Non-Linear Behavioral Modeling of Capacitive MEMS Microphones

In this work, a non-linear behavioral lumped model applicable to commercial state-of-the-art single-backplate microelectromechanical system (MEMS) microphones is described. The model allows to simulate all relevant microphone key performance indicators (KPIs), including the bias voltage dependent sensitivity, signal-to-noise ratio (SNR), and input pressure dependent total harmonic distortion (THD) of the microphone output voltage. Non-linear behavioral descriptions of the capacitive transduction and mechanical properties of a membrane are considered, which can be implemented in common circuit simulators using industry standard hardware description languages (i.e., Verilog-A). While state-of-the-art lumped models focus on purely linear microphone investigations of the sensitivity and SNR, the proposed model inherits an improved accuracy and allows to consider the system non-linearity and THD in theoretical design optimizations. Measurement results of a commercial MEMS microphone were employed to validate the precision of the developed model.