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The pseudo McMillan degree of implicit transfer functions of RLC networks

Berger, T. and Karcanias, N. ORCID: 0000-0002-1889-6314 (2018). The pseudo McMillan degree of implicit transfer functions of RLC networks. Circuits, Systems, and Signal Processing, doi: 10.1007/s00034-018-0921-6

Abstract

We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit transfer function is not a suitable measure of 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 shaw 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 independent differential equations equals the pseudo McMillan degree.

Publication Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Circuits, Systems, and Signal Processing. The final authenticated version is available online at: https://doi.org/10.1007/s00034-018-0921-6
Publisher Keywords: RLC networks, Modified nodal analysis, McMillan degree, Minimal realization
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Mathematics, Computer Science & Engineering > Engineering > Electrical & Electronic Engineering
URI: http://openaccess.city.ac.uk/id/eprint/20345
[img] Text - Accepted Version
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