System-level circuit simulation of nonlinearity in micromechanical resonators

We here present an equivalent circuit model capable of capturing the effects of nonlinearity in micromechanical resonators, particularly those driven and sensed by capacitive transducers. A charge controlled capacitor and a variable capacitor are developed to capture the nonlinear nature of the mechanical restoring force and the capacitive transducer. Distinctive features of the frequency response (like spring softening, hysteresis) induced by mechanical and capacitive nonlinearity are highlighted by illustrating the simulation results of a well-studied longitudinal beam resonator, which are verified against analytical solution of the Duffing equation. The circuit simulation approach is capable of capturing prominent parametric excitation effects in narrow-gap capacitive transducers which are commonly excluded in the approximations of the analytical model for simplicity. Finally, we constructed the full equivalent circuit for a fully differential Lamé bulk mode microresonator. The comparison between experimental and simulation results shows the proposed model can well capture the nonlinear behavior of this resonator which illustrates an approach to realize full system-level circuit simulation of microresonator based devices, such as precision resonant sensors, mechanical RF filters and MEMS oscillators.