Phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator

Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor application. It is a consensus that the synchronization region varies with phase delay with an ‘Anti-U’ mode. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator is investigated analytically and experimentally. The analytical expression for predicting the synchronization bandwidth with phase delay is derived based on the mathematic model. An additional dynamic extreme point of synchronization bandwidth actuated by nonlinearity is observed, which leads to three different types (‘U’, ‘Anti-U’ and ‘M’) of variation pattern of synchronization bandwidth 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 results validate the analytical observations. Our work provides a precise way for achieving best performance of a synchronized MEMS oscillator in the sensor application.