Determining the source of phase noise: Response of a driven Duffing oscillator to low-frequency damping and resonance frequency fluctuations

TL;DR

This paper analytically investigates how a driven Duffing oscillator responds to low-frequency fluctuations in resonance frequency and damping, providing a method to identify the noise source based on amplitude and phase noise characteristics.

Contribution

It offers a novel analytical approach to distinguish between frequency and damping noise sources in a driven Duffing oscillator.

Findings

Fluctuations in resonance frequency and damping manifest distinctly in the oscillator's response.

Amplitude and phase noise are attenuated in the strongly nonlinear regime.

Damping fluctuations significantly influence phase noise, aiding noise source identification.

Abstract

We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively, allowing them to be distinguished. In the strongly nonlinear regime, amplitude and phase noise due to resonance frequency fluctuations and amplitude noise due to damping fluctuations are strongly attenuated, while the transduction of damping fluctuations into phase noise remains of order $1$. We show that this can be seen by comparing the relative strengths of the amplitude fluctuations to the fluctuations in the quadrature components, and suggest that this provides a means to determine the source of low-frequency noise in a driven Duffing oscillator.