Mathematical proof of Leeson's oscillator noise spectrum model

Abstract

This letter presents a mathematical formulation that clearly explains the result that was heuristically introduced by Leeson for the oscillator noise spectrum. We consider the voltage and current in a simple equivalent circuit consisting of only linear components. To analyze both the oscillation and noise behaviors simultaneously without resort to frequency-domain transfer functions, we introduce dual coordinates in the time domain. Equivalent device temperature and Q factor are appropriately defined to support Leeson's result. It is successfully clarified, without taking any nonlinear effects into account, that the noise from a white source is converted up into a sharp spectrum around the oscillation frequency. © 2004, The Institute of Electronics, Information and Communication Engineers. All rights reserved.