Generalized Elements for a Structural Analysis of Circuits

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. Hereby, a classification of more evolved circuit elements is enabled. The structural analysis of circuits is expanded to systems containing such generalized elements. Several complex examples demonstrate the relevance of those definitions.