Electret microphone modeling and optimization by combined finite element analysis and lumped-element techniques

Abstract

Electret microphone performance modeling must represent detailed coupled mechanical, electrostatic, and fluid dynamics of the moving diaphragm, stationary back electrode and intervening air layer (the “motor”) while also evaluating the net performance characteristics which result. We model electret microphone response and noise by combined FEA and lumped-element methods. In detail, the diaphragm is treated as a tensioned membrane. Electrostatics are evaluated in locally parallel-plate fashion. Air layer dynamics are treated by reducing the exact thermoacoustic parallel-plate 3D squeeze solution to a 2D “transmission sheet” differential equation. Analyses (COMSOL FEA 2D PDE-mode) include initial diaphragm deflection upon back electrode polarization, then the harmonic responses to changes in frontside pressure, backside pressure, and polarization. Motor responses (frontside/backside volume flows and output current) are reduced to impedance and transfer characteristics of a three-port (front and back acoustic, electrical) element, which is then embedded in a traditional host lumped-element equivalent circuit (including amplifier). FEA-based motor characteristics over an array of frequencies lead to microphone frequency response and noise spectrum. Performance optimization is done by scripting motor geometry generation and FEA analysis as a subroutine, defining a space of adjusted parameters (motor dimensions, etc.) and running recurring FEA analyses generated by a downhill simplex algorithm.