Electrically driven CMOS-MEMS nonlinear parametric resonator design using a hierarchical MEMS circuit library

We are investigating a class of nonlinear resonators which feature parametric excitation when driven by an electrostatic force whose linear and cubic stiffness can be parametrically controlled by a pump drive oscillating voltage applied across the non-interdigitated comb fingers. The perturbation theory is employed in solving the Mathieu equation to quantitatively explain the nonlinear resonance phenomenon and to provide a closed-form solution which captures the dynamic behavior and its dependence on system parameters. We have implemented an electrically driven CMOS-MEMS nonlinear parametric resonator to validate system-level composable modeling of this complex behavior.