Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response

• Published in: Journal of microelectromechanical systems Vol. 25; no. 2; pp. 297 - 303
• Main Authors: Polunin, Pavel M., Yushi Yang, Dykman, Mark I., Kenny, Thomas W., Shaw, Steven W.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Constants; Decay; Dissipation; Duffing nonlinearity; Electrostatics; Force; Frequency measurement; Mathematical models; MEMS characterization; Micromechanical devices; nonlinear damping; Nonlinearity; quintic nonlinearity; Resonant frequency; Resonators; ringdown; Transmission line measurements; Vibration; Vibrations; ringdown; MEMS characterization; nonlinear damping; Duffing nonlinearity; quintic nonlinearity
• ISSN: 1057-7157; 1941-0158
• DOI: 10.1109/JMEMS.2016.2529296

We present a technique for estimation of the model parameters for a single-mode vibration of symmetric micromechanical resonators, including the coefficients of conservative and dissipative nonlinearities. The nonlinearities result in an amplitude-dependent frequency and a nonexponential decay, which are characterized from the ringdown response. An analysis of the amplitude of the ringdown response allows one to estimate the linear damping constant and the dissipative nonlinearity, and the zero-crossing points in the ringdown measurement can be used for characterization of the linear natural frequency and the Duffing and quintic nonlinearities of the vibrational mode, which arise from a combination of mechanical and electrostatic effects.