Tree-based characterization of low index circuit configurations without passivity restrictions
Article first published online: 15 MAY 2007
Copyright © 2007 John Wiley & Sons, Ltd.
International Journal of Circuit Theory and Applications
Volume 36, Issue 2, pages 135–160, March/April 2008
How to Cite
Encinas, A. J. and Riaza, R. (2008), Tree-based characterization of low index circuit configurations without passivity restrictions. Int. J. Circ. Theor. Appl., 36: 135–160. doi: 10.1002/cta.417
- Issue published online: 3 MAR 2008
- Article first published online: 15 MAY 2007
- Manuscript Revised: 20 MAR 2007
- Manuscript Received: 15 NOV 2006
- lumped circuit;
- differential-algebraic equation;
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.