antibiased electrostatic rf mems varactors and tunable filters

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 3971

Antibiased Electrostatic RF MEMSVaractors and Tunable Filters

Kenle Chen, Student Member, IEEE, Xiaoguang Liu, Student Member, IEEE,Andrew Kovacs, Student Member, IEEE, William J. Chappell, Member, IEEE, and Dimitrios Peroulis, Member, IEEE

Abstract—This paper presents a new approach for substantiallyenhancing the linearity and reducing the effects of bias noise forelectrostatic RF microelectromechanical systems (MEMS) devices.The proposed method relies on applying bias voltages with oppo-site polarities to cancel the dynamic vibration of the MEMS struc-tures. In this paper, the method has been applied to a shunt RFMEMS varactor and a MEMS tunable evanescent-mode tunablefilter. In the first case, the shunt MEMS varactor is split into twoidentical parts that are biased with opposite voltages. This resultsin almost complete cancelation of the odd-order modulation com-ponents, leading to 20–28-dB linearity enhancement depending onthe noise and the design. Analytical results, a computer-aided de-sign model and measurements validate the proposed approach. Inthe tunable filter case, opposite bias voltages are applied on thetuners of its resonators. Simulated and measured results are alsopresented in this case. Measurements show a sideband reductionas high as 13 dB. In both cases, the effectiveness of the proposedmethod in the presence of fabrication uncertainties are also con-sidered.

Index Terms—Evanescent-mode cavity, linearity, microelec-tromechanical systems (MEMS) diaphram, modulation, noise,resonator, RF MEMS varactor, tunable filter.

I. INTRODUCTION

R F microelectromechanical systems (RF MEMS) have re-ceived considerable research attention over the past two

decades as an enabling technology for creating highly recon-figurable wireless communications systems. Electrostatic RFMEMS devices, in particular, are known for their merits of ex-tremely low loss, high linearity, and near zero power consump-tion. Numerous tunable components have been demonstratedwith RF MEMS devices, including switches [1], tunable fil-ters [2], phase shifters [3], tunable antennas [4], and adaptivepower amplifiers [5]. Recently, continuously tunable varactorsand resonators/filters are demonstrated with high- and broadfrequency tuning range [6]–[9].

Linearity and stability are particularly important metrics forhigh- tunable components [10]. Although excellent linearity

Manuscript received July 02, 2010; revised September 26, 2010; accepted Oc-tober 01, 2010. Date of publication November 09, 2010; date of current versionDecember 10, 2010. This work was supported by the Defense Advanced Re-search Projects Agency (DARPA) under the Analog Spectral Processors (ASP)Program with a subcontract from BAE Systems. This paper is an expanded paperfrom the IEEE MTT-S International Microwave Symposium, Anaheim, CA,May 23–28, 2010.

The authors are with the School of Electrical and Computer Engineeringand the Birck Nano Technology Center, Purdue University, West Lafayette,IN 47906 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2010.2088135

has been demonstrated for RF MEMS devices, [11] and [12]show that it still remains an important issue when the deviceis biased close to its pull-in point. Stability is another concernfor high- systems, such as narrowband tunable filters [7], [8].In an integrated communication system, especially a mixed-signal system, the biasing conditions may be noisy due to signalleakage and substrate noise [13]. Moreover, obtaining a stablehigh voltage can be difficult in such a highly integrated system.Charge pumps are generally used to supply the high voltage usedto actuate MEMS tunable filters. However, in most integratedcharge pump designs, the output voltage ripple can be as highas 5% of the supplied voltage [14]–[16] and effectively appearsas bias noise to the tunable filters. Such bias noise can cause fre-quency shifts that degrade the linearity of the system.

In order to counteract these problems, an antibiased topologywas recently proposed and experimentally validated for shuntRF MEMS varactors in [17]. Fig. 1(a) shows an illustration ofthe proposed method. When a low-frequency (LF) noiseis present on the bias line and/or on the transmission line, itdynamically actuates the MEMS membrane and leads to un-wanted modulation of the RF signal [the single varactor casein Fig. 1(a)]. For the antibiased topology in Fig. 1(a), the var-actor is split into two identical parts that are individually biasedwith opposite voltages. The noise-induced dynamic vibrationsof the two membranes are 180 out of phase so that their contri-butions to the total capacitance variation are canceled, resultingin improved linearity and noise immunity.

This paper significantly expands our previous work in [17] inthe following ways. Section II presents new models that explainthe cancelation of only the odd-order modulation terms as seenin measurements of [17]. Section III presents a new approachin applying the antibias technique in tunable evanescent-modecavity filters by applying opposite bias voltages on the nearbypoles, as illustrated in Fig. 1(b). It is shown that noise-inducedmodulation is a more severe problem in high- resonant struc-tures. The application of the antibias topology successfully re-duced the sideband frequency components due to bias noise inthe tunable filter. The effects of fabrication uncertainties on theproposed technique are carefully considered in both cases.

II. ANTIBIASED VARACTOR TOPOLOGY

A. Electromechanical and RF Modeling of ElectrostaticallyActuated RF MEMS Device

This section provides a brief background of the electro-mechanical behavior of electrostatic MEMS actuators andestablishes the fundamental formulas needed for the analysis tofollow. The following analysis is mainly based on [11].

U.S. Government work not protected by U.S. copyright.

3972 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010

Fig. 1. Antibiased electrostatically actuated RF MEMS devices. (a) Varactors.(b) Two-pole tunable filter.

A typical electrostatically actuated MEMS device is shownin Fig. 2. When a voltage is applied between two electrodes, anelectrostatic force pulls the MEMS membrane towards the biaselectrode

(1)

The total capacitance of the varactor can be approximated bythe parallel-plate formula as

(2)

where is the overlapping area between the two electrodes, andis the gap between them. Note that there is also a fringing-

field capacitance between the two electrodes. The value of thefringing-field capacitance is typically 20%–50% of the paralle-plate capacitance. The effect of the fringing-field capacitance istaken into account by the computer-aided design (CAD) mod-eling presented in Section II-C.

The MEMS membrane is also subject to the mechanicalrestoring force , which is proportional to the deflection ofthe membrane

(3)

Fig. 2. Typical electrostatically actuated MEMS structure.

where is the spring constant of the movable membrane. Beforepull-in [18], the mechanical equilibrium condition gives

(4)

This third-order equation can be analytically solved and yields[6]

(5)

where

(6)

(7)

By substituting the expression of in (2), the analytical expres-sion of capacitance with respect to voltage can then be found.

Considering the MEMS varactor as a shunt capacitance on atransmission line and assuming , is given by[11]

(8)

with (low loss) and a phase modulation of

(9)

For a small displacement , the capacitance becomes [11]

(10)

Substituting expression (10) in (9) leads to

(11)

The above equation indicates that the vibration of the varactormembrane causes an instant capacitance variation and, there-fore, a phase modulation of the RF signal. If the RF signal isaccompanied by an LF voltage (e.g., modulating signal) and/orif there is biasing noise [see Fig. 3(a)], the total voltage on themembrane includes three components

(12)

where is the applied dc bias signal and is the amplitudeof the biasing noise signal (or modulating signal). Assuming that

is slightly smaller than the mechanical resonant frequency

CHEN et al.: ANTIBIASED ELECTROSTATIC RF MEMS VARACTORS AND TUNABLE FILTERS 3973

Fig. 3. Illustration of the antibias concept applied to shunt varactors. (a) SingleMEMS varactor in the presence of LF modulating signal and/or biasing noise.(b) Antibiased topology leading to out-of-phase vibrations of two MEMS mem-branes and a cancelation of the most significant sidebands [17].

of the MEMS membrane, the resultant membrane displacementis [11]

(13)

Equation (13) involves a static part and a time-varying part. Asa result, the output spectrum contains modulation sidebands at

(M1) and (M2), etc., as shown in Fig. 3(a).The antibiased topology of MEMS varactors is shown in

Fig. 3(b). Assume the LF noise is correlated, which is, ingeneral, the case when bias lines are placed close together [11].By substituting the opposite bias voltages into (13),out-of-phase vibrations at are observed. Therefore, the in-stant capacitance variations of the two varactors approximatelycompensate each other, which leads to a more constant totalcapacitance and a significant reduction of the modulation terms.

Although the previously presented analysis in [17] qualita-tively explains this idea, it does not provide quantitative resultsin terms of which modulation products are canceled and whichare not. Furthermore, (13) is derived under the assumptionof small membrane displacement, where the capacitance isless sensitive to the bias voltage. This assumption is not validfor large deflections, especially when the membrane is closeto pull-in. Fig. 4 graphically shows the gap and capacitance

Fig. 4. Gap distance and capacitance versus bias voltage with the effect of anLF variation in bias voltage.

of a typical MEMS varactor versus its bias voltage. Whenis close to the pull-in voltage, a small sinusoidal voltage

can cause a large variation of gap/capacitance,which hinders the validity of (13). The following section ad-dresses these issues.

B. Theoretical Analysis of Antibiased Varactor TopologyUsing Taylor Series

In order to accurately model the modulation characteristicsof the MEMS varactor, the C–V relationship of the antibiasedvaractor is explicitly analyzed using a Taylor-series expansion.Similar approaches have been used for the analysis of diodevaractors [19], [20].

Assuming low RF input power, the capacitance of the varactorsubject to an LF noise voltage can be expressed using a Taylor-series expansion around the bias voltage with respect to theincremental LF noise

(14)

The term in (14) denotes the static capacitance due to ,which is given by

(15)

gives rise to first-order modulation on the incident RF signal,gives rise to the second-order modulation, and so on.

and can be analytically derived using an inverse functionderivation as

(16)

(17)


Fig. 5. Equivalent circuit model of the antibiased shunt varactors.

For the antibiased topology, the single varactor is replaced bytwo identical varactors and . The superimposed voltageson and are and , respectively. It isnoted that since the capaci-tance is dependent on , which is expressed in (2) and (4). Thecapacitance on each varactor can be expanded as

(18)

(19)

As these two varactors are in parallel, the total capacitance is

(20)

The above equations (18), (19) and (20) underline that the oddterms of the Taylor series of the total capacitance are canceled.In turn, the Taylor series of the total capacitance becomes

(21)

Plugging in (21) allows us to write the time-varying capacitance as

(22)

This equation explicitly shows that the instant variation of thetotal capacitance of these two antibiased varactors only contains

components. Consequently, the phase modulation com-ponents only occur at . This means that the nonlin-earity effects due to the LF signal can be significantly reduced.

C. Simulation

A nonlinear circuit is developed to simulate the effectivenessof the antibias topology using the nonlinear varactor model pre-sented in [10], [11], and [22]. Fig. 5 shows the schematic of thesimulated circuit model. The parameters of the single varactormodel used in the ADS simulation are listed in Table I.

The simulated dynamic membrane movement in response tothe LF noise is shown in Fig. 6, which explicitly shows that thetwo varactors are vibrating in opposing directions at frequency

(60 kHz). The output spectrum of this circuit is shown inFig. 7 with the varactors same biased and antibiased. As pre-dicted by the theoretical analysis, the output spectrum of theantibiased varactor topology does not contain odd-order mod-ulation components. The results obtained from the analytical

TABLE ISUMMARY OF BASIC VARACTOR MODEL

PARAMETERS USED IN SIMULATIONS

Fig. 6. Simulated displacements of two varactors in response to the dc bias of�26 V and 60-kHz LF signal with � � � V.

Fig. 7. Simulated output spectra of: (a) same-biased and (b) antibiased varac-tors under the conditions of � � �� GHz, � � �� V, � � �� kHz, and� � � V.

model, based on the analytical C–V relation of the MEMS var-actor, are also plotted in Fig. 7, which agrees well with the sim-ulation results using the nonlinear model. It further proves thefeasibility of the Taylor-series approach in predicting the non-linear effect of MEMS varactors.

D. Fabrication Uncertainty

Sections II-B and C focus on the ideal case of the antibi-ased topology. However, in reality, these two varactors cannotbe exactly identical due to fabrication tolerances. The differencemainly comes from the initial gap distance and springconstant . As a result, the odd modulation componentscannot be perfectly canceled. As an example, Fig. 8 shows theoutput spectrum of two varactors with 0.5- m difference of gapdistance (18% of ) under the same conditions as the ideal caseshown in Fig. 7. Compared to the ideal case, the first modulationterm at (M1) is not completely canceled. However, animprovement of 30 dB is still obtained. Fig. 9 summarizes thefabrication uncertainty effects on the improvements in M1 andM3 (modulation terms at and , respectively).


Fig. 8. Simulated output spectra of two varactors with �� .(a) Same-biased. (b) Antibiased. The conditions are same as those shown inFig. 7: � � �� GHz, � � �� kHz, and � � � V.

Fig. 9. Simulated effect of fabrication uncertainty due to: (a) different initialgaps and (b) different spring constants.

As expected, less improvement is obtained as the differencesin the initial gaps and spring constants grow. Thescheme remains robust, however, even for relatively large mis-matches. For example, the improvement of M1 is 22 dB when

m (33% of ) compared to the complete cancella-tion in the ideal case. A comparison between Fig. 9(a) and (b)clearly shows that that difference of the initial gaps dominatesthe improvement degradation.

E. Experimental Validation

To experimentally validate the proposed antibiased topology,the shunt RF MEMS varactors are fabricated and measured. Thedesign and fabrication of the devices are discussed in detail in[23] and [24]. Fig. 10(a) shows the fabricated device. The twovaractors are placed on a 50- coplanar waveguide (CPW) andare separated by a large metal–insulator–metal (MIM) capac-itor (around 10 pF), which blocks the opposite bias voltageson two varactors and acts as an RF short. Fig. 10(b) shows the

Fig. 10. (a) Fabricated device for the experimental validation of the antibiasedtopology [17]. (b) Experimental setup for testing of the devices.

measurement setup. DC bias voltages on the two varactors areprovided by two Keithley 2400 voltage supplies. The LF noisesignal is generated by an Agilent 33250A function generatorand is superimposed on the dc bias voltage through decouplingcapacitors. The bias voltage is close to the pull-in voltage of thevaractor in order to get significant membrane displacements. Itis important to mention that, compared to the nonlinear testingsetup mentioned in [11], [12], and [22], no high power RF signalis needed to see the nonlinear behavior due to the LF signal.Thus, no power amplifier is needed in this setup.

Fig. 11 plots the measured results from the Agilent SpectrumAnalyzer E4448A. Comparisons are made between the two-var-actor-stack when both structures are biased with the same bias

(same-biased case) and when they are biased with oppo-site bias voltages (antibiased case). Compared to thesame-biased case, the antibiased varactor-stack does not con-tain sidebands at and , but only at , which leads toa great linearity improvement. The measurement further vali-dates the theoretical analysis. The measured results shown inFig. 11(a) match the simulation results shown in Fig. 7, whichis conducted under the same conditions. Both the simulated andmeasured results show a 20-dB linearity enhancement of theantibiased method. This enhancement is computed as the dif-ference between the most significant modulation terms of thesame-biased and antibiased cases (M1–M2). Moreover, the de-vice is measured under different conditions and the results areshown in Fig. 11(b) and (c). These results indicate 28- and 25-dBlinearity improvement, respectively.

It is interesting to note that the M1 and M3 terms are almostperfectly canceled using the antibiased approach as the mea-sured results shown in Fig. 11. This is due to the fact that the


Fig. 11. Measured output spectra of same- and antibiased varactors under dif-ferent conditions [17]. (a) � � �� GHz, � � �� kHz, � � �� V, � �

� V, and � � �� dBm. (b) � � �� GHz, � � �� kHz, � � �� V,� � � V, � � �� dBm. (c) � � �� GHz, � � �� kHz, � � �� V,� � � V, and � � �� dBm.

fabrication uncertainty is very small as these two varactors arevery close to each other on the same wafer.

III. ANTIBIASED TUNABLE TWO-POLE EVANESCENT-MODE

CAVITY FILTER

In the previous sections, we discussed the antibias concepton varactors placed on nearly matched transmission lines. Thissection shows that the same concept can also be beneficial whenapplied to high- structures. A two-pole high- tunable filteris used as a vehicle to demonstrate this.

Recently, electrostatic MEMS diaphragm tuners have beensuccessfully developed to make tunable evanescent-modecavity filters [6], [7], achieving a very high unloadedquality factor (300–650) and a broad frequency tuning range(3.04–4.71 GHz). As shown in Fig. 12(a), when a bias voltage isapplied to the top electrode, the MEMS diaphragm is actuatedto move upwards so as to change the resonant frequency of thecavity resonator. The two-pole tunable filter is composed oftwo coupled tunable evanescent-mode resonators with MEMSdiaphragm tuners. The design and implementation of thistwo-pole evanescent-mode filter have been presented in [7].

Similar to the varactor case, the LF noise from the bias linedynamically actuates the diaphragm. As mentioned in [11],MEMS tuners are subject to the same noise because the bias

Fig. 12. Evanescent-mode cavity filter with MEMS diaphragm tuners.(a) Single-cavity resonator. (b) Traditional same-biased two-pole filter.(c) Antibiased two-pole filter.

lines are close to each other and “pick-up” the same noisewaveform (correlated noise). As a result, the incident RF signal(within the passband) is modulated leading to similar sidebandsas the varactor’s case in Section II [see Fig. 12(b)]. Due to thevery high and narrow bandwidth (0.7%) of the filter, theelectromagnetic field between the diaphragm and the post ismuch stronger than that between the varactor and transmissionline [11] for the same power level. Consequently, the modu-lation effect is much more significant in filters and resonatorscompared to the varactor case.

The antibiased topology can be applied to the two-pole filter,as shown in Fig. 12(c). When subjected to an LF noise, the antib-iased topology leads to out-of-phase vibration of the two MEMSdiaphragms. In the following sections, this antibiased two-polefilter is theoretically analyzed and experimentally demonstrated.

A. Theoretical Analysis

The equivalent circuit of the two-pole filter is schematicallyshown in Fig. 13 with the matrix of the two coupled


Fig. 13. Equivalent circuit model of the two-pole tunable filter and its��matrix representation.

resonators and the inverter. and are the admittances oftwo resonators, given by

(23)

The total matrix of these three cascade sections is

(24)

Using the matrix transformation equation [25], of thesethree cascade sections can be calculated by

(25)

where , which is the port impedances of the -pa-rameter matrix transformed from the matrix in (24). ,

, and in (25) are constants given by

(26)

(27)

(28)

When the antibiased structure is subjected to an LF noise fromthe bias line, and can be expressed as

(29)

(30)

TABLE IISUMMARY OF BASIC TUNABLE-CAVITY MODEL

PARAMETERS USED IN SIMULATIONS

In (25), the term generates no modulation componentat because identical and leads to no oddTaylor-series term of , as mentioned in the previoussections. It is also noted that the odd-order modulations of the

term in (25) are perfectly canceled becauseis a even function of , which can be expressed

as

(31)

As a result, similar to the varactor case, the antibias topology oftwo-pole filter leads to a cancellation of sidebands at

.

B. Simulation

This two-pole filter is modeled and simulated using ADSwith the equivalent circuit shown in Fig. 13 and the large-signalmodel of the MEMS diaphragm tuner, which has been presentedin [10]. The model parameters of each resonator are listed inTable II. The simulated results are shown in Fig. 14. Comparedto the case of varactors on the transmission line, the effect of bi-asing noise on the evanescent-mode cavity filter is much moresignificant due to the high- resonance of the circuit. For ex-ample, as shown in Fig. 14(a), a 1-V sinusoidal noise at 1 kHzgenerates a 23-dBc sideband at for the traditionalbiasing case. For the antibiased topology, the most significantmodulation components at are almost per-fectly canceled, which falls below the 100-dBc level, as shownin Fig. 14(a). When the noise level grows to 5 V [see Fig. 14(b)],M1 is still below 100 dBc. It is also seen that the higher ordermodulation (M3) becomes more significant for the antibiasedtopology, but a significant improvement (70 dB) of M3 overthe traditional case is still achieved. The simulation verifies thetheoretical analysis. Contrary to the varactor case, M2 of thetwo-pole filter is also improved by around 6 dB by applying theantibiased approach, as observed from Fig. 14(a) and (b). Thisis due to the term in (25).

C. Discussions on Fabrication Uncertainty

The simulations and discussions in Section III-B are based onthe ideal case in which the two resonators of the two-pole filterare identical and the maximum sideband reduction is achieved.However, fabrication tolerances in the actuation gap , ca-pacitive gap , and spring constant of the MEMS tuner


Fig. 14. Simulated output spectra of two-pole filter under different conditions.(a) � � �� GHz, � � �� V, � � � kHz, � � � V, and � �

�� dBm. (b) � � �� GHz, � � �� V, � � � kHz, � � � V,and � � �� dBm.

are practically unavoidable. Particularly, the fabrication of thisMEMS-cavity filter involves manual assembly process so thefabrication differences between two resonators are expected tobe much greater than the varactor case, i.e., around 10%–20%,leading to less effective cancelation of the noise-induced mod-ulation.

ADS simulation is used to investigate these effects. Fig. 15shows the simulated improvements in M1, M2, and M3 whenthere are differences in , , and . As expected, the effectson the odd-order modulation components are the most signifi-cant and greater variation leads to less improvement of these oddcomponents. For example, suppression of M1 can be degradedas much as 10 dB when of the resonators are different by10 m (27%). It is important to note that all three factors canjointly contribute to a less effective sideband reduction.

Fig. 16 shows the simulated output spectrum of the same-bias and antibias topologies with 5 m ,

0.7 m , and . The sidebandreduction in this case is less than those achieved in the idealcase (Fig. 14). For example, at V, the reduction of M1is 9 dB; and at V, the reduction of M1 is 13 dB. It isalso found that the simulation result of antibiased filter remainsthe same when positive and negative bias voltages are switched.

D. Measurement and Experimental Validation

To validate the theory and the CAD models, a two-pole tun-able evanescent-mode cavity filter is fabricated and measured.The fabricated filter is shown in Fig. 17(a) and (b). The designand fabrication process for this filter has been presented in [7].The small-signal -parameters of the filter are measured usingan Agilent 8722ES network analyzer. Shown in Fig. 17, the filter

Fig. 15. Simulated effects of fabrication uncertainty. (a) Different dc gap.(b) Different RF gap. (c) Different spring constant, under the condition of� � ��GHz, � � � kHz, � � � V, and � � �� dBm.

is continuously tunable from 2.8 to 4.2 GHz with 0.7% frac-tional bandwidth and insertion loss of 4.8–3.5 dB (extractedof 310–450).

The nonlinear test of the two-pole filter is carried out using thesetup shown in Fig. 18. The main RF signal is generated by anAgilent 4433B signal generator and is applied to the input of thetunable filter through a 20-dB bi-directional coupler. The outputsignal is fed into an Agilent E4448 spectrum analyzer throughanother coupler. The 20-dB coupling ports of the couplers areconnected with the input and output ports of an Agilent E8361CPNA so that the frequency sweep response of the tunable filtercan be observed at the same time. First, the proper frequencyresponse of the filter is formed by gradually adjusting the biasvoltages. The signal generator is then set to output a CW signalat the center frequency of the filter and an LF noise is generatedby the function generator. The output spectrum is captured usingthe spectrum analyzer.

Fig. 19 plots the measured results. The filter is tuned to4.1165 GHz with 151 V and V voltages. The voltagesare somewhat different because the tuners and resonators are


Fig. 16. Simulated output spectra of two-pole filter with ��

�� and �� . (a) � � �� GHz, � � � kHz,� � � V, and � � �� dBm. (b) � � �� GHz, � � � kHz,� � � V, and � � �� dBm.

Fig. 17. (a) Fabricated two-pole tunable evanescent-mode cavity filter. Thebias electrodes are not shown to reveal the diaphragm tuners. (b) Fabricatedtwo-pole tunable filter with the bias electrodes. (c) Measured �-parameters ofthe tunable filter. Although only a selection of data points are shown, the filteris continuously tunable across the whole tuning range.

slightly different due to fabrication tolerances. The outputspectrum to an input signal of GHz with anLF noise signal of kHz, V is shown in thesame-biased case of Fig. 19(a). The polarity in one of the biasvoltages is subsequently reversed and the resulting spectrum is

Fig. 18. Nonlinear testing setup for the two-pole filter.

Fig. 19. Measured output spectra of same-biased and antibiased two-pole fil-ters. (a) � � ��GHz, � � � kHz, � � � V, and � � �� dBm.(b) � � ��GHz, � � � kHz, � � � V, and � � �� dBm.

shown in the antibiased case of Fig. 19(a). It is observed thatthe antibiasing of the filter results in around 9-dB improve-ment in the first modulation components (M1) and 10 dB inM2. Similar measurements are taken with noise amplitude of

V [see Fig. 19(b)]. In this case, the improvement is13 dB for M1, 20 dB for M2, and 25 dB for M3. The measuredresults agree with what the CAD modeling predicts (Fig. 16).A perfect cancellation of M1 and M3 is not achieved here dueto the dimension differences between the two resonators. Suchtolerances are typical given the specific assembly process in anacademic setting [7]. In a mass-production oriented industrysetting, the tolerances are expected to be improved by at leastan order of magnitude.

IV. CONCLUSION

We have presented a versatile antibias approach for im-proving the linearity and reducing the effects of bias noise forelectrostatic RF MEMS devices. Theoretical analysis based onTaylor-series expansion is first presented, explicitly showingthe effectiveness of the proposed method. This method has


been successfully applied to a shunt MEMS varactor (trav-eling-wave structure) and a MEMS tunable evanescent-modecavity filter (resonant structure). In the varactor case, the an-tibias topology almost completely eliminates the odd-ordermodulation components, achieving a linearity improvement of20–28 dB depending on the design and signal conditions. Inthe tunable filter case, a sideband reduction as high as 13 dBhas been observed. CAD modeling shows that the reductioncan be further improved with advanced precision fabricationtechniques that leads to lower fabrication uncertainties.

REFERENCES

[1] J. B. Muldavin and G. M. Rebeiz, “RF MEMS switches and switchcircuits,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 1, pp. 50–71,Jan. 2001.

[2] K. Entesari and G. M. Rebeiz, “A 12–18-GHz three-pole RF MEMStunable filter,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 8, pp.2566–2571, Aug. 2005.

[3] J. Hung, L. Dussopt, and G. M. Rebeiz, “Distributed 2- and 3-bit� -band MEMS phase shifters on glass substrates,” IEEE Trans.Microw. Theory Tech., vol. 52, no. 2, pp. 600–606, Feb. 2004.

[4] N. Behdad and K. Sarabandi, “Dual-band reconfigurable antenna witha very wide tunability range,” IEEE Trans. Antennas Propag., vol. 54,no. 2, pp. 409–416, Feb. 2006.

[5] W. E. Neo, J. Lin, X. Liu, L. C. N. de Vreede, L. E. Larson, M. Spirito,M. Pelk, K. Buisman, A. Akhnoukh, A. de Graauw, and L. Nanver,“Adaptive multi-band multi-mode power amplifier using integratedvaractor-based tunable matching network,” IEEE J. Solid-State Cir-cuits, vol. 41, no. 9, pp. 2166–2177, Sep. 2006.

[6] X. Liu, L. P. B. Katehi, W. J. Chappell, and D. Peroulis, “A 3.4–6.2GHz continuously tunable electrostatic MEMS resonator with qualityfactor of 460–530,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009,pp. 1149–1152.

[7] X. Liu, L. P. B. Katehi, W. J. Chappell, and D. Peroulis, “High-� con-tinuously tunable electromagnetic cavity resonators and filters usingSOI-based RF MEMS actuators,” J. Microelectromech. Syst., vol. 19,no. 4, pp. 774–784, Jul. 2010.

[8] S. Park, I. Reines, C. Patel, and G. M. Rebeiz, “High-� RF-MEMS4–6-GHz tunable evanescent-mode cavity filter,” IEEE Trans. Microw.Theory Tech., vol. 58, no. 2, pp. 381–389, Feb. 2010.

[9] A. Pothier, J. C. Orlianges, G. Zheng, C. Champeaux, A. Catherinot, D.Cros, P. Blondy, and J. Papapolymerou, “High-� RF-MEMS 4–6 GHztunable evanescent-mode cavity filter,” IEEE Trans. Microw. TheoryTech., vol. 53, no. 1, pp. 354–360, Jan. 2005.

[10] X. Liu, L. P. B. Katehi, W. J. Chappell, and D. Peroulis, “Powerhandling capability of high-� evanescent-mode RF MEMS resonatorswith flexible diaphragm,” in Asia–Pacific Microw. Conf., 2009, pp.575–578.

[11] L. Dussopt and G. M. Rebeiz, “Intermodulation distortion and powerhandling in RF MEMS switches, varactors, and tunable filters,” IEEETrans. Microw. Theory Tech., vol. 51, no. 4, pp. 927–930, Apr. 2003.

[12] G. David and O. Nerea, “Study of intermodulation in RF MEMS vari-able capacitors,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp.1120–1130, Mar. 2006.

[13] K. Makie-Fukuda, T. Anbo, and T. Tsukada, “Substrate noise measure-ment by using noise-selective voltage comparators in analog and digitalmixed-signal integrated circuits,” IEEE Trans. Instrum. Meas., vol. 48,no. 6, pp. 1068–1072, Dec. 1999.

[14] G. DiCataldo and G. Palumbo, “Design of an�th order Dickson voltagemultiplier,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.43, no. 5, pp. 414–418, May 1996.

[15] M. R. Hoque, T. Ahmad, T. McNutt, A. Mantooth, and M. M. Mo-jarradi, “Design technique of an on-chip, high-voltage charge pump inSOI,” in IEEE Int. Circuits Syst. Symp., Mar. 2006, pp. 133–136.

[16] V. Jimenez, J. Pons, M. Domingues, A. Bermejo, L. Castaner, H. Niem-inen, and V. Ermolov, “Transient dynamics of a MEMS variable capac-itor driven with a Dickson charge pump,” Sens. Actuators A. Phys., vol.128, no. 1, pp. 89–97, Mar. 2006.

[17] K. Chen, A. Kovacs, and D. Peroulis, “Anti-biased RF MEMS varactortopology for 20–25 dB linearity enhancement,” in IEEE MTT-S Int.Microw. Symp. Dig., May 2010, pp. 1142–1145.

[18] G. M. Rebeiz, RF MEMS Theory, Design, and Technology. Boston,MA: Wiley, 2003.

[19] K. Buisman, L. C. N. de Vreede, L. E. Larson, M. Spirito, A.Akhnoukh, T. L. M. Scholtes, and L. K. Nanver, “Distortion-freevaractor diode topologies for RF adaptivity,” in IEEE MTT-S Int.Microw. Symp. Dig., 2005, pp. 157–160.

[20] R. G. Meyer and M. L. Stephens, “Distortion in variable-capacitancediodes,” IEEE J. Solid-State Circuits, vol. SSC-10, no. 1, pp. 47–54,Jan. 1975.

[21] G. M. Rebeiz, “Phase-noise analysis of MEMS-based circuits andphase shifters,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 5, pp.1316–1323, May 2002.

[22] Y. Lu, “RF MEMS devices and their applications in reconfigurablerf/microwave circuits,” Ph.D. dissertation, Dept. Elect. Comput. Eng.,The Univ. Michigan at Ann Arbor, Ann Arbor, MI, 2006.

[23] H. Hsu, S. W. Lee, and D. Peroulis, “�-band loss characterization ofelectroplated nickel for RF MEMS devices,” in IEEE AP-S Int. Symp.,Jun. 2007, pp. 289–292.

[24] H. Hsu and D. Peroulis, “An experimental investigation on viscoelasticbehavior in tunable planar RF-MEMS resonators,” in IEEE MTT-S Int.Microw. Symp. Dig., Mar. 2010, pp. 1150–1153.

[25] D. M. Pozar, Microwave Engineering, Third ed. Boston, MA: Wiley,2005.

Kenle Chen (S’10) received the Bachelor’s degreein communication engineering from Xi’an JiaotongUniversity, Xi’an, China, in 2005, the Master’sdegree in electronics and information engineeringfrom Peking University, Beijing, China in 2008,and is currently working toward the Ph.D. degree atPurdue University, West Lafayette, IN.

From 2007 to 2008, he was with the Instituteof Micro Electronics, National Key Laboratory ofMicro/Nano Fabrication, Peking University, wherehis research focused on RF MEMS switches, tunable

filters, and vacuum packaging. He is currently with the School of Electrical andComputer Engineering and Birck Nanotechnology Center, Purdue University.His research interests include highly efficient broadband power amplifiers,adaptive power amplifiers and transmitters, and novel RF MEMS circuits.

Xiaoguang Liu (S’07) received the Bachelor’s de-gree in electrical engineering from Zhejiang Univer-sity, Hangzhou, China, in 2004, and the Ph.D. degreefrom Purdue University, West Lafayette, IN, in 2010.

He is currently a Postdoctoral Research Associatewith the Department of Electrical and Computer En-gineering and Birck Nanotechnology Center, PurdueUniversity. His research interests include novel RFMEMS devices and high-� tunable filters for recon-figurable radio frontends.

Dr. Liu was the recipient of the 2009 IEEE An-tenna and Propagation Society Graduate Research Fellowship.

Andrew Kovacs (S’09) received the B.S. and M.S.degrees in electrical engineering from Purdue Uni-versity, West Lafayette, IN, in 2005 and 2008, respec-tively.

He is currently a graduate student with Purdue Uni-versity. His current research specialties are harsh en-vironment sensors and uncertainty quantification inMEMS devices.


William J. Chappell (S’98–M’02) received theB.S.E.E., M.S.E.E., and Ph.D. degrees from TheUniversity of Michigan at Ann Arbor, in 1998, 2000,and 2002, respectively.

He is currently an Associate Professor with theElectrical and Computer Engineering Department,Purdue University, West Lafayette, IN, and is alsoa member of the Birck Nanotechnology Center andthe Center for Wireless Systems and Applications.His research focus is on advanced applications of RFand microwave components. He has been involved

with numerous Defense Advanced Research Projects Agency (DARPA)projects involved in advanced packaging and materials processing for mi-crowave applications. His research sponsors include the Homeland SecurityAdvanced Research Projects Agency (HSARPA), Office of Naval Research(ONR), National Science Foundation (NSF), the State of Indiana, Communica-tions-Electronics Research, Development, and Engineering Center (CERDEC),Army Research Office (ARO), as well as industry sponsors. His researchgroup uses electromagnetic analysis, unique processing of materials, andadvanced design to create novel microwave components. His specific researchinterests are the application of very high-quality and tunable componentsutilizing package-scale multilayer components. In addition, he is involved withhigh-power RF systems, packages, and applications.

Dr. Chappell was the recipient of the URSI Young Scientist Award, the JoelSpira Teaching Excellence Award, and the Eta Kappa Nu 2006 Teacher of theYear Award presented by Purdue University.

Dimitrios Peroulis (S’99–M’04) received the Ph.D.degree in electrical engineering from The Universityof Michigan at Ann Arbor, in 2003.

He has been with Purdue University, WestLafayette, IN, since August 2003, where he iscurrently leading a group of graduate students on avariety of research projects in the areas of RF MEMS,sensing and power harvesting applications, as wellas RF identification (RFID) sensors for the healthmonitoring of sensitive equipment. He has been aPrinciple Investigator (PI) or a co-PI in numerous

projects funded by government agencies and industry in these areas. He iscurrently a key contributor in two Defense Advanced Research Project Agency(DARPA) projects at Purdue, which focus on very high-quality �� RF tunable filters in mobile form factors (DARPA Analog Spectral ProcessingProgram, Phases I, II and III) and on developing comprehensive characterizationmethods and models for understanding the viscoelasticity/creep phenomenain high-power RF MEMS devices (DARPA M/NEMS S&T FundamentalsProgram, Phases I and II). Furthermore, he leads the experimental program onthe Center for the Prediction of Reliability, Integrity and Survivability of Mi-crosystems (PRISM) funded by the National Nuclear Security Administration.In addition, he heads the development of the MEMS technology in a U.S. Navyproject (Marines) funded under the Technology Insertion Program for Savings(TIPS) program focused on harsh-environment wireless microsensors for thehealth monitoring of aircraft engines. He has authored or coauthored over110 refereed journal and conference publications in the areas of microwaveintegrated circuits and antennas.

Dr. Peroulis was the recipient of the 2008 National Science Foundation CA-REER Award. His students have been the recipients of numerous Student PaperAwards and other student research-based scholarships. He has also been the re-cipient of eight teaching awards including the 2010 HKN C. Holmes MacDonaldOutstanding Teaching Award and the 2010 Charles B. Murphy Award, which isPurdue University’s highest undergraduate teaching honor.

antibiased electrostatic rf mems varactors and tunable filters

Documents