Capacitance calculation for electrostatic transducer applications

Abstract

An approach for accurate calculation of the capacitance coefficient matrix in electrostatic transducer applications is presented in this article. We consider transducers consisting of a fixed and a moving set of metal strips where strong fringing field effects may occur. The calculation method is based on an expansion of the surface charge distribution on each metal finger in terms of orthogonal functions that capture the singularity effects at the edge of the fingers. We analyze the errors both due to neglect of end effects and due to truncation of the series expansion. The complexity of the capacitance matrix calculation is significantly reduced by truncation to the first three terms of the expansion, giving errors below 1%. An example capacitance structure is analyzed in detail. The capacitance/induction coefficients roughly vary as a cosine function of the horizontal relative displacement between two electrodes. This motivates a simple approximation formula that can be used to calculate the capacitance coefficient matrix of electrostatic transducers. It gives a maximum error of 1.5% compared to the full calculation for a gap g = 5 µm and a microstrip width a = 50 µm in the example structure.