A fractal array is an antenna array which holds a property called "self-similarity". This means that parts of the whole structure are similar to the whole. A recursive procedure for evaluating the impedance matrix is allowed primarily by exploiting the self-similarity. However, numerous fractal arrays are extremely complicated in structure. Therefore, for these arrays, it is extremely elaborate to formulate explicitly a recursive relation. This paper proposes a simple procedure for evaluating, without formulating explicitly a recursive relation, the impedance matrix of fractal and fractile arrays; a fractile array is any array with a fractal boundary contour that tiles the plane without gaps or overlaps.
2. Mahatthanajatuphat, C., P. Akkaraekthalin, S. Saleekaw, and M. Krairiksh, "A bidirectional multiband antenna with modified fractal slot fed by CPW," Progress In Electromagnetics Research, Vol. 95, 59-72, 2009.
doi:10.2528/PIER09062203
3. Sangawa, U., "The origin of electromagnetic resonances in three-dimensional photonic fractals," Progress In Electromagnetics Research, Vol. 94, 153-173, 2009.
doi:10.1109/TAP.2004.823967
4. Werner, D., D. Baldacci, and P. L. Werner, "An efficient recursive procedure for evaluating the impedance matrix of linear and planar fractal arrays," IEEE Trans. Antennas Propagat., Vol. 52, No. 2, 380-387, 2004.
5. Kuhirun, W., "A recursive procedure for evaluating the impedance matrix of the peano-gosper fractal array," Proceedings of the 2006 Asia-Pacific Microwave Conference, 2082-2085, Yokohama, Japan, Dec. 2006.
6. Kuhirun, W., "A simple procedure for evaluating the impedance matrix of the peano-gosper fractal array," Proceedings of the 2008 Asia-Pacific Microwave Conference, Hongkong and Macau, Dec. 2008.
doi:10.1109/TAP.2004.832327
7. Werner, D. H., W. Kuhirun, and P. L. Werner, "Fractile arrays: A new class of tiled arrays with fractal boundaries," IEEE Trans. Antennas Propagat., Vol. 52, No. 8, 2008-2018, 2004.
8. Grunbaum, B. and G. C. Shephard, Tilings and Patterns, W. H. Freeman and Company, New York, 1987.
doi:10.1109/TAP.2003.815411
9. Werner, D. H., W. Kuhirun, and P. L.Werner, "The Peano-Gosper fractal array," IEEE Trans. Antennas Propagat., Vol. 51, No. 10, 2063-2072, 2003.
10. Edgar, G. A., Measure, Topology, and Fractal Geometry, Springer-Verlag, New York, 1990.
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