Glauco Fontgalland, Henri Baudrand, Marco Guglielmi


We present a new procedure for determining the resonant frequencies of a rectangular or a circular waveguide filled with a lossless, isotropic, and homogeneous medium. The method is applied to the integral equation. This procedure is based on the use of a monotonous function in the place of the usual determinant to solve non linear eigenvalue problems. The problem is defined on the boundary, applying the BEM. The electric field is expressed using the scalar Green's function of the rectangular or circular waveguide. Consequently, the discretized problem can be cast into the form of a real matrix eigenvalue problem, whose elements are transcendental functions of the frequency, [A][X]=0. This system can be solved by finding the eigenvalues as zeros (or minimum) of the determinant of [A]. In this paper, we use a systematic procedure to determine modes in waveguides. The efficiency of this approach consists in vanishing of a function which results from the building of a particular quadratic form of the operator appearing in the formulation of the problem rather than vanishing the determinant itself. This built function has the intrinsic property to be monotonous and to have the same zeros as the determinant. Accordingly, it is possible to save computing time and to avoid that some zeros been missed. Very agreements have been found when the solutions obtained for TM modes are compared with the ones obtained by the classical methods.

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