Capacitance microphone dynamic membrane deflections

In order to accurately describe the operation of capacitance microphones, it is necessary to have solutions for both the static and dynamic deflections of the moving electrode. The present paper describes an application of finite difference methods to the differential equations describing the dynamic membrane motion due to the acoustic excitation. The authors have previously presented numerical solution approaches to the static deflections caused by the electrical biasing of the microphone [J. Acoust. Soc. Am. 52, 711–719 (1972)]. The dynamic solution approaches presented here include the effects of the static deflections and the motion of the thin air film between the microphone's electrodes. The numerical results are compared with published results for simplified stationary electrode geometries and with experimental data on more complicated geometries at different tension levels. The predicted mode shapes change greatly, depending upon the magnitudes of the membrane tension and microphone's back chamber volume. Owing to the accuracy of these methods, they have applications in microphone optimization and characterization of the time dependent properties of electret microphones.