Noise in oscillators: a review of state space decomposition approaches

TL;DR

This paper reviews state space decomposition methods for analyzing noise in autonomous oscillators, focusing on phase and amplitude noise, and discusses theoretical foundations, projection techniques, and the impact of orbital fluctuations on phase noise.

Contribution

It introduces a generalized projection technique for decomposing oscillator noise into phase and amplitude components, highlighting the dependence on the chosen base and addressing the effects of orbital fluctuations.

Findings

Decomposition of noise into phase and amplitude components using a generalized projection.

Analysis of the influence of orbital fluctuations on phase noise.

Discussion of the use of Floquet basis in phase noise modeling.

Abstract

We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics, to optics, to biology. After presenting a rigorous definition of phase, given in terms of the autonomous system isochrons, we provide a generalized projection technique that allows to decompose the oscillator fluctuations in terms of phase and amplitude noise, pointing out that the very definition of phase (and orbital) deviations depends of the base chosen to define the aforementioned projection. After reviewing the most advanced theories for phase noise, based on the use of the Floquet basis and of the reduction of the projected model by neglecting the orbital fluctuations, we discuss the intricacies of the phase reduction process pointing out the presence of possible variations of the noisy oscillator frequency due to amplitude-related effects.