Numerical solution of transmission line problems by a network model decomposition method based on polygon discretization

A polygon discretization technique for establishing a network model suitable for both TEM (transverse electromagnetic) transmission lines and hollow waveguides is introduced. A network model decomposition algorithm, or diakoptic algorithm, is also presented for solving the transmission-line problems and is shown to be useful when a computer is not sufficiently large to accommodate a problem. The network model decomposition algorithm can be used to calculate the characteristic impedance of an arbitrarily shaped TEM transmission line and the cutoff wavenumbers of a hollow waveguide of arbitrary section. Numerical results are also presented as a demonstration of the method's validity. >

[1]  G. Kron,et al.  Equivalent Circuit of the Field Equations of Maxwell-I , 1944, Proceedings of the IRE.

[2]  F. Wu,et al.  Solution of large-scale networks by tearing , 1976 .

[3]  A. Sangiovanni-Vincentelli,et al.  A two levels algorithm for tearing , 1976 .

[4]  K. Spangenberg,et al.  Electrical Network Analyzers for the Solution of Electromagnetic Field Problems: Part I: Theory, Design and Construction , 1949, Proceedings of the IRE.

[5]  P. P. Silvester,et al.  Calculation of transformer winding resonances by a specialized finite element method employing substructures , 1988 .

[6]  Omar Wing,et al.  Circuit theory with computer methods , 1972 .

[7]  Norman Balabanian,et al.  Electrical Network Theory , 1969 .

[8]  C. Carpenter,et al.  A network approach to the numerical solution of Eddy-current problems , 1975 .

[9]  J. K. Reid,et al.  An Elliptic Eigenvalue Problem for a Reentrant Region , 1965 .

[10]  Gabriel Kron,et al.  Equivalent Circuits to Represent the Electromagnetic Field Equations , 1943 .

[11]  M. V. Schneider.  Computation of Impedance and Attenuation of TEM-Lines by Finite Difference Methods , 1965 .

[12]  J P Roth,et al.  THE VALIDITY OF KRON'S METHOD OF TEARING. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Ibrahim N. Hajj,et al.  Sparsity considerations in network solution by tearing , 1980 .

[14]  Gabriel Kron,et al.  Diakoptics : the piecewise solution of large-scale systems , 1963 .

[15]  D. Rose,et al.  Partitioning, tearing and modification of sparse linear systems , 1974 .

[16]  J. Lynn.  The use of tensor densities in equivalent circuits for field problems , 1962 .

[17]  S. Ramo,et al.  A New Approach to the Solution of High-Frequency Field Problems , 1944, Proceedings of the IRE.

[18]  Gabriel Kron,et al.  Numerical Solution of Ordinary and Partial Differential Equations by Means of Equivalent Circuits , 1945 .

[19]  A. Wexler,et al.  An Accurate Finite-Difference Method for Higher Order Waveguide Modes , 1968 .

[20]  C. Moler,et al.  APPROXIMATIONS AND BOUNDS FOR EIGENVALUES OF ELLIPTIC OPERATORS , 1967 .

[21]  Solomon Lefschetz,et al.  Applications of algebraic topology , 1975 .

[22]  H. H. Happ,et al.  Z Diakoptics - Torn Subdivisions Radially Attached , 1967 .

[23]  P. B. Johns,et al.  On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations , 1980 .