Research on the Stability Threshold and Subharmonic Oscillation in a Parametric Excitation MEMS Resonator

The parametric excitation is an effective method to improve the quality factor of nano-micro resonators, which is achieved by superimposing a twice frequency pump signal on the fundamental frequency driving signal. This paper presents a research on the stability threshold and subharmonic oscillation in a parametric excitation MEMS resonator. It is demonstrated that there is a stability boundary of the parametric excitation, which can be defined by the threshold of parametric pump signal. When the pump signal's amplitude is lower than the threshold, the resonator's response will remain a stable vibration and with the increasing of the parametric voltage the fundamental frequency driving signal will decrease. Especially, when the amplitude of the parametric pump signal reaches its stability threshold, the fundamental frequency driving voltage will drop to zero. In this case, the resonator operates in a generalized parametric resonance condition, which is called subharmonic oscillation. Compared with the stable parametric excitation, the subharmonic response proves to have an additional time-varying response in addition to a steady-state response, indicating that it is a combination of different signals and depends on the oscillation time. The work presented in this paper can help better understand the principle of stability in parametric excitation MEMS resonators and the impact of subharmonic oscillation.