This paper presents a study of the nonlinear effects introduced by MEMS varactors when excited with digitally modulated RF signals (QPSK and 16 QAM). The study is based on simulating a nonlinear model of the MEMS device using harmonic-balance and envelope solvers, and on experimental measurements of the wave reflected by the on-wafer MEMS device. It is shown that the adjacent-channel power ratio (ACPR) and error-vector magnitude (EVM) of the digital signal suffer a degradation due to the device nonlinear distortion.Peer Reviewe

Girbau Sala, David

Lázaro Guillén, Antoni

Pradell i Cara, Lluís

Microwave and Optical Technology Letters

English

UPCommons. Portal del coneixement obert de la UPC

At the outset, we mentioned that the present algorithm has beentested for a variety of wire geometries and in each case thenumerical results, that is, the current distribution and RCS com-pared very well with the standard MoM solution. In Table 1, wepresent several numerical examples involving a variety of geomet-rical shapes and incident ﬁelds. We note that the parameter Krepresents the number of nonzero elements in each column for theN  N matrix. Also, for the illustration purposes, we discuss a fewnumerical examples as follows.As a ﬁrst example, let us consider a 30 long wire that is bentinto the shape of an S, as shown in Figure 2(a). In the numericalsolution, the wire is divided into 300 equal-length linear segments,resulting in 299 unknowns. The H-plane and E-plane scatteringcross sections for the traditional MoM solution are shown in Fig.2(b) and 2(c), respectively, along with the ABF banded matrixsolution. In order to create the banded impedance matrix, 11functions are gathered into the cluster. In this plot, there is goodagreement between the traditional method and the ABF method.Next, we consider a sectoral loop, as illustrated in Figure 3(a).The total length of the loop is 32. In the numerical solution, wehave divided the sectoral wire into 315 linear divisions, giving 315unknowns. Figures 3(b) and 3(c) compare the H-plane and E-planepatterns, respectively, between the traditional MoM and ABFbanded matrix solutions. It may be noted that the two methodsmatch well, as in the previous case.In the next three examples, we consider wire junctions. Thejunctions are: (i) T-junction, (ii) Y-junction, and (iii) the three-wiremutually perpendicular junction that resembles the X–Y–Z coor-dinate axes. The geometry H-plane and E-plane patterns for eachcase are shown in Figures 4, 5, and 6, respectively. The incident-ﬁeld parameters are indicated in the inset of the ﬁgures. Onceagain, we note a favorable comparison for each case using thetraditional MoM.5. CONCLUSIONIn this work, we have presented a technique to obtain a sparsemoment matrix. We used the MoM incorporated with adaptivebasis functions for obtaining such a matrix. We have used thistechnique for a number of wire structures, especially those involv-ing junctions. Junctions are important for modeling 3D surfacestructures. The results obtained with and without implementing theadaptive basis functions were found to be quite similar.REFERENCES1. J.H. Richmond, A wire-grid model for scattering by conducting bodies,IEEE Trans Antennas Propagat AP-14 (1966), 782–786.2. A.C. Ludwig, Wire grid modeling of surfaces, IEEE Trans AntennasPropagat AP-35 (1987), 1045–1048.3. R.F. Harrington, Origin and development of the method of moments forﬁeld computation in Computational electromagnetics: Frequency-do-main method of moments, eds. E.K. Miller, L. Medgyesi-Mitschang,and E.H. Newman, IEEE Press, New York; 1992.4. D.R. Wilton and C.M. Bulter, Effective methods for solving integraland integro-differential equations, Electromagn 1 (1981), 289–308.5. E.K. Miller, L. Medgyesi-Mitschang, and E.H. Newman, Computa-tional electromagnetics: Frequency-domain method of moments, IEEEPress, New York, 1992.6. R.F. Harrington, Field computation by moment methods, Macmillan,New York, 1968.7. S.M. Rao and M.L. Waller, Development and application of adaptivebasis functions to generate diagonal moment matrix for electromagneticﬁeld problems, Microwave Opt Technol Lett 28 (2001), 357–361.8. S.M. Rao and M.L. Waller, Application of adaptive basis functions fora diagonal moment matrix solution of two dimensional ﬁeld problems:TE case, Microwave Opt Technol Lett 28 (2001), 270–273.© 2005 Wiley Periodicals, Inc.DISTORTION PRODUCED BY RF MEMSVARACTORS ON DIGITALCOMMUNICATION SIGNALSAntonio La´zaro,1 David Girbau,2 and Lluı´s Pradell21 Department of Electronics, Electrics, and Automatic EngineeringUniversitat Rovira i Virgili (URV)43007, Av. Paı¨sos Catalans26, Campus SesceladesTarragona, Spain2 Department of Signal Theory and CommunicationsUniversitat Polite`cnica de Catalunya (UPC)Campus Nord UPC—Mo`dul D3Jordi Girona 1-308034 Barcelona, Catalunya, SpainReceived 8 August 2005ABSTRACT: This paper presents a study of the nonlinear effects intro-duced by MEMS varactors when excited with digitally modulated RFsignals (QPSK and 16 QAM). The study is based on simulating a non-linear model of the MEMS device using harmonic-balance and envelopesolvers, and on experimental measurements of the wave reﬂected by theon-wafer MEMS device. It is shown that the adjacent-channel powerratio (ACPR) and error-vector magnitude (EVM) of the digital signalFigure 6 Scattering from the wire structure with geometrically shapedcoordinate axes: (a) wire structure; (b) H-plane:   90° cut; (c) E-plane:  0° cut246 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 2, February 2006 DOI 10.1002/mopsuffer a degradation due to the device nonlinear distortion. © 2005Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 246–249,2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21318Key words: MEMS; RF power handling; adjacent channel power ratio(ACPR); intermodulation distortion1. INTRODUCTIONMEMS-based variable capacitors (varactors) have demonstrated agood performance in terms of loss and tuning range, making themsuitable for RF applications such as low phase noise VCOs,capacitive switches, phase shifters, tuners, and reconﬁgurable ﬁl-ters [1, 2]. However, two phenomena arise, namely, power han-dling [3] and intermodulation distortion (IMD) [1, 5], that limit fullintegration of MEMS devices in power transmitters. These un-wanted effects are produced by the device nonlinear behaviour, notonly in MEMS varactors, but also in RF MEMS switches. Con-cerning the IMD issue, an analytical method is proposed in [1],giving expressions to predict two-tone IMD products in MEMScapacitive switches. However, the behaviour of MEMS varactorsexcited with digitally modulated communication signals (QPSK,QAM, . . . ) has not been yet studied. It is known that two-toneIMD tests cannot generally predict nonlinear effects associatedwith digital modulations, such as the adjacent-channel power ratio(ACPR). The purpose of this paper is to study the effect of theMEMS varactors’ nonlinearity on digital communication systems.The study is based on computer simulations and experimentalwork in which digitally modulated RF signals are injected into theMEMS varactor. Two effects are observed, namely, the ACPRdegrades while the bit error rate (BER) and error-vector magnitude(EVM) increase. The MEMS device was modelled as in [1, 4], andthe simulations are performed on it using the circuit solvers (har-monic balance and envelope mode) included in the Agilent ADSsimulator™ without any simpliﬁcations or linearisation of thedevice model. In this way, high-order intermodulation productscan be considered. This is advantageous with respect to the methodproposed in [5], where expressions for 5th or higher orders arepossible using Volterra series, but limited to weak nonlinearities.Simulations and on-wafer measurements at 1.2 GHz of the re-ﬂected waves in a MEMS varactor (PolyMUMPS™ process),excited by QPSK and 16-QAM signals, are presented for differenttransmission velocities and RF input powers.2. MEMS CAPACITOR MODEL, SIMULATION, ANDEXPERIMENTAL SETUPSConsider a MEMS device based on a suspended mobile mem-brane, excited by a signal composed of two RF tones at nearbyfrequencies f1 and f2. If f2  f1  fres and f1,2  fres, where fresis the mechanical resonance frequency of the membrane, then themembrane gap is modulated at a frequency f2  f1 due to thequadratic dependence of the force on the applied voltage. In [1], itwas shown that such a modulation in MEMS capacitive switchesproduces IMD products in the output RF voltage at frequencies2f1  f2 and 2f2  f1. This effect can also be seen as amodulation of the device reﬂection coefﬁcient phase at a frequencyf2  f1, which in turn produces the abovementioned IMDproducts in the reﬂected RF voltage. Measurement of the reﬂectedwave is preferred in MEMS varactors, where the reﬂection coef-ﬁcient magnitude is high [6]. If the device is excited with adigitally modulated RF signal (which can be wideband), the phasemodulation effects are noticed as a degradation of ACPR, BER andEVM. Figure 1 shows the proposed experimental setup, whichincludes a directional coupler to extract the reﬂected wave, vectorsignal generator with power ampliﬁer and circulator, wafer-probestation, and spectrum analyzer. To study those effects theoreti-cally, a nonlinear simulation is implemented using the envelopeharmonic simulation mode supported by ADS. To model theMEMS varactor, the 1D dynamic equation for equivalent mass-spring-damping model for electrostatically actuated MEMS [1] isused.Figure 2 shows the ADS schematic proposed. An input digitallymodulated signal is injected to the MEMS varactor and, by usingan ideal circulator, the reﬂected voltage wave in the nonlinearcapacitance is obtained. It is similar to the experimental setup ofFigure 1, but the reﬂectometer is implemented with an idealcirculator.Figure 1 Experimental setupFigure 2 Schematic used for envelope harmonic simulation of the var-actor model implemented using Agilent ADS. [Color ﬁgure can be viewedin the online issue, which is available at www.interscience.wiley.com.]DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 2, February 2006 247To study the nonlinear effects of a MEMS varactor on digitalmodulations, we use the model shown in Figure 2 to performsimulations of ACPR and EVM produced by the MEMS varactor(see Fig. 5 below). The simulated device is a two parallel-platevaractor manufactured using PolyMUMPs™ process. The effec-tive parameters of the device are: spring constant k  35 N/m,mechanical quality factor Q  0.3, natural resonant frequencyf0  14 kHz, initial gap distance g0  0.75 m, nominal capacity1.43 pF, parasitic capacity Cp  2.58 pF, electrical quality factorQe  13 at 1.2 GHz, and pull-in voltage Vp  2. As a conse-quence of this low pull-in voltage, we expect poor nonlinearbehaviour to be exhibited.Figure 3 shows the results of the simulated ACPR and EVM inthe reﬂected wave for a 16-QAM modulated signal as a function ofthe symbol rate (normalized to the mechanical resonant frequencyf0). ACPR and EVM worsen for signals with a symbol rate lowerthan the mechanical resonant frequency. This effect increases withincreasing RF signal power, because the mean gap decreases withthe RF voltage (self-actuation), thus enhancing the effects ofnonlinearity. For symbol rates much higher than the mechanicalresonant frequency, the ACPR level improves but the EVM re-mains almost constant because the varactor can only produce slowphase variations in the external symbols of the constellation.Figure 4 shows simulated ACPR and EVM in the reﬂected wave,for a 16-QAM modulated signal as a function of the applied DCbias voltage, normalized to the device pull-in voltage Vp. TheACPR degrades and EVM increases for increasing bias, due to alower position of the membrane.The measurements are performed at 1.2 GHz, using the exper-imental setup of Figure 1. Figure 6 shows the reﬂected powerspectrum, measured at the reﬂectometer output for two inputpowers (10 and 17 dBm) when 16 QAM is injected with a symbolrate of 10 KHz (root-cosine ﬁlter with a rollof factor of 0.3). Themeasured ACPR strongly increases with increasing RF power. Themeasured mechanical resonance frequency using the system pro-posed in [6] is about 14 kHz. Figure 7 shows the measured andsimulated ACPR produced by this device as a function of symbolrate for 16-QAM and QPSK signals with high power level (17dBm). The ACPR rapidly improves for symbol rates higher thanthe mechanical resonance, thus verifying the tendency shown inFigure 5 Measured MEMS variable capacitor. [Color ﬁgure can beviewed in the online issue, which is available at www.interscience.wiley.com.]Figure 4 Simulated ACPR (dBc) and EVM (%) for 16-QAM, Rs  10Ksym/s as a function of normalized applied DC bias (V/Vp):  P  5dBm;  P  12 dBmFigure 6 Measured reﬂected output power spectrum at 1.2 GHz for16-QAM signal (ﬁlter rollof factor  0.3). [Color ﬁgure can be viewed inthe online issue, which is available at www.interscience.wiley.com.]Figure 3 Simulated ACPR (dBc) and EVM (%) of varactor for a16-QAM signal with several input RF powers:  P  5 dBm; ▫ P  12dBm; P  15 dBm; – P  17 dBm. [Color ﬁgure can be viewed in theonline issue, which is available at www.interscience.wiley.com.]248 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 2, February 2006 DOI 10.1002/mopthe simulations. Figure 8 shows the measured ACPR for 16-QAMand QPSK signals as a function of the input power for two symbolrates: 10 KHz (f0) and 100 KHz ( f0). The ACPR degradeswith increasing RF signal input power, being higher for lowersymbol rates in both modulations.Figure 9 shows the simulated ACPR for the MEMS capacitor,as a function of input power and pull-in voltage (or spring con-stant). Good agreement between the simulated and measured re-sults is obtained. This ﬁgure also shows a rapid increase of theACPR level with the input RF power. The ACPR rapidly degradeswhen the input power is close to the power handling.3. CONCLUSIONIn this paper, the effects of the nonlinearity of MEMS-basedvaractors on digitally modulated signals have been investigated byperforming envelope harmonic-balance simulations on a 1D elec-tromechanical model and by measuring the device using the pro-posed experimental setup. Important effects such as, in particular,a degradation in ACPR and an increase in EVM, have beenobserved (in the simulations and measurements) for digitally mod-ulated signals with low-to-moderate symbol rate and high power.This effect is quite important for low pull-in voltage structures,generally designed for voltage levels compatible with standardCMOS ICs. Therefore, a limit is imposed upon the RF power thatcommunication systems using these varactors can handle. Fromthe results, it is advisable to work with high-symbol-rate signals, asthey produce lower IMD in MEMS-based circuits.ACKNOWLEDGMENTThis work was supported by the Spanish Government under grantnos. TIC2000-0144-P4-02 and ESP2004-07067-C03-03 (MCYT).REFERENCES1. L. Dussopt and G.M. Rebeiz, Intermodulation distortion and powerhandling in RF MEMS switches, varactors and tunable ﬁlters, IEEETrans Microwave Theory Tech 51 (2003), 1247–1256.2. A. Dec and K. Suyana, Microwave MEMS-based voltage-controlledoscillators, IEEE Trans Microwave Theory Tech 48 (2000), 1943–1949.3. D. Peroulis, S.P. Pacheco, and L. Katehi, RF MEMS switches withenhanced power-handling capabilities, IEEE Trans Microwave TheoryTech 52 (2004), 59–68.4. D. Mercier, P. Blondy, et al., Model for MEMS switches power han-dling and phase noise, 32nd Eur Microwave Conf, Milan, Italy, 2002,pp. 219–222.5. M. Innocent, P. Wambacq, S. Donnay, H.A.C. Tilmans, W. Sansen, andH. De Man, An analytic Volterra-series-based model for a MEMSvariable capacitor, IEEE Trans computer-aided design Integrated CircSyst 22 (2003), 124–131.6. D. Girbau, A. La´zaro, and L. Pardell, Characterization of dynamics andpower handling of RF MEMS using vector measurement techniques,IEEE Trans Microwave Theory Tech 52 (2004), 2627–2633.© 2005 Wiley Periodicals, Inc.Figure 7 Measured and simulated ACPR (dBc) for digitally modulatedQPSK () and 16 QAM () signals as a function of symbol rate Rs (RFinput power is 17 dBm). [Color ﬁgure can be viewed in the online issue,which is available at www.interscience.wiley.com.]Figure 8 Measured ACPR (dBc) vs. input power for:  16QAM/Rs 10 KHz;  16 QAM/Rs  100 KHz;  QPSK/Rs  10 KHz; ▫QPSK/Rs  100 KHz. [Color ﬁgure can be viewed in the online issue,which is available at www.interscience.wiley.com.]Figure 9 Simulated ACPR (dBc) vs. input power (dBm) for severalpull-in voltages (modulation: 16 QAM, symbol rate Rs  10 KHz)DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 2, February 2006 249

Distortion produced by RF MEMS varactors on digital communication signals

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Distortion produced by RF MEMS varactors on digital communication signals

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