Analyzing Oscillators using Describing Functions

In this manuscript, we discuss the use of describing functions as a systematic approach to the analysis and design of oscillators. Describing functions are traditionally used to study the stability of nonlinear control systems, and have been adapted for analyzing LC oscillators. We show that they can be applied to other categories of oscillators too, including relaxation and ring oscillators. With the help of several examples of oscillators from various physical domains, we illustrate the techniques involved, and also demonstrate the effectiveness and limitations of describing functions for oscillator analysis.