Modeling of parametrically excited microelectromechanical oscillator dynamics with application to filtering

A model for the dynamics of an emerging class of electrostatically driven microelectromechanical oscillators, parametrically excited MEM oscillators, has been developed. The equation of motion for these devices is a nonlinear version of the Mathieu Equation, which gives rise to rich dynamics. A standard perturbation analysis, averaging, has been adopted to analyze this complicated system. Numerical bifurcation analysis was employed and successfully verified these analytical results. Using the analytical and numerical tools developed for this model, along with the experimental results for such a device, parameters for the system are identified. This model is a pivotal design tool for the development of parametrically excited MEM filters.