Analysis of air damping in micromachined resonators

Abstract

An approach to the modeling and simulating the air damping effect on quality factor (Q) of a square plate Lamé mode microresonator is presented in this paper. Both the squeeze film damping and slide film damping are considered in the analysis procedure. The Reynolds equation and the Stoke-flow model are used to investigate the reactions of the resonant plate with the air flows in the transduction gaps and around the resonator plate surfaces, respectively. An electrical equivalent model has been derived for a microresonator operating in air. The model is realized with resistors equivalent for the slide film damping force and frequency-dependent resistors and capacitances connected in series equivalent for the squeeze film damping force. The simulated transmission characteristics are in good agreement with the experimental results for a 4.13 MHz Lamé mode microresonator.