Geometric dynamics of nonlinear circuits and jump effects

Abstract

PurposeThis paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.Design/methodology/approachA sketch of circuit theory in a differential geometric setting is given.FindingsIt 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/valueIn 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.

Simulating circuits with impasse points

“…In previous works, a geometric concept was developed to simulate those circuits without regularization (see e.g. Thiessen and Mathis (2011a), Thiessen et al (2013)). There, several electronic circuits exhibiting these behavior were studied and different approaches to calculate S, jump and hit points were analyzed (e.g.…”

“…There, several electronic circuits exhibiting these behavior were studied and different approaches to calculate S, jump and hit points were analyzed (e.g. Thiessen et al (2012b), Thiessen et al (2012a), , Thiessen and Mathis (2011b), Thiessen and Mathis (2011a)). In this work improvements in the topic of hit point calculation will be shown.…”