Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone

This paper presents the nonlinear identification of a capacitive dual-backplate microelectromechanical systems (MEMS) microphone. First, a nonlinear lumped element model of the coupled electromechanical microphone dynamics is developed. Nonlinear finite element analyses are performed to verify the accuracy of the lumped linear and cubic stiffnesses of the diaphragm. In order to experimentally extract the system parameters, an approximate solution using the second-order multiple scales method is synthesized for a nonlinear microphone model, subject to an electrical step input. A nonlinear least-squares technique is then implemented to extract system parameters from laser vibrometry data of the diaphragm motion. The results indicate that the theoretical fundamental resonant frequency, damping ratio and nonlinear stiffness parameter agree with the corresponding extracted experimental parameters with 95% confidence interval estimates.