Expansion of Bartlett's Bisection Theorem Based on Group Theory

Abstract

This paper expands Bartlett's bisection theorem. The theory of modal S-parameters and their circuit representation is constructed from a group-theoretic 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 large-scale circuits. A three-phase filter and a branch-line coupler are analyzed as application examples of circuit and electromagnetic field analysis, respectively.