Predicting the behaviour of oscillators using describing functions

Abstract

This chapter explores the application of describing functions in predicting the behaviour of non-linear oscillators. Describing functions offer an approximate method that simplifies the analysis of complex, non-linear systems by linearising their frequency response characteristics. This chapter delves into the theoretical foundations of describing functions and their practical use in predicting limit cycles in oscillators, highlighting their capacity to estimate the amplitude and the frequency of the oscillations. Through analytical derivations and case studies, this work demonstrates how describing functions bridge the gap between rigorous non-linear analysis and practical engineering approximations. The limitations, accuracy considerations, and alternative techniques are also discussed, providing a comprehensive understanding of when and how to effectively use describing functions in oscillator analysis and design. The discussion is supported by a literature survey on the use of describing functions in oscillator design and analysis and its relevance to automatic amplitude control mechanisms and the minimisation of AM-to-PM noise conversion.