Phase-delay Induced Variation of Synchronization Bandwidth and Frequency Stability in a Micromechanical Oscillator

Abstract Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor applications. It's a consensus that the synchronization region varies with phase delay with a `Anti-U' mode within 0 to pi and phase delay is typically fixed on pi/2 to achieve maximum synchronization range and best frequency stability. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator is investigated analytically and experimentally. A self-sustained oscillator is built by applying phase feedback to an electrostatically actuated micro-beam resonator and synchronization phenomenon is observed after coupling it to a weak external periodic excitation. The analytical expression for predicting the synchronization bandwidth with phase delay is derived based on the dynamic model, from which three different types (`U', `Anti-U' and `M') of variation pattern of synchronization bandwidth are observed as feedback tuning. The variation of frequency stability along phase delay is also studied. The synchronization bandwidth and the frequency stability have exactly opposite variation pattern with phase delay in linear oscillators while they are totally consistent in nonlinear oscillators. Experimental tests in vacuum environment are carried out to validate the analytical observations. Our work presented here provides a precise way for achieving best performance of a synchronized MEMS oscillator in the sensor application.