A phase-noise model for nonlinear piezoelectrically-actuated MEMS oscillators

This paper presents a new empirical exponential-series-based model that describes the measured phase-noise (PN) of a nonlinear piezoelectric MEMS oscillator. Since the order of terms in the Leeson´s model can only provide at maximum -30 dB/dec slope, a model with higher order terms is proposed to determine an effective resonator quality factor (Q_eff) and reflect the reduced contribution of the amplifier flicker-noise. The average fitting error of the proposed model to a 23 MHz in-plane shear (IPS) mode oscillator is found to be less than 1%. Nonlinear operation produces an oscillator with a PN of -130 dBc/Hz at 1kHz offset-frequency, which corresponds to an improvement of about 15 dB compared to linear operation.