Suppressing Frequency Fluctuations of Self-Sustained Vibrations in Underdamped Nonlinear Resonators

TL;DR

This paper investigates how to reduce frequency fluctuations in self-sustained nonlinear underdamped resonators, such as nano- and micro-electromechanical systems, by operating at specific extremum points in their nonlinear regime.

Contribution

It introduces a method to suppress frequency fluctuations by exploiting extremum points in the nonlinear frequency-action relationship of the resonator.

Findings

Frequency fluctuations can be significantly reduced at extremum points.

A practical implementation for nanoresonators is proposed.

Explicit model results demonstrate fluctuation suppression.

Abstract

We consider frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. An important type of such resonators are nano- and micro-electro-mechanical systems. Various noise sources are considered, with the emphasis on the fundamentally unavoidable noise that comes along with dissipation from the coupling to a thermal reservoir. The formulation in terms of the action-angle variables of the resonator allows us to study a deeply nonlinear regime. In this regime the vibration frequency as a function of the action can have an extremum. We show that frequency fluctuations can be strongly reduced by choosing the operation point at this extremum. We suggest a practical implementation of a nanoresonator that has the appropriate property and show explicit results for the corresponding model.