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Extension of the normal tree method
Author(s) -
Reißig Gunther
Publication year - 1999
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199903/04)27:2<241::aid-cta62>3.0.co;2-8
Subject(s) - gyrator , capacitor , inductor , mathematics , resistor , transformer , topology (electrical circuits) , equivalence (formal languages) , correctness , conjugate , equivalence relation , computer science , voltage , discrete mathematics , algorithm , combinatorics , mathematical analysis , engineering , electronic engineering , electrical engineering
The results of this paper are applicable to linear electrical networks that may contain ideal transformers, nullors, independent and controlled sources, resistors, inductors, and capacitors, and, under a topological restriction, gyrators. A relation between summands of some expansion of the network determinant and pairs of conjugate trees is proved, which uncovers the equivalence of known criteria on generic solvability based on matroids and those based on pairs of conjugate trees. New criteria on the solvability of active networks are given. A method to obtain complete sets of generic state co‐ordinates is established, which includes the following extension of the wellknown normal tree method: The generic order of complexity equals the sum of the number of forest capacitors and the number of co–forest inductors in any normal pair of conjugate trees, the latter term being introduced in this paper. The voltages across the forest capacitors together with the currents through the co‐forest inductors may be given initial values independently from each other. Further, a systematic method of augmentation that yields networks of generic index 1 is proposed. All results are expressed in terms of network determinants as well as in terms of network graphs, and all given criteria may be checked by efficient algorithms. Copyright © 1999 John Wiley & Sons, Ltd.