Editing Fractal antenna (section)

==Performance ==
[[File:Antenna flat panel.png|thumb|A [[planar array]] fractal antenna ([[H tree]])]]

Antenna elements (as opposed to antenna arrays, which are usually not included as fractal antennas) made from self-similar shapes were first created by Nathan Cohen<ref>{{cite web |title=Fractal Antenna Systems, Inc |website=www.fractenna.com |url=http://www.fractenna.com/nca_cohen_bio.html |access-date=22 April 2018}}</ref> then a professor at [[Boston University]], starting in 1988.<ref name=Cohen-1995>{{cite journal |author=Cohen, N. |date=Summer 1995 |title=Fractal antennas, Part&nbsp;1 |journal=Communications Quarterly |issn=1053-9433 |page=12 sidebar, ''The First Fractal Antenna'' |url=https://archive.org/details/fea_Fractal_Antennas_Part-1/page/n5/mode/1up}}</ref> Cohen's efforts with a variety of fractal antenna designs were first published in 1995,<ref name=r4/> which marked the inaugural scientific publication on fractal antennas.

Many fractal element antennas use the fractal structure as a virtual combination of [[capacitors]] and [[inductors]]. This makes the antenna so that it has many different resonances, which can be chosen and adjusted by choosing the proper fractal design. This complexity arises because the current on the structure has a complex arrangement caused by the inductance and self capacitance. In general, although their effective electrical length is longer, the fractal element antennas are themselves physically smaller, again due to this reactive loading.

Thus, fractal element antennas are shrunken compared to conventional designs and do not need additional components, assuming the structure happens to have the desired resonant input impedance. In general, the [[fractal dimension]] of a fractal antenna is a poor predictor of its performance and application. Not all fractal antennas work well for a given application or set of applications. Computer search methods and antenna simulations are commonly used to identify which fractal antenna designs best meet the needs of the application.

Studies during the 2000s showed advantages of the fractal element technology in real-life applications, such as RFID<ref>
{{cite conference
 |author1=Ukkonen, L.
 |author2=Sydanheimo, L.
 |author3=Kivikoski, M.
 |name-list-style=amp
 |date=26–28 March 2007
 |title=Read range performance comparison of Compact reader antennas for a handheld UHF RFID reader
 |pages=63–70
 |doi=10.1109/RFID.2007.346151
 |isbn=978-1-4244-1013-2
 |book-title=IEEE International Conference on RFID, 2007
}}
:
{{cite news
 |author=Sullivan, Laurie
 |date=23 May 2007
 |title=In an academic study, RFID fractal antenna wins out
 |journal=RFID Journal
 |url=http://www.rfidjournal.com/article/articleview/3334/1/1/
 |archive-url=https://web.archive.org/web/20071102055555/http://www.rfidjournal.com/article/articleview/3334/1/1/
 |archive-date=2007-11-02 |df=dmy-all
 |quote=Researchers at Finland's Tampere University of Technology found that a fractal UHF RFID handheld reader antenna performed better than four traditional antenna designs.
}}
</ref>
and cell phones.<ref>
{{cite journal
 |author1=Saidatul, N.A.   |author2=Azremi, A.A.H.
 |author3=Ahmad, R.B.      |author4=Soh, P.J.
 |author5=Malek, F.
 |name-list-style=amp
 |year=2009
 |title=Multiband fractal planar inverted&nbsp;F antenna (F-Pifa) for mobile phone application
 |journal=Progress in Electromagnetics Research B
 |volume=14 |pages=127–148
 |doi=10.2528/pierb09030802 |doi-access=free
}}
</ref>
Fractals have been used commercially in antennas since the 2010s.<ref>
{{cite book
 |author=Lau, Henry
 |year=2019
 |title=Practical Antenna Design for Wireless Products
 |page=208
 |publisher=Artech House
 |isbn=978-1630813260
}}
</ref>
Their advantages are good multiband performance, wide bandwidth, and small area.<ref>
{{cite book
 |author1=Volakis, John
 |author2=Chen, Ch-Chi
 |author3=Fujimoto, Kyohei
 |name-list-style=amp
 |year=2010
 |title=Small Antennas |at=§&nbsp;3.2.5
 |publisher=McGraw Hill
 |isbn=9780071625531
}}
</ref>
The gain with small size results from constructive interference with multiple current maxima, afforded by the electrically long structure in a small area.<ref>
{{cite book
 |author1=Frame, Michael
 |author2=Cohen, Nathan
 |year=2015
 |title=Benoit Mandelbrot: A life in many dimensions
 |chapter=ch&nbsp;8: Fractal antenna and fractal resonator primer
 |at=§&nbsp;8.4
 |publisher=World Scientific Press
 |isbn=9789814366069
}}
</ref>

Some researchers have disputed that fractal antennas have superior performance. S.R. Best (2003) observed "that antenna geometry alone, fractal or otherwise, does not uniquely determine the electromagnetic properties of the small antenna".<ref>
{{cite journal
 |last=Best |first=Steven R.
 |year=2003
 |title=A comparison of the resonant properties of small space-filling fractal antennas
 |journal=IEEE Antennas and Wireless Propagation Letters
 |volume=2 |issue=1 |pages=197–200
 |doi=10.1109/1-awp.2003.819680 |s2cid=15119380
 |bibcode=2003IAWPL...2..197B
}}
</ref>
Hansen & [[Robert E. Collin|Collin]] (2011) reviewed many papers on fractal antennas and concluded that they offer no advantage over fat dipoles, loaded dipoles, or simple loops, and that non-fractals are always better.<ref>
{{cite book
 |author1=Hansen, Robert C.
 |author2=Collin, R.E. |author2-link=Robert E. Collin
 |name-list-style=amp
 |year=2011
 |title=Small Antenna Handbook |at=ch.&nbsp;5.13
 |publisher=John Wiley & Sons
 |isbn=978-1118106853
}}
</ref>
[[Constantine A. Balanis|Balanis]] (2011) reported on several fractal antennas and found them equivalent in performance to the electrically small antennas they were compared to.<ref>
{{cite book
 |author=Balanis, C.A. |author-link=Constantine A. Balanis
 |year=2011
 |title=Modern Antenna Handbook |at=ch.&nbsp;10.9
 |publisher=John Wiley & Sons
 |isbn=978-1-118-20975-2
}}
</ref>
Log periodics, a form of fractal antenna, have their electromagnetic characteristics uniquely determined by geometry, via an opening angle.<ref>
{{cite book
 |author=Krischke, Alois
 |year=2019 |title=Rothammel's Antenna Book |at=27.5
 |publisher=DARC Verlag
 |isbn=9783000624278
}}
</ref><ref name="Rumsey, V.H pp.114-118">
{{cite conference
 |author=Rumsey, V.H.
 |year=1957
 |title=Frequency Independent Antennas
 |book-title=IRE International Convention Record
 |volume=5 |issue=Part&nbsp;1 |page=114-118
 |publisher=[[Institute of Radio Engineers]]
 |place=New York, NY
}}
</ref>