The Use of Symmetry to Simplify the Integral Equation Method with Application to 6-Sided Circulator Resonators

In this paper it is shown that for planar two-dimensional problems with symmetry, the dimensions of the matrices, which must be inverted to obtain a solution using the integral equation method, can be substantially reduced. For instance, for a three-fold symmetric hexagonal circulator junction with...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 1982-08, Vol.30 (8), p.1219-1223, Article 1219
Main Authors: Riblet, G.P., Hansson, E.R.B.
Format: Article
Language:English
Subjects:
Admittance
Backplanes
Circuits
Impedance
Integral equations
Magnetic analysis
Scattering parameters
Symmetric matrices
Transmission line matrix methods
Transmission line theory
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Summary:In this paper it is shown that for planar two-dimensional problems with symmetry, the dimensions of the matrices, which must be inverted to obtain a solution using the integral equation method, can be substantially reduced. For instance, for a three-fold symmetric hexagonal circulator junction with N segments about the periphery, the dimension of matrices to be inverted is reduced to N/3 from the usual N. It is demonstrated that for six-sided resonators with three-fold symmetry, a very good approximation to the equivalent admittance can be obtained with only 12 segments around the periphery, meaning that only 4 X 4 matrices need be inverted.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.1982.1131225