Analytical modeling of condenser microphones with nonuniform acoustic excitation and backplate perforation patterns

The present study develops an analytical model for predicting the response of condenser microphones subjected to a plane wave incident pressure field arriving from an arbitrary direction while explicitly accounting for the exact perforation pattern of the backplate. The model describes the coupled vibration of a clamped circular membrane and acoustic pressure in the air gap and incorporates thermoviscous losses. Analytical predictions are compared with reference three-dimensional finite-element simulations. The comparison includes membrane displacement fields, air-gap pressure distributions, frequency-dependent mean displacements, and-for transducers with a segmented backplate-the mean displacement differences between opposing segments and the resulting polar directivity patterns. Across a broad frequency range, including frequencies above the first membrane resonance, the analytical model shows very good agreement with the numerical reference. The results demonstrate that the framework reliably captures the influence of arbitrary backplate perforation geometries and nonuniform acoustic excitation on the microphone response.