Gunther Reißig.
Extension of the Normal Tree Method.
Int. J. Circuit Th. Appl. 27, 1999, pp. 241-265.
Erratum in vol. 28, no. 1, 2000, p. 99.
Full text. (Definitive publication; restricted access.)
Full text (Erratum). (Definitive publication; restricted access.)

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 coordinates is established, which includes the following extension of the well-known 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.
BibTeX entry:
 author = {Gunther Rei{\ss}ig},
 title = {Extension of the Normal Tree Method},
 journal = {Internat. J. Circuit Theory Appl.},
 year = 1999,
 volume = 27,
 number = 2,
 pages = {241-265},
 doi =  {10.1002/(SICI)1097-007X(199903/04)27:2<241::AID-CTA62>3.0.CO;2-8},
 note = {Erratum in vol. 28, no. 1, 2000, p. 99}

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