Generalized Circuit Elements

TL;DR

This paper introduces generalized circuit elements that extend traditional resistances, inductances, and capacitances to include complex models with internal degrees of freedom, maintaining their structural analysis properties.

Contribution

It defines generalized circuit elements capable of modeling complex behaviors while preserving the structural analysis framework of circuits.

Findings

Examples demonstrate the applicability of generalized elements.

The approach allows modeling of complex device behaviors.

Structural analysis remains valid for these generalized elements.

Abstract

The structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts of elements, e.g. behavioral models or partial differential equations stemming from refined device modelling. This paper proposes the definition of generalized circuit elements which may for example contain additional internal degrees of freedom, such that those elements still behave structurally like resistances, inductances and capacitances. Several complex examples demonstrate the relevance of those definitions.