (10) cannot be applied to find the factor including all loss components, and the following ex, which is correct under pression should be used any damping of eigenmode in the resonator. The factor related to both energy loss in the dielectric and . In the case of radiation can be determined using exciting weakly damped whispering gallery modes, accordingly factor due to loss in the conducting to (10), the resonator surface is determined by the expression . The resonator factor can be presented in the form of , taking into account . Here,

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

TABLE I CHARACTERISTICS OF THE RESONATOR WITH TM

, and taking into account [27], the relation from (12), the eigencomplex the conductor inclusion factor frequencies of the resonator (Fig. 1) can be determined by the expression

MODES

(13)

TABLE II CHARACTERISTICS OF THE RESONATOR WITH TE

Since and using (13), the real part of the eigenfrequency of a resonator with the -mode of -type can be reduced to

MODES

(14)

the conductor inclusion factor describes the interaction of the microwave field and conducting plane. It depends on the field distribution of the -mode near the resonator conducting surface and can be calculated using (12) is determined by the eigenmode Hence, the coefficient frequency and field distribution in a resonator with a perfect depends on the geometric conducting plane. In other words, parameters of a resonator and the electrophysical properties of its media including the surrounding environment and is independent of the properties of the conducting plane. The coeffiis calculated using (12) in the frame of the theory of cient eigenmodes of the resonator because the squared surface curin the resonator conducting surface and energy of rent the -type eigen -mode are determined by field components, which are represented by expressions [25], [27] containing the same constant. It should be noted that, for the resonator under can be study with a spherical interface of media, the energy obtained using an analytical solution. However, the integral relacan be found only using numerical methods. In the tionship includes only the energy of the magcase when the energy netic field, the inverse value of the conductor inclusion factor is the geometric factor [34]. Tables I and II summarize the results of numerically studying cm with the hemispherical Teflon resonator of radius and modes. The hemisphere is placed on the copper m or brass m planes. A resonator with an -type mode has the largest values of when and with an -type mode when the coefficient . This indicates the localization of eigen and mode electromagnetic fields near the conducting plane of the resonator. This case is important for increasing the sensitivity of the method for impedance determination. D. Eigenfrequencies and Impedance Plane

Factor of Resonator With

Using the solutions of (9), the solutions of the characteristic for the resonator with a perfect conducting plane equation

Frequency agrees with the resonance frequency measured experimentally in the exciting -mode of -type in the resonator under conditions of weak coupling between the resonator and exciter. The imaginary part of the eigenfrequency can be determined as (15) Equation (15) corresponds physically to the case when energy total losses in the resonator satisfy (11). This indicates that, in the case of a strong skin effect, the factor of the resonator determined by loss in its conducting surface can . be represented in the form of In real conductors with a strong skin effect, the surface reand has a sistance equals the surface reactance positive magnitude that indicates the inductive nature of the surface impedance of the conducting surface of the resonator. This can be explained by the fact that the total surface current has a phase shift in comparison with the tangential elecon the conducting surface of tric field the resonator. According to [31], only volume currents on the conducting surface are in phase with the surface electric field, and currents in the deeper layers of conductor have a phase shift from the surface electric field because of wave excitement and propagation along the direction normal to the conductor plane. In a resonator with a real conducting (i.e., impedance) plane surface, the frequency of the eigenmode can be determined using (13) by the expression (16) Therefore, from (16), the real part of the eigenfrequency of a resonator with the -mode of -type is equal to , which corresponds to the fre. At the same time, the quency determined by (14) at imaginary part of the frequency is determined by (15), which indicates the universality of (11) for calculating the total energy losses in the resonator. Besides, the real and imaginary parts of the resonator eigenfrequency are related (17)

BARANNIK et al.: WHISPERING GALLERY MODE HEMISPHERE DIELECTRIC RESONATORS WITH IMPEDANCE PLANE

Fig. 2. Eigenfrequencies of the hemispherical resonator designed from Teflon and TM modes: closed symbols—experimental data, open with TE symbols—calculation results, dashed line represents simulation results using MWS.

Thus, in the general case, the eigenfrequency of the resonator (Fig. 1) with a -mode of -type is determined by (13). At the . When same time, the resonator eigen factor is the conducting plane of the resonator is a real metal conductor, the eigenfrequencies of the resonator can be determined by (16). In the case of an isotropic dielectric hemisphere with a perfect conducting plane surface, the eigen -type and -type modes are frequency degenerated, - and -fold, respectively [27]. The finite conductivity of the plane surface of the hemisphere dielectric resonator according to (13) removes the freof (12) is expressed quency degeneration because the factor by the ratio of integral relationships for and , which contain the field components for the -mode of -type depending on the mode indices , , and . III. EXPERIMENTAL STUDY OF HEMISPHERICAL RESONATORS A. Teflon Hemisphere Teflon is an isotropic material with permittivity measured using a cylindrical disc whispering gallery mode resonator in the present work and determined as . It demonstrates relatively small losses of eigenmode energy in a resonator made of this material. Moreover, Teflon can be easily machined, which is convenient for producing resonators of different forms. Therefore, we started resonator studies using a hemispherical resonator made of Teflon. The radius of the rescm. The metal plane of the resonator (Fig. 1) onator is m . The experimental was produced from brass data on the eigenfrequency and factor were measured using Agilent Network Analyzer PNA-L N5230A in the frequency band from 30 to 40 GHz. and The eigenfrequencies of the resonator with modes at different azimuthal indices are calculated using the equation , which was obtained from (14) at . The results are compared with the measured values, as well as with those calculated using CST Microwave Studio 2008 (MWS) for the same modes (Fig. 2).

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Q factor of hemispherical resonator from Teflon with TE

and modes: closed symbols—experimental data, open symbols—calculation results.

Fig. 3.

TM

Fig. 2 demonstrates that the results of the calculated and experimental data are in good agreement for both ( -type, for which ) and for ( -type, for which ) modes. This fact confirms that the analytical approach is correct and can be used for spectrum identification of an isotropic hemisphere whispering gallery mode resonator. The experimental and calculated data deviate insignificantly, which is caused by the slight surface roughness of the spherical resonator made from Teflon and the brass plane. The roughness is difficult to take into account in the calculations. For correct identification of the resonator modes excited in the experiment, we compared the field distributions obtained by different methods: 1) calculated using a computer program developed at the Institute of Radiophysics and Electronics, National Academy of Sciences (NAS) of Ukraine; 2) calculated using the program package CST MWS 2008 (transient solver); and 3) measured experimentally using the small perturbation method, i.e., using a small-size test probe. A combination of methods allows us to determine the indices of the modes excited in the resonator. In addition, the energetic characteristics of the resonator were studied. -factor values of the Teflon resonator with and modes are shown in Fig. 3. The calculated -factor values were obtained using (11) taking into and . Fig. 3 account that shows that whispering gallery mode resonator with and modes had different values of factor. They , which, in increase with increasing azimuthal index turn, is accompanied by an increase of the eigenfrequencies. and . NevertheThe factors strongly depend on values less, the difference between the calculated and experimental energetic characteristics for both mode types does not exceed the relative error of the resonator -factor measurement , which . corresponds to the value B. Sapphire Hemisphere Resonator In order to study the special electrodynamic features of a hemispheric resonator made of uniaxial anisotropic single crystals, the spectral and energetic characteristics of a sapphire

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Fig. 4. Calculated distribution of field conducting plane using MWS.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

E

component. (a)

TE

and (b)

Al O resonator were measured. A permittivity tensor of a single-crystal sapphire can be expressed as the equation shown at the bottom of this page. cm was produced with A hemisphere with radius an optical axis perpendicular to the conducting copper plane of the resonator (see Fig. 1). The surface resistance of the copper plate was measured using a sapphire disc resonator and determined as 55 m at room temperature. Since there is no analytic solution of the electrodynamic problem for an anisotropic hemisphere with a conducting plane, the sapphire resonator was numerically simulated using the MWS package (transient and eigenmode solvers). The resonance frequencies and field redistribution of the excited modes were calculated. Fig. 4(a) and (b) shows the distributions of field components and modes, respectively, in the sapphire hemisphere whispering gallery mode res(in cross onator with a copper plate in the planes section) and (in cross section). Excitation of the resonator was realized by a quasi-image sapphire waveguide ar-

TE

modes in a hemispherical whispering gallery mode resonator with

. Fig. 4 demonstrates that the resranged in a plane onator fields of both modes are concentrated near the conducting plane. In the future, we will concentrate our studies on modes in a hemisphere sapphire resonator, because for the mode, the maximum density of the field energy spreads close to the metal plate surface [23], which indicates a preference of this mode for measurements. The frequency dependencies of the resonator -parameters are shown in Fig. 5. The experimental data were measured in the frequency band from 30 to 40 GHz. In addition, the dependencies are calculated using MWS (Fig. 5). Both the calculated and measured frequency spectra are in good agreement. The relative difference of the calculated and measured frequencies does not exceed 1% and can be decreased easy by fitting the permittivity tensor. The resonator modes are identified from a comparison of the calculated and measured mode frequencies and field structures. The slight deviation of the calculated and experimental results can be explained by a systematic inaccuracy of the numerical method defined in the program, which depends on the relation

BARANNIK et al.: WHISPERING GALLERY MODE HEMISPHERE DIELECTRIC RESONATORS WITH IMPEDANCE PLANE

Fig. 5. Spectrum of the studied whispering gallery mode resonator designed from sapphire: dashed line—results of calculation (MWS), solid line—experimental results.

Fig. 6. Spectrum of whispering gallery mode hemispherical resonator designed from sapphire, calculated using MWS (for the case without a plate).

of the resonator wavelength and the dimension of the mesh cells of the studied structure. Additional resonance peaks are resolved in the calculated spectrum, and missing or weakly pronounced peaks in the measured spectrum. The deviation can be explained by the difficulty in fulfilling the identity of excitation conditions for the resonator in these two cases. modes were exIt should be noted that the quasicited in the studied resonator, containing all six components of electromagnetic fields, space distributions of which are identical modes, except that the to those of the corresponding . The modes have only five field components because quasimodes are a result of anisotropy in the material of the spherical resonator made according to [25]. In addition, the quasi-TE modes are also registered in the hemispherical resonator without any conducting plane (Fig. 6). In the case of the isotropic material, the spherical resonator made from Teflon was only excited with the TE and TM modes, which have only five field components. To study the anisotropy effect of a uniaxial single crystal on the properties of a whispering gallery mode resonator, the case cm was calculated of hemispherical resonators of

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Fig. 7. Resonance frequencies of a hemispherical whispering gallery mode resonator with different kinds of anisotropy corresponding to the case of TE and quasi-TE modes: closed symbols—TE modes, open symbols—quasi-TE modes.

numerically for dielectrics with different anisotropy. The dielectric permittivity was considered with a longitudinal (along the optical axis of crystal) component of and with a transversal (in a perpendicular direction with respect to the optical axis of crystal) component of . The is varied in the interval from 4 to 11.59. In the resonators, the optical axis was perpendicular to the conducting plane. The calculation results of resonance frequencies for two modes are shown in Fig. 7. The indices of the resonator eigenmode was identified by analyzing field distribution in the resonator. This approach is used for experimental, as well as numerical (MWS) studies. and The results demonstrate that quasimodes have only slightly different frequencies. This fact confirms that the nature of quasi-TE modes is related to the . The resonance frequencies anisotropy of sapphire modes depend weakly on in comparison with of quasiones. For the application of a hemispherical sapphire resonator in [21], [35], microwave investigations of an HTS film surface it is necessary to determine the conductor inclusion factor . This factor cannot be calculated due to a lack of electrodynamic analysis for the case of an anisotropic resonator. Work on dein veloping a technique for the determination of coefficient an anisotropic hemispherical resonator with a conducting plane measurement is under way and will be and the method of published in a separate paper.

IV. CONCLUSION The spectral and energy characteristics of a whispering gallery mode resonator in the form of a hemisphere with an impedance plane have been studied. An electrodynamic analysis of the resonator was carried out using Maxwell equations and an impedance boundary condition: the Leontovich boundary condition. It was shown that the inclusion factor of a conductor in the resonator was determined by the field distribution and frequency of the -type eigenmode in the resonator with a perfect conducting plane.

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Results of the theoretical study and experimental measurements of the Teflon resonator frequency spectrum and factor agree well. The results were also confirmed by calculations using Microwave Studio CST 2008. It was found that the electromagnetic field localizes near the impedance plane. In the case of a sapphire hemispherical resonator with an impedance plane, the results of the experiments are compared with a numerical simulation using Microwave Studio CST 2008 because, at the present, a characteristic equation and expressions for eigenmode field components in an anisotropic hemispherical resonator with an impedance plane cannot be calculated analytically. This approach allowed us to identify the -type modes in the resonator by analyzing the distribution of the electromagnetic field. It was found that, in such a resonator, the quasi-TE modes are excited together with TE modes inherent to the isotropic resonator. It was established that the and quasimodes are excited with practically identical distribution of field components, which is confirmed by the coincidence of their mode indices. In the hemisphere sapphire resand quasimode frequenonator studied, the cies differ by approximately 1 GHz. The results obtained show that high-quality hemisphere whispering gallery mode resonators can be applied in the microwave technique. In particular, they make it possible to improve the technique for measuring electrophysical parameters for different substances including HTS films. They can be used for the development of low-phase noise microwave oscillators including millimeter-wave oscillators and advanced dielectric resonator-based devices. REFERENCES [1] S. J. Fiedziuszko and S. Holme, “Dielectric resonators,” IEEE Microw. Mag., vol. 2, no. 3, pp. 51–60, Mar. 2001. [2] V. S. Ilchenko and A. B. Matsko, “Optical resonators with whisperinggallery modes—Part II: Applications,” IEEE J. Sel. Topics Quantum Electron., vol. 12, no. 1, pp. 15–32, Jan.–Feb. 2006. [3] X. H. Jiao, P. Guillon, P. Auxtmery, and L. F. Bervudes, “Whisperinggallery modes of dielectric structures: Application to millimeter wave bandstop filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 11, pp. 1169–1175, Nov. 1987. [4] S. A. Vitusevich, K. Schieber, I. S. Ghosh, N. Klein, and M. Spinnler, “Design and characterization of an all-cryogenic low phase-noise sapphire -band oscillator for satellite communication,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 163–169, Jan. 2003. [5] E. N. Ivanov and M. E. Tobar, “Low phase noise microwave oscillators with interferometic signal processing,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 8, pp. 3284–3294, Nov. 2006. [6] C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Design techniques and noise properties of ultra-stable cryogenically-cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum., vol. 79, pp. 051301-1–12, 2008. [7] S. Kharkovsky, A. Kirichenko, and A. Kogut, “Solid-state oscillators with whispering-gallery-mode dielectric resonator,” Microw. Opt. Technol. Lett., vol. 12, no. 4, pp. 210–213, 1996. [8] J. Krupka, K. Derzakowski, A. Abramowicz, M. E. Tobar, and R. G. Geyer, “Use of whispering-gallery modes for complex permittivity determinations of ultra-low-loss dielectric materials,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 752–758, Jun. 1999. [9] R. Ratheesh, M. T. Sebastian, P. Mohanan, M. E. Tobar, J. Hartnett, R. Woode, and D. G. Blair, “Microwave characterisation of BaCe Ti O and Ba Nb O ceramic dielectric resonators using whispering gallery mode method,” Mater. Lett., no. 45, pp. 279–285, 2000. [10] N. Cherpak, A. Barannik, Y. Prokopenko, Y. Filipov, and S. Vitusevich, “Accurate microwave technique of surface resistance measurement of large-area HTS films using sapphire quasioptical resonator,” IEEE Trans. Appl. Supercond., vol. 13, no. 2, pp. 3570–3573, Jun. 2003.

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[11] N. T. Cherpak, A. A. Barannik, S. A. Bunyaev, Y. V. Prokopenko, and S. A. Vitusevich, “Measurements of millimeter-wave surface resistance and temperature dependence of reactance of thin HTS films using quasi-optical dielectric resonator,” IEEE Trans. Appl. Supercond., vol. 15, no. 2, pp. 2919–2922, Jun. 2005. [12] A. A. Barannik, S. A. Bunyaev, Y. V. Prokopenko, Y. F. Filipov, and N. T. Cherpak, “HTS surface impedance measurement device,” U.S. Patent 16620, Feb. 2, 2006. [13] J. Krupka, J. Breeze, A. Centeno, N. Alford, T. Claussen, and L. Jensen, “Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 11, pp. 3995–4001, Nov. 2006. [14] J. Krupka, D. Mouneyerac, J. G. Harnett, and M. E. Tobar, “Use of whispering-gallery modes and quasi-TE0 np-modes for broadband characterization of bulk gallium arsenide and gallium phosphide samples,” IEEE Trans. Microw. Theory Tech, vol. 56, no. 5, pp. 1201–1206, May 2008. [15] M. Hein, High-Temperature Superconductor Thin Films at Microwave Frequencies,, ser. Tracts in Mod. Phys. Berlin, Germany: SpringerVerlag, 1999, vol. 155. [16] S. N. Vlasov, “On “whispering gallery modes” in open resonators with dielectric rod,” Radiotek. Elektron., vol. 12, no. 3, pp. 572–573, 1967. [17] J. K. Wait, “Electromagnetic whispering gallery modes in a dielectric rod,” Radio Sci., vol. 2, no. 9, pp. 1005–1017, 1967. [18] M. Tobar and A. Mann, “Resonant frequencies of higher order modes in cylindrical anisotropic dielectric resonators,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 2077–2083, Dec. 1991. [19] N. T. Cherpak, A. A. Barannik, Y. V. Prokopenko, and S. A. Vitusevich, “Microwave impedance characterization of large-area HTS films: Novel approach,” Supercond. Sci. Technol., vol. 17, pp. 899–903, 2004. [20] Z. Y. Shen, High-Temperature Superconducting Microwave Circuits. Boston, MA: Artech House, 1994. [21] N. T. Cherpak, A. A. Barannik, and S. A. Bunyaev, “Quasi-optical dielectric resonator-based technique of HTS film millimeter-wave surface resistance measurements: Three types of resonators,” in Proc. 38th Eur. Microw. Conf., Amsterdam, The Netherlands, Oct. 2008, pp. 807–811. [22] S. Kharkovsky, Y. Filipov, and Z. Eremenko, “Whispering gallery modes of an open hemispherical image dielectric resonator,” Microw. Opt. Technol. Lett., vol. 21, no. 4, pp. 252–257, 1999. [23] A. A. Barannik, S. A. Bunyaev, and N. T. Cherpak, “Hemispherical quasi-optical dielectric resonators as possible sensors for impedance measurement of superconductors,” in Proc. 5th Int. Phys. Eng. Millimeter and Sub-Millimeter Waves Symp., Kharkov, Ukraine, Jun. 2004, pp. 430–432. [24] A. A. Barannik, S. A. Bunyaev, N. T. Cherpak, and S. A. Vitusevich, “Quasi-optical dielectric resonators in the form of a truncated cone,” J. Lightw. Technol., vol. 26, no. 17, pp. 3118–3123, Sep. 2008. [25] Y. V. Prokopenko, T. A. Smirnova, and Y. F. Filipov, “Eigenmodes of an anisotropic dielectric ball,” Tech. Phys., vol. 49, no. 4, pp. 459–465, 2004. [26] J.-M. LeFloch, J. D. Anstie, M. E. Tobar, J. G. Hartnett, P.-Y. Bourgeois, and D. Cros, “Whispering modes in anisotropic and isotropic dielectric spherical resonators,” Phys. Lett. A, vol. 359, no. 1, pp. 1–7, 2006. [27] Y. V. Prokopenko, Y. F. Filippov, I. A. Shipilova, and V. M. Yakovenko, “Whispering gallery modes in a hemispherical isotropic dielectric resonator with a perfectly conducting planar surface,” Tech. Phys., vol. 51, no. 2, pp. 248–257, 2006. [28] Y. V. Prokopenko and Y. F. Filippov, “Anisotropic disk dielectric resonator with conducting end faces,” Tech. Phys., vol. 47, no. 6, pp. 731–736, 2002. [29] A. M. Fatih, Y. Prokopenko, and S. Kharkovsky, “Resonance characteristics of whispering gallery modes in parallel-plates-type cylindrical dielectric resonators,” Microw. Opt. Technol. Lett., vol. 40, no. 2, pp. 96–101, 2004. [30] A. A. Barannik, Y. V. Prokopenko, Y. F. Filippov, N. T. Cherpak, and I. V. Korotash, “ factor of a millimeter-wave sapphire disk resonator with conductive end plates,” Tech. Phys., vol. 48, no. 5, pp. 621–625, 2003. [31] L. A. Vainstein, Electromagnetic Waves. Moscow, Russia: Sov. Radio, 1957. [32] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media. New York: Cambridge Univ. Press, 1992. [33] T. Van Duzer and C. W. Turner, Principles of Superconductive Devices and Circuits. New York: Elsevier, 1981.

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BARANNIK et al.: WHISPERING GALLERY MODE HEMISPHERE DIELECTRIC RESONATORS WITH IMPEDANCE PLANE

[34] J. Krupka and J. Mazierska, “Single-crystal dielectric resonators for low-temperature electronics applications,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 7, pp. 1270–1274, Jul. 2000. [35] A. A. Barannik, S. A. Bunyaev, and N. T. Cherpak, “On the low-temperature microwave response of a YBCO epitaxial film determined by a new measurement technique,” Low Temp. Phys., vol. 34, no. 12, pp. 977–981, 2008. Alexander A. Barannik was born in Kharkov, Ukraine, on April 23, 1975. He received the Diploma degree in cryogenic technique and technology from the Kharkov State Polytechnic University, Kharkov, Ukraine, in 2000, and the Ph.D. degree (physical and mathematical sciences) in radiophysics from the Kharkov National University of Radio Electronics, Kharkov, Ukraine, in 2004. Since 2000, he has been with the Institute of Radiophysics and Electronics, National Academy of Science of Ukraine, Kharkov, Ukraine, as a Junior Researcher (2000), Scientific Researcher (2005), and Senior Scientific Researcher (2007). He has coauthored over 50 scientific publications. He holds three patents. His scientific activities include the study of microwave characteristics of condensed matter, including HTS, dielectrics, and liquids by using whispering-gallery mode (WGM) dielectric resonators. He also studies electrodynamic properties of various types of WGM resonators. Sergey A. Bunyaev (S’09) was born in Kharkov, Ukraine, on November 29, 1980. He received the B.S. and M.S. degrees in electronics from the Kharkov National University of Radio Electronics, Kharkov, Ukraine, in 2001 and 2002, respectively, and the Ph.D. degree (physical and mathematical sciences) in solid-state radiophysics from the Institute of Radiophysics and Electronics, National Academy of Science of Ukraine, Kharkov, Ukraine, in 2010. From 2002 to 2009, he was with the Department of Solid State Radiophysics, Institute of Radiophysics and Electronics, National Academy of Science of Ukraine, Kharkov, Ukraine, as an Engineer (2002), doctoral student (2004), and Junior Researcher (2008). Since 2010, he has been with IFIMUP and IN-Institute of Nanoscience and Nanotechnology, Departamento de Fisica da Faculdade de Ciencias, Universidade do Porto, Porto, Portugal. He has coauthored over 20 scientific publications. He holds two patents. His research interests include electromagnetics of microwave resonant structures, microwave high-T superconductivity, and magnetic dynamics of patterned magnetic nanoelements and their arrays. Nickolay T. Cherpak (M’01–SM’02) received the Ph.D. degree in radiophysics (including quantum radiophysics) from the Institute of Low Temperature Physics and Engineering, Kharkov, Ukraine, in 1970, and the Dr.Sc. degree in radiophysics from the Leningrad Polytechnic Institute (now Technical University), St. Petersburg, Russia, in 1987. He is currently a Team Manager with the Department of Solid State Radiophysics, Institute for Radiophysics and Electronics, National Academy of Science of Ukraine, Kharkov, Ukraine, and a Professor with the Department of Technical Cryophysics, National Technical UniversityKhPI, Kharkov, Ukraine. In 1991, he was a Visiting Researcher with the University of Wuppertal, Wuppertal, Germany. In 2004, he was a Visiting Professor with the Institute of Physics, Chinese Academy of Sciences, Beijing, China. He has authored or coauthored about 280 papers in refereed journals and reports in scientific conferences. He authored Millimeter-Wave Solid-State Maser Amplifiers of Distributed Type (Naukova Dumka, 1996) and coauthored Quasi-Optical Solid-State Resonators (Naukova Dumka, 2009). He has also authored three scientific reviews. He holds 20 patents on various topics in microwave and millimeter-wave techniques. His current activity is in the area of development of techniques for millimeter-wave characterization of condensed matter, including

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high-temperature superconductors and lossy liquids. He is also interested in the millimeter-wave physical study of condensed matter, especially high-temperature superconductors and electrodynamic properties of whispering-gallery mode (WGM) dielectric resonators. Prof. Cherpak is a chairman of Commission E of the Ukrainian National URSI Committee. He was a program member of EuMW (2009 and 2010) and MMSW (1998, 2001, 2004, 2007, and 2010). He was the 1999 recipient of the I. Puljuy Award of Presidium of the National Academy of Sciences of Ukraine. Yurii V. Prokopenko was born in the Kurgan Region, Russia, on October 20, 1961. He received the Diploma degree in radiophysics and electronics from the Kharkov State University, Kharkov, Ukraine, in 1987, the Ph.D. degree (physical and mathematical sciences) from the National Scientific Centre Kharkov Institute of Physics and Technology, Kharkov, Ukraine, in 1993, and the D.S. degree (physical and mathematical sciences) from the Usikov Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine, in 2007. From 1987 to 1994, he was a Researcher Fellow and from 1994 to 2000, he was a Senior Researcher with the National Scientific Centre Kharkov Institute of Physics and Technology. In 2000, he joined the Institute of Radiophysics and Electronics, National Academy of Scinces of Ukraine. He was involved with theoretical and experimental investigations of microwave oscillations and antennas, theoretical and experimental radiophysics, physics of charge particle,s and the accelerator technique. He has authored or coauthored over 120 publications, and one monograph. He holds six invention certificates. He coauthored a high-power pulse microwave generator of a vircator type with a controlled feedback that was called the virtod. His current research activity includes theoretical electrodynamics of dielectric (and also semiconductor and ferrite) cylindrical, sphere, and hemisphere resonators. Anna A. Kharchenko (S’08) was born in Kharkov, Ukraine, on February 22, 1986. She received the B.S. and M.S. degrees in mathematics and computer science from the Kharkov National University of Radioelectronics, Kharkov, Ukraine, in 2007 and 2008, respectively, and is currently working toward the Ph.D. degree at the Usikov Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine. She has coauthored over ten scientific publications. Her main research interests are experimental microwave radiospectroscopy of periodical structure (metamaterials), investigation of Tamm-states, left-handed media (LHM) properties, metamaterial applications, and quasi-optical resonators. Svetlana A. Vitusevich received the M.Sc. degree in radiophysics and electronics from Kiev State University, Kiev, Ukraine, in 1981, and the Ph.D. degree in physics and mathematics and Dr.habil degree from the Institute of Semiconductor Physics (ISP), Kiev, Ukraine, in 1991 and 2006, respectively. From 1981 to 1997, she was with the ISP as Researcher (1981), Scientific Researcher (1992), and Senior Scientific Researcher (1994). From 1997 to 1999, she was an Alexander von Humboldt Research Fellow with the Institute of Bio- and Nanosystems (IBN) (formerly the Institute of Thin Films and Interface), Forschungszentrum Jülich (FZJ), Jülich, Germany. Since 1999, she has been a Senior Scientific Researcher with the FZJ. She has authored or coauthored 110 papers in refereed scientific journals. She holds eight patents, among which two of them are for semiconductor functional transformers. Her research interests include transport and noise properties of different types of materials for advanced electronic devices and circuits.

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High-Reliability RF-MEMS Switched Capacitors With Digital and Analog Tuning Characteristics Alex Grichener, Member, IEEE, and Gabriel M. Rebeiz, Fellow, IEEE

Abstract—This paper presents an RF microelectromechanical system switched-capacitor suitable for tunable filters and reconfigurable networks. The switched-capacitor results in a digital capacitance ratio of 5 and an analog capacitance ratio of 5–9. The analog tuning of the down-state capacitance is enhanced by a positive vertical stress gradient in the the beam, making it ideal for applications that require precision tuning. A thick greater than 100 at electroplated beam (4–4.5 m) results in – -band frequencies, switching times of 30–50 s, and power handling of 0.6–1.1 W. The design also minimizes charging in the dielectric, resulting in excellent reliability performance even under hot-switched and high-power (1 W) conditions. Index Terms—Reconfigurable network, reliability, RF microelectromechanical systems (MEMS), tunable capacitor, tunable filter.

and their effect on switch reliability. The design allows for the switched capacitor to be operated with no applied electric field across the dielectric layer, and therefore, has resulted in high-reliability operation under high RF power. Previous work have also bypassed dielectric charging by featuring a dielectricless design [3], [4], but at the expense of a lower capacitance ratio. In this design, a capacitance ratio of 5–9 is achieved, and part of this capacitance region is obtained using an analog regime, thereby allowing fine capacitance control, which is essential for tunable filters. The RF MEMS switched-capacitor has a high ( 200 at 5 GHz) and has been used in several high- tunable filters with excellent performance [5], [6]. II. DESIGN

I. INTRODUCTION F microelectromechanical systems (MEMS) switches and switched capacitors have emerged as a high-performance technology with very low loss and high linearity for use in switching networks, impedance matching networks, tunable filters, and phase shifters [1]. In particular, the Radant MEMS metal-contact switch and the Massachusetts Institute of Technology (MIT) Lincoln Laboratories and Raytheon capacitive switches have all shown excellent reliability ( 100-B cycles) and power handling ( 1 W). Metal-contact switches result in medium- (50–100) tunable networks due to their 1–2contact resistance. Capacitive switches, on the other hand, have and result in high- (100–200) a resistance of 0.25–0.5 tunable circuits at 1–6 GHz. These devices can be arrayed with fixed capacitors in a switched-capacitor bank, which is an essential variable impedance element in a tunable network. This paper presents an RF MEMS switched capacitor that is based on a thick metal process, which is ideal for 1–10-GHz applications. The work goes beyond what was done before [2] by studying the effect of cantilever beam thickness and associated vertical stress gradient, and the effect of incident RF power on the resulting device performance. This paper also advances a deeper understanding of various charging mechanisms at work

R

Manuscript received June 15, 2010; revised June 17, 2010; accepted June 17, 2010. Date of publication September 16, 2010; date of current version October 13, 2010. This work was supported by the Defense Advanced Research Projects Agency (DARPA) Science and Technology Center, University of California at Davis (UCSD)—RF MEMS Reliability and Design Fundamentals. The authors 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]). 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.2010.2065892

Fig. 1 presents the top view and cross section of the RF MEMS switched capacitor. The device is based on a thick electroplated cantilever with an isolated actuation electrode. ( , the pull-in voltage) is applied to When a voltage the actuation electrode, the cantilever beam is pulled down and touches the RF electrode, resulting in a capacitance ratio of 5. However, the capacitance ratio can be increased to 7–9 or by applying a small voltage to the RF by increasing electrode ( 10 V). This results in a movement of the cantilever, which brings the beam tip closer to the dielectric and increases the contact area (zipping effect). There are many degrees of freedom in the cantilever design depending on the requirements. The spring constant is mostly dependent on the cantilever thickness and length as . Since a higher spring constant is desirable for a robust mechanical design, the length of the cantilever was limited to less than 200 m. It is possible to increase the thickness of a long cantilever and maintain the same spring constant, but this results in a large structure and consequently a slower switching speed. The width of the cantilever was also limited to less than 200 m in order to prevent excessive curling (due to a vertical stress gradient) at the corners of the beam tip. Once the area of the cantilever beam is chosen, the overlap area between the beam and dc electrode, as well as the RF electrode, is determined. A larger overlap with the RF electrode will result in a higher capacitance, but at the expense of a smaller overlap with the dc electrode resulting in a higher is a straightforward compropull-in voltage. The air gap mise between the capacitance ratio and pull-in voltage given by kg . The device with dimensions shown in Fig. 1 was achieved with a requirement of a maximum dc operating voltage of 80 V, fF (with 10%–30% analog tuning of ), a

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Fig. 1. (top) Top view, (middle) cross section in up-state, and (bottom) cross section in down-state of switched capacitor with z -axis expanded 10 (all dimensions given in micrometers).

2

switching time of less than 50 s, and excellent yield for a ver2 MPa/ m. tical stress gradient in the cantilever beam of Since many different parameters also depend on the beam thickness (such as electrical/mechanical , switching time, power handling, spring constant, etc.), the thickness was limited to a range of 3.5–4.5 m due to the plating process. For example, an important tradeoff is while a thicker device results in shorter switching times and higher power handling, it also has a higher pull-in voltage and a smaller analog tunable range. The resulting device is 140 160 m with an air gap of 1.5 m and an RF overlap area of 36 160 m . At 2–4 GHz, eight cantilevers can be used in parallel to result in a total capacitance of 0.4/2.0 pF [6]. This solution is mechanically more robust and with higher yield than using two cantilevers, which are four times larger in area (slower switching speed, greater sensitivity to stress gradients, etc.). Fig. 2 presents the simulated spring constant, resonance freand release voltage quency, mechanical , pull-in voltage , and pull-in time and release time as a function of beam thickness. A Young’s modulus of 35 GPa taken from prior measurements on electroplated gold [7] is used in all mechanical simulations. Two spring constants are plotted, which are: 1) (natural spring constant) defined as displacement at the tip due to a distributed force over the entire beam and 2) (actuation spring constant) defined as displacement at the tip due to a distributed force above the actuation electrode. The natural spring constant is used to solve for the release time when no voltage is applied and the tip is touching the RF electrode. The actuation spring constant is used to solve for the pull-in time. The damping force encountered by the 96 160 m gold plate was simulated with CoventorWare [8] with a correction

Fig. 2. Simulated electromechanical parameters plotted as a function of beam thickness.

for the Knudsen number (0.045), which effectively lowered the viscosity by 20% [1]. Edge correction was also used for the three moving edges to model the corner-turning resistance. The resulting damping coefficient at 30–40 kHz is 390 N/(m/s) and is independent of plate thickness. Simulations also showed that the additional spring constant generated by the squeezed film damping effect was small enough to be neglected. The release and pull-in behavior are described by (1) and (2) with a zero external force and an applied electrostatic force, respectively. This results in two different quality factors, given by the natural spring constant and by the actuation , respectively. The effective mass spring constant and are equal is calculated such that both to . A beam thickness of 4–4.5 m results in a of 0.5–0.6 and a switching time of less than 50 s release

(1) pull-in

(2)

The simulated pull-in and release voltages are almost identical because the device does not actually collapse down to the actuation electrode, but is stopped when the tip touches the dielectric. For the given design, the increase in damping with dis-

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Fig. 3. Simulated C –V curve with hysteresis where

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 10, OCTOBER 2010

1 = 0 .

placement [1] results in a slightly longer pull-in time. Therefore, (2) will slightly underestimate the pull-in time. Fig. 3 shows the simulated – curves for a cantilever beam with no stress gradient. In these simulations, an was used for the dielectric and results in a down-state capaccan then be extracted using itance of 322 fF. An . The reason is low is because, as will be seen later in the simulated down-state profile [see Fig. 5(a)], the beam is not flush with the dielectric in the down-state and the . Simulations also resulting air gap significantly degrades of 20 V above the pull-in show that, for each thickness, a voltage (Fig. 3) corresponds to a change in the electrostatic of around 150 N. This increases by 85–47 fF force in a 3.5–4.5- m device, respectively. As expected, a thinner device results in a lower and a larger tuning range in the down-state position. A. Vertical Stress Gradient Effects The cantilever beam curls upwards or downwards depending on the stress gradient polarity. For a two-layer beam, the deflection at the tip due to a stress gradient is given by [1] (3) where is the stepped stress gradient is the effective Young’s modulus calculated and using Poisson’s ratio for gold . The simulated dem flection (using CoventorWare) in the -direction for MPa/ m is shown in Fig. 4(a). Table I presents and the calculated tip deflection using (3) and the simulated tip de. flection averaged across the width of the cantilever beam Excellent agreement is seen between (3) and CoventorWare. Finite-element method (FEM) simulations show that a stress gradient in the cantilever beam can significantly impact the resulting – curve. Fig. 4(b) and (c) shows the – and – curves of a 4.0- m-thick beam with three different stress gra) results in a significant dients. A downward curl (negative depreciation of the down-state capacitance and poor tuning with and (a partial collapse of the beam occurs at V). An upward curl, on the other hand, results in a high down-state capacitance with an excellent linear tuning range with both and .

2

Fig. 4. Simulated cantilever. (a) Up-state profile (z -axis expanded 25). (b) C –V curves with hysteresis. (c) C –V curves with hysteresis where  : m. is in the range of 2–2 MPa/m and t

0

=40

1

TABLE I CALCULATED AND SIMULATED TIP DEFLECTION AND UP-STATE CAPACITANCE AS A FUNCTION OF 

1

Simulated cross sections of a 4.0- m beam with three different stress gradients [see Fig. 5(a)] show that an upward curled beam is most flush with the dielectric in the down-state (although the corners at the beam tip are slightly lifted, which is is not higher), and therefore, can be deformed why the initial more easily with an electrostatic force at the actuation electrode or at the RF electrode . A beam with a downward curl,

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Fig. 6. Fabricated devices shown in: (a) one-port and (b) two-port configurations.

Fig. 7. Circuit model of: (a) one-port and (b) two-port device. Fig. 5. Simulated down-state profile of a 4.0-m-thick beam with z -axis expanded 25 where: (a)  ; ; MPa/m and (b)  MPa/m with different V and V applied.

2

1 = 02 0 +2

1 = +2

on the other hand, makes a larger angle with the dielectric in the down-state, and therefore, results in a smaller down-state capacitance and tuning range. The cross section of a beam with an MPa/ m) pulled down with different upward curl ( voltage combinations is shown in Fig. 5(b).

beams. Finally, the second metal is etched, the cantilevers are released in a standard photoresist stripper, and the sample is dried in a CO critical point dryer. The fabricated devices are shown in Fig. 6. As seen in the one-port configuration, the pad is dc isolated from the coplanar waveguide (CPW) ground using a large metal–insulator–metal (MIM) capacitor (14.5 pF). IV. MEASUREMENTS A. RF

III. FABRICATION The RF MEMS devices are fabricated on a 500- m-thick quartz substrate and are implemented in a CPW configuration. First, a SiCr layer (1200 Å) is sputtered and patterned to form the high-resistance bias lines. Second, a metal layer consisting of Ti/Au (200 Å/3000 Å) is sputtered and patterned to form the bottom electrodes. An Si N layer (0.15 m) is then deposited with PECVD and patterned with reactive ion etching (RIE) to form the dielectric layer. A PMMA layer (1.5 m) is coated as the sacrificial and patterned with RIE. Next, a second metal layer consisting of Ti/Au/Ti (200 Å/3000 Å/200 Å) is sputtered and selectively electroplated to form the 3.5–4.5- m-thick

The device circuit models are shown in Fig. 7 and the corresponding measured and fitted -parameters are shown in Fig. 8. For a flat beam, the fitted up-state capacitance is 48 fF and the down-state capacitance is 240 fF. The relationship between the measured and simulated capacitance and vertical stress gradient is 37–53 fF, is shown in Fig. 9. It is seen that the measured and is in excellent agreement with simulations. The is calcuof a one-port device, which does lated from the measured not yield accurate results for greater than 100 (see error bars of around 0.5 is extracted from the meain Fig. 10). An surements, and is dominated by the loss of the RF electrode, which is 0.3- m thick.

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Fig. 10. Extracted up- and down-state Q with error bars.

Fig. 8. Measured and fitted S -parameters of: (a) one-port and (b) two-port device.

Fig. 9. Measured and simulated up- and down-state capacitance (and resulting ratio) as a function of stress gradient.

– curves were obtained by fitting the measured -parameters to the circuit models. As predicted by the FEM simulations, the down-state capacitance tuning slope is enhanced with a positive stress gradient (upward curl) and a thinner beam (Fig. 11). Measurements also show that the 4.0- m cantilever pulls in at 54 V, while the 4.5- m cantilever pulls in at 65 V, which is in excellent agreement with the simulated pull-in voltages (Fig. 2). B. Mechanical Measurements The setup in Fig. 12 can be adapted to different mechanical measurements. For the mechanical resonance frequency and

= 4:0 m and 1 = +1 MPa/m. = 4 0 4 5 m and 1 =

Fig. 11. (a) Measured C –V curves with hysteresis where t  ; MPa/m and where t : m and  : ; : (b) Measured C –V curves with hysteresis where t MPa/m.

1 = 0 +1 +1

= 45

measurement, the function generator is used to excite the cantilever beam with a sinusoidal voltage and a dc-offset voltage. This results in an amplitude modulation (AM) for an RF signal passing through the two-port device and the resulting spectrum is detected using a spectrum analyzer [1]. The resonance frequency and are extracted by fitting the measured AM response to a normalized second-order system (Fig. 13 and Table II). Note that the extracted is the actuation since the device is being displaced with a voltage at the acis lower than simulated for tuation electrode. The extracted

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Fig. 12. Core measurement setup used for resonance frequency, switching time, power, and reliability measurements.

t = 3:5–4:5 m. (b) Measured V =V = 1:00–1:25.

Fig. 14. (a) Measured release time shown for pull-in time ( m) shown for

t = 4:0 

C. Power Handling RF power incident on a two-port device induces an effec, which is plotted in Fig. 15(a), for both the up- and tive down-state positions. This rms voltage generates an electrostatic force on the cantilever and decreases both its pull-in and release voltage. It also increases the release switching time. These are plotted in Fig. 15 as a function of the incident power level at 10 GHz. It is seen that a 4–4.5- m device can handle 0.6–1.1 W before failing to release in a hot-switched condition. Fig. 13. Measured and fitted mechanical gain as a function of excitation frequency for three different beam thicknesses.

TABLE II , AND SWITCHING MEASURED RESONANCE FREQUENCY, TIMES AS A FUNCTION OF BEAM THICKNESS

Q

D. V

Versus Temperature

The temperature stability of a device ( m) was studied by measuring the change in the pull-in voltage as a function of temperature (Fig. 16). Measurements show the pull-in voltage decrease by 3 V with a 100 C change in temperature. This is most likely due to gold softening at the higher temperatures leading to a decrease in the spring constant. E. Reliability Tests

a 3.5- m beam, and higher than simulated for a 4.5- m beam. The discrepancy is due to stress gradients in the fabricated devices and the resulting gap deviation from . To measure the switching time, a two-port device was hot switched with a 50% duty cycle unipolar square waveform and the resulting power detector output was used to record the switching dynamics (Fig. 14 and Table II). Overall there is good agreement between measured and calculated release times, while the measured pull-in times are 20%–40% longer than calculated for reasons discussed in Section II.

The reliability of the device was studied with a setup similar to one used by Blondy et al. (Fig. 12) [9]. The response of a device hot switched with three different bias waveforms (shown in Fig. 17) applied to the actuation electrode was measured using an RF power detector connected to an oscilloscope. The incident (rms). RF power was limited to 100 mW so as not to induce a Every bias waveform included two successive triangular pulses of opposite polarity (each 15-ms wide), which allowed for an automated detection (with the help of a PC) of both the positive and negative pull-in and release voltage. The triangular pulses were applied at a frequency of 1 Hz, and therefore, lasted for 3% of the time. The other 97% of the bias waveform, depending on the specific experiment, consisted of one of the following:

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Fig. 17. Three typical bias conditions that allow for an automatic recording (with the use of narrow triangular pulses) of the evolution of V and V .

then pulled down with a unipolar [see Fig. 18(a)]. The steady decrease of and is indicative of bulk charging, which is caused by the injection of positive charge by the electrode, into the quartz substrate. This is different from top charging, which is caused by the injection of negative surface charge by the cantilever beam into the dielectric, as shown in Fig. 19. The change and can be fitted to a Curie-Von Schweidler equation in [9] as (4) Fig. 15. (a) Calculated effective V (rms) in the up- and down-state positions. Measured: (b) release voltage and (c) release time for t : – : m as a function of incident RF power at 10 GHz.

= 35 45

Fig. 16. Measured pull-in voltage as a function of temperature (t Data from [2].

= 4:0 m).

1) (discharge mode); 2) Unipolar (unipolar (bipolar charge mode). charge mode); and 3) bipolar and could be automatically In this way, the evolution of recorded under different biasing conditions. Charging effects induced by a unipolar voltage at the actua) were characterized by measuring tion electrode (with and . To get a baseline, the setup was the evolution of run in discharge mode for the first half hour, and the switch was

V, s, and . with Fig. 18(a) shows that after around 5 h of charging, and a and , the switch quickly recovers shift of 11–12 V in to a steady-state condition when released. The short recovery time constant is further evidence of bulk charging where the path from the charge traps to the closest conductor is relatively short, as compared to top charging [11], [12]. However, it is seen that the switch does not recover to its original pull-in and release voltages, which is indicative of additional charging mechanisms with much slower discharge time constants, such as surface charging due to humidity in the surrounding ambient atmosphere [13]. and due to a In a similar fashion, the evolution of bipolar voltage at the actuation electrode (with ) were V, s, and [see measured and fitted with Fig. 18(b)]. Note that the pull-in and release voltages nearly recover to their original levels. The excellent fit to the given exponentials is consistent with previous charging measurements in dielectricless capacitive RF MEMS [9]. for a given duty cycle can be exThe voltage shift , where pressed as is the voltage % % shift due to a 100% duty cycle [9]. Also, an extrapolation of the Curie-Von fit allows for a prediction of the switch lifetime: if only substrate charging is considered for the case of unipolar actuation, then it would take 24 days for to fall to zero (stuck down) with a 100% duty cycle and 240 days with a 50% duty

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Fig. 20. Simulated electric field distribution in air gap and quartz substrate of switch in down-state position with 60-V applied to actuation electrode and with RF electrode and beam grounded.

Fig. 21. Evolution of measured pull-in voltage when the device is pulled down V: unipolar and bipolar. with a bipolar V and V

= 10

Fig. 18. Evolution of measured and fitted pull-in and release voltage when the device is pulled down with: (a) unipolar V and (b) bipolar V .

Fig. 19. Two charging mechanisms shown: bulk charging in the quartz substrate and top charging in the dielectric.

cycle. The values are 24 and 768 years, respectively, for bipolar actuation. A 2-D electrostatic simulation of the electric field distribuV was performed using Maxwell SV [10]. tion with Fig. 20 shows that most of the electric field is contained inside the air gap between the beam and actuation electrode. However, the field also expands several micrometers into the substrate underneath the edge of the electrode. The simulated field magnitude in this region is 10–30 MV/m, which is sufficient to induce charge injection. Charging effects produced by a unipolar and bipolar voltage V) at the RF electrode was also studied. Fig. 21 shows ( the evolution of the pull-in voltage when the switch is pulled V unipolar and down with a bipolar , and with V bipolar. Before the application of a , the switch was left in the down-state with a bipolar for over 2 h in order

to allow substrate charging to stabilize so that the effect of a could be studied nearly independently of substrate charging. The measurement shows that a unipolar causes the to increase by almost 2 V before stabilizing at the 4-h mark, while does not result in a significant shift of . This a bipolar demonstrates the importance of using only a bipolar voltage at the RF electrode. PECVD Si N introduces a high density of charge traps associated with silicon dangling bonds [14]. An increase in the pull-in voltage suggests an injection of top charge into the dielectric, which sets up an electric field that directly opposes the applied field. It is important to note that all charging experiments were performed in ambient atmosphere. In contrast to bulk charging, surface charging can be significantly impacted by humidity [11], and Si N is susceptible to moisture-related surface charging. This is unexpected because Si N is generally hydrophobic. However, it can be made hydrophilic after aggressive surface treatments such as oxygen plasma cleaning [15], which was the case with devices used here. For the time duration that the dielectric is subjected to , the accumulation of injected charge can be modeled as [14] (5) where is the charging time constant of the species of trap, is the corresponding steady-state charge density and is and by related to (6)

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Fig. 22. Evolution of measured and fitted release voltage when the device is pulled down with a bipolar V and V V unipolar.

= 10

where and are fitting parameters for each species of trap. The voltage shift that results from the trapped charge sheet is given by (7) where is the distance between the bottom electrode and the was limited charge sheet (typically a fitted parameter). Since to 10 V, the charge time constants of the nitride are seen most clearly by measuring the shift in the release voltage. Fig. 22 shows the measured release voltage immediately dropping to V unipolar (this is ex16 V with an application of is applied pected), and then slowly rising to 45 V. As before, for at to a switch that has been pulled down with a bipolar least several hours. It follows from (5)–(7) that the change in the . release voltage can be fitted to A good fit is achieved with two species of charge traps (where V and h), as shown in Fig. 22. Charging also leads to a change in the down-state capacitance for each of over time. Fig. 23 shows the measured change in the four voltage combinations studied previously. It is seen that , and also a bipolar the application of a bipolar and results in a stable down-state capacitance over time. As expected, bulk charging due to a unipolar acts to increase the down-state capacitance, while top charging due to a unipolar acts to decrease the down-state capacitance. Several high-cycle tests were performed with different bias waveforms. The first test was performed in ambient atmosphere using the standard setup (Fig. 12). A 4.5- m device was hotswitched with 29 dBm of incident RF power at 10 GHz with a 4-kHz 50% duty cycle unipolar bias waveform of amplitude (the beam and RF electrode were dc grounded). 1.1 times It is known that incident RF power can accelerate charging by raising the temperature of the MEMS device [16]. The bias waveform and power detector output were monitored on an oscilloscope and are shown in Fig. 24 at the start of the test and after 17 days of continuous switching (a total of 6 billion cycles). – curves, measured before and after the high-cycle test, showed a 15% increase in the up-state capacitance, which is attributed to substrate charging, and a 10% decrease in the down-state capacitance, which is attributed to the accumulation of contaminants in the area where the beam touches the dielectric.

Fig. 23. Evolution of measured down-state capacitance when the device is pulled down with: (a) bipolar V and unipolar V and (b) bipolar V and V V unipolar and V V bipolar.

10

=

= 10

Fig. 24. Power detector output recorded at beginning and end of reliability test.

A second high-cycle test was again performed in ambient atmosphere with another 4.5- m device. The device was hot switched with 29 dBm of incident RF power at 12 GHz. The main difference was that the bias waveform used was bipolar (8-kHz switching frequency, 50% duty cycle, and amplitude ). The device switched for 15.5 days equal to 1.2 times (10.5 billion cycles) before a similar drift of the power detector voltage was observed, as in the previous test. V. CONCLUSION This paper has demonstrated a cantilever-based RF MEMS switched capacitor with digital and analog tuning capabilities, which is ideal for 1–10-GHz applications. The design features two independent electrodes under the beam, allowing for precise control of the capacitance, resulting in an up- and down-state capacitance of 50 fF/250 fF. A beam with a positive stress gradient

GRICHENER AND REBEIZ: HIGH-RELIABILITY RF-MEMS SWITCHED CAPACITORS

(upward curl) has been found to be more flush with the dielectric in the down-state position, resulting in a tunable capacitance ratio of 5-9. Measurements also showed that a beam thickness of 4–4.5 m is optimal and results in a pull-in voltage of 50–65 V, a switching time of less than 50 s, and a greater than 200 at 5 GHz. The power handling was limited by an induced (rms), which caused the switch to not release in hot-switched conditions with greater than 1.1 W of incident RF power at 10 GHz m). An investigation of the various charging mecha( nisms also revealed that a bipolar voltage at the actuation electrode minimizes bulk substrate charging and a bipolar voltage at the RF electrode ( 10 V) minimizes top charging in the dielectric layer. Separating the electrodes also allows the device to be operated with a relatively low electric field across the dielectric. This results in high-reliability performance with greater than 10-B cycles demonstrated under hot switched and high-power conditions. ACKNOWLEDGMENT The authors would like to thank J.-M. Kim, Chonbuk National University, Jeonju, Korea, and B. Lakshminarayanan, Skyworks, Boston, MA, for their help with the project. REFERENCES [1] G. M. Rebeiz, RF MEMS Theory, Design, and Technology. New York: Wiley, 2003. [2] 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. [3] A. Grichener, D. Mercier, and G. M. Rebeiz, “High-power high-reliability high- switched RF MEMS capacitors,” in IEEE MTT-S Int. Microw. Symp. Dig., San Fransisco, CA, Jun. 2006, pp. 31–34. [4] P. Blondy, A. Crunteanu, C. Champeaux, A. Catherinot, P. Tristant, O. Vendier, J. L. Cazaux, and L. Marchand, “Dielectric less capacitive MEMS switches,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, vol. 2, pp. 573–576.

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[5] S. J. Park, I. Reines, and G. M. Rebeiz, “High- RF-MEMS tunable evanescent-mode cavity filter,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 2, pp. 381–389, Feb. 2010. [6] M. A. El-Tanani and G. M. Rebeiz, “High performance 1.5–2.5-GHz RF MEMS tunable filters for wireless applications,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 6, pp. 1629–1637, Jun. 2010. [7] C. W. Baek, Y. K. Kim, Y. Ahn, and Y. H. Kim, “Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures,” Sens. Actuators A, vol. 117, pp. 17–27, 2005. [8] CoventorWare ver. 2008, Coventor, Cary, NC, 2008. [Online]. Available: http://www.coventor.com [9] D. Mardivirin, A. Pothier, A. Crunteanu, B. Vialle, and P. Blondy, “Charging in dielectricless capacitive RF-MEMS switches,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 1, pp. 231–236, Jan. 2009. [10] Maxwell SV Ansoft Corporation, Pittsburgh, PA, 2004. [Online]. Available: http://www.ansoft.com/maxwellsv [11] Z. Peng, C. Palego, J. C. M. Hwang, D. I. Forehand, C. L. Goldsmith, C. Moody, A. Malczewski, B. W. Pillans, R. Daigler, and J. Papapolymerou, “Impact of humidity on dielectric charging in RF MEMS capacitive switches,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 5, pp. 299–301, May 2009. [12] Z. Peng, X. Yuan, J. C. M. Hwang, D. Forehand, and C. L. Goldsmith, “Top vs. bottom charging of the dielectric in RF MEMS capacitive switches,” in Asia–Pacific Microw. Conf., Yokohama, Japan, Dec. 2006, pp. 1535–1538. [13] P. Blondy, A. Crunteanu, A. Pothier, P. Tristant, A. Catherinot, and C. Champeaux, “Effects of atmosphere on the reliability of RF-MEMS capacitive switches,” in Eur. Microw. Integr. Circuit Conf., Munich, Germany, Oct. 2007, pp. 548–550. [14] X. Yuan, J. C. M. Hwang, D. Forehand, and C. L. Goldsmith, “Modeling and characterization of dielectric-charging effects in RF MEMS capacitive switches,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2005, pp. 753–756. [15] C. Cheung, K. Luo, D. Li, P. Ngo, L. Dang, J. Uyeda, J. Wang, and M. Barsky, “Silicon nitride surface preparation to prevent photoresist blister defects,” in GaAs Manuf. Technol. Conf. Dig., 2005, p. 14.10. [16] D. Mardivirin, A. Pothier, J. C. Orlianges, A. Crunteanu, and P. Blondy, “Charging acceleration in dielectric less RF MEMS switched varactors under CW microwave power,” in IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2009, pp. 1649–1652. Alex Grichener (S’02–M’03), photograph and biography not available at time of publication.

Gabriel M. Rebeiz (S’86–M’88–SM’93–F’97), photograph and biography not available at time of publication.

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Considerations for Developing an RF Exposure System: A Review for in vitro Biological Experiments Alessandra Paffi, Francesca Apollonio, Member, IEEE, Giorgio Alfonso Lovisolo, Carmela Marino, Rosanna Pinto, Michael Repacholi, and Micaela Liberti, Member, IEEE

Abstract—This paper provides a detailed review and classification of exposure systems used in RF in vitro research from 1999 up to 2009. Since different endpoints and protocols are used in bioelectromagnetics studies, exposure systems cannot be standardized. However, a standardized procedure to achieve the optimum design of the exposure system is suggested. Following this procedure will lead to a known dose distribution within the biological sample and allow a better comparison with other in vitro studies. In addition, the quality of the study will be such that it will be more likely to be included in assessment procedures such as health-risk assessments. Index Terms—Exposure systems, in vitro biological experiments, review, RF.

I. INTRODUCTION

T

HE SCIENTIFIC literature on electromagnetic (EM) fields contains a large number of conflicting results, especially among those studies evaluating whether exposure to RF fields causes biological effects. Much of this conflict can be attributed to inaccurate dosimetry and to a lack of well-characterized exposure conditions. In many cases, especially in studies published prior to the 1990s, insufficient effort was made by investigators to ensure that their biological samples were exposed to a known “dose,” e.g., the specific absorption rate (SAR) or SAR distribution, to within, say, 3 dB. Only information about the incident field was provided and little or no attention given to field strengths induced within tissue samples or cells. In terms of dosimetry, this is considered insufficient since the ratio between induced fields and incident fields can be highly variable depending on the exposure conditions [1]. In particular, in [2], it was explained how numerical calculations can give proper information on distribution of the induced fields Manuscript received April 19, 2010; revised June 23, 2010; accepted June 24, 2010. Date of publication September 13, 2010; date of current version October 13, 2010. A. Paffi, F. Apollonio, and M. Liberti are with the Italian Inter-University Center of Electromagnetic Fields and Biosystems (ICEmB) and the Department of Electronic Engineering, “La Sapienza” University of Rome, 00184 Rome, Italy (e-mail: [email protected]; [email protected]; liberti@die. uniroma1.it). G. A. Lovisolo, C. Marino, and R. Pinto are with the Technical Unit of Radiation Biology and Human Health, RC Casaccia, ENEA, 00123 Rome, Italy (e-mail: [email protected]; [email protected]; [email protected]). M. Repacholi is with the Department of Electronic Engineering, “La Sapienza” University of Rome, 00184 Rome, Italy (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.2010.2065351

within the sample showing that variation can be enormous. For example, in experiments with poor dosimetry, having in vitro samples exposed to highly nonuniform RF fields, but having low average intensities, may produce positive results. However, if researchers claim that low nonthermal RF fields produced the effect, one cannot rule out that it was due to highly localized peak fields. Since the International EM Field Project was established at the World Health Organization (WHO) in 1996, WHO’s EM field research agendas have emphasized the importance of accurate dosimetry in all scientific studies. Well-defined and characterized exposure conditions are necessary for health-risk assessments [3]. The reason for this is clear, unless the “dose” is accurately known, the results of EM field studies will have little value for determining exposure thresholds for health risks or for development of exposure limits in standards. Some authors have tried to provide the necessary characteristics for RF exposure systems to increase the accuracy of the dose induced. For example, [4] and [5] provided information concerning optimization of exposure and how to evaluate the fundamental designs of in vitro exposure setups including their advantages and disadvantages. During the past ten years, several cooperative European and national RF research programs have been carried out. At the commencement of the first European Commission project on EM field studies, discussion on quality assurance led to shared objectives. In particular, a number of European Cooperation in Science and Technology (COST) workshops have been devoted to defining exposure conditions that lead to reproducible and scientifically meaningful results. For example, the COST workshop “Exposure Systems and their Dosimetry,” held in Zurich, Switzerland, in February 1999 [6], [7], and the workshop on “Forum on Future European Research on Mobile Communications and Health,” held in Bordeaux, France, in April 1999 [8]. Following these discussions, the exposure systems adopted in the European projects (see [9, Table I]) were: wire patch cells, TEM cells, and coplanar waveguides used in RAMP2001 (Risk Assessment for Exposure of Nervous System Cell to Mobile Telephone EMF: from in vitro to in vivo Studies); short-circuited waveguides in REFLEX (Risk Evaluation of Potential Environmental Hazards from Low Energy EM Fields Exposure Using Sensitive in vitro Methods); rectangular waveguides in CEMFEC (Combined Effects of EM Fields with Environmental Carcinogens); short-circuited waveguides, TEM cells, and wire patch cells in Perform B (In vitro and in vivo Replication Studies Related to Mobile Telephones and Base Stations); and wire patch cells in the CRADA-CTIA

0018-9480/$26.00 © 2010 IEEE

PAFFI et al.: CONSIDERATIONS FOR DEVELOPING AN RF EXPOSURE SYSTEM

(Cooperative Research and Development Agreement with the International Association for the Wireless Telecommunications Industry) Project (USA-EU). The necessity of conducting coordinated research activities in laboratories of different countries has raised the question of whether standardized exposure systems and protocols should be used. This was discussed at the EMF-NET (Effects of the Exposure to Electromagnetic Fields: from Science to Public Health and Safer Workplace) workshop “EM Field Health Risk Research Lessons Learned and Recommendations for the Future” held in Monte Verita, Switzerland, in 2005 [10]. It was concluded that, because of the different endpoints and protocols used in bioelectromagnetics studies, exposure setups could not be standardized. However, the workshop did conclude that strong quality control on dosimetry is mandatory to assure repeatability and reproducibility of results, even when different exposure systems are used [10]. Some of the authors contributing to these discussions provided specifications that have to be met when designing an in vitro exposure system [9]. The issues to be discussed for exposure system design include the biological parameters (biological target, statistical power, exposure environment, end-point(s) to be studied, and the effect of the sample holder) and exposure characteristics (signal, dose, control, and monitoring of dose, sham versus blind conditions, and EM compatibility) [9]. To address these issues, we carried out a detailed review of exposure systems used in RF in vitro research from 1999 up to 2009, providing a classification and evolving a standardized procedure for optimal exposure design. More than 100 papers from 28 journals have been reviewed, resulting in the assessment of 51 exposure systems. The purpose of our review is to discuss the strengths and weaknesses of the various systems used, the frequency ranges over which they are applicable, the type and number of sample holders that can be contemporaneously exposed, the exposure features, and their usefulness for exposing the target tissue or cell sample. Current exposure systems have been designed for frequencies up to about 5 GHz, but systems are now required for investigations at higher frequencies, maybe as high as 10 GHz. This paper will also identify features of exposure systems that lead to optimal conditions needing to be incorporated for these higher frequency studies.

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and distinction between offline or real-time systems (Table I). Offline exposure systems, most used by research groups, presuppose experimental data are collected at the end of the exposure, while for real-time setups, data are collected during the RF exposure. This basic subdivision is further classified according to their reference RF structure and divided in three main families: radiating, propagating, and resonant. Radiating systems usually consist of commercial or ad hoc antennas, such as horn and microstrip antennas, generally exposing samples in the far-field region. They allow simultaneous exposure of many samples, but generally have low uniformity of dose among samples and reduced efficiency in terms of SAR per unit of input power. Propagating systems are used in many bioelectromagnetics investigations and include different RF structures such as TEM cells and various waveguides (rectangular, circular, radial, coplanar). Their main advantages are versatility and RF field uniformity. Resonant systems, such as short-circuited waveguides, are closed and compact structures, which can be easily placed inside an incubator when strict environmental control is needed. They are characterized by high efficiency, but the positioning of the sample is critical due to the extremely localized region of field uniformity. A special type of resonant system is the wire patch cell, based on a wire patch antenna, with the samples positioned inside the structure between the two patches that are short-circuited by metallic rods [11]. In Table I, each system is described by the number and type of sample holders that can be exposed, the operating frequency or the frequency range for wideband systems, the efficiency, and the SAR homogeneity in the sample that is expressed in terms of the coefficient of variation (CV: equal to standard deviation divided by mean value). The information is omitted if it is not provided or cannot be easily determined from the paper. Some of the papers included in the table do not report efficiency or homogeneity. However, all of them give a dosimetric evaluation based on numerical simulations and/or experimental measurements. These parameters allow an initial comparison among different systems and are described in detail in Sections II-B and C.

II. CLASSIFICATION B. Offline Systems A. Classification Criteria From the more than 100 papers, some focused on the design and characterization of in vitro exposure systems, whereas others reported biological experiments involving exposure of cell cultures and tissues to RF fields. Among them, only those reporting a new system or ones adapted to new experimental conditions have been considered. Moreover, biological papers where the exposure system is not described or the dose delivered in terms of the SAR is not given have not been included. The list of the 51 exposure systems with their reference is given in Table I. Our classification of exposure systems was based on those of the authors in [9]. They are based on the experimental protocol

Among offline exposure systems, the most commonly used RF structures are propagating ones, but resonant and radiating structures are also employed according to the experimental requirements. 1) Propagating Structures: Propagating structures are mostly closed and confine the RF field inside, and provide good versatility to different situations, usually guaranteeing a uniform field in the biological sample. Based on their propagating structures, 24 different exposure systems were collected. Most of them are based on TEM cells (ten) [12] and rectangular waveguides (six) because these are the best-established structures. However, cylindrical and radial waveguides (three) have also been used.

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TABLE I CLASSIFICATION OF EXPOSURE SYSTEMS WITH THEIR REFERENCE, NUMBER, AND TYPE OF SAMPLE HOLDERS, OPERATING FREQUENCY, SAR EFFICIENCY, SAR HOMOGENEITY, AND NOTES ON TYPE OF DOSIMETRY CONDUCTED

The TEM cell provides exposure conditions similar to those of free-space and presents great versatility for adaptation to

different experimental requirements [2], [13]. As an example, TEM cells have been used in the European Union (EU) projects

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TABLE I (Continued.) CLASSIFICATION OF EXPOSURE SYSTEMS WITH THEIR REFERENCE, NUMBER, AND TYPE OF SAMPLE HOLDERS, OPERATING FREQUENCY, SAR EFFICIENCY, SAR HOMOGENEITY, AND NOTES ON TYPE OF DOSIMETRY CONDUCTED

cited above, with different sample holders, such as flasks [14] and multiwells (see Fig. 1) [15]. They are preferred for in vitro studies since they can be easily placed in a standard incubator. The typical efficiency values are around 1 (W/kg)/W although there is great variability. For example, the efficiency changes from 0.02 (W/kg)/W for 5-mL round-bottom tubes [16] to 0.144 (W/kg)/W for 35-mm Petri dishes [17] up to 6 (W/kg)/W for exposure of four T25 flasks filled with 5 mL of culture medium [13]. Moreover, Guy et al. [2] showed, through a numerical study, the differences in SAR values and distributions in various in vitro preparations within commonly used

sample holders, such as tubes and Petri dishes. They noted that uniformity of SAR distribution strongly depends on the vessel used and the field polarization. The most uniform SAR for a layer of cells occurred in Petri dishes with the bottom parallel to the -field. For cell suspensions inside standard vessels, it was not possible to achieve satisfactory uniformity of the SAR 70% [2]. All the TEM cells reviewed operated at frequencies from 835 to 915 MHz in the uplink bands of the GSM850 and GSM900 standards. Some authors used commercial TEM cells [13], [15], [18]–[21] with a SAR evaluation, either numerical

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Fig. 1. Two TEM cells for multiwells, as reported in [15, Fig. 1].

Fig. 2. Short-circuited rectangular waveguide with Petri dish samples inside as used in the laboratories of the Department of Biotechnology, Health and Ecosystems Protection, ENEA.

[17]–[20] or experimental [14], [21], for the frequency and sample holders employed. For example, Capri et al. [19] used the same system as [18] at the same frequency, but with well microplates instead of flasks. In [20], the same TEM cell used in [18] was employed, but at a higher frequency (1950 MHz). Under each condition, a new numerical dosimetry was conducted, even though neither the efficiency, nor the dose uniformity were quantified. Two commercial GTEM cells were used in [22] and [23] to expose tubes of lymphocytes at 930 MHz and flasks of fibroblasts at 935 MHz, respectively. In both cases the average SAR in the sample was only theoretically estimated. The GTEM cell has broad bandwidth (up to several gigahertz) application and potentially large capacity, but is characterized by a very low volume efficiency (ratio between the target volume and the space of the entire exposure unit). Due to its quite large dimension, it does not fit inside an incubator so ad hoc systems to maintain environmental control have to be adopted. Even the rectangular waveguide is quite a versatile structure, allowing, with satisfactory efficiency values, exposure from 900 MHz up to 2.45 GHz of different kinds of sample holders: cuvettes (1950 MHz [24]), multiwells (2.45 GHz [25]), and flasks (900 MHz [26], [27]; 1800 MHz [28]; 2.45 GHz [29]). A common characteristic of both TEM cells and rectangular waveguides is the small volume of sample (up to eight flasks) they can expose under similar conditions. A radial transmission line can overcome such limitations as presented in [30]–[32]. It can also be used over a wide frequency band (up to 3 GHz) to simultaneously expose 16 T75 flasks [30], [32] or 24 pineal glands located in cylindrical receptacles [31]. Nevertheless, the efficiency is significantly lower: 0.016 (W/kg)/W at 835 MHz [30], 0.34 (W/kg)/W at 900 MHz [31], and 0.245 (W/kg)/W at 2.45 GHz [30]. The exposure system used in [33] was a truncated cylindrical waveguide based on a totally different principle. The efficiency is high (8.6 (W/kg)/W) and the dose homogeneity good, but due to the fact that only one Petri dish can be exposed at a time, the whole system was made up of six waveguides to have enough statistical power. Moreover, this system allows only the exposure of cells not needing CO since it does not fit into an incubator so an arrangement has to be set up to control the environment of the sample.

Other systems supporting a traveling wave are the two described in [34] and [35]. The first is based on two parallel conductors with bent lateral edges to limit the RF radiation and supports plane wave transmission. In [35], a modified coaxial cable was developed that includes a special glass tube used as the sample holder, reaching a very high efficiency (120 (W/kg)/W), as determined by experimental measurements. 2) Resonant Structures: There were 11 systems classified as resonant, in particular, eight short-circuited rectangular waveguides. Resonant systems are generally closed structures that allow standing waves inside due to total reflection. They have high volume efficiency and are usually compact systems enabling the placement of both active and sham systems in the same incubator. As they are based on resonance, they are strongly affected by the position and size of the biological samples, and have a narrow operating frequency band. In spite of this, they guarantee high SAR efficiency for cells in monolayers or suspensions since samples can be located at the - or -field maxima. The temperature is usually controlled by forced airflow through the guides [36]. Most of the resonant structures reviewed are based on shortening the rectangular waveguide at one end, as reported in Fig. 2. These structures permit the simultaneous exposure of different sample holders: tubes [37] and Petri dishes (from one 100 mm [38] up to eight 35 mm [39] or 60 mm [40] dishes). They are used at most frequencies typical of mobile communications: 800 MHz [37], 900 MHz [39], [41], 1710 MHz [40], 1800 MHz [36], and 1950 MHz [42]. The efficiency and SAR homogeneity vary strongly with the frequency. For 900-MHz exposures of cell monolayers [39], the efficiency is about 1.3 (W/kg)/W and homogeneity 20%; for 1800 MHz [36], the homogeneity is 30%–40% for both monolayers and suspensions, while the efficiency is much better than 10 (W/kg)/W for suspensions and 50 for monolayers. Such differences depend on the dominant coupling mechanism (inductive or capacitive). For example, Schuderer et al. [36] exposed monolayers to the -field and cell suspensions to -field maxima to improve both the SAR value and homogeneity. The custom-made resonant structure used in [37] allowed the simultaneous exposure of eight tubes. Numerical and experimental dosimetry was performed for all tubes, but only two

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Fig. 3. Wire patch cell operating at 1800 MHz with four Petri dishes and a thermostated water jacket as reported in [45, Fig. 11].

of them were chosen to expose the biological samples to two different doses at the same time. Efficiencies were 1.61 and 2.28 (W/kg)/W for the two tubes and good homogeneities of 6.8% and 12.1%, respectively. A short-circuited modified rectangular waveguide, operating at 2.45 GHz, was used in [43], and an ad hoc rectangular culture dish placed outside the structure over two slits on the top wall of the waveguide. With this arrangement the maximum SAR was around 70 W/kg, but the SAR distribution varied strongly along the length of the waveguide. A different solution was adopted in [44] where a culture flask was exposed to an 830-MHz field with an efficiency of 9.4 (W/kg)/W. A parallel-plate resonator fed by a coaxial cable through a tapered transition section was used. The entire exposure system (6-cm length, 5-cm width, and 2.4-cm height) was installed within an incubator. Finally, the wire patch cell is a structure first proposed by [11] and constructed of two squared parallel metallic plates short circuited by special props at the corners (see Fig. 3). One of the two plates is fed from above through a coaxial cable whose inner conductor extends to the plate below. The biological sample is placed in Petri dishes between the two plates. The dimensions of this system depend on the operating frequency. In spite of the need for an EM compatible arrangement for the wire patch cell, its reduced size permits it to fit inside an incubator. This system allows simultaneous exposure of eight Petri dishes filled with cell suspensions or monolayers at 900 MHz [11] and four at 1800 MHz [45] due to its reduced dimensions. The efficiency of the two systems is low compared to resonant structures, but comparable to the propagating ones: 0.5 (W/kg)/W at 900 MHz and 1.25 (W/kg)/W at 1800 MHz. SAR homogeneity for monolayers decreases with frequency and remains below 30%, which is acceptable according to [4] and [5]. Local temperature control of the samples can be maintained using two spiral plate water jackets (Fig. 3) [45]. 3) Radiating Structures: Radiating systems allow large experiments where many samples can be simultaneously exposed. These are the only systems currently used for frequencies over 2.45 GHz. Nevertheless, they have low efficiency, due to the low incident power densities, and poor homogeneity. They also need

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EM compatible arrangements due to the lack of enclosures confining the field. Moreover, if environmental control is needed, the setup may become complex. Five radiating systems have been reviewed. A horn antenna was used [46] to conduct 2.45-GHz exposures of 96-well culture plates in a Plexiglass incubator. They determined the SAR to be 4 W/kg. Zhao [47] used a horn antenna for millimeter waves (50 GHz) to irradiate one, two, or four Petri dishes with a SAR distribution varying below 20%. Vijayalaxmi [48] also used two horn antennas operating at 2.45 and 8.2 GHz to expose T25 flasks in an incubator inside an anechoic room. Exposures were conducted at 1.75 m from the opening of the antenna at a frequency of 2.45 GHz and 1.46 m at 8.2 GHz. Numerical dosimetry confirmed low efficiencies (0.1 and 0.34 (W/kg)/W at 2.45 and 8.2 GHz, respectively). SAR homogeneities were given in terms of a dose distribution function. The system described in [49] allowed exposures of up to 25 or 49 Petri dishes. It was comprised of a horn antenna operating at 2142.5 MHz and a dielectric lens that focused the beam onto the samples. The efficiency was low (0.175 (W/kg)/W), but the SAR variation was high (CV of 59%). In this case, the environmental control was very complex with two different forced air sources placed in the culture room and in the anechoic chamber. The exposure system described in [50] consisted of six microstrip antennas operating at 2.1 GHz and placed on each face of a cubic box. The system attempts to replicate the field distribution of radio base stations in an area of 6 cm 6 cm at the center of the box. Only the electric field inside the sample (Petri dish filled with Dulbecco solution) was provided using numerical simulations. C. Real-Time Systems Special attention has recently been given to real-time data acquisition during RF exposures to identify possible cumulative or reversible effects. In particular, electrophysiological techniques are now widely used to study interactions between the nervous system and RF fields. Real-time analysis imposes additional requirements of easy access to the biological sample and minimal coupling with the data acquisition setup. Most real-time systems are propagating structures with the exceptions of one resonant [51] and one radiating [52] system. 1) Propagating Structures: Propagating systems for realtime studies are generally closed structures, such as TEM cells or rectangular waveguides, modified with holes for sample observation and perfusion, and for online monitoring of biochemical or biophysical parameters. In [53], Meyer et al. used a TEM cell at 180 and 900 MHz [54] and two rectangular waveguides at 900 and 1800 MHz to expose myocyte cultures during patch-clamp recordings of electrophysiological activity [53]. These systems had two holes in their top and bottom plates: one to insert the recording electrodes and the other to observe the sample with a microscope. To avoid interference between the -field inside the guide and the wire of the patch-clamp electrode, long glass microelectrodes were used between the solution and a wire positioned outside the exposure device. The calculated efficiency was 1.66 (W/kg)/W for the waveguide at 900 MHz and 3.16 (W/kg)/W for 1800 MHz.

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A rectangular waveguide operating between 0.75–1.12 GHz was proposed by [55] to evaluate effects on skeletal muscle contraction exposed to continuous wave (CW), amplitude modulated, or pulse modulated fields. The muscle was inserted in a bath placed in the center of the waveguide. A force transducer continuously measured muscle contractions induced by a voltage difference between the two metal electrodes. The waveguide walls contained slots to allow connection with measurement, control, and stimulating devices outside the system. Their detailed numerical dosimetry in the muscle sample accounted for the bath, metal electrodes inside the guide, and openings in the walls. The efficiency was higher than 3 and homogeneity . around 79%, calculated as A modified rectangular waveguide giving CW or Universal Mobile Telecommunications System (UMTS) signals was used for electrophysiological recordings of neuronal networks cultivated on microsensor chips [56]. The chip is fitted into a recess in the guide to avoid short circuiting the measuring probes while exposing the neuronal cells. To expose heart slices [57] and brain slices [58] to high-power microwave pulses (repetition frequency 9.2 GHz), a WR90 waveguide was used terminated with an exposure cell containing the sample and a sapphire matching plate below. An extremely high efficiency of 3.3 kW/kg/W was measured at 0.5 mm above the matching plate, but decreased about twofold per millimeter with distance from it. To expose brain slices to 700-MHz CW fields while recording electrophysiological activity, Tattersall et al. [59] employed a parallel-plate waveguide apparatus. In this case, as in [53], the top and bottom plates of the guide had holes to illuminate the sample and allow insertion of both stimulating and recording electrodes. The electrodes were placed at an angle of about 45 to the -field raising the possibility of artifacts in the recorded traces [60]. The SAR in the slice was estimated to be less than 0.01 W/kg for an input power of 0.126 W, giving an efficiency value lower than 0.03 (W/kg)/W. An open coplanar waveguide was used for studies involving patch-clamp recordings of neuronal cells [61] and field potential recordings of brain slices [62]. Fig. 4 shows the system of [61] mounted on a microscope. The two systems operate in the 800–2000-MHz band, encompassing all typical frequencies for mobile telephony. They differ from each other by the distance between the central and lateral conductors because of the different size samples to be irradiated. The open planar geometry allows easy access to the samples and the - and -fields are confined in a small volume around the surface that guarantees the avoidance of interference with the data acquisition setup. Field confinement also provides highefficiency values, higher than 17 (W/kg)/W, for both systems at all frequencies. A modified stripline system was used to evaluate effects of a CW 2.45-GHz field on the activity of ascorbate oxidase trapped in liposomes [63]. In this system, both the sample cuvette and the temperature regulating chamber were adjacent parts of the dielectric substrate of the stripline. The whole system was located inside a spectrophotometer monitoring the enzymatic activity during exposure (Fig. 5).

Fig. 4. CPW system for patch-clamp recordings while mounted on a microscope, as used in the laboratory of the Department of Human and General Physiology, University of Bologna.

Fig. 5. Modified stripline system reported in [63] installed in a spectrophotometer at the laboratory of the Institute of Neurobiology and Molecular Medicine-CNR, Rome, Italy.

2) Resonant Structures: A resonant system employed by Hagan et al. [51] was based on a WR-975 rectangular waveguide terminated with a shorting plate. It was designed to expose neural cells in the frequency range of 0.75–1.12 GHz while monitoring catecholamine release online. The cell perfusion apparatus was placed inside the waveguide and communicates with the exterior through slots on the guide plates. The highest calculated SAR was achieved when the cell perfusion chamber was located at the -field maximum. 3) Radiating Structures: Yoon et al. [52] had the same biological protocol as Hagan et al. [51], but exposed at frequencies from 1 to 6 GHz. For this higher frequency range, a standard waveguide is too small to accommodate the sample and the cell-perfusion apparatus. Thus, a radiating system was chosen using a horn antenna with the perfusion chamber placed in the far-field region. This solution required a special arrangement to avoid perturbing the field and interfering with the experimental equipment. All instruments were shielded in a conducting box behind the perfusion chamber and a layer of absorber material used to prevent -field reflection. In addition, the whole system was placed within an anechoic chamber. While Yoon et al. [52] recognized the need for exposure systems that could operate at higher frequencies, in their system

PAFFI et al.: CONSIDERATIONS FOR DEVELOPING AN RF EXPOSURE SYSTEM

SAR homogeneity became critical due to the higher conductivity of the medium and the dimensions of the sample holder becoming comparable to the wavelength of the incident field. D. Considerations From Table I, it is evident that the majority of experiments in bioelectromagnetics in the last ten years used offline analysis, but in recent years there has been an increasing trend toward real-time systems. Most offline exposure systems are based on standard RF structures dimensioned to operate at the frequency of interest and accommodate the biological sample in holders required by the protocol. Real-time systems generally require modifications of standard RF structures and features that allow continuous monitoring of the sample while avoiding RF coupling and interference with the recording apparatus. As is evident from Table I, real-time investigations generally require the use of nonstandard sample holders. Currently the majority of exposure systems operate at typical mobile communication frequencies. However, some papers report systems designed to expose biological samples at higher frequencies: 2.45 GHz [25], [29], [30], [32], [43], [46], [48], [63], millimeter waves [47], 6.00 GHz [52], 8.20 GHz [48], and 9.20 GHz [57]. Different strategies exist for exposure system development. In some, the same reference structure is maintained for exposures at different frequencies. For example, for wire patch cells, at 1800 [45] and 2450 MHz [64], [65], a resizing and a new dosimetry are necessary [11]. In others, the change of exposure frequency imposes a change of reference structure, such as in the real-time systems used at 1 GHz by Hagan et al. [51] and at 6 GHz by Yoon et al. [52]. However, systems operating at the same frequency and delivering the same dose can be based on completely different structures, determined by the experimental protocol (e.g., for real-time and offline experiments). The efficiency (see Table I) depends strongly on the type of RF structure (e.g., open, closed, resonant) and frequency while SAR homogeneity also depends on the sample volume and holder shape. III. RESULTS A. From the Classification to a Procedure for Developing an Appropriate Exposure System From Table I, it is evident that many different exposure systems have been developed and employed for a great variety of experimental protocols in the last ten years. As already noted in [9] and [10], the concept of using a standardized exposure system for all types of studies is not possible. However, the choice, design, and characterization of the system can be standardized to obtain repeatable and reproducible results from biological experiments. The effect of the exposure depends only on the RF dose characteristics, while the reliability of the observed effect depends on avoiding any confounding factor due to RF interference, changes in environmental parameters, or loss in the well being of the cells. In turn, an accurate knowledge of the dose and control of possible confounding factors depend on proper

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design and characterization of the system employed, which can be achieved following a standardized procedure, as suggested in Section III-B. Analysis of the experimental protocol requirements allows one to choose the RF structure with the required features or to design a system through a sequence of standardized steps. One sees from Table I that some studies do not match all the procedural steps. B. Standardized Procedure The proposed procedure for reaching the optimum exposure design is shown in the flowchart (Fig. 6) and consists of seven main steps. First, an experimental hypothesis is formulated (step 1), leading to the choice of an appropriate biological system to be exposed. The experiment to test the hypothesis is then defined (step 2), including biological models, endpoints, techniques, and exposure parameters. The outcome of these analyses determines the requirements of the exposure system. The best RF structure is then chosen (step 3). If one chooses to adopt an existing system, then determine whether it has already been reported in literature, or whether it is necessary to design one (step 4) that leads to a first dimensioning of the structure. The final design parameters (dimensions, materials, sample position, etc.) are obtained through numerical simulations with and without the sample (step 5), using an iterative adjustment procedure to optimize sensitive parameters. The next two steps are the manufacture (step 6) and experimental validation (step 7) of the exposure system. Measurements should be conducted first with the structure empty and then loaded with the biological sample to validate the behavior of the system and to experimentally evaluate the dosimetry. If acceptable agreement between measurement and simulation is not achieved, one must return to steps 5, 6, or 7 depending on the degree of mismatch. To explain how this procedure can be applied in actual situations, some practical examples are given in Section III-C. C. Some Examples The following two examples provide some practical guidance on how to use the standardized procedure. 1) How to Start to Identify the Exposure System: Assume we want to test the hypothesis that an RF field typical of wireless technologies (i.e., Wi-Fi) at a frequency of 2.45 GHz can produce genotoxic effects in blood cells. From a review of available publications, an experimental protocol like the one used in [20] for UMTS may be considered. The biological test system is human leucocytes and is used to detect primary DNA damage, i.e., strand breaks using alkaline comet assays. This endpoint suggests the use of an offline system and an incubator with at least six donors to obtain sufficient statistical power. Assume the exposure protocol requires 24 h of intermittent RF exposure at a SAR ranging from 1 to 4 W/kg. Different vessels could be used; flasks, Petri dishes, or tubes. Referring to Table I, we note that seven exposure systems for 2.45 GHz exist. The first two are radiating structures from [46] and [48], which do not seem adequate due to their low efficiency and poor RF characterization.

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Fig. 6. Flowchart of the proposed standardized procedure for reaching the optimum exposure system design.

The system in [25] is not adaptable because it uses a nonstandard vessel (polystyrene block with ten holes) and has inadequate sample volume exposed (approximately 0.5 mL per each hole). Similarly, in [43], an ad hoc vessel is used that is divided into four compartments to simultaneously expose to four different SARs. Of the two remaining systems, the radial waveguide of [30] and [32] and the rectangular one of [29], the first cannot be used since it is not possible to insert it inside an incubator. Therefore the rectangular waveguide seems to be the appropriate choice

for this study. Nevertheless, to expose samples from at least six donors it would be necessary to perform six separate experiments since the system from [29] can hold only one flask at a time. This disadvantage may be overcome by a wire patch cell system like the one proposed in [64] and [65], which permits the exposure of four Petri dishes at a time. Otherwise one can choose to use a completely new design by going through steps from 4 to 7 (Fig. 6). 2) Use of Different Systems in Cooperative Studies: This example addresses the evaluation of RF effects on biological sys-

PAFFI et al.: CONSIDERATIONS FOR DEVELOPING AN RF EXPOSURE SYSTEM

tems of different levels of complexity, as part of a cooperative study program, such as the RAMP2001 Project (Table I in [9]). From that table, both real-time and offline protocols were used with many biological endpoints. The primary hypothesis was that RF fields (900 and 1800 MHz) may affect nerve cells, thus the interaction targets were neuroblastoma cells and hippocampal and cortical neural cultures from a rat brain. The endpoints were proliferation, apoptosis, gene expression, cell differentiation, activation, and inactivation kinetic changes in the ratio of the different calcium channel subtypes and ionic currents. Doses in the range of 1–4 W/kg were chosen for all experiments, requiring a low number of samples. This excludes radiating structures due to their low efficiency. For neuronal phenotype maturation, neuroblastoma cell lines were used. A reduced number of neurites, possibly related to increased expression of a specific mRNA, was observed [66]. For this study, a multiwell sample holder was used in an incubator. From the literature, the possibility of using a TEM cell has been identified (step 3 of Fig. 6) and its functioning and dosimetry have been evaluated [15]. Cell proliferation and gene expression have been evaluated using standard Petri dishes. For this purpose, the wire patch cell was chosen and used at 900 MHz with the same operating modality as in [11]. For exposures at 1800 MHz, a resizing was carried out. Details on steps from 4 to 7 are given in [45]. Finally, for an ionic currents endpoint, a real-time analysis with a microscope and current recorder is necessary. In this case, the specific requirements are described in [61], which are: 1) a transparent dielectric substrate to achieve visibility of the sample; 2) the exposure region where the external electrode is placed is large enough; 3) a substrate thickness less than the microscope optical length; 4) avoiding RF power losses due to dissipation effects in the substrate; 5) avoiding RF power losses due to RF radiation; and 6) a characteristic impedance of 50 to achieve good impedance matching when the structure is connected to a standard coaxial cable. From the literature, no systems for both frequencies of interest are available, therefore a new design is necessary. All steps from 4 to 7 in Fig. 6 are discussed in [61]. This system has been used in [67] to investigate the effects of 900-MHz CW fields on Ba currents through voltage-gated calcium channels in rat cortical neurons. IV. DISCUSSION AND CONCLUSION The appropriate exposure system for in vitro RF research depends on the biological endpoints and the exposure parameters required. The WHO has placed great importance on accurate dosimetry if studies are to be useful for determining any health risks of exposure to RF fields. While standardized exposure systems are not necessary, there is a place for a standardized design procedure to ensure that the appropriate exposure system is identified and used. When determining the exposure structure, some priorities must be kept in mind. The ability to accurately determine the dose in the exposed sample and the well being of the cells. Furthermore, a sham group and blind modality must be adopted when possible [9].

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This paper has provided practical information on the processes necessary to arrive at the best exposure system to properly test the study hypothesis. Our approach has been to review papers in the literature (summarized in Table I) to: 1) divide the exposure systems into categories defined by their RF structure; 2) identify their strengths and weaknesses, efficiencies, and ability to expose the sample volume and numbers necessary to achieve good statistical power; and 3) finally provide a flowchart of information necessary to achieve the best results. Two guidance examples on how to use such a flowchart have been provided. The first one for identifying the best exposure system for a new experiment and the second describes how to manage exposure systems in a large cooperative study. The two examples describe three different ways to use the flowchart. In the first case, the suggestion is the use of an existing system (“use it in the same operating modality,” step 3 in Fig. 6). The second example describes how to develop two new exposure systems, a wire patch cell and a real-time one, following the overall procedure to step 7 of Fig. 6 (“ready to use”). For TEM cells, a reference system was adopted with a proper characterization (“evaluate functioning and dosimetry,” step 3 of Fig. 6). During the last ten years, the quality of exposure systems has greatly improved and the use of well-grounded experimental protocols (sham exposure, blinding of exposure and biological tests, positive and negative controls) has become a reference for the scientific community. Standardized criteria for the choice of exposure system represent a solid base for conducting highquality investigations, as required by bodies such as the International Commission on Non-Ionizing Radiation Protection (ICNIRP), IEEE, International Agency for Research on Cancer (IARC), and WHO, to have confidence in the results so they can be included in the process of health-risk assessment. The procedure proposed in this paper can help to provide a quality exposure system. REFERENCES [1] C. H. Durney, H. Massoudi, and M. F. Iskander, Radiofrequency Radiation Dosimetry Handbook, 4th ed. Brooks AFB, TX: USAF SAM, 1986, Rep. USAFSAM-TR-85-73. [2] A. W. Guy, C. K. Chou, and J. A. McDougall, “A quarter century of in vitro research: A new look at exposure methods,” Bioelectromagnetics, vol. 20, pp. 21–39, Dec. 1999, Suppl. 4. [3] “Health and environmental effects of exposure to static and time varying electric and magnetic fields: Guidelines for quality research,” WHO, Geneva, Switzerland, 1996. [Online]. Available: www.who.int/peh-emf/research database/en/index.html, WHO Int. EMF Project. [4] N. Kuster and F. Schönborn, “Recommended minimal requirements and development guidelines for exposure setups of bio-experiments addressing the health risk concern of wireless communications,” Bioelectromagnetics, vol. 21, pp. 508–514, Oct. 2000. [5] F. Schönborn, K. Pokovic, M. Burkhardt, and N. Kuster, “Basis for optimization of in vitro exposure apparatus for health hazard evaluations of mobile communications,” Bioelectromagnetics, vol. 22, pp. 457–559, Dec. 2001. [6] F. Schönborn, K. Pokovic, and M. Burkhardt, “In vitro setups for HF exposure,” in Proc. 6th COST 244bis Exposure Syst. and Their Dosimetry Workshop, Zurich, Switzerland, Feb. 14–15, 1999, pp. 12–23. [7] A. Bitz, J. Steckert, and V. Hansen, “Exposure setups for a large number of samples: In vitro setups for HF exposure,” in Proc. 6th COST 244bis Exposure Syst. and Their Dosimetry Workshop, Zurich, Switzerland, Feb. 14–15, 1999, pp. 24–30. [8] N. Kuster and F. Schönborn, “Requirements for exposure systems,” in Proc. COST 244bis Forum on Future Eur. Res. on Mobile Commun. and Health Workshop, Bordeaux, France, Apr. 19–20, 1999, pp. 53–59.

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[9] G. A. Lovisolo, F. Apollonio, L. Ardoino, M. Liberti, V. Lopresto, C. Marino, A. Paffi, and R. Pinto, “Specifications of in vitro exposure setups in the radiofrequency range,” Radio Sci. Bull., no. 331, pp. 21–30, Dec. 2009. [10] T. Samaras, N. Kuster, and S. Nebovetic, “Scientific report: Workshop on EMF health risk research lessons learned and recommendations for the future,” presented at the Centro Stefano Franscini, Monte Verita, Switzerland, Nov. 20–24, 2005. [11] L. Laval, P. Leveque, and B. Jecko, “A new in vitro exposure device for the mobile frequency of 900 MHz,” Bioelectromagnetics, vol. 21, no. 4, pp. 255–263, May 2000. [12] M. L. Crawford, “Generation of standard EM fields using TEM transmission cells,” IEEE Trans. Electromagn. Compat., vol. EMC-16, no. 4, pp. 189–195, Nov. 1974. [13] N. Nikoloski, J. Frohlich, T. Samaras, J. Schuderer, and N. Kuster, “Reevaluation and improved design of the TEM cell in vitro exposure unit for replication studies,” Bioelectromagnetics, vol. 26, no. 3, pp. 215–224, Apr. 2005. [14] A. B. Desta, R. D. Owen, and L. W. Cress, “Non thermal exposure to radiofrequency energy from digital wireless phones does not affect ornithine decarboxylase activity in L929 cells,” Radiat. Res., vol. 160, pp. 488–491, Oct. 2003. [15] G. D. Vecchio, A. Giuliani, M. Fernandez, P. Mesirca, F. Bersani, R. Pinto, L. Ardoino, G. A. Lovisolo, L. Giardino, and L. Calza, “Effect of radiofrequency electromagnetic field exposure on in vitro models of neurodegenerative disease,” Bioelectromagnetics, vol. 30, pp. 564–572, Oct. 2009. [16] R. Sarimov, L. O. G. Malmgren, E. Markova, B. R. R. Persson, and Y. Belyaev, “Non-thermal GSM microwaves affect chromatin conformation in human lymphocytes similar to heat shock,” IEEE Trans. Plasma Sci., vol. 32, no. 8, pp. 1600–1608, Aug. 2004. [17] H. B. Lim, G. G. Cook, A. T. Barker, and L. A. Coulton, “Effect of 900 MHz electromagnetic fields on nonthermal induction of heat-shock proteins in human leukocytes,” Radiat. Res., vol. 163, pp. 45–52, Jan. 2005. [18] O. Zeni, A. Schiavoni, A. Sannino, A. Antolini, D. Forigo, F. Bersani, and M. R. Scarfì, “Lack of genotoxic effects (micronucleus induction) in human lymphocytes exposed in vitro to 900 MHz electromagnetic fields,” Radiat. Res., vol. 160, no. 2, pp. 15–158, Aug. 2003. [19] M. Capri, E. Scarcella, C. Fumelli, E. Bianchi, S. Salvioli, P. Mesirca, C. Agostani, A. Antolini, A. Schiavoni, G. Castellani, F. Bersani, and C. Franceschi, “In vitro exposure of human lymphocytes to 900 MHz CW and GSM modulated radiofrequency: Studies of proliferation, apoptosis and mitochondrial membrane potential,” Radiat. Res., vol. 162, no. 2, pp. 211–218, Aug. 2004. [20] O. Zeni, A. Schiavoni, A. Perrotta, D. Forigo, M. Deplano, and M. R. Scarfì, “Evaluation of genotoxic effects in human leukocytes after in vitro exposure to 1950 MHz UMTS radiofrequency field,” Bioelectromagnetics, vol. 29, pp. 177–184, Apr. 2008. [21] J. Y. Kim, S. Y. Hong, Y. M. Lee, S. A. Yu, W. S. Koh, J. R. Hong, T. Son, S. K. Chang, and M. Lee, “In vitro assessment of clastogenicity of mobile-phone radiation (835 MHz) using the alkaline comet assay and chromosomal aberration test,” Environmental Toxicol., vol. 23, no. 3, pp. 319–327, Jun. 2008. [22] M. Zmyslony, P. Politanski, E. Rajkowska, W. Szymczak, and J. Jaite, “Acute exposure to 930 MHz CW electromagnetic radiation in vitro affects reactive oxygen species level in rat lymphocytes treated by iron ions,” Bioelectromagnetics, vol. 25, no. 5, pp. 324–328, Jul. 2004. [23] I. Pavicic and I. Trosic, “In vitro testing of cellular response to ultra high frequency electromagnetic field radiation,” Toxicol. in Vitro, vol. 22, pp. 1344–1348, Aug. 2008. [24] E. Bismuto, F. Mancinelli, G. d’Ambrosio, and R. Massa, “Are the conformational dynamics and the ligand binding properties of myoglobin affected by exposure to microwave radiation?,” Eur. Biophys. J. Biophys. Lett., vol. 32, no. 7, pp. 628–634, Nov. 2003. [25] G. Sajin, E. Kovacs, R. P. Morau, T. Savopol, and M. Sajin, “Cell membrane permeabilization of human erytrocytes by athermal 2450 MHz microwave radiation,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 11, pp. 2072–2075, Nov. 2000. [26] O. Zeni, M. Romano, A. Perrotta, M. B. Lioi, R. Barbieri, G. d’Ambrosio, R. Massa, and M. R. Scarfi, “Evaluation of genotoxic effects in human peripheral blood leukocytes following an acute in vitro exposure to 900 MHz radiofrequency fields,” Bioelectromagnetics, vol. 26, no. 4, pp. 258–265, May 2005. [27] G. D. Prisco, G. d’Ambrosio, M. L. Calabrese, R. Massa, and J. Juutilainen, “SAR and efficiency evaluation of a 900 MHz waveguide chamber for cell exposure,” Bioelectromagnetics, vol. 29, pp. 429–438, Sep. 2008.

[28] A. Schirmacher, S. Winters, S. Fischer, J. Goeke, H. J. Galla, U. Kullnick, E. B. Ringelstein, and F. Stogbauer, “Electromagnetic fields (1.8 GHz) increase the permeability to sucrose of the blood brain barrier in vitro,” Bioelectromagnetics, vol. 21, no. 5, pp. 338–345, Jul. 2000. [29] H. L. Gerber, A. Bassi, M. H. Khalid, C. Q. Zhou, S. M. Wang, and C. C. Tseng, “Analytical and experimental dosimetry of a cell culture in T-25 flask housed in a thermally controlled waveguide,” IEEE Trans. Plasma Sci., vol. 34, no. 4, pp. 1449–1454, Aug. 2006. [30] E. G. Moros, W. L. Straube, and W. F. Pickard, “The radial transmission line as a broad-band shielded exposure system for microwave irradiation of large number of culture flask,” Bioelectromagnetics, vol. 20, no. 2, pp. 65–80, Feb. 1999. [31] V. W. Hansen, A. K. Bitz, and J. R. Streckert, “RF exposure of biological systems in radial waveguides,” IEEE Trans. Electromagn. Compat., vol. 41, no. 4, pp. 487–493, Nov. 1999. [32] W. F. Pickard, W. L. Straube, and E. G. Moros, “Experimental and numerical determination of SAR distributions within culture flasks in a dielectric loaded radial transmission line,” IEEE Trans. Biomed. Eng., vol. 47, no. 2, pp. 202–208, Feb. 2000. [33] G. B. Gajda, J. P. McNamee, A. Thansandote, S. Boonpanyarak, E. Lemay, and P. V. Bellier, “Cylindrical waveguide applicator for in vitro exposure of cell culture samples to 1.9 GHz radiofrequency fields,” Bioelectromagnetics, vol. 23, pp. 592–598, Dec. 2002. [34] F. Belloni and V. Nassisi, “A suitable transmission line at 900 MHz RF fields for E. coli DNA studies,” Rev. Sci. Instrum., vol. 76, no. 5, pp. 1–6, May 2005. [35] M. H. Gaber, N. Abd El Halim, and W. A. Khalil, “Effect of microwave radiation on the biophysical properties of liposomes,” Bioelectromagnetics, vol. 26, no. 3, pp. 194–200, Apr. 2005. [36] J. Schuderer, T. Samaras, W. Oesch, D. Spät, and N. Kuster, “High peak SAR exposure unit with tight exposure and environmental control for in vitro experiments at 1800 MHz,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 2057–2066, Aug. 2004. [37] R. Mazor, A. Korenstein-Ilan, A. Barbul, Y. Eshet, A. Shahadi, A. Jrby, and R. Korenstein, “Increased levels of numerical chromosome aberration after in vitro exposure of human peripheral blood lymphocytes to radiofrequency electromagnetic fields for 72 hours,” Radiat. Res., vol. 169, no. 1, pp. 28–37, Jan. 2008. [38] J. S. Lee, T. Q. Huang, T. H. Kim, J. Y. Kim, H. J. Kim, J. K. Pack, and J. S. Seo, “Radiofrequency radiation does not induce stress response in human T-lymphocytes and rat primary astrocytes,” Bioelectromagnetics, vol. 27, pp. 578–588, Oct. 2006. [39] J. Schuderer, D. Spat, T. Samaras, W. Oesch, and N. Kuster, “In vitro exposure systems for RF exposures at 900 MHz,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 2067–2075, Aug. 2004. [40] F. Schönborn, K. Pokovic, A. M. Wobus, and N. Kuster, “Design, optimization, realization and analysis of an in vitro setup for the exposure of embryonal stem cells at 1.71 GHz,” Bioelectromagnetics, vol. 21, no. 5, pp. 372–384, Jul. 2000. [41] A. Markkanen, P. Penttinen, J. Naarala, J. Pelkonen, A. Sihvonen, and J. Juutilainen, “Apoptosis induced by ultraviolet radiation is enhanced by amplitude modulated radiofrequency radiation in mutant yeast cells,” Bioelectromagnetics, vol. 25, no. 2, pp. 127–133, Feb. 2004. [42] M. L. Calabrese, G. d’Ambrosio, R. Massa, and G. Petraglia, “A highefficiency waveguide applicator for in vitro exposure of mammalian cells at 1.95 GHz,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2256–2264, May 2006. [43] Y. Takashima, H. Hirose, S. Koyama, Y. Suzuki, M. Taki, and J. Miyakoshi, “Effects of continuous and intermittent exposure to RF fields with a wide range of SARs on cell growth, survival, and cell cycle distribution,” Bioelectromagnetics, vol. 27, pp. 392–400, Jul. 2006. [44] M. Mashevich, D. Folkman, A. Kesar, A. Barbul, R. Korenstein, E. Jerby, and L. Avivi, “Exposure of human peripheral blood lymphocytes to electromagnetic fields associated with cellular phones leads to chromosomal instability,” Bioelectromagnetics, vol. 24, no. 2, pp. 82–90, Dec. 2003. [45] L. Ardoino, V. Lopresto, S. Mancini, R. Pinto, and G. A. Lovisolo, “A 1800 MHz in vitro exposure device for experimental studies on the effects of mobile communication systems,” Radiat. Protection Dosimetry, vol. 112, no. 3, pp. 419–428, 2004. [46] A. Peinnequin, A. Piriou, J. Mathieu, V. Dabouis, C. Sebbah, R. Malabiau, and J. C. Debouzy, “Non-thermal effects of continuous 2.45 GHz microwaves on FAS-induced apoptosis in human jurkat T-cell line,” Bioelectrochemistry, vol. 51, no. 2, pp. 157–161, Jun. 2000. [47] J. X. Zhao, “Numerical dosimetry for cells under millimetre-wave irradiation using Petri dish exposure set-ups,” Phys. Med. Biol., vol. 50, pp. 3405–3421, Jul. 2005.

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[48] Vijayalaxmi, “Cytogenetic studies in human blood lymphocytes exposed in vitro to 2.45 GHz or 8.2 GHz radiofrequency radiation,” Radiat. Res., vol. 166, no. 3, pp. 532–538, Sep. 2006. [49] T. Iyama, H. Ebara, Y. Tarusawa, S. Uebayashi, M. Sekijima, T. Nojima, and J. Miyakoshi, “Large scale in vitro experiment system for 2 GHz exposure,” Bioelectromagnetics, vol. 25, pp. 599–606, Dec. 2004. [50] R. Araneo and S. Celozzi, “Design of a microstrip antenna setup for bio-experiments on exposure to high-frequency electromagnetic field,” IEEE Trans. Electromagn. Compat., vol. 48, no. 4, pp. 792–804, Nov. 2006. [51] T. Hagan, I. Chatterjee, D. McPherson, and G. L. Craviso, “A novel waveguide-based radiofrequency/ microwave exposure system for studying nonthermal effects on neurotransmitter release-finite difference time domain modeling,” IEEE Trans. Plasma Sci., vol. 32, no. 4, pp. 1668–1676, Aug. 2004. [52] J. Yoon, I. Chatterjee, D. McPherson, and G. L. Craviso, “Design, characterization, and optimization of a broadband mini exposure chamber for studying catecholamine release from Chromaffin cells exposed to microwave radiation: Finite-difference time-domain technique,” IEEE Trans. Plasma Sci., vol. 34, no. 4, pp. 1455–1469, Aug. 2006. [53] K. W. Linz, C. von Westphalen, J. Streckert, V. Hansen, and R. Meyer, “Membrane potential and currents of isolated heart muscle cells exposed to pulsed radio frequency fields,” Bioelectromagnetics, vol. 20, no. 8, pp. 497–511, Dec. 1999. [54] S. Wolke, U. Neibig, R. Elsner, F. Gollnick, and R. Meyer, “Calcium homeostasis of isolated heart muscle cells exposed to pulsed high frequency electromagnetic fields,” Bioelectromagnetics, vol. 17, pp. 144–153, Dec. 1996. [55] M. R. Lambrecht, I. Chatterjee, D. McPherson, J. Quinn, T. Hagan, and G. L. Craviso, “Design, characterization, and optimization of a waveguide-based RF/MW exposure system for studying nonthermal effects on skeletal muscle contraction,” IEEE Trans. Plasma Sci., vol. 34, no. 4, pp. 1470–1479, Aug. 2006. [56] P. Koester, J. Sakowski, W. Baumann, H. Glock, and J. Gimsaa, “A new exposure system for the in vitro detection of GHz field effects on neuronal networks,” Bioelectrochemistry, vol. 70, pp. 104–114, Jan. 2007. [57] A. G. Pakhomov, S. P. Mathur, J. Doyle, B. E. Stuck, J. L. Kiel, and M. R. Murphy, “Comparative effects of extremely high power microwave pulses and a brief CW irradiation on pacemaker function in isolated frog heart slices,” Bioelectromagnetics, vol. 21, no. 4, pp. 245–254, May 2000. [58] A. G. Pakhomov, J. Doyle, B. E. Stuck, and M. R. Murphy, “Effects of high power microwave pulses on synaptic transmission and long term potentiation in hippocampus,” Bioelectromagnetics, vol. 24, pp. 174–181, Apr. 2003. [59] J. E. H. Tattersall, I. R. Scott, S. J. Wood, J. J. Nettel, M. K. Bevir, Z. Wang, N. P. Somasiri, and X. Chen, “Effects of low intensity radiofrequency electromagnetic fields on electrical activity in rat hippocampal slices,” Brain Res., vol. 904, no. 1, pp. 43–53, Jun. 2001. [60] N. C. D. Misfud, I. R. Scott, A. C. Green, and J. E. H. Tattersall, “Temperature effects in brain slices exposed to radiofrequency fields,” in Book of Abstract of 8th Int. Congr. Eur. BioElectromagn. Assoc., Bordeaux, France, Apr. 11–13, 2007. [61] M. Liberti, F. Apollonio, A. Paffi, M. Pellegrino, and G. d’Inzeo, “A coplanar waveguide system for cells exposure during electrophysiological recordings,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 11, pp. 2521–2528, Nov. 2004. [62] A. Paffi, M. Pellegrino, R. Beccherelli, F. Apollonio, M. Liberti, D. Platano, G. Aicardi, and G. d’Inzeo, “A real-time exposure system for electrophysiological recording in brain slices,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 2463–2471, Nov. 2007. [63] A. R. Orlando, M. Liberti, G. Mossa, and G. d’Inzeo, “Effects of 2.45 GHz microwave fields on liposomes entrapping glycoenzyme ascorbate oxidase: Evidence for oligosaccaride side chain involvement,” Bioelectromagnetics, vol. 25, no. 5, pp. 338–345, Jul. 2004. [64] A. Paffi, F. Apollonio, M. Liberti, L. Grandinetti, S. Chicarella, and G. d’Inzeo, “A new wire patch cell for the exposure of cell cultures to electromagnetic fields at 2.45 GHz: Design and numerical characterization,” in Proc. 39th Eur. Microw. Conf., Rome, Italy, Oct. 29, 2009, pp. 870–873. [65] A. Paffi, F. Apollonio, M. Liberti, G. A. Lovisolo, R. Lodato, C. Merla, S. Mancini, S. Chicarella, and G. d’Inzeo, “A wire patch cell for “in vitro” exposure at the Wi-Fi frequencies,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, May 23–28, 2010, pp. 772–775.

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[66] G. Del Vecchio, A. Giuliani, M. Fernandez, P. Mesirca, F. Bersani, R. Pinto, L. Ardoino, G. A. Lovisolo, L. Giardino, and L. Calzà, “Continuous exposure to 900 MHz GSM-modulated EMF alters morphological maturation of neural cells,” Neurosci. Lett., vol. 455, pp. 173–177, May 2009. [67] D. Platano, P. Mesirca, A. Paffi, M. Pellegrino, M. Liberti, F. Apollonio, F. Bersani, and G. Aicardi, “Acute exposure to 900 MHz CW and GSM-modulated radiofrequencies does not affect Ba2+ currents through voltage-gated calcium channels in rat cortical neurons,” Bioelectromagnetics, vol. 28, no. 8, pp. 598–606, Dec. 2007.

Alessandra Paffi was born in Rome, Italy, in 1971. She received the Laurea degree (cum laude) in electronic engineering and Doctorate degree from “La Sapienza,” University of Rome, Rome, Italy, in 1999 and 2005, respectively. From 2005 to 2006, she was a Post-Doctoral Fellow with the Italian Inter-University Center of Electromagnetic Fields and Biosystems (ICEmB). She is currently Post-Doctoral Fellow with the Department of Electronic Engineering, “La Sapienza” University of Rome. Her main research activities include theoretical and experimental studies for modeling interactions between EM fields and biological systems at different levels of biological complexity. Among her research activities, special interest is devoted to the design and fabrication of EM field exposure systems in the RF range.

Francesca Apollonio (M’06) was born in Rome, Italy, in 1968. She received the Laurea degree (cum laude) in electronic engineering and Doctorate degree from “La Sapienza,” University of Rome, Rome, Italy, in 1994 and 1998, respectively. In 1994, she began her research in bioelectromagnetics, during which time she was involved with experimental dosimetry techniques. In 2000, she became an Assistant Professor with the Department of Electronic Engineering, “La Sapienza” University of Rome. Her research interests include the interaction of EM fields with biological systems using both theoretical and experimental approaches. In particular, she is involved in molecular dynamic studies, modeling mechanisms of interaction, dosimetry techniques, and design of exposure systems.

Giorgio Alfonso Lovisolo was born in Turin, Italy, in 1945. He received the Aeronautic Engineering degree from the Politecnico of Turin, Turin, Italy, in 1970. He was involved with computer scientific programming and hyperthermic treatment control on cancer therapy in a clinical research institute in Rome, Italy. In 1982, he joined Italian Agency for New Technologies, Energy and Environment (ENEA), initially as a Researcher with the Dosimetry and Biophysics Laboratory, then as Head of the Medical Physics Division, as Scientific Advisor of the Environmental Department Direction, and currently as Project Coordinator. He is a Contract Professor of dosimetry and protection of non ionizing radiations with the Post-graduate School of Health Physics, “Tor Vergata” University of Rome. Since 1979, he has been involved with ionizing and nonionizing radiation applications in biomedical technologies. In particular, his research has concerned the design and setup of microwave (MW) and RF apparatus for hyperthermia, Q.A. problems, and recently, EM dosimetry in the field of radio-biological and radio-protection studies.

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Carmela Marino was born in Cosenza, Italy, in 1959. She received the Biology degree from “La Sapienza” University of Rome, Rome, Italy, in 1982. She is currently a Research Scientist and Coordinator of bioelectromagnetic research activity with the Department of Biotechnology, Health and Ecosystems Protection, ENEA, Rome, Italy, and a Contract Professor of radiobiology and thermobiology and biological effects of EM fields with the Post-graduate School of Health Physics, “Tor Vergata” University of Rome, Rome, Italy. After previous experience in the studies of biological effect of ionizing and nonionizing radiation applied to cancer therapy, in in vivo system in particular (she spent an extended period as a Scientific Research Fellow with the Gray Laboratory, Cancer Research Campaign, Mount Vernon Hospital, Nothwood, U.K.), she has been involved in experimental studies on risk assessment of EM fields. In particular, she was Coordinator of the research activity Subject 3 Interaction between sources and biosystems on behalf of ENEA (MURST/ENEA-CNR program “Human and Environmental Protection from Electromagnetic Emissions”), and she was involved in several projects of the 5 and 6 FP as a member of the Steering Committee and Coordinator of the research unit. She is a consulting expert of the International Commission on Non-Inonizing Radiation Protection (ICNIRP) Commission II. She has authored or coauthored over 40 referred papers and 140 national and international conference contributions. She is an Associate Editor of the Bioelectromagnetics Society’s journal. Ms. Marino is president of the European Bioelectromagnetics Association (EBEA). She is a member of the Bioelectromagnetic Society (BEMS) and the Italian Society for Radiation Research (SIRR).

Rosanna Pinto was born in Torre del Greco, Italy, in 1970. She received the Laurea degree in electronic engineering from “La Sapienza” University of Rome, Rome, Italy, in 1998. She had a two-year training period with the Bioelectromagnetic Laboratory, Section of Toxicology and Biomedical Science, ENEA, Rome, Italy. Since 2000, she has been with this same laboratory. Her research field concerns the numerical and experimental dosimetry of EM fields devoted to bioelectromagnetic research, especially in the design and realization of exposure apparatus for in vivo and in vitro experiments devoted to the knowledge of the effects of EM fields on biological systems according to the international criteria for quality assurance of experimental design.

Michael Repacholi was born in Taree, Australia, in 1944. He received the Ph.D. degree in biology from the University of Ottawa, Ottawa, ON, Canada in 1980. He is currently a Visiting Professor with the Department of Electronic Engineering, “La Sapienza” University of Rome, Rome, Italy. For 12 years, until June 2006, he was the Coordinator of the Radiation and Environmental Health Unit, World Health Organization (WHO), Geneva, Switzerland. Dr. Repacholi was the first chair of the International Commission on Non-Ionizing Radiation Protection. He also established the International EMF Project of the WHO in 1996.

Micaela Liberti (M’04) was born in Genova, Italy, in 1969. She received the Laurea degree in electronic engineering and Doctorate degree from “La Sapienza” University of Rome, Rome, Italy, in 1995 and 2000, respectively. From 2001 to 2002, she was a Post-Doctoral Fellow with the Italian Inter-University Center of Electromagnetic Fields and Biosystems (ICEmB). In 2002, she became an Assistant Professor with the Department of Electronic Engineering, “La Sapienza” University of Rome. Her scientific interests include interaction mechanisms between EM fields and biological systems, dosimetric evaluations at the microscopic level, exposure systems dosimetry, and design. Dr. Liberti has been a member of the Scientific Council of the European Bioelectromagnetic Association (EBEA) since 2008.

Digital Object Identifier 10.1109/TMTT.2010.2084890

Digital Object Identifier 10.1109/TMTT.2010.2084891

EDITORIAL BOARD Editor-in-Chief: GEORGE E. PONCHAK Associate Editors: H. ZIRATH, W. VAN MOER, J.-S. RIEH, Q. XUE, L. ZHU, K. J. CHEN, M. YU, C.-W. TANG, B. NAUWELAERS, J. PAPAPOLYMEROU, N. S. BARKER, C. D. SARRIS, C. FUMEAUX, D. HEO

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Digital Object Identifier 10.1109/TMTT.2010.2084895

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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