Characterizing MEMS nonlinearities directly: The ring-down measurements

We present a technique for direct estimation of the conservative and dissipative nonlinearities of symmetric MEMS resonators. The technique is based on measuring the ring-down response, during which the nonlinearities result in an amplitude-dependent frequency and non-exponential decay. Here we show how analysis of the amplitude and phase of the ring-down response allows one to estimate conservative and dissipative nonlinearities, in addition to the linear natural frequency and quality factor, associated with a vibrational mode. The coefficients obtained from the test allow one to predict the nonlinear open and closed loop responses of the resonator.