A Brief Historical Review


The fractal design of antennas and arrays results from the blend of two aparently
disjoint disciplines: electromagnetic theory and geometry. From the early spiral
and logperiodic antennas developed in the early sixties by Carrel, Mayes et
al, and from the works of Benoit Mandelbrot on fractal geometry, the fractal
design of antennas appears as a natural way to explore for a multifrequency
operation and for an antenna size reduction. This document reviews the development
of such a novel concept and gives the reader some references for
further reading.
Background
 40's. L.J.Chu and H.Wheeler stablish a fundamental limit on
the performance of small antennas.
 60's. Several research teams at the University of Illinois at UrbanaChampaign, University of
California and Ohio State University introduce the concept of frequencyindependent
antennas. The selfscaling concept gives place to the logperiodic dipole array
and to the spiral antennas.
 70's. B.
Mandelbrot coins the term 'Fractal'. Such a name is used to describe a
family of geometrical objects that defy the traditional rules of the Euclidean geometry.
Later on, Mandelbrot states that such a weird fractal shapes are, in fact, among the most
common forms in nature.
 80's. D.Jaggard et al. coin the term 'Fractal
Electrodynamics'. Electromagnetics and Fractal Geometry blend into a
novel discipline. The interaction of fractal bodies and electromagnetic waves are
investigated and some relationships between common fractal properties and the
scattered electromagnetic waves are stablished.
 90's. The first reported fractal
multiband antennas are introduced by C.Puente et al.
from the Universitat Politècnica de Catalunya. Also, the potentiallity of fractals
to become small antennas is introduced by the same
research team and by N.Cohen from the University of Boston.
Some Significant Milestones
 19861993. Several authors theoretically investigate
the relationships between fractal arrays and their array factors.
Some fractal and array properties such as Fractal Dimension and Secondary
Lobe Ratio are linked for the first time.
 1993, November. The potentiallity of fractal arrays
to become multifrequency arrays is introduced by C.Puente
at the University of Illinois at UrbanaChampaign during a graduate course
discussion.
 1994. Some prelimar ideas on multiband fractal arrays
are presented by C.Puente at an URSI meeting in Las
Palmas, Gran Canaria, Spain. Further work on such ideas gives place to a paper that is
submitted to the IEEE Transactions on Antennas and Propagation in May 1994, and
published in May 1996.
 1995, May. After several months working on the invention of
the Sierpinski antenna, the Universitat Politècnica de Catalunya finally
applies for the patent on Fractal and Multifractal
Antennas . Such results proved the feasibility of fractals to become multiband
antennas (i.e., antennas that keep the same parameters at several frequency
bands). A paper reporting the first results is submitted to IEE Electronics
Letters.
 1995, Summer. Some preliminar ideas on fractal small
antennas are suggested by N.Cohen from the Boston University.
 1998. The Koch monopole becomes
the first reported fractal small antenna that improves the features of some
classical antennas in terms of bandwidth, resonance frequency and radiation
resistance. Whether such antennas are bounded to the fundamental limits on
small antennas is still a topic under investigation.
References
Fractal Shape Antennas
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Multifractales", Invention Patent, nº: P9501019. Presented at the Oficina
Española de Patentes y Marcas. Owner: Universitat Politècnica de Catalunya, May 1995.
 C.Puente,J.Romeu,R.Pous,X.Garcia, F.Benítez, “Fractal
Multiband Antenna Based on the Sierpinski Gasket”, IEE Electronics Letters,
vol.32, no.1, pp.12, January 1996.
 C.Puente, R.Pous, "Fractal Design of Multiband and Low SideLobe Arrays",
IEEE Transactions on Antennas and Propagation, vol.44, no.5, pp.730739, May 1996.
 C.Puente,J.Romeu, R.Bartolomé, R.Pous, “Perturbation of the Sierpinski antenna
to allocate the operating bands”, IEE Electronics Letters, vol. 32, no.24,
pp. 21862188, November 1996.
 C.Puente, J.Claret, F.Sagués,J.Romeu, M.Q.LopezSalvans, R.Pous, “Multiband
properties of a fractal tree antenna generated by electrochemical deposition,”
IEE Electronics Letters, vol.32, no.5, pp. 22982299, December 1996.
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Antennas and Arrays”, in Fractals in Engineering, J.L.Véhel, E.Lutton,
C.Tricot editors, Springer, New York 1997.
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de los Parámetros de Entrada de una Antena Fractal de Sierpinski”, XII Simposium
Nacional URSI, vol.I, pp.363371, Bilbao, Septiembre 1997.
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