An Empirical Phase-Noise Model for MEMS Oscillators Operating in Nonlinear Regime

Nonlinearity of a silicon resonator can lead to improved phase-noise performance in an oscillator when the phase shift of the sustaining amplifier forces the operating point to a steeper phase-frequency slope. As a result, phase modulation on the oscillator frequency is minimized because the resonator behaves as a high-order phase filter. The effect of the increased filtering translates into phase-noise shaping that reflects superior overall performance. Nonlinear effects in MEMS oscillators can be induced via sufficient driving power, generating low-frequency nonwhite noise processes that need to be considered in a phase-noise description. Since the phase-frequency response is not symmetric for a nonlinear detuned resonator, an empirical model based on power series is proposed to describe its effect in the noise sources and to account for the observed higher effective quality factor of the oscillator, the reduction in the corner frequency, and elevated levels of flicker noise very close-to-carrier. The applicability of the presented phase-noise model is shown for three piezoelectric MEMS oscillators, producing a relative fitting error below 1% in all cases.