Another approach to the study of phase noise in electrical oscillators

TL;DR

This paper reexamines the fundamental mechanisms of phase noise in electrical oscillators, deriving the Lorentzian spectral distribution and clarifying the roles of amplitude suppression and resonator quality factor.

Contribution

It provides a first-principles analysis of phase noise, deriving key spectral properties and clarifying the impact of amplitude suppression and resonator Q on noise behavior.

Findings

Lorentzian spectral power distribution derived from first principles

Expression for the line-width parameter clarified

Role of Q factor in noise suppression discussed

Abstract

The mechanism at the base of phase noise generation in electrical oscillators is reexamined from first principles. The well known Lorentzian spectral power distribution is obtained, together with a clearcut expression for the line-width parameter. The mechanism of suppression of the amplitude fluctuations and its effects are discussed and the true role of the figure of merit $Q_0$ of the resonator is restated. The up conversion of low frequency components from a non-white noise source is also considered. A number of simple numerical experiments is presented to illustrate and clarify the mathematical results.