A behavioral nonlinear modeling implementation for MEMS capacitive microphones

Abstract

We are highlighting the behavioral nonlinear system-level modeling approach for MEMS capacitive microphones. The combination of finite element modeling and large signal nonlinear circuit modeling provides a strong capability to predict electroacoustical performance for capacitive transductions. Circuit simulation tools such as Cadence Virtuoso have emerged as powerful aids in designing behavioral models in both linear and nonlinear regimes. Typical small signal lumped element models fail to capture the MEMS behavior which changes over pressure and electrical bias conditions. The models described herein capture diaphragm displacement and capacitance change over large pressure ranges for a simply supported circular plate. This can be coupled with the electrostatic force, due to the applied bias voltage, and converted back to pressure, thereby realizing a feedback loop in the circuit model. The nonlinear model capability is extended to predict capacitance-bias behavior and estimate pull-in of the MEMS device. The microphone sensitivity, signal-to-noise ratio, and harmonic distortions are accurately predicted using the nonlinear large signal model when compared to measured microphone data.