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Non-uniform deflection of a pressure condenser microphone diaphragm causes a nonlinear relationship between the deflection of the diaphragm and the induced voltage. This paper describes how the numerical dynamic analysis carried out with the second order finite difference method in space and forward difference in time domain to determine more accurately this nonlinearity and moreover, to determine the influence of the nonlinear electric field force on the mechanical system of the microphone with respect to time. For this purpose unsteady one dimensional equation of diaphragm vibration has been considered in the cylindrical coordinate. The damping and stiffness coefficients have been calculated using the squeeze film theory. Unlike the past analytical solutions, in this article the dependence of damping coefficient on the number of holes and rings, holes radius and relative angle is studied in detail. The dependence of the microphone capacitance on the diaphragm deflection can be well calculated by solving the Laplace equation using a numerical mapping. The numerical frequency response obtained for a condenser microphone has been compared with analytical solution exists in the literature. The numerical results obtained indicate a very good accuracy of the code. Such a dynamic analysis unlike the past numerical static simulation gives a deeper view into the reasons of the nonlinearity of this important measuring transducer.

Condenser microphones are widely used in electronic and acoustic applications. Although, various mechanical and electro-mechanical methods have been developed to design and analyze these sensors. However, due to the difficulty of fluid-structural-electrical couplings, none of them can introduce a method that consider all parameters of the design together. This research concerns the effects of four main parameters: a) Air gap size; b) Number of holes on the back-plate; c) holes radius size and d) location of the holes in back plate, on the response of the microphones. This analysis have been carried out based on coupled finite element and finite volume method using ANSYS-CFX software to simulate fluid-structure interaction between the diaphragm and air in the air-gap region. By using this method, the effects of the geometric parameters on the response of the microphone have been investigated. Results show that, increasing air gap size, holes radius, and holes number decrease the damping effects of the air between diaphragm and back plate. On the other hand, increasing the distance between the holes has the opposite effect. In addition, results reveal that among these four parameters, increasing the number of holes on back plate is the most efficient method in reducing air-gap damping effects.