A non-dimensional time-domain lumped model for externally DC biased capacitive microphones with two electrodes

Microphones that utilize externally biased capacitive transduction (condenser microphones) are typically being modeled in lumped parameter networks where the mechanical, acoustical, and electrical elements are all represented as passive electronic circuit components. Those models have been shown to be insufficient to fully describe crucial aspects of this type of transducer, such as the pull-in phenomenon in which, after a certain distance and for a certain bias voltage, the moving electrode, typically a flexible membrane, attaches itself to the stationary. In this paper, we account for several non-linearities present in an extended simplified model of such a transducer in the time domain and identify the different factors related to its nonlinear response. We derive a time-domain non-linear non-dimensional system of equations for the coupled lumped model where we also take into account parasitic capacitances that are usually present and can significantly affect the overall electroacoustic performance as well as the fringing fields due to the nonhomogeneous electric field between the electrodes and nonlinearities related to damping due to the thin-film of air between the electrodes. We present the nondimensionalization method we used that allows for the identification of a novel set of nondimensional parameters that characterize the non-linear behavior of our system in the time-domain. A designer can use these parameters to optimize for linearity in the voltage response of the transducer. We post-process our time-domain solution to calculate the response to the fundamental excitation frequency and discuss the harmonic distortion. It is shown that coupling the electrical nonlinearities to the mechanical can significantly contribute to the nonlinear voltage response of the transducer. Our model agrees well with nonlinear measurements of analog microelectroelectromechanical (MEMS) microphones for a set of physical values of the nondimensional parameters.