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.
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Full text (Erratum).
(Definitive publication; restricted access.)

**Abstract:**

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:**

@article{Reissig99a,
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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