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Genetic and self-similar approaches for the fractal antennas designing


A. A. Potapov – Dr.Sci. (Eng.), Professor, Kotel'nikov's Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences (Moscow). E-mail:
Y. S. Shifrin – Dr.Sci. (Eng.), Professor, Kharkiv National University of Radio Electronics (Ukraine), IEEE Life Fellow. E-mail:
R. R. Kuzeyev – Head of department of Information and Telecommunication Technologies, JSC «NPO «Radioelectronika» n.a. V. I. Shimko (Kazan). E-mail:

In Introduction a history of the fractal and fractal antennas is reported briefly. Basic fractal geometry-related terms are introduced. In Chapter 1 different fractal shapes are shown. Both advantages and drawbacks of their implementations in antennas' design is discussed. In Chapter 2, specifics of Genetic algorithm of global extremum search is discussed focusing on design of polyfractal array antennas. Multiple examples of in-line array antenna synthesis are presented. Chapter 3 reviews self-affine fractal multiband PCB-based patch antenna design which is presented in [10]. Chapter 4 is a review of [11] in which a triple-band radiating element is presented. The antenna is five-element stacked combination of patch dual-band and patch monoband antennas with broadside radiation pattern. The dual-band antenna successfully implements Sierpinski fractal shapes for driven and parasitic patch elements. This antenna uses the surface of parasitic patch director of the monoband antenna as a required screen plane. It is stressed that all the parasitic elements allows broadband behavior in each of three operating bands. Results of surface current distribution calculation are discussed. In Conclusion it is said that although the fractal antennas are very promising for multifrequency and broadband operation, they have not spreaded wide in modern telecommunication equipment. This is mostly because of absence of effective synthesis methods for fractal geometry dedicated to electromagnetics and radiating structures.

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  2. Potapov A.A. Fraktaly' v radiofizike i radiolokaczii: Topologiya vy'borki / Izd. 2‑e, pererab. i dop. M.: Universitetskaya kniga. 2005.
  3. Potapov A.A. Fraktaly' i xaos kak osnova prory'vny'x texnologij v sovremenny'x radiosistemax. Dopolnenie k kn.: Kronover R. Fraktaly' i xaos v dinamicheskix sistemax / Per. s angl. / Pod red. T.E`. Krenkelya. M.: Texnosfera. 2006
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  8. Petko J.S., Werner D.H. An Autopolyploidy-Based Genetic Algorithm for Enhanced Evolution of Linear Polyfractal Arrays // IEEE Trans. on Antennas and Propag. 2007. V. 55. №. 3. P. 583–593.
  9. Petko J.S., Werner D.H. The Evolution of Optimal Linear Polyfractal Arrays Using Genetic Algorithms // IEEE Trans. on Antennas and Propag. 2005. V. 53. №. 11. P. 3604–3615.
  10. Sinha S.N., Jain M. A Self-Affine Fractal Multiband Antenna // IEEE Antennas and Wireless Propagation Letters. 2007. V. 6. № 3. P. 110–112.
  11. Anguera J., Martínez-Ortigosa E., Puente C., Borja C., Soler J. Broadband Triple-Frequency Microstrip Patch Radiator Combining a Dual-Band Modified Sierpinski Fractal and a Monoband Antenna // IEEE Trans. on Antenna and Propag. 2007. V. 54. № 11. P. 3367–3373.
  12. Maci S., Gentili G.B. Dual-Frequency Patch Antennas // IEEE Antennas and Propag. Magazine. 1997. V. 39. № 6. P. 13–20.
  13. Anguera J., Martínez E., Puente C., Borja C., J. Soler J. BroadBand Dual-Frequency Microstrip Patch Antenna with Modified Sierpinski Fractal Geometry // IEEE Trans. on Antenna and Propag. 2004. V. 52. P. 66–73.
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  15. Potapov A.A. Fraktal`ny'e modeli i metody' na osnove skejlinga v fundamental`ny'x i prikladny'x problemax sovremennoj fiziki // Sb. nauch. tr. «Neobratimy'e proczessy' v prirode i texnike» / Pod red. V.S. Gorelika i A.N. Morozova. M.: MGTU im. N.E`. Baumana. 2008. Vy'p. II. S. 5–107.
  16. Matveev E.N., Potapov A.A.  Chislennoe modelirovanie antenn s fraktal`noj geometriej // Nelinejny'j mir. 2009. T. 7. № 9. S. 689–693.
  17. Potapov A.A., Matveev E.N. Fraktal`naya e`lektrodinamika, skejling fraktal`ny'x antenn na osnove kol`czevy'x strukturi mul`timasshtabny'e chastotno-izbiratel`ny'e 3D–sredy' ili fraktal`ny'e «se`ndvichi»: perexod k fraktal`ny'm nanostrukturam // Radiotexnika i e`lektronika. 2010. T. 55. № 10. S. 1157–1177.
  18. Potapov A.A. Fraktal`ny'e antenny', nanotexnologii, rezonansy' i plazmony' // Uspexi sovremennoj radioe`lektroniki. 2011. № 5. S. 5–12.
  19. Potapov A. A. The Base of Fractal Antenna Theory and Applications: Utilizing in Electronic Devices // Proc. of the 2013 IX Int. Conf. on Antenna Theory and Techniques, 16–20 September, 2013, Odessa, Ukraine. Odessa: Odessa National O.S. Popov Academy of Telecommunications, 2013. P. 62–67.

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