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Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators
Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM), P.O. Box 91775-1111, Mashhad, Iran
* Author to whom correspondence should be addressed.
Received: 6 July 2012; in revised form: 6 August 2012 / Accepted: 16 August 2012 / Published: 22 August 2012
Abstract: A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring resonators is obtained. Moreover, to avoid dynamic pull-in instability, the choices of the quality factor, ac-drive and DC-bias voltages of the ring resonators, with a given geometry are limited by a resonant pull-in condition. Using the perturbation technique and the method of harmonic balance, the expressions for describing the effect of nonlinearities on the resonance frequency and displacement are derived. The results are discussed in detail, showing the effect of varying operating conditions and the quality factor on the harmonic distortions and third-order intermodulation distortion. The detailed nonlinear modeling and distortion analysis are applied as appropriate tools to design bulk-mode ring resonators with low motional resistance and high linearity.
Keywords: harmonic distortions; intermodulation distortion; micromechanical device; nonlinear system; perturbation method
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Bijari, A.; Keshmiri, S.-H.; Babazadeh, F. Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators. Micromachines 2012, 3, 582-603.
Bijari A, Keshmiri S-H, Babazadeh F. Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators. Micromachines. 2012; 3(3):582-603.
Bijari, Abolfazl; Keshmiri, Sayyed-Hossein; Babazadeh, Farshad. 2012. "Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators." Micromachines 3, no. 3: 582-603.