A multi-scale (MS) approach combined to the generalized equivalent circuit (GEC) modeling is applied to compute the input impedance of pre-fractal structures with incorporated PIN diodes. Instead of treating the whole complex problem at once, the MS method splits the complex structure into a set of scale levels to be studied separately. The computation is done gradually from the lowest level. Each scale level is artificially excited by N modal sources to compute its input impedance matrix. The MS method is based on converting this input impedance matrix into an impedance operator to achieve the transition toward the subsequent level. The PIN diodes were easily integrated in the MS approach thanks to their surface impedance model. The main advantage of the MS-GEC method is the significant reduction of the problem's high aspect ratio since fine details are studied separately of the larger structure. Consequently, the manipulated matrices are well conditioned. Moreover, the reduced size of matrices manipulated at each level leads to less memory requirement and faster processing than the MoM. Values obtained with the MS-GEC approach converge to those given by the MoM method when a su±cient number of modal sources are used at each scale level. For frequencies between 1 GHz and 6.8 GHz, the agreement between the two methods is conspicuous.
2. Werner, D. H. and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antennas and propagation Magazine, Vol. 45, No. 1, 38-53, Feb. 2003.
3. Vardaxoglou, J. C., Frequency Selective Surfaces, Analysis and Design, John Wiley and Sons, 1997.
4. Munk, B. A., Frequency Selective Surfaces, Theory and Design, John Wiley and Sons, 2000.
5. Tennant, A. and B. Chambers, "A single-layer tuneable microwave absorber using an active FSS," IEEE Microwave and Wireless Components Letters, Vol. 14, No. 1, 46-47, Jan. 2004.
6. Tennant, A. and B. Chambers, "Adaptive radar absorbing structure with PIN diode controlled active frequency selective surface," Smart Materials and Structures, Vol. 13, 122-125, 2004.
7. Chang, K., S. I. Kwak, and Y. J. Yoon, "Active frequency selective surfaces using incorporated PIN diodes," IEICE Transactions on Electronics, Vol. 91, No. 12, 1917-1922, 2008.
8. Kiani, G. I., K. P. Esselle, A. R. Weily, and K. L. Ford, "Active frequency selective surface using PIN diodes," International Symposium on Antennas and Propagation Society, 4525-4528, Honolulu, HI, Jun. 9-17, 2007.
9. Chang, K., S. I. Kwak, and Y. J. Yoon, "Equivalent circuit modeling of active frequency selective surfaces," IEEE Radio and Wireless Symposium, 663-666, 2008.
10. Harrington, R. F., Field Computation by Moment Methods, IEEE Press, 1993.
11. Aubert, H., "The concept of scale-changing network in the global electromagnetic simulation of complex structures," Progress In Electromagnetics Research B, Vol. 16, 127-154, 2009.
12. Perret, E., H. Aubert, and H. Legay, "Scale-changing technique for the electromagnetic modeling of MEMS-controlled planar phase-shifters," IEEE Trans. Microwave Theory and Tech., Vol. 54, No. 9, 3594-3601, Sep. 2006.
13. Voyer, D., H. Aubert, and J. David, "Scale-changing technique for the electromagnetic modeling of planar self-similar structures," IEEE Trans. Antennas Propagation, Vol. 54, No. 10, 2783-2789, Oct. 2006.
14. Larbi Aguili, C., A. Bouallegue, and H. Baudrand, "Utilisation d'un processus de renormalisation pour l'étude électromagnétique des structures fractales bidimensionnelles," Annales des Télecommunications, Vol. 60, No. 7-8, 1023-1050, Juillet-Août, 2005.
15. Larbi Aguili, C., T. Ben Salah, T. Aguili, A. Bouallegue, and H. Baudrand, "Study of the sierpinski's Carpet fractal planar antenna by the renormalization method," International Journal of Microwave and Optical Technology, 58-65, 2005.
16. Larbi Aguili, C., T. Ben Salah, T. Aguili, A. Bouallegue, and H. Baudrand, "Study of the electromagnetic waves diffraction by bi-dimensional fractal structures using the renormalization method," International Journal of Electronics and Communications, Vol. 63, 720-727, Elsevier, AEU, 2009.
17. Ben Salah, T., C. Larbi 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.
18. Baudrand, H., "Representation by equivalent circuit of the integral methods in microwave passive elements," European Microwave Conference, Vol. 2, 1359-1364, Budapest, Hungary, Sep. 10-13, 1990.
19. Aguili, T., "Modélisation des composants S. H. F planaires par la méthode des circuits équivalents généralisés,", Thesis, National Engineering School of Tunis ENIT, May 2000.
20. Aubert, H. and H. Baudrand, "l'électromagnétisme par les schémas équivalents," Editions Cepadues, 2003.