Oscillator Modeling Using the Averaging Principle

摘要

This article introduces a method for modeling and analysis of perturbed oscillator behavior, i.e. the behavior of "ideal" oscillators subjected to weak interactions with the outside world. These interactions can e.g. involve an amplitude-regulating mechanism, as in harmonic oscillators, couplings to other oscillators, as in quadrature-type oscillators, and noise, both white and colored. The method is grounded on perturbation theory and averaging. Perturbation techniques allow us to separate the analysis of the unperturbed, ideal, oscillator from the analysis of the perturbed one. Averaging is used to separate the fast-varying and the slow-varying components of the oscillator's behavior. Applications of this method include oscillator phase noise analysis and the construction of compact behavioral models for harmonic oscillators.