Modeling of nonlinear micromechanical resonators and their simulation with the harmonic-balance method

A model for a micromachined electrostatically driven high-Q beam resonator is constructed of nonlinear voltage-controlled current and charge sources. Its characteristics are simulated with the harmonic-balance method in the RF simulation program APLAC demonstrating both the spring softening and hardening effects in the capacitive transducer and in the nonlinear mass-spring systems. Measured large-signal frequency-domain transfer characteristics of a test resonator structure at various signal levels were accurately reproduced by model simulations.