Amplitude response and square wave describing functions

TL;DR

This paper introduces a novel describing function method using square waves instead of sinusoids, enabling better prediction of oscillations that are approximately square in feedback systems.

Contribution

It develops a square wave-based describing function framework, extending classical methods to analyze nonlinear systems with square wave responses.

Findings

Accurately predicts oscillations that are approximately square.

Generalizes classical describing function method to square wave inputs.

Provides a new analytical tool for nonlinear system analysis.

Abstract

An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is characterized by their response to square waves of varying amplitude - their amplitude response. The output of an LTI system to a square wave input is approximated by a square wave, to give an analog of the describing function. The classical describing function method for predicting oscillations in feedback interconnections is generalized to this square wave setting, and gives accurate predictions when oscillations are approximately square.