Asymptotic stochastic characterization of phase and amplitude noise in free-running oscillators

Fabio L. Traversa; Fabrizio Bonani

doi:10.1142/S021947751100048X

Asymptotic stochastic characterization of phase and amplitude noise in free-running oscillators

Fabio L. Traversa, Fabrizio Bonani

Department of Electronic Engineering

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker-Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account. © 2011 World Scientific Publishing Company.

Original language	English
Pages (from-to)	207-221
Journal	Fluctuation and Noise Letters
Volume	10
Issue number	2
DOIs	https://doi.org/10.1142/S021947751100048X
Publication status	Published - 1 Jun 2011

Keywords

Fokker-Planck equation
orbital noise
Oscillator
stochastic integral calculus

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abstract = "Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker-Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account. {\textcopyright} 2011 World Scientific Publishing Company.",

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T1 - Asymptotic stochastic characterization of phase and amplitude noise in free-running oscillators

AU - Traversa, Fabio L.

AU - Bonani, Fabrizio

PY - 2011/6/1

Y1 - 2011/6/1

N2 - Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker-Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account. © 2011 World Scientific Publishing Company.

AB - Starting from the definition of the stochastic differential equation for amplitude and phase fluctuations of an oscillator described by an ordinary differential equation, we study the associated Fokker-Planck equation by using tools from stochastic integral calculus, harmonic analysis and Floquet theory. We provide an asymptotic characterization of the relevant correlation functions, showing that within the assumption of a linear perturbative analysis for the amplitude fluctuations phase noise and orbital fluctuations at the same time are asymptotically statistically independent, and therefore the nonlinear perturbative analysis of phase noise recently derived still exactly holds even if orbital noise is taken into account. © 2011 World Scientific Publishing Company.

KW - Fokker-Planck equation

KW - orbital noise

KW - Oscillator

KW - stochastic integral calculus

U2 - 10.1142/S021947751100048X

DO - 10.1142/S021947751100048X

M3 - Article

VL - 10

SP - 207

EP - 221

JO - Fluctuation and Noise Letters

JF - Fluctuation and Noise Letters

SN - 0219-4775

IS - 2

ER -