1 Oscillator noise: a nonlinear perturbative theory including orbital fluctuations and phase-orbital correlation Fabio L. Traversa, Fabrizio Bonani, Senior Member, IEEE Abstract We derive a full statistical characterization of the noise spectrum of a free running oscillator perturbed by white Gaussian noise sources, including the effect of orbital fluctuations and of their correlation with phase noise, thus extending the previous theory based on the Floquet decomposition of the linearized oscillator equations [1]. This allows to derive explicit relationships for the relevant phase, amplitude and correlation spectra. The examples provide a validation of the theoretical results, and allow to assess the importance of the Floquet exponents and eigenvectors on the magnitude of the orbital noise contribution. Index Terms Circuit simulation, Autononmous systems, Oscillator noise, Floquet theory I. I NTRODUCTION Noise in free running oscillators is a classical topic in circuit analysis, mainly because of its practical importance in the design and optimization of high sensitivity telecommunication systems [2]. The autonomous nature of oscillator operation makes noise analysis particularly challenging: the absence of a fixed time reference due to the lack of applied generators results in the appearance of fluctuations both into the timing properties of the circuit (expressed in terms of phase noise or, equivalently, timing jitter) and into the amplitude of the oscillator working point [1], [2], [3] (amplitude or orbital noise). In most practical cases, the very effects assuring the stability of the oscillator operation imply also a quenching of the amplitude noise component, thus making phase noise the dominant fluctuation effect [3]: amplitude noise, however, usually becomes important at frequencies far away from the nominal oscillation frequency and its harmonics. Notice that, in particular in presence of a strong adjacent channel, also the noise components far from the oscillation harmonics might have a significant impact on the dynamic range of the receiver [2]. Therefore, the assessment of amplitude noise, besides being important per se to fully characterize the circuit noise performance, also has, at least for specific applications, significant practical effects. F.L. Traversa is with the Departament d’Enginyeria Electr` onica, Universitat Aut` onoma de Barcelona, 08193-Bellaterra (Barcelona), Spain. F. Bonani is with the Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. February 14, 2011 DRAFT (c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.