Nonlinear frequency response of comb-driven microscanners

Accurate prediction of the dynamic behavior of comb-driven MEMS microscanners is important to optimize the actuator and structure design. In this paper, a numerical and an analytical model for the dynamic analysis of comb-driven microscanners under different excitation schemes are presented. The numerical model is based on a second order nonlinear differential equation. Due to the nature of the torque function, this governing equation of motion is a parametric nonlinear ODE, which exhibits hysteretic frequency domain behavior and subharmonic oscillations. Experimental results and approximate analytical expressions for this nonlinear torque function of the comb-drive are presented. Amplitude and phase relationship between the excitation signal and the resultant oscillations at different excitation frequencies are measured and we show that they are in close agreement with the numerical simulations. Analytical model uses perturbation methods to reach approximate close-form expressions for the dynamic behavior of the device in the first parametric resonance region. It is also utilized to predict the stability regions on the frequency-excitation voltage plane, where the device exhibit hysterical characteristics. Analytical and numerical modeling approaches proposed in this paper provides a simple yet powerful way to analyze the nonlinear frequency response of comb-driven actuators and simplify the design process for a microscanner based system