The biasing of capacitance microphones by a constant voltage or electret charges places electrostatic forces on the microphone’s membrane diaphragm. Due to the dependence of the electrostatic forces on the deflections, the final membrane position is governed by a nonlinear differential equation. Because of this nonlinearity, certain ranges of the parameter values exist for which stable static deflections cannot be obtained. Numerical methods are usually used to obtain the deflections and their critical or highest stable values. The results of two past investigations using different forms for the nondinemsionalized nonlinear differential equation are reviewed and compared [Warren et al., J. Acoust. Soc. Am. 52, 711–719 (1972); Friam et al., J. Acoust. Soc. Am. 53, 1601–1608 (1973)]. A third, and perhaps more appropriate, form for the nondimensionalized differential equation is presented and discussed. Using this third form, deflection and stability results are reviewed for circular and annular membranes. Recent results are then presented for rectangular strip membranes with the tension applied along one axis and supported only on the edges perpendicular to that axis. In general, annular membranes are more stable than the other two types of membrane systems. The effect of openings in the stationary electrode was found to increase the stability in all three types of membrane systems. The amount of increase was found to be dependent upon the size and location of the openings. The static deflections and their stability values are of importance since they determine the operating position of the membrane diaphragm and the operating range of many microphone parameters. Application of the stability results to membrane switches may also be possible [Sessler et al., IEEE Trans, Commun. COM-21(1), 61–65 (Jan. 1973)]. Subject Classification: 85.44, 85.62.
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Joseph E. Warren (1975) studied this question.