Harmonic Balance Nonlinear Identification of a Capacitive Dual-Backplate MEMS Microphone

This paper describes the application of a nonlinear identification method to extract model parameters from the steady-state response of a capacitive dual-backplate microelectromechanical systems microphone. The microphone is modeled as a single-degree-of-freedom second-order system with both electrostatic and mechanical nonlinearities. A harmonic balance approach is applied to the nonlinear governing equation to obtain a set of algebraic equations that relate the unknown system parameters to the steady-state response of the microphone. Numerical simulations of the governing equation are also performed, using theoretical system parameters, to validate the accuracy of the harmonic balance solution for a weakly nonlinear microphone system with low damping. Finally, the microphone is experimentally characterized by extracting the system parameters from the response amplitude and phase relationships of the experimental data.