"E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

TL;DR

This paper presents methods to derive single higher-order differential equations that characterize output quantities in both linear and nonlinear analog circuits, utilizing symbolic linear algebra and computer algebra tools based on differential algebra.

Contribution

It introduces a systematic approach combining linear algebra and computer algebra for deriving single-equation descriptions of circuit outputs, including nonlinear cases.

Findings

Successfully derives single differential equations for linear circuits using symbolic methods.

Employs Maple-based differential algebra tools to handle nonlinear circuit equations.

Provides examples demonstrating the effectiveness of the approach.

Abstract

In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differential equations which is used to model the analog circuit. For nonlinear circuits and their corresponding nonlinear differential equations, we show how to employ computer algebra tools implemented in Maple, which are based on differential algebra.