Nonlinear circuit analysis technique for microelectromechanical systems with a time-variant capacitor and an AC power source

Microelectromechanical systems (MEMS) utilise time-variant capacitors as transducers in many applications. However, this kind of component can introduce harmonics and disturbances into the circuit with an AC power source, which is difficult to evaluate through closed-form solutions. This Letter proposes an iterative solution to analyse the dynamics of MEMS devices which contain a time-variant capacitor and an AC source. First, the expressions of the time-variant capacitor, AC source and their derivatives with respect to time are determined. Then, an initial solution that is sufficiently close to the actual solution is determined using linear circuit analysis. On the basis of the previous steps and the principles of the iterative method, an approximated solution combining the initial solution and its iteratively-derived higher-order terms is reached. Adding additional higher-order terms can improve the accuracy of the solution. A case study considering a MEMS device which has an AC power source and sinusoidal motion was performed using MATLAB Simulink. The simulation study further demonstrated that: (i) this iterative solution can effectively analyse the dynamics of MEMS devices with a time-variant capacitor and an AC power source; and (ii) computing additional higher-order terms derived from the initial solution can further improve the solution's accuracy.