Numerical analysis for waveguides of arbitrary cross section

Abstract

This paper presents the use of an integral operator formulation approach to wave propagation in uniform hollow conducting waveguides of arbitrary cross section. Cutoff wavenumbers, wall currents, and modal field distributions are obtained from this formulation using the method of moments. Waveguides with simply or multiply connected cross sections of any shape including septum can be accepted. The expansion functions at the junction in terms of the tree representation are suggested and applied to calculate the cutoff wavenumbers, wall currents, and modal field distributions for the waveguides with a septum of zero thickness. Treatments of septum for both TM and TE modes are discussed. The suggested expansion functions are used to calculate the charge densities and equipotential lines on the transmission lines with the junction. Two methods, null positioning and root finding, are considered to determine the cutoff wavenumbers. We have shown that these two independent methods, actually, yield the same solutions. By finding the complex roots of the determinant for the eigenvalue equation, convergence estimation on the computed cutoff wavenumbers are made to show the convergence characteristics with respect to the number of employed expansion functions. Cutoff wavenumbers, etc. are numerically calculated for cylindrical waveguides, with and without septum, rectangular waveguides, a coaxial cable, and compared with exact solutions to validate the accuracy of this method. This method is also applied to a single ridge and quadridge waveguide involving complicated shapes that do not lend themselves to exact solutions.