On phase feedback for nonlinear MEMS resonators

In oscillator circuits, a resonator acts as a frequency selective network. Nonlinearities in the resonator may influence oscillator performance and may limit the signal to noise ratio. In this paper, a phase feedback approach for increasing the signal to noise ratio in MEMS resonators is investigated. The approach consists of fine-tuning the frequency at which the resonator oscillates by means of setting the oscillation phase condition in the amplifier of the oscillator circuit. The approach is explained for a nonlinear Duffing resonator, which is representative for certain types of MEMS resonators. Here, this approach is applied to a nonlinear clamped-clamped beam MEMS resonator. On simulation level, closed-loop phase feedback yields an increase in S/N-ratio of several decades compared to the open-loop system. Furthermore, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined.