Observation of the Effect of Fractional Synchronization on Amplitude and Frequency Stability in Micromechanical Oscillators

In this paper, we present observations of the amplitude and frequency noise of two self-sustained oscillating modes of a single micromechanical resonator under fractional synchronization. The resonant modes which comprise the self-sustained oscillators have a 3: 1 ratio of frequencies. Increasing the amplitude of the low-frequency oscillator increases the range of frequencies over which the oscillations synchronize; inversely, increasing the amplitude of the high-frequency oscillator decreases the synchronization range. We show that by increasing the amplitude of either mode, the white noise in amplitude and frequency of the higher mode will decrease in the synchronized regime. We also show that when synchronized the frequency fluctuations of the higher frequency mode can be reduced by four times in comparison with the fluctuations of the same oscillator operating at the same amplitude when not synchronized. The same amount of reduction is also observed in the amplitude fluctuations of the higher frequency mode. These observations create a path toward exploitation of fractional synchronization for the purposes of noise reduction in both amplitude and frequency of micromechanical oscillators.