ALTHOUGH microwave mixer design is well developed, it

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1 3106 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 Compact and Broad-Band Millimeter-Wave Monolithic Transformer Balanced Mixers Pei-Si Wu, Chi-Hsueh Wang, Tian-Wei Huang, Senior Member, IEEE, and Huei Wang, Senior Member, IEEE Abstract Three broad-band miniature monolithic transformer singly balanced diode mixers for operation in the microwave and millimeter-wave bands are reported in this paper. The coupledline equivalent models are used to synthesize the initial design of these transformers up to 50 GHz. The first one is a broad-band spiral transformer mixer, and the second one is a 21-GHz Marchand-type transformer mixer. These two mixers with chip sizes around 0.29 mm 2 exhibit bandwidths of 105% and 54.5%, respectively. We also propose a 30-GHz single-coiled transformer mixer, which has comparable performance with the first two mixers and reduced chip size. The single-coiled transformer mixer achieves a bandwidth of 100% with the chip size smaller than 0.25 mm 2. In order to save chip area, all these transformers provide broad-band matching to the diodes directly. To the authors knowledge, these mixers achieve the widest bandwidths with the smallest chip sizes among all passive balanced mixers using monolithic-microwave integrated-circuit processes in dc 40-GHz frequency range. Index Terms Diode, mixer, monolithic microwave integrated circuit (MMIC), transformer. I. INTRODUCTION ALTHOUGH microwave mixer design is well developed, it still remains a challenge to develop high-performance and low-cost monolithic mixers [1], [2]. For low-frequency applications, Gilbert-cell mixers have good performance and small chip area. Above 10 GHz, Gilbert-cell mixers also have attractive function, but they need an extra matching circuit to enhance their bandwidth [3] [5]. Gilbert-cell mixers are fully differential circuits, but may require single-ended to balanced transformation for connection with other circuit components. Passive balanced mixers, which use Lange couplers [6], Marchand baluns [7], or rat-race baluns [8], are widely used in microwave and millimeter-wave frequencies. The balun sizes of these passive balanced mixers are proportional to the wavelength and often occupy most of the chip area. Alternatively, the transformer mixer with meandered coupled lines demonstrates a compact design in the - and -band [9], [10]. In [9] and [10], the sizes of the transformer mixers are reduced significantly (4 13 times) compared to the mixers using the above-mentioned passive baluns. Manuscript received January 13, 2005; revised April 7, This work was supported in part by the National Science Council under Grant NSC E PAE, Grant NSC E , Grant NSC E , Grant NSC E PAE, and Grant NSC E The authors are with the Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei 106, Taiwan, R.O.C. ( twhuang@cc.ee.ntu.edu.tw). Digital Object Identifier /TMTT Fig. 1. Mixer structure of: (a) conventional singly balanced mixer and (b) transformer mixer. In this paper, we discuss three singly balanced transformer mixers using GaAs-based monolithic-microwave integratedcircuit (MMIC) technology. The first one is the broad-band spiral transformer mixer. The second is the 21-GHz Marchand-type one [11] [13], which demonstrates the first -band Marchand-type transformer. We further proposed a 30-GHz single-coiled transformer mixer. The single-coiled transformer is modified from an -band CMOS design in [14] and [15], and extended to -band in this study. To minimize the chip sizes, all these three transformers provide broad-band matching to the diodes directly. Among these three mixers, the broad-band spiral transformer mixer has the widest bandwidth, the 21-GHz Marchand-type mixer obtains the best isolation, and the 30-GHz single-coiled mixer achieves comparable performance and the smallest chip size. To the authors knowledge, these mixers achieve the widest bandwidths with the smallest chip sizes among all passive balanced mixers using MMIC processes. II. DESIGN METHODOLOGY The conventional singly balanced mixer uses a four-port hybrid, such as a 180 rat-race balun or a 90 Lange coupler [16], as shown in Fig. 1(a). In this mixer, RF has the same phase and the local oscillator (LO) has 180 phase difference to the diodes. A low-pass filter is often utilized to filter out the IF signal. Using this mixer type, LO-to-RF isolation is determined by the port-to-port isolation of the four-port hybrid. An alternative configuration, which is shown in Fig. 1(b), is utilized in this paper. Since the transformer is a three-port element, only the LO feeds through it and the signal has 180 phase difference to the diodes. RF feeds through a high-pass filter and IF is taken out through a low-pass filter. The LO-to-RF and LO-to-IF isolation are directly related to the magnitude and phase balance of the transformer /$ IEEE

2 WU et al.: COMPACT AND BROAD-BAND MILLIMETER-WAVE MONOLITHIC TRANSFORMER BALANCED MIXERS 3107 The circuits are designed using a m GaAs pseudomorphic high electron-mobility transistor (phemt) MMIC process provided by WIN Semiconductors, Taoyuan, Taiwan, R.O.C. 1 In order to design a miniature transformer mixer, a diode size should be selected for the best conversion loss at matched impedance. To save the chip area of matching circuits, the transformer balun can be designed to provide broad-band matching to the diodes directly instead of matched for 50.For minimum size consideration, only a single and small capacitor is used for the RF high-pass filter, and a series inductor and a shunt capacitor are used for the IF low-pass filter. Three different types of transformers are utilized to implement the mixers. For these three types of transformers, the multicoupled-line model in EDA software such as ADS and Microwave Office are utilized to synthesize the transformers in the initial designs. A full-wave electromagnetic (EM) simulator (Sonnet Software, Liverpool, NY) [17] is used after the initial design to predict the performance more precisely. A. Conventional Transformer The first type of transformer is the conventional transformer using two oppositely wrapped twin coils connected in series. A simplified circuit diagram of it is shown in Fig. 2(a). Port 1 is connected through two coils to ground; ports 2 and 3 are connected from ground to coil. At the center frequency, an excitation signal at port 1 will couple to ports 2 and 3 with equal magnitude and phase difference of 180. This transformer is divided into two coils; each coil can be modeled utilizing multicoupled-line elements. Fig. 2(b) shows one coil layout structure of the transformer. The line length from port a to port c (gray line) is the same and symmetric as the line from port b to port d (black line). The gray and black lines are metals on the same layer. The total line length of one coil (including the gray and black lines) is (1) where is the inner square width in Fig. 2(b), is the number of coupled lines on each side, and and are, respectively, the linewidth and line gap. Each linewidth is equal and, thus, so is each line spacing. The area of one coil is By neglecting the corner effect, one coil can be modeled using four -coupled lines [18], as shown in Fig. 2(c). Instead of modeling coupled lines i and iii individually, one eight-coupled microstrip line can be used for the coupling consideration. Similarly, coupled lines ii and iv are modeled by another set of eight-coupled microstrip lines. In order to use a simpler eight-coupled-line model, as shown in Fig. 2(d), coupled line iv is interchanged with coupled line iii. It turns out that the simulation results for Fig. 2(c) and (d) are nearly identical, when is the same or larger than the line gap and the total line length is less than twice the center frequency wavelength, which 1 WIN 0.15 m Power (10 V) phemt Design Kit (rev ), (2) Fig. 2. (a) Simplified circuit diagram. (b) One coil layout structure of the conventional transformer. (c) Equivalent multicoupled line. (d) Simplified 2n-coupled-line model (n =4)of one coil. is true for most cases. Therefore, one coil can be modeled utilizing one -coupled microstrip lines, as shown in Fig. 2(d). The line length of each microstrip line in Fig. 2(d) is the average of the total line length of one coil, and it can be calculated by In Fig. 2(c), the current flow of coupled line i (ii) is in the reverse direction of coupled line iii (iv) so the insertion loss (3)

3 3108 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 Fig. 3. Insertion losses of the conventional transformer as a function of the ratio of the inner square width to the substrate height ID=H. Fig. 4. Chip photograph of the conventional transformer. The chip size is mm. and magnitude imbalance will both deteriorate as decreases. Fig. 3 shows insertion losses of the conventional transformer as a function of the ratio of the inner square width to the substrate height. In order to further decrease the coupling effect, we place a ground at the center of the coils. If via-holes are placed in the coil center directly, the imbalance can be improved. For size consideration, small squares connected to via-holes are utilized in this case. The chip photograph of this transformer is shown in Fig. 4. The chip size is mm. The design procedure of this transformer is summarized as follows. 1) Calculate of the designed center frequency. 2) To minimize the chip area, the linewidths and line gaps are selected to the design rule limit of 5 m. 3) Determine the inner square width. For both size and coupling consideration, 50 m is selected. 4) Let, then the number of turns of one coil can be calculated by (3). 5) Use a multicoupled microstrip line model to synthesize the initial design of this transformer. 6) Finally, the full-wave EM simulator is utilized to determine the final layout. The transformer was tested via on-wafer probing. We used an HP8510C network analyzer to measure the small-signal data up to 50 GHz. The three-port -parameters are extracted from the two-port measurements using a port-reduction method [19], [20]. However, since the transformer is designed to match to the diodes instead of 50, the simulated and measured -parameters under the 50- system do not exactly reflect the performance of the transformer in the mixer circuit. Fig. 5(a) shows the measured total power losses of this transformer, it is below 9 db from 5 to 30 GHz. The simulated and measured insertion losses and phase differences between ports 2 and 3 of the transformer are shown in Fig. 5. The multicoupled-line model can be used to predict the initial values of line gaps, widths, and lengths. After that, we can start from these initial values for the optimization of the transformer performance. Neglecting the corner effect of the coils makes the multicoupled-line model results slightly different from EM simulations. The magnitude difference between EM simulation and measured results are less than 2 db up to 30 GHz. B. Marchand-Type Transformer The second type of transformer is the Marchand-type transformer [11], [12]. Unlike the design in [11] and [12], the linewidths and line gaps of this transformer are adapted to the design rule limit of 5 m to minimize the chip area, therefore, this transformer operates in the higher frequency and occupies a much smaller chip area. A simplified circuit diagram of the Marchand-type transformer is shown in Fig. 6. This configuration is very similar to the conventional transformer, but with port 1 connected through two coils and then to an open circuit instead of to ground. This transformer can be considered as a Marchand balun with each coil to be a quadrature coupler. For the mixer to match the diodes, the total line length of one coil is approximately of the center frequency. The inner square width of the coils is still a concern for magnitude balance and insertion loss. In order to obtain good insertion loss and little imbalance of and, via holes are placed in the center of the coils to improve them, as mentioned before in the conventional transformer design. The chip photograph of this transformer is shown in Fig. 7. The chip size is mm. The simulated and measured results are shown in Fig. 8. The imbalance of this transformer is very small (from 10 to 25 GHz). Fig. 8(a) also shows the measured total power losses of this transformer (it is below 7 db from 10 to 30 GHz). The coupled-line model can be also used as the initial design, and the agreement between EM simulations and measured results is less than 2 db up to 30 GHz. C. Single-Coiled Transformer The third type of transformer is the single-coiled transformer. This transformer is modified from an -band CMOS design [14], [15]. Due to the restriction of the air-bridge design rule, we modified the structure to the GaAs process and extended it to the -band. A simplified circuit diagram of the single-coiled transformer is shown in Fig. 9(a). Its simplified circuit diagram is similar to the conventional one; the difference is that all the lines are intertwined to one coil instead of two coils. By this single-coiled structure, the size of this transformer is more compact than the other two transformers. The structure of this trans-

4 WU et al.: COMPACT AND BROAD-BAND MILLIMETER-WAVE MONOLITHIC TRANSFORMER BALANCED MIXERS 3109 Fig. 6. Simplified circuit diagram of Marchand-type transformer. Fig. 7. Chip photograph of the Marchand-type transformer. The chip size is mm. for the clarity. The total line length in the -direction ( ) and in the -direction ( ) are where and are the inner square widths in the - and -directions in Fig. 9(b), respectively; is the number of turns parallel to the -axis, which is an even number. and are, respectively, the linewidth and line gap. The line lengths from ports 2 and 3 to ground are the same, but they are not a half length of port 1 to ground as the other two transformers. The area of this transformer is (4) (5) (6) Fig. 5. Simulated and measured results of: (a) js j, (b) js j, and (c) amplitude and phase difference of S and S of the conventional transformer. Measured result of total power loss (10jS j 0jS j 0jS j ) is also shown in (a). former is shown in Fig. 9(b). The gray metal, the metal with polka dots, and the metal with oblique stripes are all metals on the same layer. The difference in pattern between metals is only The total line number of upper and lower sides, which is different from the number of left and right sides,is. Instead of using one section coupled line to model the transformer, one -coupled line and one -coupled microstrip line are used to synthesize this transformer. The line length of the - and -coupled microstrip line are and, respectively. Similar to the previous two transformers, the inner square width is also an important factor of this transformer. One viahole is put in the center to decrease the coupling effect between the opposing sides of the coil. The design procedure of this transformer is similar to the conventional transformer; the only difference is that the number of turns is decided by (7)

5 3110 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 Fig. 9. (a) Simplified circuit diagram. (b) Structure of the single-coiled transformer. Fig. 10. Chip photograph of the single-coiled transformer. The chip size is mm. The simulated and measured results are shown in Fig. 11. The imbalance between ports 2 and 3 is similar to the conventional transformer. Fig. 11(a) also shows the measured total power losses of this transformer; it is below 8.7 db from 5 to 35 GHz. The coupled-line model is still valid for the initial design, while the EM simulations are within 1.5-dB differences to the measured results up to 25 GHz. Fig. 8. Simulated and measured results of: (a) js j, (b) js j, and (c) amplitude and phase difference of S and S of the Marchand-type transformer. Measured result of total power loss (10jS j 0jS j 0jS j ) is also shown in (a). which means that the line length from ports 2 or 3 to ground is equal to. The chip photograph of this transformer is shown in Fig. 10. The chip size is mm. III. MIXER IMPLEMENTATIONS AND MEASUREMENT RESULTS The three transformers are separately applied to three singly balanced mixer designs. The diode sizes of these mixers are all two-finger 20- m devices. The diode is realized by connecting the drain and source of a phemt as the cathode of the Schottky diode, while the gate metallization is realized as the anode. The cutoff frequency of the two-finger 20- m Schottky diode is 301 GHz. The whole circuits are simulated by the circuit simulator (HP/EEsof Libra). All these mixers are measured via on-wafer probing. We used an Agilent E8247C PSG as the LO source, and an HP83650B signal generator as the RF or IF source. A. Broad-Band Spiral Transformer Mixer The chip photograph of the broad-band spiral transformer mixer with the conventional transformer is shown in Fig. 12. The chip size is mm. The simulated and measured

6 WU et al.: COMPACT AND BROAD-BAND MILLIMETER-WAVE MONOLITHIC TRANSFORMER BALANCED MIXERS 3111 Fig. 12. Chip photograph of the broad-band spiral transformer mixer. The chip size is mm. Fig. 11. Simulated and measured results of: (a) js j, (b) js j, and (c) amplitude and phase difference of S and S of the single-coiled transformer. Measured result of total power loss (10jS j 0jS j 0jS j ) is also shown in (a). results of this mixer are shown in Fig. 13. The conversion loss is better than 10 db from 10 to 32 GHz. Between GHz, the conversion loss of this mixer is better than 6 db. The RF-to-IF Fig. 13. Simulated and measured: (a) conversion losses, RF-to-IF isolations, (b) LO-to-IF isolations, and LO-to-RF isolations of the broad-band spiral transformer mixer for down conversion, of which LO power is 13 dbm and IF is fixed at 1 GHz. isolation is not good at low frequency because only a series inductor and shunt capacitor are used for the IF low-pass filter.

7 3112 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 Fig. 14. Chip photograph of the Marchand-type transformer mixer. The chip size is mm. The LO-to-RF isolation is good at low frequency, but degrades at high frequency. The degredation is due to the imbalance from the transformer, specifically the magnitude imbalance. Since the imbalance of this transformer at low frequency is very small, and the low-pass filter has good rejection at high frequency, the LO-to-IF isolation is better than 33 db from 9 to 34 GHz. B. Marchand-Type Transformer Mixer The chip photograph of the Marchand-type transformer mixer is shown in Fig. 14. The chip size is mm. Fig. 15 shows the simulated and measured results of this mixer. It can be observed that the conversion loss is better than 10 db from 12 to 21 GHz. Between GHz, the conversion loss is better than 6 db. Due to the same reason as the broad-band spiral transformer mixer, the RF-to-IF isolation is not good at low frequency. The LO-to-RF and LO-to-IF isolations are better than 30 db from 12 to 21 GHz due to the good magnitude and phase balance of the Marchand-type transformer. C. Single-Coiled Transformer Mixer The chip photograph of the single-coiled transformer mixer is shown in Fig. 16. The chip size is mm. The simulated and measured results of this mixer are shown in Fig. 17. It can be seen that the conversion loss is better than 10 db from 10 to 30 GHz. From 15 to 23 GHz, the conversion loss is better than 5 db. The poor RF-to-IF isolation at low frequency is similar to the other two transformer mixers. The imbalance of the transformer degrades the LO-to-RF isolation. Due to the characteristic of the single-coiled transformer, the LO-to-RF isolation is good at low frequency, but becomes worse at high frequency. The LO-to-IF isolation is better than 30 db from 9 to 33 GHz because the imbalance of this transformer at low frequency is very small, as shown in Fig. 11(c), and the low-pass filter has good rejection at high frequency. In these three mixers, the LO-to-RF isolations are directly affected by the magnitude and phase imbalance of the transformers. The Marchand-type transformer has the lowest imbalance among these three transformers, therefore, its LO-to-RF isolation is also the best. The LO-to-IF isolation is not only caused by the imbalance of the transformer, but also by the rejection of the low-pass filter at the IF port. All these mixers have better than 30-dB LO-to-IF isolations. The RF-to-IF isolations are determined by the rejection level of the high-pass filter in Fig. 15. Simulated and measured: (a) conversion losses, RF-to-IF isolations, (b) LO-to-IF isolations, and LO-to-RF isolations of the Marchand-type transformer mixer for down conversion, of which LO power is 13 dbm and IF is fixed at 2 GHz. Fig. 16. Chip photograph of the single-coiled transformer mixer. The chip size is mm. the RF port and the low-pass filter in the IF port, therefore, the isolations of the mixers are about the same. The cause for the variation of conversion losses is more complicated, and cannot be determined directly from the transformers.

8 WU et al.: COMPACT AND BROAD-BAND MILLIMETER-WAVE MONOLITHIC TRANSFORMER BALANCED MIXERS 3113 approximately 0.29 mm. The proposed single-coiled mixer have a bandwidth of 100%, the conversion loss is better than 10 db between GHz and below 5 db from 15 to 23 GHz. Its chip size is very compact, only 0.25 mm. ACKNOWLEDGMENT The chip was fabricated by WIN Semiconductors, Taoyuan, Taiwan, R.O.C., through the Chip Implementation Center of Taiwan, Taiwan, R.O.C. The authors would like to thank H.-Y. Chang, M.-F. Lei, and M.-C. Yeh, all with National Taiwan University, Taiwan, R.O.C., Prof. Y.-S. Lin, National Central University, Taiwan, R.O.C., and J.-S. Fu, The University of Michigan at Ann Arbor, for their helpful suggestions. Fig. 17. Simulated and measured: (a) conversion losses, RF-to-IF isolations, (b) LO-to-IF isolations, and LO-to-RF isolations of the single-coiled transformer mixer for down conversion, of which LO power is 13 dbm and IF is fixed at 1 GHz. Among these three mixers, the broad-band spiral transformer mixer has the widest bandwidth with an aspect ratio of greater than 1 : 3. The Marchand-type one has the best isolations, but the bandwidth is much smaller than the others. The bandwidth is limited due to the impedance matching between the diodes and transformer. The single-coiled transformer mixer has comparable performance compared to the other two with the smallest chip area. IV. CONCLUSION Three broad-band compact singly balanced transformer mixers have been designed, fabricated, and tested. The multicoupled-line equivalent models are proposed to synthesize these transformer mixers in the initial designs. Conventional and Marchand-type transformers have been used to realize the mixers with bandwidths of 105% and 54.5%, and conversion losses better than 10 db from 10 to 32 and 12 to 21 GHz, respectively. The individual chip size of each chip is only REFERENCES [1] S. A. Maas, Mixer technologies for modern microwave and wireless systems, in Proc. GaAs 2002 Conf., Sep. 2002, pp [2] H. J. Siweris and H. Tischer, Monolithic coplanar 77 GHz balanced HEMT mixer with very small chip size, in IEEE MTT-S Int. Microwave Symp. Dig., Jun. 2003, pp [3] K. Osafune and Y. Yamauchi, 20-GHz 5-dB-gain analog multipliers with AlGaAs/GaAs HBTs, IEEE Trans. Microw. Theory Tech., vol. 42, no. 3, pp , Mar [4] B. Tzeng, C.-H. Lien, H. Wang, Y.-C. Wang, P.-C. Chao, and C.-H. Chen, A 1 17 GHz InGaP GaAs HBT MMIC analog multiplier and mixer with broad-band input-matching networks, IEEE Trans. Microw. Theory Tech., vol. 50, no. 11, pp , Nov [5] M.-D. Tsai, C.-S. Lin, C.-H. Wang, C.-H. Lien, and H. Wang, A GHz SiGe BiCMOS analog multiplier and mixer based on attenuationcompensation technique, in IEEE RFIC Symp. Dig., Jun. 2004, pp [6] Alpha Industries Inc., Woburn, MA, AMD038S1-00 Data Sheet, [7] S. A. Maas, F. M. Yamada, A. K. Oki, N. Matovelle, and C. Hochuli, An GHz monolithic ring mixer, in IEEE RFIC Symp. Dig., Jun. 1998, pp [8] S. J. Mahon and J. T. Harvey, Wide-band MMIC Kowari mixer/phase shifters, IEEE Trans. Microw. Theory Tech., vol. 49, no. 7, pp , Jul [9] C. J. Trantanella, Ultra-small MMIC mixers for K- and Ka-band communications, in IEEE MTT-S Int. Microwave Symp. Dig., Jun. 2000, pp [10] P.-S. Wu, C.-H. Tseng, T.-W. Huang, and H. Wang, A singly balanced millimeter-wave mixer using a compact transformer, in Asia Pacific Microwave Conf. Dig., vol. 3, Nov. 2003, pp [11] K. S. Ang, S. B. Economides, S. Nam, and I. D. Robertson, A compact MMIC balun using spiral transformers, in Asia Pacific Microwave Conf., vol. 3, Dec. 1999, pp [12] Y. J. Yoon, Y. Lu, R. C. Frye, M. Y. Lau, P. R. Smith, L. Ahlquist, and D. P. Kossives, Design and characterization of multilayer spiral transmission-line baluns, IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp , Sep [13] M. Shimozawa, K. Itoh, Y. Sasaki, H. Kawano, Y. Isota, and O. Ishida, A parallel connected Marchand balun using spiral shaped equal length coupled lines, in IEEE MTT-S Int. Microwave Symp. Dig., Jun. 1999, pp [14] A. M. Niknejad and R. G. Meyer, Design, Simulation and Applications of Inductors and Transformers for RF ICs. Norwell, MA: Kluwer, [15] J. R. Long, Monolithic transformers for silicon RF IC design, IEEE J. Solid-State Circuit, vol. 35, no. 9, pp , Sep [16] S. A. Maas, Microwave Mixers, 2nd ed. Boston: Artech House, [17] Sonnet User s Manual, Release 8.53, Sonnet Software Inc., Liverpool, NY, [18] J. R. Long and M. A. Copeland, The modeling, characterization, and design of monolithic inductors for silicon RF IC s, IEEE J. Solid-State Circuit, vol. 32, no. 3, pp , Mar [19] M. Davidovitz, Reconstruction of the S-matrix for a 3-port using measurements at only two ports, IEEE Microw. Guided Wave Lett., vol. 5, pp , Oct [20] H.-C. Lu and T.-H. Chu, Port reduction methods for scattering matrix measurement of an n-port network, IEEE Trans. Microw. Theory Tech., vol. 48, no. 6, pp , Jun

9 3114 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 Chi-Hsueh Wang was born in Kaohsiung, Taiwan, R.O.C. in He received the B.S. degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1997, and the Ph.D. degree from National Taiwan University, Taipei, Taiwan, R.O.C. in He is currently a Post-Doctoral Research Fellow with the Graduate Institute of Communication Engineering, National Taiwan University. His research interests include the design and analysis of microwave and millimeter-wave circuits and computational electromagnetics. Pei-Si Wu was born in Changhua, Taiwan, R.O.C., in He received the B.S. degree in electric engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 2002, and is currently working toward the Ph.D. degree at the National Taiwan University. He is currently with the Graduate Institute of Communication Engineering, National Taiwan University. His research interests include microwave and millimeter-wave circuit designs. Huei Wang (S 83 M 87 SM 95) was born in Tainan, Taiwan, R.O.C., on March 9, He received the B.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 1980, and the M.S. and Ph.D. degrees in electrical engineering from Michigan State University, East Lansing, in 1984 and 1987, respectively. During his graduate study, he was engaged in research on theoretical and numerical analysis of EM radiation and scattering problems. He was also involved in the development of microwave remote detecting/sensing systems. In 1987, he joined the Electronic Systems and Technology Division, TRW Inc. He was a Member of the Technical Staff and Staff Engineer responsible for monolithic-microwave integrated-circuit (MMIC) modeling of computer-aided design (CAD) tools, MMIC testing evaluation, and design. He then became the Senior Section Manager of the Millimeter Wave Sensor Product Section, RF Product Center, TRW Inc. In 1993, he visited the Institute of Electronics, National Chiao-Tung University, Hsin-Chu, Taiwan, R.O.C., and taught MMIC-related topics. In 1994, he returned to TRW Inc. In February 1998, he joined the faculty of the Department of Electrical Engineering, National Taiwan University, as a Professor. Dr. Wang is a member of Phi Kappa Phi and Tau Beta Pi. Tian-Wei Huang (S 91 M 98 SM 02) received the B.S. degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1987, and the M.S. and Ph.D. degree in electrical engineering from the University of California at Los Angeles (UCLA), in 1990 and 1993, respectively. In 1993, he joined the TRW RF Product Center, Redondo Beach, CA. From 1998 ti 1999, he was with Lucent Technologies, where he was involved with local multipoint distribution system (LMDS) fixed wireless systems. From 1999 to 2002, he was involved with RF/wireless system testing with Cisco Systems. In August 2002, he joined the faculty of the Department of Electrical Engineering, National Taiwan University. His research has focused on the design and testing of monolithic microwave integrated circuits (MMICs) and RF integrated circuits (RFICs). His current research interests are MMIC/RFIC design, packaging, and RF system-on-chip (SOC) integration.