Frequency stabilization in a pseudo-linear micromechanical parametric oscillator

Micromechanical oscillator sustains oscillation through a velocity-proportional feedback force. Stabilization of the oscillation frequency is typically achieved by increasing the amplitude of the resonator while remaining in its linear regime. However, nonlinear effects and parasitic cross-talk unavoidably emerge with the reduction of oscillator size, severely limiting its performance. To overcome these limitations, in this paper, a novel and robust frequency stabilization scheme that employs the interaction of intrinsic high-order nonlinearities in a parametrically driven arch beam resonator is proposed and verified. Firstly, a micromechanical resonator with intrinsic high-order nonlinearities is specifically designed. Upon parametrically driving the resonator into resonance at large vibrational amplitudes, the bending of the resonance curve changes direction. This mixed behavior forms a pseudo-linear region without the need for auxiliary electrostatic tuning, simplifying the circuits and enhancing the robustness of the system. Secondly, significant frequency stability enhancement is observed when driving the resonator into self-sustained parametric oscillation in the pseudo-linear regime where output frequency decouples from the amplitude noise. Besides, the phase noise suppression effect of the parametrically driven oscillator is experimentally demonstrated when compared with the conventional directly driven oscillator. Finally, a theoretical phase noise model is developed, which well reproduces the observed frequency stabilization in the pseudo-linear regime and phase noise suppression effect of parametric oscillations.