Resonant pull-in of high-Q MEMS oscillators with arbitrary closed-loop phase shift
Résumé
In this article, we develop a simple closed-form expression of the resonant pull-in instability of high-Q MEMS resonators actuated with arbitrary periodic waveforms and arbitrary closed-loop phase shifts. The instability of MEMS oscillators operated under a low bias voltage is shown to be independent of the dimensions and physical properties of the resonator and fully-determined by the quadrature component of the actuation. The results are illustrated on parallel-plate capacitive MEMS actuated with sine-, square- and pulsed-wave voltages. Input-design methods optimizing the pull-in conditions of sensors and switches can be built based on our conclusions.