Thermal boundary layer limitations on the performance of micromachined microphones

Abstract

The extent to which thermal boundary layer effects limit the performance of micromachined microphones is examined. A lumped element network model for a micromachined microphone is presented which includes a ladder network in parallel with the adiabatic back volume compliance to account for the transition of the enclosure from adiabatic to isothermal conditions when the thermal boundary layer becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive component which contributes thermal-acoustic noise to the system. The model results are compared to measurements taken from commercially available microphone units with various back volume sizes, and the simulated relative noise power contribution of each acoustic noise source is calculated. The impedance of the back volume, including the thermal correction factor, is compared to the adiabatic compliance and the impedance derived from thermoacoustic finite element analysis. It is shown that the noise due to the thermal component of the back volume impedance becomes significant in microphones with small back volumes and effectively sets an upper bound on the signal-to-noise ratio of a microphone of given package dimensions.