Noise Analysis of Stable Oscillators

Abstract

In Chapter 3 we developed a new perturbation analysis technique suitable for stable oscillators. We showed that it is not mathematically consistent to view the perturbed oscillator response as the sum of pure tones (unperturbed oscillator response) and a small deviation. Rather, the perturbed oscillator output should be viewed as a sum of two signals: unperturbed oscillator output phase shifted by α(t) along the limit cycle (Definition 3.4) and a small deviation away from the limit cycle. In case of stochastic perturbations, the oscillator output is a stochastic process which can also be viewed as a sum of two stochastic processes: phase noise and amplitude noise process. Since phase noise is the dominant effect in the oscillator response we will not concentrate on amplitude noise at present. We begin by obtaining a stochastic characterization of the phase deviation α(t) which we use to obtain the time domain and frequency domain characterization of the output of noisy oscillator. We give efficient numerical techniques, both in time and frequency domain for characterization of the output of a noisy oscillator. We conclude this chapter with some examples of electrical circuits which have been analyzed with this technique.