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A generalization of the Leeson effect

The oscillator, inherently, turns the phase noise of its internal components into frequency noise, which results into a multiplication by 1/f^2 in the phase-noise power spectral density. This phenomenon is known as the Leeson effect. This report extends the Leeson effect to the analysis of amplitude noise. This is done by analyzing the slow-varying complex envelope, after freezing the carrier. In the case of amplitude noise, the classical analysis based on the frequency-domain transfer function is possible only after solving and linearizing the complete differential equation that describes the oscillator. The theory predicts that AM noise gives an additional contribution to phase noise. Beside the detailed description of the traditional oscillator, based on the resonator governed by a second-order differential equation (microwave cavity, quartz oscillators etc.), this report is a theoretical framework for the analysis of other oscillators, like for example the masers, lasers, and opto-electronic oscillators. This manuscript is intended as a standalone report, and also as complement to the book E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge University Press, 2008. ISBN 978-0-521-88677-2 (hardback), 978-0-521-15328-7 (paperback).