A novel family of fractal curves is proposed which provides the designer a systematic way of miniaturizing the microwave components with the freedom of choosing among form factor, design complexity and achieved miniaturization. The proposed fractal curve is characterized by two integer values m and n. The m value determines the form factor of the fractal while n value governs the iteration number. The equations governing the geometry of fractals are also presented. The proposed fractal is characterized for miniaturization by designing a printed monopole antenna for various values of m and n. The results from the full wave simulations and experiments are analysed and explained. The effect of fractal on reducing the resonant frequency is quantified by an equation based on its physical interpretation. Based on this analysis, saturation point for miniaturization is established. The curves being symmetric around a straight line, distortionless radiation patterns are seen.
2. Werner, D. H. and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antennas and Propagation Magazine, Vol. 45, No. 1, 38-57, 2003.
3. Best, S. R., "A discussion on the significance of geometry in determining the resonant behavior of fractal and other non-Euclidean wire antennas," IEEE Antennas and Propagation Magazine, Vol. 45, No. 3, 9-28, 2003.
4. Chen, W. and G. Wang, "Effective design of novel compact fractal-shaped microstrip coupledline bandpass filters for suppression of the second harmonic," IEEE Microwave and Wireless Components Letters, Vol. 19, No. 2, 74-76, 2009.
5. Sharma, S., R. Kumar, R. V. S. Ram Krishna, and R. Khokle, "Design of defected ground bandpass filters using stepped impedance resonators," Progress In Electromagnetics Research B, Vol. 54, 203-225, 2013.
6. Volakis, J. L., C. Chen, and K. Fujimoto, Small Antennas: Miniaturization Techniques and Applications, McGraw Hill Publications, 2010.
7. Gianvittorio, J. P. and Y. Rahmat-Samii, "Fractal antennas: A novel antenna miniaturization technique, and applications," IEEE Antennas and Propagation Magazine, Vol. 44, No. 1, 20-36, 2002.
8. Werner, D. H., R. L. Haupt, and P. L.Werner, "Fractal antenna engineering: The theory and design of fractal antenna arrays," IEEE Antennas and Propagation Magazine, Vol. 41, No. 5, 37-59, 1999.
9. Mahatthanajatuphat, C., S. Saleekaw, P. Akkaraekthalin, and M. Krairiksh, "A rhombic patch monopole antenna with modified Minkowski fractal geometry for UMTS, WLAN, and mobile WiMAX application," Progress In Electromagnetics Research, Vol. 89, 57-74, 2009.
10. Khan, O. M., Z. U. Islam, I. Rashid, F. A. Bhatti, and Q. U. Islam, "Novel miniaturized Koch pentagonal fractal antenna for multiband wireless applications," Progress In Electromagnetics Research, Vol. 141, 693-710, 2013.
11. 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.
12. Li, D. and J.-F. Mao, "Multiband multimode arched bow-shaped fractal helix antenna," Progress In Electromagnetics Research, Vol. 141, 47-78, 2013.
13. Li, D. and J.-F. Mao, "Sierpinskized Koch-like sided multifractal dipole antenna," Progress In Electromagnetics Research, Vol. 130, 207-224, 2012.
14. Farswan, A., A. K. Gautam, B. K. Kanaujia, and K. Rambabu, "Design of Koch fractal circularly polarized antenna for handheld UHF RFID reader applications," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 2, 771-775, 2016.
15. Dhar, S., K. Patra, R. Ghatak, B. Gupta, and D. R. Poddar, "A dielectric resonator-loaded Minkowski fractal-shaped slot loop heptaband antenna," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 4, 1521-1529, 2015.
16. Jalil, M. E. B., M. K. Abd Rahim, N. A. Samsuri, N. A. Murad, H. A. Majid, K. Kamardin, and M. Azfar Abdullah, "Fractal Koch multiband textile antenna performance with bending, wet conditions and on human body," Progress In Electromagnetics Research, Vol. 140, 633-652, 2013.
17. Azaro, R., F. D. Natale, M. Donelli, E. Zeni, and A. Massa, "Synthesis of a prefractal dualband monopolar antenna for GPS applications," IEEE Antennas and Wireless Propagation Letters, Vol. 5, No. 1, 361-364, 2006.
18. Azaro, R., G. Boato, M. Donelli, A. Massa, and E. Zeni, "Design of a prefractal monopolar antenna for 3.4–3.6GHz Wi-Max band portable devices," IEEE Antennas and Wireless Propagation Letters, Vol. 5, No. 1, 116-119, 2006.
19. Ghatak, R., D. R. Poddar, and R. K. Mishra, "Design of Sierpinski gasket fractal microstrip antenna using real coded genetic algorithm," IET Microwaves, Antennas and Propagation, Vol. 3, No. 7, 1133-1140, 2009.
20. Donelli, M. and P. Febvre, "Design of a superconducting antenna integrated with a diplexer for radio-astronomy applications," Journal of Telecommunications and Information Technology, Vol. 3, 113-118, 2014.
21. Ma, Y., H.-W. Zhang, Y. Li, Y. Wang, and W. Lai, "Terahertz sensing application by using fractal geometries of split-ring resonators," Progress In Electromagnetics Research, Vol. 138, 407-419, 2013.
22. Miyamoto, Y., H. Kanaoka, and H. Kirihara, "Terahertz wave localization at a three-dimensional ceramic fractal cavity in photonic crystals," Journal of Applied Physics, Vol. 103, 103106, 2008.
23. Sangawa, U., "The origin of electromagnetic resonance in three-dimensional photonic fractals," Progress In Electromagnetics Research, Vol. 94, 153-173, 2009.
24. De la Mata Luque, T. M., N. R. K. Devarapalli, and C. G. Christodoulou, "Investigation of bandwidth enhancement in volumetric left-handed metamaterials using fractals," Progress In Electromagnetics Research, Vol. 131, 185-194, 2012.
25. Sengupta, K. and K. J. Vinoy, "A new measure of lacunarity for generalized fractals and its impact in the electromagnetic behaviour of Koch dipole antennas," Fractals, Vol. 14, No. 4, 271-282, 2006.
26. Comisso, M., "On the use of dimension and lacunarity for comparing the resonant behavior of convoluted wire antennas," Progress In Electromagnetics Research, Vol. 96, 361-376, 2009.