Modeling of measurement condenser microphones at low frequencies: Numerical issues

Numerical modeling of condenser microphones is a challenging task. In these devices, there is a strong coupling between the exterior medium, the metallic stretched membrane, and the interior domain. Viscous and thermal losses in the narrow gap between membrane and back plate play a central role in the precise damping of the membrane's first resonance and the definition of the sensitivity at high frequencies. The inclusion of losses means a drastic increase in the computational load and makes the modeling of the most complicated units very cumbersome. The difficulty is even higher when whole calibration systems, such as primary reciprocity setups, need to be modeled. There is a need for such models from the metrological community. In previous publications, the Boundary Element Method (BEM) has shown to be able to model several measurement condenser microphones, some of them containing many holes in the backplate. There is, however, a difficulty when low frequencies are modeled. The limit for “low” frequency depends on the unit, but it is generally below the membrane resonance. This issue is the consequence of the instability of the BEM at low frequencies for interior domains, where the pressure in the cavity is almost uniform. Some solutions have been found for microphone models that minimize this effect, but a complete removal would be more desirable. In this paper, the issue will be examined from the practical point of view. Some new remedies will be proposed, including numerical approaches that preserve the advantages of the BEM and can become more stable in the referred cases.