The Impact of Damping on the Frequency Stability of Nonlinear MEMS Oscillators

Linear models for oscillator noise predict an improvement in frequency stability with increasing quality factor. Although it is well known that this result does not apply to oscillators embedding nonlinear resonators, systematic experimental investigations of the impact of damping on frequency stability of nonlinear microelectromechanical system (MEMS) oscillators has not been previously reported. This paper studies the frequency stability of a nonlinear MEMS oscillator under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave oscillator embedding a double-ended tuning fork resonator driven into the nonlinear regime is introduced. The experimental results indicate that for a preset drive level, the variation of air damping changes the onset of nonlinear behavior in the resonator, which not only impacts the output frequency, but also the phase/frequency noise of a nonlinear MEMS square wave oscillator. The random walk frequency noise and flicker frequency noise levels are strongly correlated with the nonlinear operating point of the resonator, whereas the white phase and white frequency noise levels are impacted both by the output power and by operative nonlinearities.