A generalized model of coupled oscillator phase‐noise response

Abstract

Model frameworks, based on Floquet theory, have been shown to produce effective tools for accurately predicting phase-noise response of single (freerunning) oscillator systems. This method of approach, referred to herein as macro-modeling, has been discussed in several highly influential papers and now constitutes an established branch of modern circuit theory. The increased application of, for example, injection-locked oscillators and oscillator arrays in modern communication systems has subsequently exposed the demand for similar rigorous analysis tools aimed at coupled oscillating systems. This paper presents a novel solution in terms of a macro-model characterizing the phaseresponse of synchronized coupled oscillator circuits and systems perturbed by weak noise sources. The framework is generalized and hence applicable to all circuit configurations and coupling topologies generating a synchronized steady-state. It advances and replaces the phenomenological descriptions currently found in the published literature pertaining to this topic and, as such, represents a significant breakthrough w.r.t. coupled oscillator noise modeling. The proposed model is readily implemented numerically using standard routines.