Parametric Noise Reduction in a High-Order Nonlinear MEMS Resonator Utilizing Its Bifurcation Points

An electrostatically actuated non-linear microelectromechanical systems (MEMS) resonator can describe double hysteresis behavior in the measured frequency response due to the interplay between electrical and mechanical non-linearities in the system. This paper provides the first experimental mapping of the stable and unstable branches of the frequency response of a MEMS resonator describing a double hysteretic frequency response using a closed-loop phase feedback oscillator. Furthermore, the frequency stability of the oscillator is compared for varying amplitude and phase feedback conditions, and it is experimentally demonstrated that parametric noise up-conversion can be suppressed in such a system by suitably biasing the resonator at one of the four bifurcation points in such a system. This result is qualitatively consistent with theoretical prediction and demonstrates that improved frequency stability in a non-linear MEMS oscillator is possible by suitably biasing the resonator using simultaneous amplitude and phase feedback.