New Formula for Evaluating the Number of Unit Cell of a Finite Periodic Structure Considered as Infinite Periodic One

Samia Bouali, Taoufik Aguili

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DOI: 10.4236/jemaa.2011.39055                

Abstract

This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure. The transmission matrix for the N identical cascaded cells has been successfully used to obtain an efficient and easy-to-use formula giving the necessary number of cells such that they can be considered infinite. As an illustrative example, the formula is applied and verified to finite size TL periodically loaded with obstacles. Scattering parameters and the input impedance of the structure are expressed and plotted.

Keywords

Periodic Structure, Floquet Theorem, Dispersion Relation, Scattering Parameters, Input Impedance

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. Brillouin, “Wave Propagation in Periodic Structures,” Dover, New York, 1953.
[2]	R. Collin, “Foundations for Microwave Engineering,” 2nd Edition, Wiley-IEEE Press, 2000.
[3]	D. Pozar, “Microwave Engineering,” Addison-Wesley, Reading, 1990.
[4]	D. J. Mead, “Wave Propagation in Continuous Periodic Structures: Research Contribution from Southampton 1964-1995,” Journal of Sound and Vibration, Vol. 190, No. 3, 1996, pp. 495-524.
[5]	B. A. Munk, “Frequency Selective Surfaces: Theory and Design,” Wiley, New York, 2000.
[6]	E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Physical Review Letters, Vol. 58, No. 20, 1987, pp. 2059-2062.
[7]	Y. Rahmat-Samii and H. Mosallaei, “Electromagnetic Band-Gap Structures: Classification, Characterization, and Applications,” 11th International Conference on Antennas and Propagation, Manchester, 17-20 April 2001, pp. 560-564.
[8]	J. D. Joannopoulos, et al., “Photonic Crystals: Molding the Flow of Light,” 2nd Edition, Princeton University Press, Princeton, 2008.
[9]	C. Caloz and T. Itoh, “Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications,” John Wiley & Sons, Inc., Hoboken, 2006.
[10]	K. Yasumoto and K. Yoshitomi, “Efficient Calculation of Lattice Sums for Free-Space Periodic Green’s Function,” IEEE Transactions on Antennas and Propagation, Vol. 47, No. 6, 1999, pp. 1050-1055.
[11]	P. Harms, R. Mittra and W. Ko, “Implementation of the Periodic Boundary Condition in the Finite-Difference Time-Domain Algorithm for FSS Structures,” IEEE Transactions on Antennas and Propagation, Vol. 42, No. 9, 1994, pp. 1317-1324. doi:10.1109/8.318653
[12]	V. V. S. Prakash and R. Mittra, “Characteristic Basis Function Method: A New Technique for Efficient Solution of Method of Moments Matrix Equations,” Microwave and Optical Technology Letters, Vol. 36, No. 2, 2003, pp. 95-100. doi:10.1002/mop.10685
[13]	T. J. Cui, W. B. Lu, Z. G. Qian, X. X. Yin and W. Hong, “Accurate Analysis of Large-Scale Periodic Structures Using an Efficient Sub-Entire-Domain Basis Function Method,” IEEE Transactions on Antennas and Propagation, Vol. 52, No. 11, 2004, pp. 3078-3085.
[14]	W. B. Lu, T. J. Cui, Z. G. Qian, X. X. Yin and W. Hong, “Fast Algorithms for large-Scale Periodic Structures,” IEEE Antennas and Propagation Society International Symposium, Monterey, 20-25 June 2004, pp. 4463-4466.
[15]	P. Yeh, “Optical Waves in Layered Media,” John Willey and Sons Inc., Hoboken, 1988.