Algorithm for Calculating the Output Signal of Electret Capacitive Transducers of the Receiving Type

Introduction. Electret capacitive receiving transducers with moving plates are used in various devices, particularly as microphones in mobile phones. However, methods for calculating their sensitivity, including taking into account the electrical load parameters and other characteristics of such transducers, are insufficiently developed.
Aim. To develop a mathematical model of membrane-type electret sensors for evaluating their sensitivity, taking into account the static deflection of the membrane, the characteristics of mechanical vibrations under the influence of an external periodic force of various origins, and the influence of the electrical load.
Materials and methods. Computer simulation in the MATLAB environment.
Results. The proposed calculation procedure is divided into three interconnected stages. The static stage accounts for membrane deflection under the influence of the electret-induced electric field. The dynamic stage describes membrane vibrations caused by an external periodic disturbance. The electrical stage determines the resulting electrical voltage at the transducer terminals. Analytical expressions for the static deflection of the membrane are derived, and the limits of its steady state are determined as functions of the parameters of the electret transducer capsule, including membrane tension, air gap thickness, electret film thickness, relative permittivity of the electret material, membrane and counter-electrode dimensions, etc. The technique for calculating membrane vibrations uses equivalent lumped parameters (membrane mass, acting forces, etc.) instead of distributed parameters, thereby eliminating the need to solve partial differential equations.
Conclusion. The proposed calculation procedure provides a basis for the rational selection of electret transducer parameter values depending on the target performance requirements. The derived expressions enables the calculation of the amplitude–frequency characteristics of various electret transducer generators. The results obtained are useful for those designing new and optimizing existing electret transducer designs

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