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Tree‐based characterization of low index circuit configurations without passivity restrictions

The present paper addresses index characterizations in differential‐algebraic models of electrical circuits without the need for passivity assumptions. Positive definiteness conditions on the conductance, capacitance and inductance matrices are replaced by certain algebraic assumptions on the so‐called proper trees for augmented node analysis and normal trees for modified node analysis. The current discussion is restricted to index‐0 and index‐1 systems; for the latter, the analysis is based upon certain matrix factorizations which split the topological information from the electrical features of the devices. Several examples illustrate the scope of our framework. Copyright © 2007 John Wiley & Sons, Ltd.