Modelling of a MEMS Transducer with a Moving Electrode in Form of Perforated Square Plate
Résumé
Several realizations of electroacoustic MEMS transducers where the moving electrode is perforated for technological reasons have been published recently. Since the presence of the holes changes the vibration characteristics of the plate (in terms of eigenmodes) and the coupling between the incident acoustic pressure and the pressure inside the transducer through these holes influences significantly the behaviour of the transducer, a precise modelling of such devices is of interest. The modelling approach proposed herein employs an approximated expression of the eigenfunctions of the perforated clamped plate in form of two-dimensional series expansion over the system of functions related to the solution for one-dimensional beam clamped at both ends, the coefficients of the series being calculated from the numerical solution for the eigenfunctions of the perforated clamped plate. The convergence issues and the dependence of the approximation error on the number of terms in the series are discussed. An integral formulation providing the acoustic pressure field inside the air gap between the moving electrode and the fixed one is then proposed. It takes into account the strong coupling between the acoustic pressure field in the air gap and the displacement field of the plate, the thermal and viscous boundary layer effects and the acoustic short circuit between both sides of the perforated plate through the holes.
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