1 Department of Electrical Engineering, Technical University of Denmark
In this thesis a study of analytical and numerical models of coupled oscillating systems, perturbed by delta-correlated noise sources, is undertaken. These models are important for the attainment of a qualitative understanding of the complex dynamics seen in various physical, biological, electronic systems and for the derivation of fast and computationally efficient CAD routines. The text concentrates on developing models for coupled electronic oscillators. These circuit blocks find use in RF/microwave and optical communication systems as coherent multi-phase signal generators, power combiners and phase-noise filters; to name but a few of the possible applications areas. Taking outset in the established single-oscillator phase-macro model, a novel numerical algorithm for the automated phase-noise characterization of coupled oscillators, perturbed by noise, is developed. The algorithm, which is based on stochastic integration and Floquet theory and is independent of circuit topology and parameters, proceeds by deriving the invariant manifold projection operators. This formulation is easily integrated into commercial CAD environments, such as SPICE™ and SPECTRE™. The algorithm improves the computational efficiency, compared to brute-force Monte-Carlo techniques, by several orders of magnitude. Unilateral ring-coupled oscillators have proven a reliable and power efficient way to create coherent multi-phase signal generators in the RF/microwave frequency range. A complete and self-contained study of this complex multi-mode system is undertaken. The developed model explains the existence of a so-called dominant mode, ensuring a consistent signal phase pattern following start-up. A linear response model is derived to investigate linear stability and noise properties. It is shown that a linear coupling transconductor will cancel the coupling induced noise contribution in the single-side band phase-noise spectrum. This phenomena was not discussed in any of the previous publications considering this circuit. The model gives a general insight into the qualitative properties of unilateral ring-coupled oscillators, perturbed by white noise.