Gain and noise spectral density in an electronic parametric amplifier with added white noise

TL;DR

This study analyzes the spectral density and behavior of a classical linear parametric amplifier under white noise, providing theoretical estimates validated by experiments, and explores noise precursors to instability.

Contribution

It offers analytical estimates for noise spectral density and amplification bandwidth in a parametric amplifier, validated through experimental data and analysis of noise precursors.

Findings

High gains achieved near the instability threshold

Wider tunable bandwidth in quasi-degenerate mode

Spectral components due to noise precursors match theoretical predictions

Abstract

In this paper, we discuss the behavior of a linear classical parametric amplifier (PA) in the presence of white noise and give theoretical estimates of the noise spectral density based on approximate Green's functions obtained by using averaging techniques. Furthermore, we give analytical estimates for parametric amplification bandwidth of the amplifier and for the noisy precursors to instability. To validate our theory we compare the analytical results with experimental data obtained in an analog circuit. We describe the implementation details and the setup used in the experimental study of the amplifier. Near the threshold to the first parametric instability, and in degenerate-mode amplification, the PA achieved very high gains in a very narrow bandwidth centered on its resonance frequency. In quasi-degenerate mode amplification, we obtained lower values of gain, but with a wider bandwidth that is tunable. The experimental data were accurately described by the predictions of the model. Moreover, we noticed spectral components in the output signal of the amplifier which are due to noise precursors of instability. The position, width, and magnitude of these components are in agreement with the noise spectral density obtained by the theory proposed here.