Entrainment Phenomena in Nonlinear Oscillations
Entrainment or injection locking is the underlying effect of synchronization. It can therefore be observed in a variety of fields including physics, biology and electronic engineering. In recent years various circuit designs have been developed using injection locking for the design of i.e. quadrature oscillators, frequency dividers and circuits exhibiting low phase noise. On the other hand, unwanted temporary entrainment known as pulling can be a severe cause of performance degradation for zero-IF or low-IF transceivers. Therefore entrainment effects have been studied since decades (i.e. Andronov and Witt, Adler, Kurokawa). A general theory is still missing.
In this paper, we give a theory of injection phenomena based on a perturbation technique employing Floquet’s theory. The theory is valid as long as the injected signal power is sufficiently small.
KeywordsPhase Noise Nonlinear Oscillation Impulse Train Arnold Tongue Colpitts Oscillator
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