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.
3. Rong, Y. and K. A. Zak, "Characteristics of generalized rectangular and circular ridge waveguides," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 2, 258-265, 2000. doi:10.1109/22.821772
4. Tsandoulas, G. N. and G. H. Knittel, "The analysis and design of dualpolarization square-waveguide phased arrays," IEEE Transactions on Antennas and Propagation, Vol. 21, No. 6, 796-808, 1973. doi:10.1109/TAP.1973.1140605
5. De Villiers, D. I. L. , P. Meyer and K D Palmer, "Broadband offset quad-ridged waveguide orthomode transducer," Electronics Letters, Vol. 45, No. 1, 60-62, 2009. doi:10.1049/el:20092887
6. Ding, S., B. Jia, F. Li, and Z. Zhu, "3D simulation of 18-vane 5.8 GHz magnetron," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 14-15, 1925-1930, 2008. doi:10.1163/156939308787537946
7. Singh, K., P. K. Jain, and B. N. Basu, "Analysis of a coaxial waveguide corrugated with wedge-shaped radial vanes considering azimuthal harmonic effects," Progress In Electromagnetics Research, Vol. 47, 297-312, 2004. doi:10.2528/PIER04010201
8. Singh, K. , P. K. Jain, and B. N. Basu, "Analysis of a corrugated coaxial waveguide resonator for mode rarefaction in a gyrotron," IEEE Trans. Plasma Science, Vol. 33, 1024-1030, 2005. doi:10.1109/TPS.2005.848604
9. Barroso, J. J., R. A. Correa, and P. J. de Castro, "Gyrotron coaxial cylindrical resonators with corrugated inner conductor: Theory and experiment," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 9, 1221-1230, 1998. doi:10.1109/22.709460
10. Iatrou, C. T., S. Kern, and A. B. Pavelyev, "Coaxial cavities with corrugated inner conductor for gyrotrons," IEEE Trans. Microwave Theory Tech., Vol. 44, No. 1, 56-64, Jan. 1996. doi:10.1109/22.481385
11. Agrawal, M., G. Singh, P. K. Jain, and B. N. Basu, "Analysis of tapered vane-loaded structures for broadband gyro-TWTs," IEEE Trans. Plasma Science, Vol. 29, 439-444, 2001. doi:10.1109/27.928941
12. Qiu, C. R. , Z. B. Ouyang, S. C. Zhang, H. B. Zhang, and J. B. Jin, "Self-consistent nonlinear investigation of an outer-slotted-coaxial waveguide gyrotron traveling-wave amplifier," IEEE Trans. Plasma Science, Vol. 33, No. 3, 1013-1018, 2005. doi:10.1109/TPS.2005.848600
13. Chen, M. H., G. N. Tsandoulas, and F. G. Willwerth, "Modal characteristics of quadruple-ridged circular and square waveguides," IEEE Trans. Microwave Theory Tech., Vol. 22, No. 8, 801-804, 1974. doi:10.1109/TMTT.1974.1128341
14. Sun, W. and C. A. Balanis, "Analysis and design of quadruple-ridged waveguides," IEEE Trans. Microwave Theory Tech., Vol. 4, No. 12, 2201-2207, 1994. doi:10.1109/22.339743
15. Tang, Y. , J. Zhao, and W. Wu, "Analysis of quadruple-ridged square waveguide by multilayer perceptron neural network model," Asia-Pacific Microwave Conference, APMC 2006, 1912-1918, 2006. doi:10.1109/APMC.2006.4429782
16. Tang, Y., J. Zhao, and W. Wu, "Mode-matching analysis of quadruple-ridged square waveguides," Microwave and Optical Technology Letters, Vol. 47, No. 2, 190-194, 2005. doi:10.1002/mop.21120
17. Sexson, T., "Quadruply ridged hom,", Tech. Rep., ECOM-018 1-M1 160, Army Electronics Command., US, Mar. 1968.
18. Canatan, F., "Cutoff wavenumbers of ridged circular waveguides via Ritz-Galerkin approach," Electronics Letters, Vol. 25, 1036-1038, 1989. doi:10.1049/el:19890692
19. Rong, Y., "The bandwidth characteristics of ridged circular waveguide," Microwave and Optical Technology Letters, Vol. 3, 347-350, 1990. doi:10.1002/mop.4650031006
20. Zheng, Q. , F. Xie, B. Yao, and ect., "Analysis of a ridge waveguide family based on subregion solution of multipole theory," Automation Congress, 1-4, WAC, World, 2008.
21. Skinner, S. J. and G. L. James, "Wide-band orthomode transducers," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 2, 294-300, 1991. doi:10.1109/22.102973
22. Schiff, B., "Eigenvalues for ridged and other waveguides containing corners of angle 3π/2 or 2π by the finite element method," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 6, 1034-1039, 1991. doi:10.1109/22.81677
23. Song, C. H. and J. P. Wolf, "The scaled boundary finite-element method --- Alias consistent infinitesimal finite-element cell method --- For elastodynamics," Computer Methods in Applied Mechanics and Engineering, Vol. 147, 329-355, 1997. doi:10.1016/S0045-7825(97)00021-2
24. Wolf, J. P. and C. M. Song, The Scaled Boundary Finite Element Method, Wiley Press, Chichester, England, 2003.
25. Liu, J., et al., "The scaled boundary finite element method applied to electromagnetic field problems," IOP Conference Series: Materials Science and Engineering, Vol. 10, No. 1, 2245, Syndey, Jul. 2010.
26. Song, C. M., "The scaled boundary finite element method in structural dynamics," International Journal for Numerical Methods in Engineering, Vol. 77, 1139-1171, 2009. doi:10.1002/nme.2454
27. Deeks, A. J. and J. P. Wolf, "A virtual work derivation of the scaled boundary finite-element method for elastostatics,", Vol. 28, 489-504, 2002.
28. Hu , Z., G. Lin, Y. Wang, J. Liu, "A hamiltonian-based derivation of scaled boundary finite element method for elasticity problems," IOP Conference Series: Materials Science and Engineering, Vol. 10, No. 1, 2213, Syndey, Jul. 2010.