Perturbation Analysis of Stable Oscillators

Abstract

As pointed out in Chapter 2, noise analysis in electrical circuits is based on perturbation analysis. It is well known that linear perturbation analysis is not valid for oscillatory circuits. In order to develop a noise analysis technique for oscillators we first need to develop a rigorous perturbation analysis technique. In this chapter we first show that traditional linear perturbation analysis is not valid for oscillators. This also helps us introduce the notations which we use when we describe our perturbation analysis technique. We show that this incorrect linearization leads to nonphysical results such as infinite oscillator output phase noise power in presence of white noise. We then describe our perturbation analysis technique in detail. This analysis is not limited to any specific type electrical oscillator. In fact this analysis is valid for any autonomous system of equations with oscillatory solution. We also demonstrate our technique with an example.