Vol. 14
Latest Volume
All Volumes
PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2010-08-25
Simple Procedure for Evaluating the Impedance Matrix of Fractal and Fractile Arrays
By
Progress In Electromagnetics Research M, Vol. 14, 61-70, 2010
Abstract
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.
Citation
Waroth Kuhirun, "Simple Procedure for Evaluating the Impedance Matrix of Fractal and Fractile Arrays," Progress In Electromagnetics Research M, Vol. 14, 61-70, 2010.
doi:10.2528/PIERM10071405
References

1. Kuhirun, W., "A new design methodology for modular broadband arrays based on fractal tilings,", Ph.D. Thesis, The Pennsylvania State University, 2003.
doi:10.2528/PIER09061603

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.