Gain and noise spectral density in a parametric amplifier with added white noise: Theory and experiment

Abstract

In this paper, we discuss the behavior of a linear classical parametric amplifier 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. To validate our theory, we compare the analytical results with experimental data from an analog circuit and with numerical simulations of the model’s stochastic differential equations. The experimental data were accurately described by our model. Moreover, we noticed spectral components in the output signal of the amplifier, which are due to noisy 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.