Abstract
SummaryModel frameworks, based on Floquet theory, have been shown to produce effective tools for accurately predicting phase‐noise response of single (free‐running) 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 phase‐response 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.
Highlights
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 state of time-domain oscillator noise modeling has evolved over the years culminating with the invention of phase-noise macro-model (PMM), first proposed by Kärtner[5] and later further developed and refined by Demir et al as well by other research groups including the authors of this paper.[6,7,8]
We present a novel macro-model aimed at predicting phase-noise performance of a general coupled synchronized oscillator ensemble perturbed by weak noise sources
Summary
Rigorous phase-noise modeling tools represent a critical part of accessing the performance of any system involving oscillators/clocks operating at, or around, room temperature.[1,2,3,4] The state of time-domain oscillator noise modeling has evolved over the years culminating with the invention of phase-noise macro-model (PMM), first proposed by Kärtner[5] and later further developed and refined by Demir et al as well by other research groups including the authors of this paper.[6,7,8] the term macro-model is introduced as a handle to refer to the category of Floquet-theory-based methodologies discussed in other studies.[5,6,7] The PMM delivers a rigorous, coordinate independent description which is the objectively correct mathematical solution approach to the presented problem. The C-OSC framework, described directly reduces to the previously proposed S-OSC description in other studies[5,6,7] for the trivial case of a single oscillator ensemble (free-running oscillator with no coupling), that is, the proposed C-OSC PMM implicitly contains the S-OSC PMM as a special case
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