Ing. Karina Šimonová, Ph.D.

This study investigates the directivity of electrostatic (condenser) microphones featuring a circular membrane and a back-plate segmented into four parts. We analyze the relationship between the direction of arrival of incoming sound pressure waves and the non-axisymmetrical displacement field of the membrane using both analytical and numerical models. Since the output voltage of an electrostatic microphone is proportional to the mean value of the membrane displacement over the fixed electrode surface, the membrane displacement field influenced by the acoustic pressure field inside the transducer must be accurately calculated. By subtracting the output voltage signals from two opposite electrodes, we obtain two directional outputs with bidirectional directivity patterns perpendicular to each other. To validate our theoretical findings, we conduct measurements on an experimental transducer specimen. The experimental results, obtained using a scanning laser vibrometer to analyze the membrane displacement field and directivity measurements performed in an anechoic chamber, confirm our theoretical predictions. Bidirectional patterns at both outputs, which are perpendicular to each other, are observed in the frequency range corresponding to the pass band of the transducer, except at very low frequencies where phase problems occur.

The paper is mainly concerned with the analytical approach of the behaviour of a two-dimensional miniaturized MEMS transducer, namely a rectangular or square clamped plate loaded by a fluid-gap (squeeze film), surrounded by a small cavity (reservoir), and excited by an incident acoustic field (assume to be uniform on the plate). Until now, the problem has not been analytically solved owing to the geometry of the device in conjunction with the nature of the diaphragm (elastic plate) and its boundary conditions (zero deflection and zero normal slope along all edges); namely analytical eigenfunctions do not exist for the clamped plate. On the other hand, the analytical approach classically used to express the acoustic field in the fluid-gap relies on a modal expansion which does not match correctly with both the displacement field of the diaphragm and the boundary conditions at the entrance of the reservoir. Then, two particular questions arise: how to derive analytically the modal behaviour of the loaded clamped plate, and what analytical approach for the acoustic field in the fluid gap is convenient to describe its coupling with the displacement field of the plate? The aim of the paper is both to provide basically an exact analytical approach and to handle a numerical implementation (FEM) against which the analytical results are tested.