Behavioral Modeling of a CMOS–MEMS Nonlinear Parametric Resonator

Predictive design of nonlinear microelectromechanical systems featuring parametric resonance provides motivation to refine mixed MEMS/analog behavioral composable modeling and simulation methodologies. Toward this end, a schematic of a canonical parametric resonator testbed is built with primitive beam, plate, and gap models from a MEMS Verilog-AMS library along with a macro model of a non-interdigitated comb with electrostatic spring coefficients extracted from finite element analysis. A CMOS-MEMS parametric resonator for validation experiments exploits the well known non-interdigitated finger design to create a voltage-controlled spring constant as the parametric stimulus. Behavioral modeling and the analytic perturbation solutions are validated by optical vibration measurements matching to 0.2% and 2.1%, respectively.