Nonlinear circuit analysis for time‐variant microelectromechanical system capacitor systems

Abstract

Electrostatic transducers, consisting of time-variant capacitors, are utilised in many types of microelectromechanical system (MEMS) devices. Linear circuit theory is based on the premise of time-invariant passive devices. Time-variant capacitors generally result in one or more nonlinear differential equations that must be solved to obtain expressions for the voltage across or the current through the capacitor. An iterative approach can be used to provide an approximate solution to the nonlinear differential equation model of the Thevenin equivalent RC circuit. This solution technique is verified through comparison with a MATLAB Simulink ® simulation of a MEMS capacitor that sinusoidally varies with time because of external stimuli.