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.
Highlights
Today, in this rapidly-developing world of micro-communications, how to develop micromechanical oscillators and filters with high linearity, high power handling capability and low motional resistance, is a matter of debate
Unlike HD2 products, the presence of third-order intermodulation (IM3) products can greatly deteriorate the performance of the micromechanical filter and mixer-filter, and this indicates the importance of characterizing the IM3 in micromechanical resonators
This paper deals with the nonlinear behavior of distortion in silicon bulk-mode ring resonators with electrostatic actuation and capacitive detection on both inner and outer sides of the ring
Summary
In this rapidly-developing world of micro-communications, how to develop micromechanical oscillators and filters with high linearity, high power handling capability and low motional resistance, is a matter of debate. Mestrom et al [7] studied the frequency responses and the nonlinear dynamic properties of clamped-clamped (C-C) beam resonators and predicted the hardening behavior. They compared their analytical results with experimental results and found a reasonable agreement. Navid et al [10] and Lin et al [11] derived analytical formulations for IMD using the third-order input intercept point (IIP3) They measured IIP3 at the offset of Δω = 2π × (200 kHz) for a clamped-clamped beam resonator and contour-mode disk resonator, respectively. The effect of operating conditions including the ac-drive and DC-bias voltages and quality factor on the harmonic and third-order intermodulation distortions are investigated
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