Capacitance Microphone Static Membrane Deflections—Comments and Further Results

Abstract

The static deflections of the membrane diaphragm of capacitance microphones due to electrical biasing are governed by a nonlinear differential equation. Since the governing equation is nonlinear, deflection and stability results are usually obtained using numerical methods. The static deflections and their stability values determine the operating range of certain microphone parameters and influence the sensitivity and frequency response. The results of two past investigations using different forms for the nondimensionalized nonlinear differential equations are reviewed and compared. [J. E. Warren, A. M. Brzezinski, and J. F. Hamilton, J. Acoust. Soc. Amer. 52, 711–719 (1972); F. W. Fraim et al., J. Acoust. Soc. Amer. 53 (to be published)]. Results are presented for circular, annular, and strip membranes using a third and perhaps more appropriate form for the nonlinear differential equation. Stability results for the three types of membrane systems for flat stationary electrodes with openings are also presented. Since the third nondimensionalized form is similar to that used by Teer, his results for an optimum stationary electrode curvature for circular membranes may now be applied to situations with two dielectric layers of different thicknesses and permittivities [K. Teer, Acustica 15, 256–263 (1955)].