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Expansion of Bartlett's Bisection Theorem Based on Group Theory
Yoshikazu FUJISHIRO Takahiko YAMAMOTO Kohji KOSHIJI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.8
pp.16231639 Publication Date: 2017/08/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E100.A.1623 Type of Manuscript: PAPER Category: Circuit Theory Keyword: irreducible representation, modal equivalent circuit, stabilizer subgroup, symmetryadapted mode, unitarytransformed Smatrix,
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Summary:
This paper expands Bartlett's bisection theorem. The theory of modal Sparameters and their circuit representation is constructed from a grouptheoretic perspective. Criteria for the division of a circuit at a fixed node whose state is distinguished by the irreducible representation of its stabilizer subgroup are obtained, after being inductively introduced using simple circuits as examples. Because these criteria use only circuit symmetry and do not require human judgment, the distinction is reliable and implementable in a computer. With this knowledge, the entire circuit can be characterized by a finite combination of smaller circuits. Reducing the complexity of symmetric circuits contributes to improved insights into their characterization, and to savings of time and effort in calculations when applied to largescale circuits. A threephase filter and a branchline coupler are analyzed as application examples of circuit and electromagnetic field analysis, respectively.

