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Geometric dynamics of nonlinear circuits and jump effects

Tina Thiessen (Faculty of Electrical Engineering and Computer Science, Institute of Theoretical Electrical Engineering, Leibniz Universität Hannover, Hannover, Germany)
and
Wolfgang Mathis (Faculty of Electrical Engineering and Computer Science, Institute of Theoretical Electrical Engineering, Leibniz Universität Hannover, Hannover, Germany)

Abstract

Purpose

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

Design/methodology/approach

A sketch of circuit theory in a differential geometric setting is given.

Findings

It is shown that the structure of circuit theory can be given in a much better way than by means of a description of circuits using concrete coordinates. Furthermore, the formulation of a concrete jump condition is given.

Originality/value

In this paper, an outline is given about the state of the art of nonlinear circuits from a differential geometric point of view. Moreover, differential geometric methods were applied to two example circuits (flip flop and multivibrator) and numerical results were achieved.

Keywords

Citation

Thiessen, T. and Mathis, W. (2011), "Geometric dynamics of nonlinear circuits and jump effects", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 4, pp. 1307-1318. https://doi.org/10.1108/03321641111133217

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited