Phase noise analysis of a mechanical autonomous impact oscillator with a MEMS resonator

In this paper, phase noise analysis of a mechanical autonomous impact oscillator with a MEMS resonator is performed. Since the circuit considered belongs to the class of hybrid systems, methods based on the variational model for the evaluation of either phase noise or steady state solutions cannot be directly applied. As a matter of fact, the monodromy matrix is not defined at impact events in these systems. By introducing saltation matrices, this limit is overcome and the aforementioned methods are extended. In particular, the unified theory developed by Demir is used to analyze the phase noise after evaluating the asymptotically stable periodic solution of the system by resorting to the shooting method. Numerical results are presented to show how noise sources affect the phase noise performances.