Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences


UC Berkeley


2008 Research Summary

Linearity and Q-Boosting of Vibrating Micromechanical Resonators

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Clark Nguyen and Li-Wen Hung

This project aims to study and analytically model the nonlinear behavior of vibrating micromechanical resonators pursuant to accurate prediction of 1/f3 and 1/f4 close-to-carrier phase noise in micromechanical resonator oscillators. Once the mechanisms are understood, methods for suppressing these noise sources will then be conceived and applied towards achieving phase noise performance exceeding that of existing portable wireless communication oscillators, and perhaps approaching that of radar-grade oscillators.

Capacitively-driven vibrating micromechanical resonators have been demonstrated with resonant frequencies in the GHz range with Q's larger than 11,000 [1], making them promising in on-chip frequency selecting elements for oscillators and filters in wireless communications. Despite these advantages, there are lingering questions concerning the linearity of these devices which must be sufficient to avoid noise aliasing in oscillators and to maintain the needed minimum cumulative receiver linearity specification for the targeted wireless communication application. A modeled understanding of the nonlinear behavior of micromechanical devices will be instrumental in maximizing the performance of micromechanical signal processors for communication and other applications. To date, an analytical model for determining intermodulation distortion in capacitively-transduced radial-mode disk resonators has been developed and evaluated. Using an IIP3 measurement setup that avoids the use of an input power combiner, a 156-MHz contour-mode disk resonator with Q = 20,500 has been demonstrated to have PIIP3 = 19.49 dBm, which is very close to the predicted value of 18.95 dBm.

One method under current study to enhance the linearity of micromechanical resonators is to combine them into mechanically coupled arrays [2]. This mechanical circuit-based approach has now been shown to also boost the Q of a vibrating micromechanical resonator [3]. In particular, if a low Q resonator is embedded into a mechanically-coupled array of much higher Q resonators (Figure 1), its functional Q increases by a factor approximately equal to the number of resonators in the array. This is illustrated in Figure 2, where the low Q of 7,506 for a deficient resonator is effectively raised by about 9X to 63,207 when emplaced into a mechanically-coupled array of eight very high-Q wine-glass disks that then form a composite resonator.

Figure 1
Figure 1: SEM of a 3-resonator version of the mechanically-coupled wine-glass disk resonator array which is composed of one low-Q and two high-Q resonators

Figure 2
Figure 2: Measured frequency characteristics for: (a) a high-Q wine-glass disk resonator and a mechanically-coupled array of three such resonators, and (b) wine-glass disk resonators and arrays with one low-Q resonator and several high-Q resonators, showing that mechanically-coupled arrays can "fix" the Q of a bad resonator

J. Wang, J. E. Butler, T. Feygelson, and C. T.-C. Nguyen, "1.51-GHz Polydiamond Micromechanical Disk Resonator with Impedance-Mismatched Isolating Support," Proceedings, MEMS'04, Maastricht, The Netherlands, January 2004, pp. 641-644.
Y.-W. Lin et al., "Low Phase Noise Array-Composite Micromechanical Wine-Glass Disk Oscillator," Technical Digest, IEDM, Washington, DC, December 2005, pp. 287-290.
Y.-W. Lin et al., "Quality Factor Boosting via Mechanically-Coupled Arraying," Technical Digest, Transducers'07, Lyon, France, June 2007, pp. 2453-2456.