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This paper explores the many interesting implications for oscillator design, with optimized phase-noise performance, deriving from a newly proposed model based on the concept of oscillator conjugacy. For the case of 2-D (planar) oscillators, the model prominently predicts that only circuits producing a perfectly symmetric steady-state can have zero amplitude-to-phase (AM-PM) noise conversion, a so-called zero-state. Simulations on standard industry oscillator circuits verify all model predictions and, however, also show that these circuit classes cannot attain zero-states except in special limit-cases which are not practically relevant. Guided by the newly acquired design rules, we describe the synthesis of a novel 2-D reduced-order LC oscillator circuit which achieves several zero-states while operating at realistic output power levels. The potential future application of this developed theoretical framework for implementation of numerical algorithms aimed at optimizing oscillator phase-noise performance is briefly discussed.
Model 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.
