Thermal boundary layer limitations on the performance of micromachined microphones

This work examines the extent to which thermal boundary layer effects limit the performance of micromachined microphones. The acoustic impedance of the cavity formed by the microphone enclosure is calculated using both analytical and finite-element methods. A thermal correction to the cavity impedance is included to account for the transition of compression and expansion within the enclosure from adiabatic to isothermal when the thermal boundary layer that forms at the walls of the enclosure becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive term that results from thermal relaxation losses and contributes thermal-acoustic noise to the system. A lumped-element network model for the microphone response which includes the thermally corrected enclosure impedance is presented and compared to measured results for a case study device. The relative noise power contribution of each noise source considered in the model is calculated. It is shown that the noise due to the resistive term of the enclosure cavity impedance becomes significant when the enclosure volume is small. This sets a theoretical limit on the noise floor that can be achieved by a micromachined microphone with given enclosure dimensions.