This paper proposes a new modal analysis based on Floquet's theorem which is needful for the study of a 1-D periodic phased array antenna excited by arbitrary located sources. This analysis requires an accurate estimation for calculation of the mutual coupling parameters (for example: mutual impedances or admittances...) between the array elements and their effects integrating a large planar radiating structure. Two different formulations are suggested, in spectral and spatial domains, to solve the problem and to calculate the coupling coefficients between the neighbouring elements in a periodic environment. Important gain in the running time and used memory is obtained using Floquet analysis. One numerical method is used for modeling the proposed structures: the moment method combined with Generalized Equivalent Circuit (MoM-GEC).
2. Ishimaru, A., R. J. Coe, G. E. Miller, and W. P. Green, "Finite periodic structure approach to large scanning array problems," IEEE Trans. Antennas Propagat., 1213-1220, 1985.
3. Mekkioui, Z. and H. Baudrand, "Bi-periodic centered-fed microstrip leaky-wave antenna (LWA) analysis by a source modal decomposition in spectral domain," IET, 1141-1149, 2009.
4. Baudrand, H., M. Titaouine, N. Raveu, and G. Fontgland, "Electromagnetic modeling of planar almost periodic structures," SBMOI/IEEE MTT-S International Microwave and Optoelectronics Conference, 427-431, 2009.
5. El Gouzi, M. E. A. and M. Boussouis, "Hybrid method for analyse discontinuities in shielded microstrip," International Journal of Engineering Science and Technology, Vol. 2, No. 7, 2010.
6. Eleftheriades, G. V. and J. R. Mosig, "On the network characterization of planar passive circuits using the method of moments," IEEE Transaction on Microwave Theory and Techniques, Vol. 44, No. 3, 438-445, March 1996.
7. Bhattacharyya, K. A., "Phased Array Antennas: Floquet Analysis, Synthesis, BFNs, and Active Array Systems," Wiley and Sons, March 2006.
8. Chou, H.-T., L.-R. Kuo, and S.-C. Tuan, "General analysis of Floquet modes for an one-dimensional,infinite phased array antennas," IEEE Antennas and Propagation Society International Symposium (APSURSI), 1-2, Chicago, IL, July 2012.
9. Valerio, G., P. Baccarelli, P. Burghignoli, A. Galli, R. Rodrguez-Berral, and F. Mesa, "Analysis of periodic shielded microstrip lines excited by nonperiodic sources through the array scanning method," Radio Science, Vol. 43, 2008.
10. Bhattacharyya, K. A., "Floquet modal based analysis of finite and infinite phased array antennas," Macquarie University and IEEE Joint Lecture, Vol. 43, No. 1, November 2012.
11. Watanabe, K. and K. Yasumoto, "Two-dimensional electromagnetic scattering of non-plane incident waves by periodic structures," Progress In Electromagnetics Research, Vol. 74, 241-271, 2007.
12. Mili, S., C. Larbi Aguili, and T. Aguili, "Study of fractal-shaped structures with pin diodes using the multi-scale method combined to the generalized equivalent circuit modeling," Progress In Electromagnetics Research B, Vol. 27, 213-233, 2011.
13. Rodrguez-Berral, R., F. Mesa, P. Baccarelli, and P. Burghignoli, "Excitation of a periodic microstrip line by an aperiodic delta-gap source," IEEE Trans. Antennas Propagat. Letters, Vol. 8, 641-644, 2009.
14. Watanabe, K., "Spectral-domain approach to electromagnetic scattering from imperfectly periodic," 13th International Conference on Mathematical Methods in Electromagnetic Theory, 1-6, Ukraine, September 2010.
15. Sze, K. Y. and L. Shafai, "Reflection properties of infinite periodic arrays of rectangular conducting patches," Can. J. Elect. Comput. Eng., Vol. 24, No. 1, January 1999.
16. Skrivervik, K. and L. R. Mosig, "Finite phased array of microstrip patch antennas: The infinite array approach," IEEE Trans. Antennas Propagat., Vol. 40, No. 5, 579-582, 1992.
17. Craeye, C., "Expoitation of infinte-array results for accurate solution of finite widebands arrays," EMTS, 2007.
18. Baudrand, H., Circuits Passifs en Hyperfrequences, Editions Cepadues, January 2001.
19. BenSalah, T., C. L. Aguili, and T. Aguili, "Renormalization group application to multi-port model for studying fractal-shaped structures' diffraction," PIERS Proceedings, 1629-1633, Beijing, China, March 23-27, 2009.
20. Ayari, M., T. Aguili, H. Temimi, and H. Baudrand, "An extended version of transverse wave approach (TWA) for full-wave investigation of planar structures," Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 7, No. 2, December 2008.
21. Makarov, S., A. Puzella, and V. Iyer, "Scan impedance for an infinite dipole array: Accurate theoretical model compared to numerical software," IEEE Antennas and Propagation Magazine, Vol. 50, 132-149, December 2008.
22. Zhang, K. and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, Springer, Berlin, Heidelberg, New York, 1998.
23. Vardaxoglou, J. C., Frequency Selective Surfaces, Analysis and Design, John Wiley and Sons, 1997.
24. Mekkioui, Z. and H. Baudrand, "A full-wave analysis of uniform microstrip leaky-wave antenna with arbitrary metallic strips," Electromagnetics, Vol. 28, No. 4, 296-314, 2008.
25. Riabi, M. L., M. Ahmadpanah, H. Benzina, H. Baudrand, and V. Fouad Hanna, "Performance of the LSBRM using e±cient weighting functions for planar structures," IEEE Trans. Antennas Propagat., Vol. 142, No. 4, 364-368, August 1995.
26. Aguili, T., "Modelisation des composants S. H. F planaires par la methode des circuits equivalents generalises," Thesis, National Engineering School of Tunis ENIT, May 2000.
27. Sultan, K. S., H. H. Abdullah, and E. A. Abdallah, "Method of moments analysis for antenna arrays with optimum memory and time consumption," PIERS Proceedings, 1353-1356, Kuala Lumpur, Malaysia, March 27-30, 2012.
28. Li, D. and C. D. Sarris, "Efficient finite-difference time-domain modeling of periodic structures under non-periodic sources," Antennas and Propagation Society International Symposium, 2007.