Analysis of resonant pull-in of micro-electromechanical oscillators

In this paper, the equations governing the pull-in of electrostatic (micro-electromechanical systems MEMS) oscillators are established and analyzed. This phenomenon defines the maximal oscillation amplitude that can be obtained without incurring instability and, hence, an upper limit to the performance of a given device. The proposed approach makes it possible to accurately predict pull-in behavior from the purely resonant case, in which the electrostatic bias is very small, to the static case. The method is first exposed in the case of a parallel-plate resonator and the influence of the excitation waveform on the resonant pull-in characteristics is assessed. It is then extended to the more complex case of clamped-clamped and cantilever beams. The results are validated by comparison with transient simulations.