Dynamic behavior of the circular membrane of an electrostatic microphone: Effect of holes in the backing electrode

Abstract

Today, several applications require using electrostatic microphones in environments and/or in frequency ranges, which are significantly different from those they were designed for. When low uncertainties on the behavior of acoustic fields, generated or measured by these transducers, are required, the displacement field of the diaphragm of the transducers (which can be highly nonuniform in the highest frequency range) must be characterized with an appropriate accuracy. An analytical approach, which leads to results depending on the location of the holes in the backing electrode (i.e., depending on the azimuthal coordinate) not available until now (regarding the displacement field of the membrane in the highest frequency range, up to 100 kHz), is presented here. The holes and the slit surrounding the electrode are considered as localized sources described by their volume velocity in the propagation equation governing the pressure field in the air gap (not by nonuniform boundary conditions on the surface of the backing electrode as usual). Experimental results, obtained from measurements of the displacement field of the membrane using a laser scanning vibrometer, are presented and compared to the theoretical results.

Microphone with Planar Nano-Gauge Detection: Fluid-Structure Coupling Including Thermoviscous Effects

“…Analytical solutions to the Kirchhoff equations in viscothermal fluids [13] presenting a good agreement with experimental results, but only for acoustic devices with simpler shapes [14] or higher dimensions [15]. The microsystem studied has a complex shape, small dimensions and strong fluid-structure coupling.…”

Analytical and numerical modeling of an axisymmetrical electrostatic transducer with interior geometrical discontinuity

“…The analytical method relies on eigenmodes expansions of both the membrane and the fluidfilled elements loading the membrane (air gap and peripheral cavities), along with general solutions of the associated homogeneous propagation equations (see, for example, Refs. 1,[4][5][6][7][8]. The analytical approach used to provide the results given in this paper has been validated previously from comparison with experimental results obtained on similar transducers available in the literature.…”

“…The analytical approach used to provide the results given in this paper has been validated previously from comparison with experimental results obtained on similar transducers available in the literature. 5,7 Regarding the numerical method which could be given also for final designs of devices, numerical simulation using an adaptive mesh and accounting for the viscous and thermal boundary layer effects 9-11 has been handled herein; particularly here, it provides more results against which the approximate analytical results can be tested.…”

An analytical-numerical method for determining the mechanical response of a condenser microphone

“…The paper by Lavergne et al 13 contains the displacement field of the B&K 1/2 in. microphone obtained experimentally using a scanning laser vibrometer.…”

“…12. Very recently, Lavergne et al 13 developed a theory for electrostatic acoustical transducers used in environments and/or frequency ranges which are significantly different from those for which they have been designed according to the previous described work. By using a lubrication-type approximation they obtained a Helmholtz-type equation for the pressure in the gap and used a similar equation for the pressure in the backchamber.…”