406 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 21, NO. 8, AUGUST 2011

Impact of Mechanical Vibration on the Performanceof RF MEMS Evanescent-Mode Tunable Resonators

Xiaoguang Liu, Member, IEEE, Joshua Small, David Berdy, Student Member, IEEE,Linda P. B. Katehi, Fellow, IEEE, William J. Chappell, Member, IEEE, and Dimitrios Peroulis, Member, IEEE

Abstract—This letter presents the first experimental investiga-tion on the impact of mechanical vibration on the performance ofMEMS evanescent-mode tunable resonators. It is shown both con-ceptually and experimentally that mechanical vibration can intro-duce distortions to the RF signal. Signal distortions are found tobe very small ( �� ��� of sideband or � �� change in-error vector magnitude) for a diaphragm based MEMS tunableresonator with a diaphragm size of 7 7��� and mechanical vi-bration amplitude of 1g. A novel MEMS tunable evanescent-moderesonator based on two arrays of cantilever beams that replace thediaphragm is also presented to achieve even lower distortion in thepresence of mechanical vibration. A 15–25 dB reduction in the vi-bration-induced sideband is observed.

Index Terms—Error vector magnitude (EVM), RF MEMS, tun-able resonator, vibration.

I. INTRODUCTION

R ECENTLY, highly-loaded MEMS tunable evanes-cent-mode cavity resonators have attracted a lot of

research attention as a promising candidate for making widelytunable RF/microwave filters with very high unloaded qualityfactors ( ) [1], [2]. In such resonators, the resonant frequencyis very sensitive to this gap between the capacitive post andthe top wall of the cavity. Frequency tuning is achieved bychanging this gap.

Environmental perturbations, such as electrical noise[3], tem-perature variation, shock and vibration, may potentially degradethe performance of such highly-tunable resonators when theyare deployed in the field. Fig. 1 shows a scenario in which ex-ternal mechanical perturbation can cause the diaphragm tunerto vibrate, creating an instantaneous change in the RF resonantfrequency [Fig. 1(b)]. This frequency variation can lead to RFsignal distortions by introducing unwanted amplitude and phasemodulation of the RF signal that passes through the resonator[Fig. 1(b)] [4].

This letter studies the impact of mechanical vibration onthe performance of MEMS tunable evanescent-mode cavityresonators by measuring RF signal distortion. The amplitude

Manuscript received February 05, 2011; revised May 19, 2011; accepted June14, 2011. Date of publication July 08, 2011; date of current version August 10,2011. This work was supported by the Defense Advanced Research ProjectsAgency.

X. Liu, J. Small, D. Berdy, W. J. Chappell, and D. Peroulis are with the Schoolof Electrical and Computer Engineering, Purdue University, West Lafayette, IN,47906 USA (e-mail: liu79@purdue.edu; dperouli@purdue.edu.

L. P. B. Katehi is with the University of California, Davis, CA 95616 USA.email: katehi@ucdavis.edu.

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

Digital Object Identifier 10.1109/LMWC.2011.2160159

Fig. 1. (a) MEMS tunable evanescent-mode resonator[1], [2]; (b) Electro-mechanical model showing the effect of vibration; (c) signal distortion due tothe vibration-induced frequency shift.

of the vibration-induced modulation sideband and the errorvector magnitude (EVM) are used to quantify the amount ofdistortions. In addition, we present a novel vibration-resistantdesign using fringing-field actuated cantilever beam arrays.Measured results show 15–25 dB reduction in the modulationsideband with this design.

II. EXPERIMENTS

A. Experiment Setup

Fig. 2(a) shows the block diagram of the measurement setup.The MEMS tunable resonator is mounted on an electrodynamicshaker platform by a rigid fixture [inset of Fig. 2(b)]. Theamount of actual vibrations is detected by an Analog DeviceADXL001-70 MEMS accelerometer mounted on the samefixture. The direction of sensing is aligned with the direction ofthe vibration (perpendicular to the shaker platform).

An Agilent 4433B signal generator generates the RF signal,which is fed through the MEMS tunable resonator to a Tek-tronix real time spectrum analyzer (RTSA). Both continuouswave (CW) and digitally-modulated signals are used in the ex-periments. In the CW case, the vibration induced sideband mod-ulation products are recorded while in the digital modulationcase, EVM is recorded to quantify the amount of distortions dueto vibration.

B. Results and Discussion

A strongly-coupled evanescent-mode resonator is used inthe tests. The tested resonator has a resonant frequency of

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LIU et al.: IMPACT OF MECHANICAL VIBRATION ON THE PERFORMANCE OF RF MEMS EVANESCENT-MODE TUNABLE RESONATORS 407

Fig. 2. (a) Block diagram of the measurement setup; (b) Pictures of the mea-surement setup.

Fig. 3. Typical measured spectrum of the received signal from the MEMS tun-able resonator subject to mechanical vibration (� � ��� ��� and � � ��).

3.44 GHz, insertion loss of 0.75 dB, a loaded quality factorof 25 and a mechanical resonant frequency of approximately1.7 kHz. Since the electromagnetic resonant frequency is mostsensitive to change when the is the smallest, all tests areperformed without applying a dc bias to the tunable resonator.

Fig. 3 shows a typical output spectrum when a CW signal isfed through the resonator in the presence of vibration. The mag-nitude of the first modulation sideband is recorded for differentvibration frequencies ( ) and amplitudes (Fig. 4). Two peaksin the sideband amplitude are observed in Fig. 4(a). The peakat 1.7 kHz corresponds to the natural mechanical resonant fre-quency of the MEMS tuner. The peak at 1.4 kHz is attributedto a resonance in the measurement fixture, which is further con-firmed in Fig. 8.

Fig. 4(b) shows the relationship between the sideband ampli-tude and the peak magnitude of acceleration. For common vi-bration conditions ( and [5]), the sidebandamplitude is quite low ( ).

Fig. 4. Measured sideband magnitude for the MEMS resonator subject to dif-ferent (a) vibration frequencies and (b) amplitudes.

Fig. 5. Comparison of the received constellation diagrams (a) with and (b)without external vibration (� � ��� ��� and � � ��).

Fig. 6. Measured EVM for different (a) vibration frequencies and (b) ampli-tudes.

Signal distortions can also be characterized by the amount ofmodulation error introduced by the RF link. For this purpose, aQPSK modulated signal is passed through the tunable resonatorand demodulated by the RTSA. Fig. 5 shows a comparison ofthe received constellation diagram with and without external vi-bration.

Fig. 6 shows the measured EVM values with different vi-bration frequencies and amplitudes. The measured EVM valuesfollow a similar trend as that of the sideband magnitude (Fig. 4).Again, very low distortion is observed for common vibrationconditions.

III. MEMS TUNABLE RESONATOR WITH

REDUCED VIBRATION SENSITIVITY

To further reduce the susceptibility to external mechanicalvibration, we present a novel tunable resonator design usingminiature MEMS cantilever beam array. It is well-known thattraditional miniature RF MEMS devices are virtually immune to

408 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 21, NO. 8, AUGUST 2011

Fig. 7. Novel MEMS tunable evanescent-mode cavity resonator with electro-static fringing-field beam array, (a) fringing-field actuated cantilever beam; (b)MEMS beam array; (c) tunable evanescent-mode cavity design; and (d) mea-sured frequency tuning characteristics for a weakly-coupled tunable resonator.

Fig. 8. Measured sideband magnitude for the fringing-field MEMS resonatorsubject to different (a) vibration frequencies and (b) amplitudes.

vibration due to their extremely small mass and relatively highspring constant (tens of N/m) [6], [7]. However, these MEMSdevices usually have very limited deflection, which limits thefrequency tuning range in our design.

The authors have previously demonstrated a biasing tech-nique to extend the tuning range of electrostatically actuatedMEMS without significantly increasing their size [8]. As illus-trated in Fig. 7(a), the pull-down electrodes are laterally offsetfrom the movable cantilever as opposed to being directly be-neath it. This configuration utilizes the electrostatic fringing-field to actuate the cantilever and has been shown to eliminatethe “pull-in” effect that limits the deflection range in typicalparallel-plate electrostatic designs. The fringing-field actuatedcantilever can be designed to linearly deflect the full movablerange (up to 60 – 70 ). The mass of these cantilevers isextremely small. For example, a gold cantilever with dimen-sions of 300 50 2.5 has a mass of 7.3 anda spring constant of 1.5 N/m. Under an acceleration of 1g, thetip displacement is no more than 4.7 nm.

Fig. 7(b,c) show the concept design of the fringing-fieldMEMS tunable evanescent-mode resonator. The array of

cantilevers is deflected to change the gap between the postand the cavity; therefore, the resonant frequency is changed.Fig. 7(d) shows a picture of the assembled device. The bodyof the evanescent-mode cavity is machined from copper, andcoaxial connectors are used as feeds. This resonator tunes from15.7–16.3 GHz with of 623–785. The mechanical resonantfrequency of the MEMS beams is estimated to be 7.5 kHz. Theinitial gap and loaded quality factor are adjusted to be similarto the resonator tested in Section II.

Due to a limitation in the bandwidth of the RTSA, only CWsignal tests were conducted for the fringing-field MEMS tunableresonator. Fig. 8 shows the measured results. The same peak at1.4 kHz confirms that there is a resonance in the measurementfixture. The small resonance at 500 Hz is believe to be a weakerresonance in the fixture due the difference in the resonator fix-ture geometry. At vibration frequencies below 200 Hz, the mod-ulation sidebands remain very low ( ). A 15–25 dB re-duction in the vibration-induced sideband can be observed com-pared to the diaphragm based tunable resonator (Fig. 4) underthe same tested conditions. This reduction is primarily attributedto two factors: a) the smaller mass and b) the higher mechanicalresonant frequency of the cantilever beams.

IV. CONCLUSION

This letter presents the first experimental investigation of theimpact of mechanical vibration on the performance of MEMSevanescent-mode tunable resonators. For the diaphragm basedMEMS tunable resonator, signal distortion is found to be verysmall ( modulation sideband and EVMincrease under common vibration conditions). A novel MEMStunable evanescent-mode resonator design using electrostaticfringing-field MEMS beams has also been demonstrated toachieve a further reduction of 15–25 dB in the vibration-in-duced sideband.

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