Chapter 7

Perturbation Models for Stability, Phase Noise, and Modulation

The complex dynamics of coupled-oscillator arrays lead to the existence of a multitude of steady-state solutions. In addition to finding or selecting a desired steady-state solution, one further needs to guarantee its stability. In this section, perturbation methods are described that allow the designer to examine both the existence and the local stability of the various steady-state solutions of coupled oscillator arrays. An introduction to stability analysis of nonlinear dynamical systems is presented [94], followed by its application to coupled oscillator systems [95, 96].

The perturbation nature of noise, leads to phase-noise analysis methods that are closely related to the formulation used in the stability analysis. Analytical models are presented that demonstrate the attractive properties of coupled inter-injection locked oscillator systems, among them improved phase-noise performance compared to single elements [97].

A straightforward application of coupled-oscillator arrays has been in power-combining arrays where, by controlling the phase shift within an array of synchronized oscillator elements, one can direct the radiated beam toward a desired direction taking advantage of free-space power combining and eliminating the use of lossy power-combining networks. The simple topologies associated with such arrays have led to their consideration in communication system applications where one introduces ...

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