Analysis of quadruple corner-cut ridged square waveguide using a scaled boundary finite element method

This paper describes the development of an efficient semi-analytical method, namely scaled boundary finite-element method (SBFEM) for a quadruple corner-cut ridged square waveguide. Thinking about its symmetry, only a quarter of its cross-section needs to be considered and divided into a few sub-domains. Only the boundaries of the sub-domains are discretized with line elements leading to great flexibility in mesh generation. The singularities in the re-entrant corners are represented analytically by locating the scaling center in those points. Variational principle approach is presented to formulate the basis SBFE equations for the sub-domains. Then, an equation of the ‘stiffness matrix’ on the discretized boundary is established. Finally, by using the continued-fraction solution and introducing auxiliary variables, a generalized eigenvalue equation with respect to the cutoff wave number is obtained without introducing an internal mesh. Numerical results are presented to verify the accuracy and efficiency of the present technique. Variations of the cutoff wave numbers of the dominant and higher-order modes for both TE and TM cases with the corner-cut ridge dimensions are investigated in details. Simple approximate equations are found to accurately predict the cutoff wave number of TE_20U, TE₂₂, TM₁₁ and TM_13L modes. The single mode bandwidth of the waveguide is also calculated.