volume | PIER Journals

Abstract

This article presents a theoretical characterization of the regular polygonal waveguide (RPW) having n-sides. Based on the symmetrical circular symmetry of the RPW and the circular waveguide (CW), the analogy between the electromagnetic (EM) behaviors of these to waveguide (WG) is established. After a brief recall about the state of the art concerning the WG engineering and its application, we introduce a basic theory of the WG presenting a regular polygonal cross-section with n-sides. By considering, the fundamental mode TE₁₁, we develop the main mathematical formulas summarizing the different characteristics (cut-off frequency, f_c, propagating constant, k₁₁ and S-parameters) appropriated to any RPW in function of its physical parameters (number of sides, n, diameter, D and height, h). In order to verify the validation of the developed analytical expressions, comparisons between the HFSS simulated and theoretical dispersion diagrams of regular pentagonal (n=5), hexagonal (n=6), heptagonal (n=5) metallic (copper) WG with for example, 50 mm outer diameter are presented. So, it was demonstrated that very good correlation between the theoretical predictions (f_c(n), k₁₁(n)) is found with a relative error less than 1%. As application of the present study in terms of EM wave shielding, simulation of metallic wall with hexagonal aperture is also performed. Finally, discussion about the future work is drawn in conclusion.

1. Auld, B. A., "The synthesis of symmetrical waveguide circulator," IEEE Tran. MTT, Vol. 7, 238-246, 1959.
doi:10.1109/TMTT.1959.1124688

2. Akaiwa, Y., "Bandwidth enlargement of a millimeter wave Y-circulator with half-wavelength line resonantors," IEEE Tran. MTT, Vol. 22, 1283-1286, 1974.
doi:10.1109/TMTT.1974.1128477

3. http://www.microwaves101.com/encyclopedia/waveguide.cfm.

4. Li, C., D. Wu, and K. Seo, "Rectangle waveguide to substrate integrated waveguide transition and power divider," MOTL, Vol. 52, No. 2, 375-378, Feb. 2010.
doi:10.1002/mop.24902

5. Simon, W., M. Werthen, and I. Wolff, "A novel coplanar transmission line to rectangular waveguide transition," Microwave Symposium Digest, 1998 IEEE MTT-S Int., Vol. 1, No. 7-12, 257-260, Jun. 1998.

6. Jia, H., K. Yoshitomi, and K. Yasumoto, "Rigorous analysis of rectangular waveguide junctions by Fourier transform technique," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 12, 1597-1598, 1998.
doi:10.1163/156939398X00539

7. MacPhie, R. H. and K.-L. Wu, "Scattering at the junction of a rectangular waveguide and a larger circular waveguide," IEEE Tran. MTT, Vol. 43, No. 9, 2041-2045, Sep. 1995.
doi:10.1109/22.414538

8. Arcambal, C., Introduction des contraintes de propagation et rayonnement electromagnetiques dans l'etude et la conception d'emetteurs/recepteurs de puissance, Ph.D. Thesis, Univ. Rouen, France, Jul. 2003 (in French).

9. Kao, K. C. and G. A. Hockham, "Dielectric-fibre surface waveguides for optical frequencies," IEE Proc., Vol. 133, Pt. J, No. 3, Jun. 1986.

10. Queffelec, P., P. Talbot, M. L. Floc'h, and P. Gelin, "Broad-band measurement of all complex permeability tensor components and complex permittivity of ferrites using a rectangular waveguide," J. Phys. IV, Vol. 7, 294-304, 1997.

11. Soleimani, H., Z. Abbas, K. Khalid, N. Yahya, and H. Soleimani, "Determination S-parameters of PTFE at X-band frequency using FEM modeling rectangular waveguide," European Journal of Scientific Research, Vol. 39, No. 1, 105-110, 2010.

12. http://www.hollandshielding.com/honeycomb.php.

13. Honeycomb sandwich design technology, Hexcel Composites, Publication No. AGU 075b, Dec. 2000.

14. Bahadorzadeh, M., M. N. Moghaddasi, and A. R. Attari, "Improving the shielding effectiveness of a rectangular metallic enclosure with aperture by using extra shielding wall," Progress In Electromagnetics Research Letters, Vol. 1, 45-50, 2008.
doi:10.2528/PIERL07110706

15. Lozano-Guerrero, A. J., A. Daz-Morcillo, M. A. Garca-Fernandez, and J. V. Balbastre-Tejedor, "Fast computation of shielding effectiveness of metallic enclosures with apertures and inner elements," MOTL, Vol. 51, No. 12, 2832-2836, Dec. 2009.
doi:10.1002/mop.24745

16. Dehkhoda, P., A. Tavakoli, and R. Moini, "Fast calculation of the shielding effectiveness for a rectangular wall thickness and with numerous small apertures," Progress In Electromagnetics Research, Vol. 86, 341-355, 2008.
doi:10.2528/PIER08100803

17. Araneo, R. and G. Lovat, "An efficient MoM formulation for the evaluation of the shielding effectiveness of rectangular enclosures with thin and thick apertures," IEEE Tran. EMC, Vol. 50, No. 2, 294-304, May 2008.

18. Lucido, M., G. Panariello, and F. Schettino, "Full wave analysis of arbitrary polygonal section waveguides," IEEE Int. Symp. MTT, 1675-1678, Jun. 3-8, 2007.

19. Mazumdar, J. and D. Hill, "A note on the determination of cutoff frequencies of hollow waveguides by a contour line-conformal mapping technique," Applied Acoustics, Vol. 21, No. 1, 23-37, 1987.
doi:10.1016/0003-682X(87)90072-7

20. Du, L., R. S. Chen, and Y. Yang, "Perfectly matched layers backed by the second-order waveguide impedance boundary condition for the time-domain finite-element solution of waveguide problems ," MOTL, Vol. 51, No. 12, 2870-2874, Dec. 2009.
doi:10.1002/mop.24774

Prof. Blaise Ravelo

Dr. Belahcene Mazari