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.

background

/pdf/geometric-dynamics-of-nonlinear-circuits-and-jump-effects-53eag9f2ac.pdf

On singular points of electrical circuits

Geometric dynamics of nonlinear circuits and jump effects

In this paper an outline about the geometric concept of nonlinear electronic circuits is given. With this geometric concept the fast switching behavior of circuits, i.e. the jumps in their state space, is illustrated and a jump condition is formulated. Furthermore, the developed geometric approach is adapted to MNA based systems of equations. This new method enables the simulation of such ill-conditioned circuits without regularization and presents an implementation approach for common circuit simulators like SPICE.

Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach

Along the line suggested by our previous paper [7], we give a mathematical formulation of nonlinear time-varying electrical circuits and examine the transversality and local-solvability which assure that the dynamics of the circuit can be defined as a unique vector field on a manifold. Especially, in the case of circuits whose time-varying elements are only voltage and current sources we have sufficient conditions for transversality and local-solvability in terms of the time-invariant circuits obtained by deleting voltage and current sources.

Nonlinear time-varying circuits: Transversality and local- solvability

/pdf/on-the-mathematical-foundations-of-electrical-circuit-theory-4r2jbrdr3k.pdf

On singular points of electrical circuits

Citations

Geometric dynamics of nonlinear circuits and jump effects

Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach

Nonlinear time-varying circuits: Transversality and local- solvability

References

On the mathematical foundations of electrical circuit theory

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