Modal characteristics of crossed rectangular waveguides

An integral-eigenvalue problem is formulated for a crossed rectangular waveguide and solved numerically by applying the Ritz-Galerkin method. Theoretical formulas for determining cutoff frequencies and modal-field expressions are obtained for the specific case of a symmetrical rectangular waveguide, cutoff frequencies are calculated numerically, and the results are verified by comparison with available experimental data. The modal fields are expressed in terms of Fourier series for both TE and TM modes. It is found that the bandwidth can be increased to a maximum of 38% when the waveguide dimensions are properly selected and that the numerical results are in agreement with those computed by the method of partial regions. Some practical applications of the modal-field equations are briefly noted.