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

Abstract

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.

Survey of integrated‐circuit‐oscillator phase‐noise analysis

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This tutorial distills the salient phase-noise analysis concepts and key equations developed over the last 75 years relevant to integrated circuit oscillators. This resonator can take the form of an LC tank circuit, dielectric puck, quartz crystal, SAW or bulk acoustic wave transducer, yttrium iron garnet resonator, or ceramic disk resonator to name a few [43,147,148]. Furthermore, we demonstrate that all these methods boil down to obtaining three things: (1) noise modulation function; (2) noise transfer function; and (3) current-controlled oscillator gain.

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Phase Noise Analysis for the Drive Loop of Capacitive MEMS Gyroscopes

“…The Formula (13), and (14), shows that both the low-frequency or high-frequency current injection will cause the original stable phase of drive signal changes. When the phase changes by the injection current is contained, the drive frequency excitation signal can be expressed as:…”

High-<inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> AlN-on-Silicon Resonators With Annexed Platforms for Portable Integrated VOC Sensing

“…Because one particular electrode configuration can excite several modes in piezoelectric resonators, gain and phase conditions are often met for many frequencies. Therefore, both adequate compensation of resonator electrical loading [14] and spurious mode suppression are crucial in safeguarding the circuit from locking into oscillations at undesired frequencies.…”