Computation of the Propagation Characteristics of TE and TM Modes in Arbitrarily Shaped Hollow Waveguides Utilizing the Conjugate Gradient Method

Abstract

This paper describes the use of the conjugate gradient method in conjunction with the finite difference method for the calculation of the propagation characteristics of TE and TM modes, including cutoff wavenumbers and field distribution, of hollow conducting waveguides of arbitrary cross sections. This method is quite fast and accurate and can be applied in a straightforward fashion for the analysis of both TE and TM modes in waveguides of arbitrary cross sections. In order to check the accuracy of this method, the new approach has been applied to compute the cutoff wavelength of a rectangular waveguide as analytical results are available for this problem. This method has also been applied to compute the first six TE and TM modes for L-shaped, single ridge, vaned rectangular, T-septate and rectangular coaxial waveguides. Comparison of accuracy is made whenever data is available. Since the conjugate gradient method is an iterative method, computer storage is 6N instead of N² for conventional matrix methods. Hence problems with a million unknowns can easily be solved on a VAX 11/785. As the conjugate gradient method directly solves the eigenvalue problem, the propagation characteristics can be obtained efficiently with an a priori specified degree of accuracy.