Numerical Modeling and Simulation of a Condenser Microphone

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.