MEMS Tutorial: Nonlinearity in Micromechanical Resonators

In this tutorial, we cover the effect of nonlinear spring forces on (micro)resonators. The motivation of analysis is: i. to understand the nonlinear effects observed with real resonators and ii. to estimate the maximum vibration amplitude where vibrations are almost linear. Knowing the range for linear vibrations sets the dynamic range for resonators. On the lower end, the usable range is limited by intrinsic noise in the MEMS system. The upper end is limited by the resonator power handling capacity which, as we’ll see shortly, is limited by nonlinear effects. The analysis in this tutorial follows closely to Landau [2] but the presentation has been slightly modernized.