This paper presents an extension of the recently-developed efficient semi-analytical method, namely scaled boundary finite element method (SBFEM) to analyze quadruple corner-cut ridged circular waveguide. Owing to its symmetry, only a quarter of its cross-section needs to be considered. The entire computational domain is divided into several sub-domains. Only the boundaries of each sub-domain are discretized with line elements leading to great flexibility in mesh generation, and a variational approach is used to derive the scaled boundary finite element equations. SBFEM solution converges in the finite element sense in the circumferential direction, and more significantly, is analytical in the radial direction. Consequently, singularities around re-entrant corners can be represented exactly and automatically. By introducing the "dynamic stiffness" of waveguide, using the continued fraction solution and introducing auxiliary variables, a generalized eigenvalue equation with respect to cutoff wave number is obtained without introducing an internal mesh. Numerical results illustrate the accuracy and efficiency of the method with very few elements and much less consumed time. Influences of corner-cut ridge dimensions on the cutoff wave numbers of modes are examined in detail. The single mode bandwidth of the waveguide is also discussed. Therefore, these results provide an extension to the existing design data for ridge waveguide and are considered helpful in practical applications.
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