A Numerical Study on the Viscous Damping Effect for a Condenser Microphone

Exposing a condenser microphone to incident pressure causes a nonuniform diaphragm deflection and a nonlinear relationship with the induced voltage. This paper describes how the second order finite difference method is implemented to solve governing equations including diaphragm motion, Reynolds and Laplace equations 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 an unsteady 1-D equation of diaphragm motion has been considered in the cylindrical coordinates. The damping and stiffness coefficients of this equation 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, a holes radius and relative angle is studied in detail. It has also shown that the back plate holes damping effect strongly depends on the position and the pattern of holes. Using numerical mapping to solve the Laplace equation, microphone capacitance variation with respect to diaphragm deflection is calculated. The numerical frequency response obtained for a condenser microphone has been compared with prior analytical solutions. The numerical results obtained indicate a very good accuracy of the code. The damping coefficient effect on the frequency range which is also studied in detail is very important in designing a practical microphone. Unlike past numerical static simulation such a dynamic analysis gives a deeper view of nonlinearity of this important measuring transducer.