A State-Space Phase-Noise Model for Nonlinear MEMS Oscillators Employing Automatic Amplitude Control

This paper presents a new phase-noise model for nonlinear microelectromechanical-system (MEMS) oscillators. Two widely recognized existing phase-noise models, namely, the linear time-invariant and time-variant models, are first reviewed, and their limitations on nonlinear MEMS oscillators are examined. A new phase-noise model for nonlinear MEMS oscillators is proposed according to the state-space theory. From this model, a closed-form phase-noise expression that relates the circuit and device parameters with the oscillator phase noise is derived and, hence, can be used to guide the oscillator design. The analysis also shows that, despite the nonlinearity in the MEMS resonator, the phase noise is still governed by its linear transfer function. This finding encourages the designers to operate the MEMS resonator far beyond its Duffing bifurcation point to maximize the oscillation signal power and put more emphasis on the low-noise automatic-amplitude-control-loop design to minimize the noise aliasing through amplitude-stiffening effect without concerning the nonlinear chaotic behavior.