Nonlinear dynamics of a dual-backplate capacitive MEMS microphone

This work presents an investigation of the electromechanical nonlinear dynamics of a dual-backplate capacitive MEMS (microelectromechanical systems) microphone. A large displacement solution via an energy method has been utilized to provide linear and cubic lumped stiffnesses of the circular diaphragm of the microphone. A nonlinear dynamic model of the microphone is developed using lumped element modeling. Theoretical lumped stiffnesses of the diaphragm are verified by nonlinear finite element analyses and the errors for the linear and cubic stiffnesses are approximately 1.3% and 5.0% respectively.;The critical quasi-static pull-in voltage of the microphone is found to be approximately 41V both analytically and numerically. The phenomenon of quasi-static pull-in due to an applied DC voltage is illustrated by a subcritical pitchfork bifurcation. By using a phase portrait and basin of attraction, a mechanical shock load is related to dynamic pull-in. Further study shows that dynamic pull-in could potentially take place below the critical quasi-static pull-in voltage when the microphone is subject to a large mechanical shock load. The dynamic pull-in due to an acoustical pulse, in the form of an N-wave, has been investigated by using numerical simulation. A dynamic pull-in threshold curve has been obtained in terms of the duration time and amplitude of the N-wave for a given DC bias voltage.;Studies of dynamic pull-in also show that several nonlinearities (geometric, electrostatic and mechanical/acoustical shock) compete with each other. An increased electrostatic nonlinearity and/or an increased mechanical/acoustical shock load destabilize the system while an increased geometric nonlinearity helps to stabilize the microphone and expands the stable operational range.;The multiple time scales and harmonic balance methods are applied to obtain approximate solutions of the nonlinear governing equations under the electrical square, electrical sinusoidal and sinusoidal acoustical excitations. Based on the two approximate solutions for the electrical excitations and a nonlinear least-squares curve-fitting technique, system parameters are extracted from two types of experimental data. The preliminary uncertainty analysis, which includes only the uncertainties caused by fabrication, shows that the experimentally extracted linear natural frequency, damping ratio and nonlinear stiffness parameter fall within their conservative theoretical ranges for a 95% confidence level.