WITH THE rapid growth of the demand for low-power,

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1 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 55, NO. 11, NOVEMBER Accurate Systematic Mode-Parameter Extraction for On-Chip Spira Inductors Hao-Hui Chen, Member, IEEE, Huai-Wen Zhang, Shyh-Jong Chung, Senior Member, IEEE, Jen-Tsai Kuo, Senior Member, IEEE, and Tzung-Chi Wu Abstract A systematic mode-parameter-extraction technique is presented for accuratey modeing on-chip spira inductors in radio frequency integrated circuits (RFICs). The mode is a π-circuit with an additiona parae RC network connecting both vertica branches to account for substrate couping. The extraction starts with extracting the series inductance and resistance at ow frequencies. Then, the oxide capacitance is evauated in an intermediate frequency range. Afterward, the substrate effects incuding the substrate resistance and capacitance, as we as couping, are extracted at higher frequencies. A the umped circuit eement vaues are anayticay determined by the network anaysis from the measured network parameters (S- ory -parameters). The proposed approach thus can provide better circuita interpretations of the inductor behaviors for faciitating the design of RFIC inductors. Square and circuar CMOS spira and octagona BiCMOS7 spira inductors are investigated to test this technique. Highy accurate frequency responses by the extracted parameters are obtained over a wide frequency band without any optimization. This reveas the vaidation and capabiity of the proposed parameter-extraction method. Index Terms Inductor mode, parameter extraction, spira inductors. I. INTRODUCTION WITH THE rapid growth of the demand for ow-power, ow-cost, and high-integration wireess communication systems, the deveopment of on-chip passive devices for radio frequency integrated circuits (RFICs) has emerged as a critica issue recenty. Among the passive circuit designs, on-chip spira inductors are particuary important and widey used in RFICs such as mixers, ow-noise ampifiers, and osciators. To faciitate the circuit simuation and optimization of RFICs, various modern inductor modes such as modified π-modes [1] [8], doube-π modes [9], [10], higher order intrinsic modes [11], and T-modes [12] [14] have been deveoped to characterize RFIC inductors in a wide frequency band. As the circuit scheme of a comprehensive inductor mode generay Manuscript received May 22, 2008; revised August 19, Current version pubished October 30, This work was supported in part by the MoE ATU program, Taiwan, and in part by the SRC program under Contract 2003-TJ The review of this paper was arranged by Editor V. R. Rao. H.-H. Chen was with the Department of Eectronic Engineering, Huafan University, Taipei 22301, Taiwan, R.O.C. He is now with the Department of Eectronic Engineering, Nationa Kaohsiung First University of Science and Technoogy, Kaohsiung 824, Taiwan, R.O.C. (e-mai: hhchen@huafan. hfu.edu.tw). H.-W. Zhang is with the United Microeectronics Corporation, Hsinchu 300, Taiwan, R.O.C. S.-J. Chung and J.-T. Kuo are with the Department of Communication Engineering, Nationa Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. T.-C. Wu is with Inventec Corporation, Taoyuan 335, Taiwan, R.O.C. Digita Object Identifier /TED consists of severa series and shunt branches, to accuratey extract the circuit eements in such a compicated mode is a chaenging task. Physics-based formuation and quasi-static eectromagnetic cacuation have been proposed for evauating the eements in the circuit mode [2] [4], [9]. However, the resuts predicted by these approaches are normay estimated soutions. A parameter-extraction technique based on measurement data is therefore indispensabe for accurate extraction of the mode parameters. Curve fitting approaches using various mathematica techniques such as genetic agorithm, partice swarm optimization, vector fitting procedure, and augmentation method have been appied to extract the mode parameters from the measured data [8], [13] [16]. In genera, these mathematica treatments can greaty improve the mode accuracy, but they often require considerabe computing resources, as we as proper initia guesses to obtain accuratey converged soutions. Moreover, it is difficut to acquire the reated physica conceptions of the effects of mode parameters on the inductor characteristics from these mathematics-based methodoogies. On the other hand, anaytica extraction techniques based on the network anaysis, such as those reported in [12] [14] and [17] [19], are much more efficient and capabe of providing physica aspects of the inductor behaviors. In these anaytica approaches, approximations that are vaid at reativey ow or high frequencies are usuay utiized to decompose the compicated circuit mode into severa subcircuits. The eements are then extracted step by step from the simpified subcircuits. Athough these network-based extraction techniques are effective and suitabe for physica modeing, there are sti chaenges and need for further improvements. As mentioned earier, the subcircuits treated in each extracting procedure are approximated resuts of the whoe circuit mode in certain frequency ranges. Determining the frequency bands appicabe for the approximations woud be an important concern to the accurate extraction of the eement vaues. This critica issue, however, has not been given the attention it needs. Furthermore, even in the anaysis of the simpified subcircuits, numerica manipuation and/or assumption, such as vector fitting [13], [14], iterative computation [18], power-series approximation [19], and symmetrica assumption [12], [18], [19], were often required to dea with the parameter extraction. Due to the errors stemmed from the approximations and numerica treatments appied in the extracting procedures, further optimization is generay required to improve the accuracy of the fina resuts. In this paper, an accurate systematic parameter-extraction technique for on-chip spira inductors is presented. Fig. 1 shows the circuit mode for inductors to be investigated. This mode is /$ IEEE

2 3268 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 55, NO. 11, NOVEMBER 2008 Fig. 1. Enhanced circuit mode for on-chip spira inductors. Fig. 2. Top view of the tested 4.5-turn square spira inductor. first proposed in [1] and has been used in various RF circuit designs [20], [21]. It is named as the enhanced mode herein. To extract the 12 eements in the mode, the circuit is decomposed into severa subcircuits based on suitabe approximations in certain frequency ranges. By the network anaysis of the simpified subcircuits, the series inductance and resistance of the spira meta coi (L s0, R s0, L s1, and R s1 ) are first extracted from the measured Y -parameters at ow frequencies. The oxide capacitance between the spira and the siicon substrate (C ox1 and C ox2 ) is then evauated in an intermediate frequency range. Afterward, the eements representing the substrate resistance (R Si1 and R Si2 ) and capacitance (C Si1 and C Si2 ), as we as the atera couping among the meta ines (R sub and C sub )are extracted at higher frequencies. To mitigate the possibe errors resuted from the approximations, the frequency bands suitabe for the considered subcircuits are quantitativey determined by the Y -parameters. Such a procedure can aso be utiized to assess the contributions of oxide and substrate parasitics at a specified operating frequency. It wi be seen that the circuita equations for soving the mode parameters derived in the proposed approach are very simpe. No compex mathematica manipuation (such as vector fitting or iterative cacuation) is required. The extraction is therefore very efficient and easy to be automaticay impemented. Meanwhie, since the mode parameters are anayticay extracted by the network anaysis, this technique can provide better circuita interpretations of the inductor behaviors for faciitating the RFIC inductor designs. Square and circuar CMOS spira and octagona BiCMOS7 spira inductors are used to test the presented technique. Highy accurate simuations by the extracted parameters are obtained over a wide frequency band without a need for further optimization, indicating the vaidation and capabiity of the proposed extraction method. II. PARAMETER-EXTRACTION PROCEDURE To iustrate the proposed parameter-extraction method, a 4.5-turn square spira fabricated by the 0.18-μm 1P6M CMOS process with 2-μm top meta thickness is used as an exampe. Fig. 2 shows the top view of the inductor, where the inewidth (W ), ine spacing (S), and inner radius (R) are 14.5, 2, and 60 μm, respectivey. The underpass is ocated on the meta-five ayer. The substrate resistivity is approximatey 10 Ω cm, and the thickness of the oxide dieectric Fig. 3. Comparison of shunt and series admittances of the π-network for the inductor circuit. is about 7.5 μm. It is noticed that this exampe has been investigated and characterized by the enhanced mode in [1] and [19]. One can therefore objectivey compare the resuts obtained by the proposed technique with the pubished data. Moreover, to obtain the measured network parameters (S- or Y -parameters) for performing the extraction, one notes that the enhanced mode with the eements cacuated by optimization can accuratey simuate the measured S- and Y -parameters [1]. It woud be reasonabe to treat the resuts modeed by the optimized eements as the measured data. We thus utiize these pseudomeasurement resuts to extract the mode parameters in the foowing. A. Low-Frequency Approximation As shown in Fig. 1, the enhanced mode can be treated as a parae combination of the upper and ower subcircuits. Due to the dc-bocking property of the oxide capacitances C ox1 and C ox2, one can remove the ower subcircuit and approximatey characterize the inductor by the upper subcircuit at ow frequencies. Such an approximation has been widey appied to find the series inductance and resistance in many iteratures (e.g., [17] [19]). To mitigate the errors resuted from the approximation, however, the upper frequency imit appicabe to the approximation shoud be specified. For vaidation, a π-network shown in the inset of Fig. 3 is used to temporariy mode the inductor. In the network, the series admittance Yseries m = Y 12 m, and the two shunt ones Yshunt1 m = Y 11 m + Y12 m and Yshunt2 m = Y22 m + Y12 m, where Y11 m, Y22 m, and Y12 m are the measured twoport Y -parameters of the entire inductor. Fig. 3 shows the

3 CHEN et a.: ACCURATE SYSTEMATIC MODEL-PARAMETER EXTRACTION FOR ON-CHIP SPIRAL INDUCTORS 3269 magnitudes of the shunt admittances normaized with respect to that of the series admittance. It can be observed that, the ower the frequency, the smaer are the normaized magnitudes and, thus, the better the shunt branches behave ike an open path. The upper frequency imit f 1 can therefore be specified by sufficient sma normaized magnitudes. Here, 1% is chosen as the upper bound of both magnitudes. For the particuar exampe, f 1 = 0.52 GHz is obtained. B. Extraction of L s0, R s0, L s1, and R s1 When f f 1, the upper subcircuit can approximatey represent the entire inductor. The impedance Z u of the series arm is then represented by the measured Y12 m as Z u = R u (ω)+jωl u (ω) =Re[ 1/Y m 12 ]+jim[ 1/Y m 12 ]. Moreover, from simpe network anaysis, Z u can be expressed in terms of the unknown eements L s0, R s0, L s1, and R s1 as Fig. 4. R u(ω) R dc as functions of (a) L dc L u(ω) and (b) (1 + T 2 /ω 2 ) 1. The sopes T and M are derived in the ow frequency range f f 1. R u (ω) =R s0 R s1 R t + ω 2 L 2 s1 R 2 t + ω 2 L 2 s1 R2 s0l s1 L u (ω) =L s0 + Rt 2 + ω 2 L 2 s1 (1) where R t = R s0 + R s1. The dc resistance and inductance are then equa to (1) evauated at ω = 0 R dc = R s0r s1 R t L dc = L s0 + R2 s0l s1 Rt 2. (2) From (1) and (2), it can be readiy verified that where R u (ω) R dc = T (L dc L u (ω)) (3) R u (ω) R dc = M(1 + T 2 /ω 2 ) 1 (4) T = R t M = R s0 R dc. (5) L s1 Note that R u (ω) and L u (ω) in (3) and (4) are obtained by the measured Y12 m data, whereas R dc and L dc are determined by Y12 m measured at the ow frequency imit. Then, R u (ω) R dc as a function of L dc L u (ω) can be potted as shown in Fig. 4(a). (The frequency is aso abeed on the upper horizonta axis in Fig. 4 for reference). It can be observed that R u (ω) R dc is very cose to a inear function of L dc L u (ω) for f f 1, and the coefficient T in (3) can then be computed from its sope. Moreover, it is worthy to note that, when frequency goes beyond about 0.75 GHz, where Yshunt1,2 m / Y series m 0.02 (see Fig. 3), the variation of R u (ω) R dc with regard to L dc L u (ω) graduay deviates from inear characteristics. Since the inear behavior exists ony when the ow-frequency approximation is effective, the vaue of Yshunt1,2 m / Y series m used to determine the upper frequency imit f 1 discussed in Section II-A shoud be imited to This finding can serve as a guideine for the choice of the upper bound of Yshunt1,2 m / Y series m in determining the ow-frequency band. By the T vaue, R u (ω) R dc versus (1 + T 2 /ω 2 ) 1 is shown in Fig. 4(b). A good inear dependence of R u (ω) R dc Fig. 5. Comparison of shunt and series admittances of the π-network for the ower subcircuit. on (1 + T 2 /ω 2 ) 1 is observed again for f f 1, and the coefficient M in (4) can then be evauated by finding the sope. With the cacuated coefficients T and M, and the measured R dc and L dc, the vaues of L s0, R s0, L s1, and R s1 can then be cacuated from (2) and (5) as C. Extraction of C ox R s0 = M + R dc (6a) R s1 = R s0r dc M (6b) L s0 = L dc M T (6c) L s1 = R s0 + R s1. T (6d) When f>f 1, the ower subcircuit has to be taken into account. Since the enhanced mode is a parae connection of the upper and ower subcircuits (see Fig. 1), the admittance Y -matrix of the ower subcircuit [Y ] can be then cacuated as [Y ]=[Y m ] [Y u ], where [Y m ] is the measured Y -matrix of the entire inductor and [Y u ] is that of the upper subcircuit which can be obtained once L s0, R s0, L s1, and R s1 are known. By the matrix [Y ], an equivaent π-network with the series admittance Yseries = Y 12 and the shunt ones Yshunt1 = Y 11 + Y12 and Yshunt2 = Y 22 + Y12 is then constructed to characterize the ower subcircuit, where Y11, Y22, and Y12 are the entries of [Y ]. Fig. 5 shows the pot of the ratios Yseries / Y shunt1,2

4 3270 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 55, NO. 11, NOVEMBER 2008 Fig. 6. ( 1/Im[Z i ]) and (1/Re[Z i ]) as functions of frequency. The inear sope for ( 1/Im[Z i ]) is derived in the intermediate frequency range f 1 f f 2. for 0.5 GHz f 2 GHz. One can see that the ratios are much smaer than unity over the frequency band. A frequency f 2 beow which Yseries Y shunt1 and Yshunt2 can be then defined to approximate the series branch as an open path. Here, 0.05 is adopted for the upper bound of the ratios to define f 2. Such a condition impies that the parae network of R sub and C sub woud behave ike an open circuit in the intermediate frequency range f 1 f f 2, and the impedance of the eft part of the ower subcircuit (see the inset of Fig. 6) can consequenty be written as Z i =1/(Y11 + Y12), which yieds 1 Re [ 1/ ( Y11 + Y )] 12 = 1 Re[Z i ] = 1 + ω 2 C R Si1R 2 Si1 Si1 1 Im [ 1/ ( Y11 + Y )] 12 = 1 Im[Z i ] = ( 1 ωc ox1 + ωc Si1 1/R 2 Si1 + ω2 C 2 Si1 (7a) ) 1. (7b) Moreover, a further investigation, as shown in Fig. 6, indicates that ( 1/Im[Z i ]) shows a good inear variation, whereas (1/Re[Z i ]) is amost invariant as frequency is changed in f 1 f f 2. These reationships exist since both 1/ωC ox1 and 1/ωC Si1 are reativey high impedances in comparison with R Si1 in the band. Equation (7b) is therefore simpified as 1 Im [ 1/ ( Y11 + Y )] 12 = 1 Im[Z i ] ωc ox1. (8) From the inear regression in (8) in f 1 f f 2, C ox1 can then be extracted. A simiar treatment can be appied to the right part of the ower subcircuit to extract C ox2 by using the Y22 data. In addition, it is worthy mentioning that R Si1 coud be comparabe with 1/ωC Si1 when a high-resistivity siicon substrate is considered. In such a scenario, the inear variation of (1/Re[Z i ]) with regard to ω 2, as characterized by (7a), can be potted to extract R Si1 and C Si1. With the obtained R Si1 and C Si1, C ox1 is then cacuated from (7b). Fig. 7. Representation of the ower subcircuit by (a) a combination of the substrate body and C ox1,2, and (b) an equivaent T-network. D. Extraction of R Si, C Si, R sub, and C sub Having determined C ox1 and C ox2, the remaining eements R Si1,2, C Si1,2, R sub, and C sub are next extracted over f f 2. As shown in Fig. 7(a), the ower subcircuit can be treated as a combination of the substrate body and C ox1,2, where the substrate body is formed by a π-network with the series admittance Yseries s = 1/R sub + jωc sub and the two shunt ones Yshunt1,2 s = 1/R Si1,2 + jωc Si1,2. By using an equivaent T-network with the series impedances Z a,b and the shunt one Z c to mode the substrate body, the whoe ower subcircuit can be represented by a T-network, as shown in Fig. 7(b). One then obtains Z a = Z11 (jωc ox1 ) 1, Z b = Z22 Z12 (jωc ox2 ) 1, and Z c = Z12, where Z11, Z22, and Z12 are the Z-parameters of the ower subcircuit; they can be readiy computed by the Y -matrix of the ower subcircuit [Y ] obtained in Section II-C. Finay, by appying the T to π transformation, the T-network of the substrate body can be transformed into the desired π equivaent circuit to find the admittances Yshunt1,2 s and Yseries s, which eads to Yseries s = 1/R sub + jωc sub = Z c /F Yshunt1 s = 1/R Si1 + jωc Si1 = Z b /F Yshunt2 s = 1/R Si2 + jωc Si2 = Z a /F (9a) (9b) (9c) where F = Z a Z b + Z b Z c + Z c Z a. The eements R Si1,2, C Si1,2, R sub, and C sub can be further extracted. Fig. 8 shows the cacuated Yseries s and Y shunt1,2 s as functions of frequency. Frequency-independent resuts for Re[Yseries s ] and Re[Yshunt1,2 s ], which correspond to 1/R sub and 1/R Si1,2,are ceary observed in f f 2. Meanwhie, it is found that the variations of Im[Yseries s s ] and Im[Yshunt1,2 ] with regard to frequency exhibit good inear behavior at high frequencies. The eements C sub and C Si1,2 can be then simpy extracted from the sopes of these inear curves.

5 CHEN et a.: ACCURATE SYSTEMATIC MODEL-PARAMETER EXTRACTION FOR ON-CHIP SPIRAL INDUCTORS 3271 Fig. 8. Yseries s and Y shunt1,2 s as functions of frequency. TABLE I MODEL PARAMETERS FOR THE TESTED 4.5-TURN SQUARE SPIRAL INDUCTOR.LINEWIDTH W = 14.5 μm, LINE SPACING S = 2 μm, AND INNER RADIUS R = 60 μm Fig. 9. Comparison of measured and modeed inductance, resistance, and quaity factor for the tested 4.5-turn CMOS square spira inductor. Line width W = 14.5 μm, ine spacing S = 2 μm, and inner radius R = 60 μm. TABLE II MODEL PARAMETERS FOR THE 2.5- AND 6.5-TURN INDUCTORS. LINEWIDTH W = 14.5 μm, LINE SPACING S = 2 μm, AND INNER RADIUS R = 60 μm III. RESULTS AND DISCUSSION A. Comparison of the Extracted Resuts and Pubished Data Tabe I ists the extracted mode parameters for the inductor tested in Section II. The resuts are compared with the optimization soutions in [1] and the data by an aternative extraction technique in [19]. It can be seen that our resuts are very cose to the optimization soutions. The ony significant deviation is the vaue of R sub. Note that the parae R sub C sub network is used to mode the atera couping among the spira meta ines. The couping is dominated by R sub at ow frequencies and by C sub at high frequencies [1], [22]. The accuracy of R sub vaue is therefore important ony at reativey ow frequencies, where, at the same time, the characteristics of the whoe inductor circuit are mainy governed by the upper subcircuit (L s0, R s0, L s1, and R s1 ) since C ox1 and C ox2 bock ow-frequency signas. Thus, it is reasonabe to concude that the accuracy of R sub vaue woud not be critica to the prediction of the inductor characteristics. Based on the extracted umped circuit eement vaues, Fig. 9 shows the simuated responses of the key characteristics of the inductor, incuding the series inductance L s =Im[ 1/Y12 m ]/ω, series resistance R s =Re[ 1/Y12 m ], and quaity factor Q = Im[Y11 m ]/Re[Y11 m ] and compared with the measured data [1]. The resuts with removing the R sub is aso potted for comparison. Very good agreement between the simuations and measurements can be observed in the whoe frequency range of interest. The root-mean-square deviations for L s, R s, and Q are 0.30%, 1.73%, and 1.38%, respectivey. Athough not shown in this paper, good coincidence between the simuation and measurement for the S-parameters has aso been examined. In addition, it is found that the resuts predicted by the mode without R sub are amost identica to those cacuated by the origina enhanced mode. This observation justifies the trivia effect of R sub on the inductor performance. The enhanced circuit mode can be therefore further simpified by eiminating R sub with itte cost. The proposed method has further been checked by investigating inductors with different numbers of turns. Tabe II compares the extracted mode parameters for inductors with

6 3272 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 55, NO. 11, NOVEMBER 2008 Fig. 11. Comparison of measured and modeed inductance, resistance, and quaity factor for an eight-turn BiCMOS7 octagona spira inductor. Linewidth W = 4 μm, ine spacing S = 3 μm, and outer diameter OD = 160 μm. Fig. 10. Comparison of measured and modeed inductance, resistance, and quaity factor for 0.13-μm CMOS circuar spira inductor with various outer diameters. Coi number N =3.5, inewidth W = 6 μm, and ine spacing S = 2 μm. 2.5 and 6.5 turns given in [1]. Again, the resuts by the proposed approach have cose agreement with the optimization for both the exampes. B. Experimenta Verification To aow for actua industria appications, three 3.5-turn circuar spiras with the outer diameters (ODs) being 100, 150, and 200 μm have been fabricated and measured to perform the experimenta verification of the proposed technique. These inductors were impemented in the UMC 0.13-μm 1P8M mixedmode/rf CMOS process. The spiras with meta thickness being 2 μm were fabricated on the meta-eight ayer, and the underpass was deposited on the meta-seven ayer. The inewidth W and ine spacing S are 6 and 2 μm, respectivey. Moreover, the measured raw data are de-embedded with a twostep (open and short) procedure [23] to remove the undesired pad parasitics. Fig. 10 shows the comparison of the modeed and measured L s, R s, and Q of the tested sampes. It is seen that the modeed resuts based on the extracted parameters fit accuratey to the measurement data over a wide frequency range from 0.1 to 20 GHz, indicating the wideband modeing capabiity of the proposed extraction technique, as we as the enhanced mode. C. Appicabiity to Other IC Fabrication Technoogy In addition to the aforementioned CMOS inductors, the modeing of inductors impemented by other IC fabrication technoogy is aso considered. Fig. 11 shows the L s, R s, and Q of an eight-turn octagona spira fabricated by the BiCMOS7 process [8]. The inewidth W, ine spacing S, and outer diameter OD of the considered inductor are 4, 3, and 160 μm, respectivey. It is observed that the resuts simuated by the enhanced mode with the proposed parameter-extraction method match we with the measurements in [8]. This indicates that the presented approach and the enhanced circuit mode are suitabe for deaing with various RFIC inductors. IV. CONCLUSION A systematic technique for accuratey extracting mode parameters of on-chip spira inductors has been presented. By introducing suitabe approximations, the circuit eements in the mode can be anayticay extracted in different frequency bands using the network anaysis. The vaidation and capabiity of the proposed extraction method have been demonstrated by the modes of square and circuar CMOS spira and octagona BiCMOS7 spira inductors. Moreover, it is found that the atera resistive couping R sub has negigibe effects on the prediction of inductor characteristics. The enhanced circuit mode can be therefore further simpified by eiminating R sub without sacrificing the mode accuracy. ACKNOWLEDGMENT The authors woud ike to thank the staff members of UMC for the fabrication and measurement of the test sampes and the reviewers for the vauabe comments that heped to improve the content of this paper. REFERENCES [1] J. Gi and H. Shin, A simpe wide-band on-chip inductor mode for siicon-based RF ICs, IEEE Trans. Microw. Theory Tech., vo. 51, no. 9, pp , Sep [2] J. R. Long and M. A. Copeand, The modeing, characterization, and design of monoithic inductors for siicon RF ICs, IEEE J. Soid State Circuits, vo. 32, no. 3, pp , Mar [3] A. M. Niknejad and R. G. Meyer, Anaysis, design, and optimization of spira inductors and transformers for Si RF ICs, IEEE J. Soid State Circuits, vo. 33, no. 10, pp , Oct [4] C. P. Yue and S. S. Wong, Physica modeing of spira inductors on siicon, IEEE Trans. Eectron Devices, vo. 47, no. 3, pp , Mar [5] I. C. H. Lai and M. Fujishima, A new on-chip substrate-couped inductor mode impemented with scaabe expressions, IEEE J. Soid State Circuits, vo. 41, no. 11, pp , Nov [6] D. Meendy, P. Francis, C. Picher, K. Hwang, G. Srinivasan, and A. Weisshaar, A new wide-band compact mode for spira inductors

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Lee, Current reused LC VCOs, IEEE Microw. Wireess Compon. Lett., vo. 15, no. 11, pp , Nov [22] W. Jin, Y. Eo, J. I. Shim, W. R. Eisenstadt, M. Y. Park, and H. K. Yu, Siicon substrate couping noise modeing, anaysis, and experimenta verification for mixed signa integrated circuit design, in Proc. IEEE MTT-S Int. Microw. Symp. Dig., 2001, pp [23] Y. Cheng, M. J. Deen, and C.-H. Chen, MOSFET modeing for RF IC design, IEEE Trans. Eectron Devices, vo. 52, no. 7, pp , Ju Huai-Wen Zhang received the B.S.E.E. degree and M.S. degree in communication engineering from the Nationa Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2004 and 2006, respectivey. He is currenty with the United Microeectronics Corporation, Hsinchu. His research interests incude active and passive RF devices and advance processes for RFICs. Shyh-Jong Chung (M 92 SM 06) received the B.S.E.E. and Ph.D. degrees from the Nationa Taiwan University, Taipei, Taiwan, R.O.C., in 1984 and 1988, respectivey. Since 1988, he has been with the Department of Communication Engineering, Nationa Chiao Tung University, Hsinchu, Taiwan, where he is currenty a Professor. From 1995 to 1996, he was a Visiting Schoar with the Department of Eectrica Engineering, Texas A&M University, Coege Station. His areas of interest incude the design and appications of active and passive panar antennas, communications in inteigent transportation systems, LTCC-based RF components and modues, packaging effects of microwave circuits, and c eectromagnetics. Jen-Tsai Kuo (S 88 M 92 SM 04) received the Ph.D. degree from the Institute of Eectronics, Nationa Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in Since 1984, he has been with the Department of Communication Engineering, NCTU, where he is currenty a Professor. In , he was a Visiting Schoar with the Eectronic Engineering Department, University of Caifornia, Los Angees. His research interests incude anaysis and design of microwave integrated circuits and numerica techniques in eectromagnetics. Dr. Kuo is currenty an Editoria Board member of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS. He was one of the recipients of the best paper award of the 2002 Nationa Teecommunication Conference, Taiwan, and the Asia Pacific Microwave Conference Prize, Bangkok, Thaiand, December He aso received the Taiwan Citation Laureate 2006 from the Thomson Scientific and the 2007 Distinguished Research Award from the Nationa Science Counci, Taiwan. Hao-Hui Chen (M 99) received the B.S. degree in physics from the Nationa Centra University, Taoyuan, Taiwan, R.O.C., in 1991 and the Ph.D. degree in communication engineering from the Nationa Chiao Tung University, Hsinchu, Taiwan, in From 1998 to 2008, he was with the Department of Eectronic Engineering, Huafan University, Taipei, Taiwan. Since 2008, he has been with the Department of Eectronic Engineering, Nationa Kaohsiung First University of Science and Technoogy, Kaohsiung, Taiwan, where he is currenty an Associate Professor. His research interests incude passive component and circuit designs for RFICs, RF and microwave circuit designs, RFIC device modeing, panar antenna design, and computationa eectromagnetics. Tzung-Chi Wu was born in Yunin, Taiwan, R.O.C., in He received the B.S.E.E. degree from the Technoogy and Science Institute of Northern Taiwan, Taipei, Taiwan, in He is currenty with Inventec Corporation, Taoyuan, Taiwan. His current research interests focus on the modeing of on-chip spira inductors.