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Description
The study of a number of nonlinear oscillators has led to great advancements in science and engineering. In particular, the Colpitts oscillator has shown great promise in a number of applications ranging from communications to temperature sensors. Current work is being conducted in implementing a precision time keeping device based on Colpitts oscillators. Precision timing is of great importance in day to day activities ranging from communication systems, location services, financial transactions, and agriculture. Currently the majority of the world relies on global positioning systems (GPS) for precise time. In the event that the GPS satellites were to fail it would lead to a number of worldwide problems. Thus, the need for a precision time keeping device that is independent of GPS is crucial. In this thesis we propose the Colpitts oscillator be the building block of this precise time keeping device. We conduct a comprehensive analysis on the collective response of bidirectionally coupled oscillators. In particular, we study the collective patterns of oscillations that are manifested via symmetry-breaking bifurcations in a network of bidirectionally coupled Colpitts oscillators. The objective is to determine which patterns of oscillation lead to the least amount of phase error. This is done by studying the phase shift synchronization of various patterns of oscillations. We demonstrate that traveling wave patterns, in which consecutive Colpitts oscillate with a constant phase difference, leads to phase drift that scales as 1/N, where N is the number of oscillators. This is a significant improvement with respect to the 1/√N scaling that is achieved by uncoupled ensembles of oscillators.
