Phase Noise Reduction in an MEMS Oscillator Using a Nonlinearly Enhanced Synchronization Domain

We investigate the phase dynamics of a closed-loop MEMS-based oscillator and demonstrate how one can exploit nonlinear behavior to improve oscillator phase noise characteristics by synchronizing the oscillator with a weak harmonic drive. Analytical predictions are based on an oscillator model that incorporates a resonator element with a weak cubic (i.e., Duffing type) nonlinearity, weak coupling to a clean external harmonic drive, and both thermal and frequency noise terms. The method of stochastic averaging is used to derive an expression for the rate of phase diffusion induced by the noises, and the results predict a remarkable phase noise reduction of three order of magnitude when the oscillator is synchronized to the weak external field. The predictions are experimentally demonstrated using a closed-loop oscillator with a double-anchored double-ended-tuning-fork MEMS resonator with coupling to a small external sinusoidal signal from a signal generator, demonstrating a 30 dB/Hz drop in phase noise. The results show how one can generate a clean high-power signal from a relative noisy oscillator by synchronizing it with a low-power external signal. The results also confirm recent studies showing that the parameter range of synchronization is significantly expanded when the resonator operates in its nonlinear regime.