The Pseudo-McMillan Degree of Implicit Transfer Functions of RLC Networks

We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit network transfer function is not a suitable measure for the complexity of the network, we introduce the pseudo-McMillan degree to overcome these shortcomings. Using modified nodal analysis models...

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Bibliographic Details
Published in:Circuits, systems, and signal processing systems, and signal processing, 2019-03, Vol.38 (3), p.967-985
Main Authors: Berger, Thomas, Karcanias, Nicos, Livada, Maria
Format: Article
Language:English
Subjects:
Capacitors
Circuits and Systems
Differential equations
Electrical Engineering
Electronics and Microelectronics
Engineering
Inductors
Instrumentation
Signal,Image and Speech Processing
Transfer functions
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Summary:We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit network transfer function is not a suitable measure for the complexity of the network, we introduce the pseudo-McMillan degree to overcome these shortcomings. Using modified nodal analysis models, which are linked directly to the natural network topology, we show that the pseudo-McMillan degree equals the sum of the number of capacitors and inductors minus the number of fundamental loops of capacitors and fundamental cutsets of inductors; this is the number of independent dynamic elements in the network. Exploiting this representation, we derive a minimal realization of the given RLC network, that is one where the number of involved (independent) differential equations equals the pseudo-McMillan degree.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-018-0921-6