Phase Feedback for Nonlinear MEM Resonators in Oscillator Circuits

Abstract

In this paper, a phase feedback approach for using nonlinear microelectromechanical (MEM) resonators in oscillator circuits is investigated. Phase feedback makes use of the oscillation phase condition for oscillator circuits and enables fine-tuning of the frequency at which the resonator oscillates by means of setting the phase in the feedback amplifier. The principle of the approach is illustrated for a nonlinear Duffing resonator, which is representative of many types of MEM resonators. Next, the approach is applied to an electrostatically actuated nonlinear clamped-clamped beam MEM resonator, on simulation level. Phase feedback allows for operation of the resonator in its nonlinear regime. The closed-loop technique enables control of both the frequency of oscillation and the output power of the signal. Additionally, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined. Application of phase feedback results in more robustness with respect to dynamic pull in than in open-loop case, however, at the cost of a deteriorated phase noise response.