  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).
