Signal to noise ratio in parametrically-driven oscillators

TL;DR

This paper develops an analytical model using Green's functions and averaging techniques to estimate the signal to noise ratio in parametrically-driven oscillators near the first instability zone, considering added ac drive and thermal noise.

Contribution

It introduces a theoretical approach that provides analytical estimates of SNR in parametrically-driven oscillators, accounting for phase dependence and noise measures.

Findings

SNR strongly depends on the phase between external drive and parametric pump.

High SNR occurs for certain phase ranges, while others show flat or decreasing SNR.

Analytical estimates agree well with numerical simulations.

Abstract

Here we report a theoretical model based on Green's functions and averaging techniques that gives ana- lytical estimates to the signal to noise ratio (SNR) near the first parametric instability zone in parametrically- driven oscillators in the presence of added ac drive and added thermal noise. The signal term is given by the response of the parametrically-driven oscillator to the added ac drive, while the noise term has two dif- ferent measures: one is dc and the other is ac. The dc measure of noise is given by a time-average of the statistically-averaged fluctuations of the position of the parametric oscillator due to thermal noise. The ac measure of noise is given by the amplitude of the statistically-averaged fluctuations at the frequency of the parametric pump. We observe a strong dependence of the SNR on the phase between the external drive and the parametric pump, for some range of the phase there is a high SNR, while for other values of phase the SNR remains flat or decreases with increasing pump amplitude. Very good agreement between analytical estimates and numerical results is achieved.