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{{Short description|Antenna with a fractal shape}} |
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{{Use dmy dates|date=June 2020}} |
{{Use dmy dates|date=June 2020}} |
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[[File:6452553 Vicsek Fractal Antenna.png|thumb|right|An example of a fractal antenna: a space-filling curve called a "[[Minkowski Island]]"<ref name=r4>{{cite journal|last1=Cohen|first1=Nathan|title=Fractal antennas Part 1|journal=Communications Quarterly|issn=1053-9433|date=Summer 1995|volume=5|pages=7–22|url=https://archive.org/stream/fea_Fractal_Antennas_Part-1/Fractal_Antennas_Part-1_djvu.txt}}</ref> or "Minkowski fractal"<ref>Ghosh, Basudeb; Sinha, Sachendra N.; and Kartikeyan, M. V. (2014). ''Fractal Apertures in Waveguides, Conducting Screens and Cavities: Analysis and Design'', p.88. Volume 187 of ''Springer Series in Optical Sciences''. {{ISBN|9783319065359}}.</ref>]] |
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{{Antennas|expanded=types}} |
{{Antennas|expanded=types}} |
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A '''fractal antenna''' is an [[Antenna (radio)|antenna]] that uses a [[fractal]], [[Self-similarity|self-similar]] design to maximize the effective length, or increase the perimeter (on inside sections or the outer structure), of material that can receive or transmit [[electromagnetic radiation]] within a given total surface area or volume. |
A '''fractal antenna''' is an [[Antenna (radio)|antenna]] that uses a [[fractal]], [[Self-similarity|self-similar]] design to maximize the effective length, or increase the perimeter (on inside sections or the outer structure), of material that can receive or transmit [[electromagnetic radiation]] within a given total surface area or volume. |
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Such fractal antennas are also referred to as multilevel and [[space filling curves]], but the key aspect lies in their repetition of a motif over two or more scale sizes,<ref name=r1>Nathan Cohen (2002) "Fractal antennas and fractal resonators" {{US Patent|6452553}}</ref> or "iterations". For this reason, fractal antennas are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications. |
Such fractal antennas are also referred to as multilevel and [[space filling curves]], but the key aspect lies in their repetition of a motif over two or more scale sizes,<ref name=r1>Nathan Cohen (2002) "Fractal antennas and fractal resonators" {{US Patent|6452553}}</ref> or "iterations". For this reason, fractal antennas are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications. |
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A fractal antenna's response differs markedly from traditional antenna designs, in that it is capable of operating with good-to-excellent performance at many different frequencies simultaneously. |
A fractal antenna's response differs markedly from traditional antenna designs, in that it is capable of operating with good-to-excellent performance at many different frequencies simultaneously. Normally, standard antennas have to be "cut" for the frequency for which they are to be used—and thus the standard antennas only work well at that frequency. |
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In addition the fractal nature of the antenna shrinks its size, without the use of any components, such as inductors or capacitors. |
In addition, the fractal nature of the antenna shrinks its size, without the use of any components, such as inductors or capacitors. |
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[[File:6452553 Vicsek Fractal Antenna.png|thumb|right|An example of a fractal antenna: a space-filling curve called a "[[Minkowski Island]]"<ref name=r4>{{cite journal|last1=Cohen|first1=Nathan|title=Fractal antennas Part 1|journal=Communications Quarterly|issn=1053-9433|date=Summer 1995|volume=5|pages=7–22|url=https://archive.org/stream/fea_Fractal_Antennas_Part-1/Fractal_Antennas_Part-1_djvu.txt}}</ref> or "Minkowski fractal"<ref>Ghosh, Basudeb; Sinha, Sachendra N.; and Kartikeyan, M. V. (2014). ''Fractal Apertures in Waveguides, Conducting Screens and Cavities: Analysis and Design'', p.88. Volume 187 of ''Springer Series in Optical Sciences''. {{ISBN|9783319065359}}.</ref>]] |
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== Log-periodic antennas and fractals == |
== Log-periodic antennas and fractals == |
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[[Log-periodic antenna]]s are arrays invented in 1952 and commonly seen as TV antennas. This was long before Mandelbrot coined the word ''fractal'' in 1975.<ref>{{cite book |title=Mathematical people |
[[Log-periodic antenna]]s are arrays invented in 1952 and commonly seen as TV antennas. This was long before [[Benoit Mandelbrot|Mandelbrot]] coined the word ''fractal'' in 1975.<ref>{{cite book |title=Mathematical people: profiles and interviews |last1=Albers |first1=Donald J. |last2=Alexanderson |first2=Gerald L. |publisher=AK Peters |year=2008 |isbn=978-1-56881-340-0 |location=Wellesley, MA |page=214 |chapter=Benoît Mandelbrot: In his own words |author2-link=Gerald L. Alexanderson}}</ref> Some authors (for instance Cohen)<ref>Nathan Cohen, "Fractal antenna and fractal resonator primer", p. 218, ch.8 in, Michael Frame, Nathan Cohen (eds), ''Benoit Mandelbrot: A Life In Many Dimensions'', World Scientific, 2015 {{ISBN|9814635537}}.</ref> consider log-periodic antennas to be an early form of fractal antenna due to their infinite self similarity at all scales. However, they have a finite length even in the theoretical limit with an infinite number of elements and therefore do not have a [[fractal dimension]] that exceeds their [[topological dimension]] – which is one way of defining fractals. More typically, (for instance Pandey)<ref>Anil Pandey, ''Practical Microstrip and Printed Antenna Design'', p. 5, Artech House, 2019 {{ISBN|1630816701}}.</ref> authors treat them as a separate but related class of antenna. |
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== Fractal element antennas and performance == |
== Fractal element antennas and performance == |
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[[File:Antenna flat panel.png|thumb|A [[planar array]] fractal antenna ([[H tree]])]] |
[[File:Antenna flat panel.png|thumb|A [[planar array]] fractal antenna ([[H tree]])]] |
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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 |
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 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. |
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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. |
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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. |
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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 need of the application. |
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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. |
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In the last few decades different aspects of theoretical study and practical applications of fractal antennas have been researched and refined, including but not necessarily limited to: properties of wire antenna with fractal configuration of radiating elements<ref>{{Cite journal|last=Karpukov|first=L.M.|last2=Onufrienko|first2=V.M.|last3=Romanenko|first3=S.N.|date=2002|title=The properties of the fractal wire antennas|url=https://www.researchgate.net/profile/Dmitry-Zelenchuk/publication/3980152_Diffraction_of_electromagnetic_wave_by_an_array_of_complex_shape_microstrip_reflectors/links/0c96052a75c3e54e0a000000/Diffraction-of-electromagnetic-wave-by-an-array-of-complex-shape-microstrip-reflectors.pdf#page=307|journal=MATHEMATICAL METHODS|pages=310-312}}</ref>; requirements of the frequency independence of fractal structured antennas<ref>{{Cite journal|last=Onufrienko|first=V. M.|date=2013|title=The frequency independence of fractal antennas|url=https://ieeexplore.ieee.org/document/6650768/|journal=2013 IX Internatioal Conference on Antenna Theory and Techniques|pages=332–334|doi=10.1109/ICATT.2013.6650768}}</ref>; the possibility of controlling wave characteristics in a fractal meta-material wave-guide with the help of variation of positive and negative phase gain and direct and inverse wave displacement ([[Goos–Hänchen effect|Goos-Hänchen effect]])<ref>{{Cite journal|last=Onufrienko|first=V. M.|last2=Slyusarova|first2=T. I.|last3=Onufrienko|first3=L. M.|date=2018|title=Planar fractally-shaped terahertz waveguide: On the Goos-Hänchen effect|url=https://ieeexplore.ieee.org/document/8336418/|journal=2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET)|location=Lviv-Slavske|publisher=IEEE|pages=1237–1240|doi=10.1109/TCSET.2018.8336418|isbn=978-1-5386-2556-9}}</ref> etc. |
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Studies during the 2000s showed advantages of the fractal element technology in real-life applications, such as RFID<ref> |
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Studies during the 2000s showed advantages of the fractal element technology in real-life applications, such as RFID<ref>{{cite conference|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|vauthors=Ukkonen L, Sydanheimo L, Kivikoski M|book-title=IEEE International Conference on RFID, 2007|lay-url=http://www.rfidjournal.com/article/articleview/3334/1/1/}}</ref> and cell phones.<ref>{{cite journal |author1=N. A. Saidatul |author2=A. A. H. Azremi |author3=R. B. Ahmad |author4=P. J. Soh |author5=F. Malek |title=Multiband Fractal Planar Inverted F Antenna (F-Pifa) for Mobile Phone Application |journal=Progress in Electromagnetics Research B |volume=14 |pages=127–148 |year=2009 |doi= 10.2528/pierb09030802|doi-access=free }}</ref> Fractals have been used in antennas since 1988<ref name="Cohen-1995">{{cite journal |author=Cohen, N. |title=Fractal Antennas Part 1|journal=Communications Quarterly |issn=1053-9433|page=12 sidebar, 'The First Fractal Antenna' |date=Summer 1995}}</ref> and their advantages<ref>John Volakis, Ch-Chi Chen, and Kyohei Fujimoto," Small Antennas", ch. 3.2.5, McGraw Hill, 2010 {{ISBN|9780071625531}}</ref> are good multiband performance, wide bandwidth, and small area<ref>Michael Frame, and Nathan Cohen, "Benoit Mandelbrot: A Life in Many Dimensions", ch 8: "Fractal Antenna and Fractal Resonator Primer", ch 8.4, World Scientific Press, 2015 {{ISBN|9789814366069}}</ref> and that reference showed that the gain with small size results from constructive interference with multiple current maxima, afforded by the electrically long structure in a small area. |
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{{cite conference |
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|author1=Ukkonen, L. |
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|author2=Sydanheimo, L. |
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|author3=Kivikoski, M. |
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|name-list-style=amp |
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|date=26–28 March 2007 |
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|title=Read range performance comparison of Compact reader antennas for a handheld UHF RFID reader |
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|pages=63–70 |
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|doi=10.1109/RFID.2007.346151 |
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|isbn=978-1-4244-1013-2 |
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|book-title=IEEE International Conference on RFID, 2007 |
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}} |
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: |
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{{cite news |
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|author=Sullivan, Laurie |
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|date=23 May 2007 |
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|title=In an academic study, RFID fractal antenna wins out |
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|journal=RFID Journal |
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|url=http://www.rfidjournal.com/article/articleview/3334/1/1/ |
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|archive-url=https://web.archive.org/web/20071102055555/http://www.rfidjournal.com/article/articleview/3334/1/1/ |
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|archive-date=2007-11-02 |df=dmy-all |
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|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. |
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}} |
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</ref> |
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and cell phones.<ref> |
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{{cite journal |
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|author1=Saidatul, N.A. |author2=Azremi, A.A.H. |
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|author3=Ahmad, R.B. |author4=Soh, P.J. |
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|author5=Malek, F. |
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|name-list-style=amp |
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|year=2009 |
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|title=Multiband fractal planar inverted F antenna (F-Pifa) for mobile phone application |
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|journal=Progress in Electromagnetics Research B |
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|volume=14 |pages=127–148 |
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|doi=10.2528/pierb09030802 |doi-access=free |
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}} |
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</ref> |
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Fractals have been used commercially in antennas since the 2010s.<ref> |
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{{cite book |
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|author=Lau, Henry |
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|year=2019 |
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|title=Practical Antenna Design for Wireless Products |
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|page=208 |
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|publisher=Artech House |
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|isbn=978-1630813260 |
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}} |
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</ref> |
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Their advantages are good multiband performance, wide bandwidth, and small area.<ref> |
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{{cite book |
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|author1=Volakis, John |
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|author2=Chen, Ch-Chi |
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|author3=Fujimoto, Kyohei |
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|name-list-style=amp |
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|year=2010 |
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|title=Small Antennas |at=§ 3.2.5 |
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|publisher=McGraw Hill |
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|isbn=9780071625531 |
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}} |
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</ref> |
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The gain with small size results from constructive interference with multiple current maxima, afforded by the electrically long structure in a small area.<ref> |
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{{cite book |
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|author1=Frame, Michael |
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|author2=Cohen, Nathan |
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|year=2015 |
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|title=Benoit Mandelbrot: A life in many dimensions |
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|chapter=ch 8: Fractal antenna and fractal resonator primer |
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|at=§ 8.4 |
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|publisher=World Scientific Press |
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|isbn=9789814366069 |
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}} |
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</ref> |
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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> |
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Some researchers have disputed that fractal antennas have superior performance. Steven R. Best in 2003 observed "that antenna geometry alone, fractal or otherwise, does not uniquely determine the electromagnetic properties of the small antenna".<ref>{{cite journal|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|last1=Best|first1=S.R.|bibcode=2003IAWPL...2..197B|s2cid=15119380}}</ref> In 2011, Robert C. Hansen and [[Robert E. Collin]] reviewed many papers on fractal antennas and concluded that they offer no advantage over fat dipoles, loaded dipoles, or simple loops, and that nonfractals are always better.<ref>Robert C. Hansen, Robert E. Collin, ''Small Antenna Handbook'', ch. 5.13, John Wiley & Sons, 2011 {{ISBN|1118106857}}</ref> Balanis reported on several fractal antennas and found them equivalent in performance to the electrically small antennas they were compared to.<ref>Constantine A. Balanis, "Modern Antenna Handbook", ch. 10.9, John Wiley & Sons, 2011 {{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>Alois Krischke, "Rothammel's Antenna Book", 27.5, DARC Verlag, 2019 {{ISBN|9783000624278}}</ref><ref name="Rumsey, V.H pp.114-118">Rumsey, V.H. "Frequency Independent Antennas", IRE International Convention Record, Vol. 5, Part 1, pp.114-118, 1957</ref> |
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{{cite journal |
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|last=Best |first=Steven R. |
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|year=2003 |
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|title=A comparison of the resonant properties of small space-filling fractal antennas |
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|journal=IEEE Antennas and Wireless Propagation Letters |
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|volume=2 |issue=1 |pages=197–200 |
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|doi=10.1109/1-awp.2003.819680 |s2cid=15119380 |
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|bibcode=2003IAWPL...2..197B |
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}} |
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</ref> |
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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> |
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{{cite book |
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|author1=Hansen, Robert C. |
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|author2=Collin, R.E. |author2-link=Robert E. Collin |
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|name-list-style=amp |
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|year=2011 |
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|title=Small Antenna Handbook |at=ch. 5.13 |
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|publisher=John Wiley & Sons |
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|isbn=978-1118106853 |
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}} |
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</ref> |
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[[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> |
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{{cite book |
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|author=Balanis, C.A. |author-link=Constantine A. Balanis |
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|year=2011 |
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|title=Modern Antenna Handbook |at=ch. 10.9 |
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|publisher=John Wiley & Sons |
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|isbn=978-1-118-20975-2 |
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}} |
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</ref> |
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Log periodics, a form of fractal antenna, have their electromagnetic characteristics uniquely determined by geometry, via an opening angle.<ref> |
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{{cite book |
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|author=Krischke, Alois |
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|year=2019 |title=Rothammel's Antenna Book |at=27.5 |
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|publisher=DARC Verlag |
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|isbn=9783000624278 |
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}} |
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</ref><ref name="Rumsey, V.H pp.114-118"> |
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{{cite conference |
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|author=Rumsey, V.H. |
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|year=1957 |
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|title=Frequency Independent Antennas |
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|book-title=IRE International Convention Record |
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|volume=5 |issue=Part 1 |page=114-118 |
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|publisher=[[Institute of Radio Engineers]] |
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|place=New York, NY |
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}} |
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</ref> |
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== Fractal antennas, frequency invariance, and Maxwell's equations == |
== Fractal antennas, frequency invariance, and Maxwell's equations == |
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One different |
One different and useful attribute of some fractal element antennas is their self-scaling aspect. In 1957, V.H. Rumsey<ref name="Rumsey, V.H pp.114-118"/> presented results that angle-defined scaling was one of the underlying requirements to make antennas invariant (have same radiation properties) at a number, or range, of frequencies. Work by Y. Mushiake in Japan starting in 1948<ref>{{Cite journal|url=http://www.sm.rim.or.jp/~ymushiak/sub.docu.1.htm##%% |first=Y. |last=Mushiake |title=Origination of self-complementary structure and discovery of its constant-impedance property |journal=The Journal of the Institute of Electrical Engineers of Japan |volume=69 |issue=3 |page=88 |date=March 1949 |language=ja}}</ref> demonstrated similar results of frequency independent antennas having [[self-complementary antenna|self-complementarity.]] |
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It was believed that antennas had to be defined by angles for this to be true, but in 1999 it was discovered<ref>{{cite journal | author = Hohlfeld R, Cohen N | year = 1999 | title = Self-similarity and the geometric requirements for frequency independence in Antennae | journal = Fractals | volume = 7 | issue = 1| pages = 79–84 | doi = 10.1142/S0218348X99000098 }}</ref> that ''[[self-similarity]] was one of the underlying requirements to make antennas frequency and bandwidth invariant''. In other words, the self-similar aspect was the underlying requirement, along with origin symmetry, for frequency independence. Angle-defined antennas are self-similar, but other self-similar antennas are frequency independent although not angle-defined. |
It was believed that antennas had to be defined by angles for this to be true, but in 1999 it was discovered<ref>{{cite journal | author = Hohlfeld R, Cohen N | year = 1999 | title = Self-similarity and the geometric requirements for frequency independence in Antennae | journal = Fractals | volume = 7 | issue = 1| pages = 79–84 | doi = 10.1142/S0218348X99000098 }}</ref> that ''[[self-similarity]] was one of the underlying requirements to make antennas frequency and bandwidth invariant''. In other words, the self-similar aspect was the underlying requirement, along with origin symmetry, for frequency independence. Angle-defined antennas are self-similar, but other self-similar antennas are frequency independent although not angle-defined. |
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== Other uses == |
== Other uses == |
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In addition to their use as antennas, fractals have also found application in other antenna system components including loads, [[Counterpoise (ground system)|counterpoises]], and ground planes. |
In addition to their use as antennas, fractals have also found application in other antenna system components, including loads, [[Counterpoise (ground system)|counterpoises]], and ground planes. |
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Fractal inductors and fractal tuned circuits (fractal resonators) were also discovered and invented simultaneously with fractal element antennas.<ref name=r1/><ref>{{cite patent |inventor=Cohen, Nathan |pubdate=2007-08-14 |title=Fractal antennas and fractal resonators |number=7256751 |country=US}}</ref> An emerging example of such is in [[metamaterial]]s. A recent invention demonstrates using close-packed fractal resonators to make the first wideband [[metamaterial]] invisibility cloak at microwave frequencies.<ref>{{US patent|8,253,639}}</ref><ref>{{cite journal |author=Cohen, N. |title=Body sized wide-band high fidelity invisibility cloak |journal=Fractals |volume=20 |issue=3n04 |pages=227–232 |year=2012 |doi=10.1142/s0218348x1250020x|bibcode=2012Fract..20..227C }}</ref> |
Fractal inductors and fractal tuned circuits (fractal resonators) were also discovered and invented simultaneously with fractal element antennas.<ref name=r1/><ref>{{cite patent |inventor=Cohen, Nathan |pubdate=2007-08-14 |title=Fractal antennas and fractal resonators |number=7256751 |country=US}}</ref> An emerging example of such is in [[metamaterial]]s. A recent invention demonstrates using close-packed fractal resonators to make the first wideband [[metamaterial]] invisibility cloak at microwave frequencies.<ref>{{US patent|8,253,639}}</ref><ref>{{cite journal |author=Cohen, N. |title=Body sized wide-band high fidelity invisibility cloak |journal=Fractals |volume=20 |issue=3n04 |pages=227–232 |year=2012 |doi=10.1142/s0218348x1250020x|bibcode=2012Fract..20..227C }}</ref> |
Afractal antenna is an antenna that uses a fractal, self-similar design to maximize the effective length, or increase the perimeter (on inside sections or the outer structure), of material that can receive or transmit electromagnetic radiation within a given total surface area or volume.
Such fractal antennas are also referred to as multilevel and space filling curves, but the key aspect lies in their repetition of a motif over two or more scale sizes,[3] or "iterations". For this reason, fractal antennas are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications. A fractal antenna's response differs markedly from traditional antenna designs, in that it is capable of operating with good-to-excellent performance at many different frequencies simultaneously. Normally, standard antennas have to be "cut" for the frequency for which they are to be used—and thus the standard antennas only work well at that frequency.
In addition, the fractal nature of the antenna shrinks its size, without the use of any components, such as inductors or capacitors.
Log-periodic antennas are arrays invented in 1952 and commonly seen as TV antennas. This was long before Mandelbrot coined the word fractal in 1975.[4] Some authors (for instance Cohen)[5] consider log-periodic antennas to be an early form of fractal antenna due to their infinite self similarity at all scales. However, they have a finite length even in the theoretical limit with an infinite number of elements and therefore do not have a fractal dimension that exceeds their topological dimension – which is one way of defining fractals. More typically, (for instance Pandey)[6] authors treat them as a separate but related class of antenna.
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[7] then a professor at Boston University, starting in 1988.[8] Cohen's efforts with a variety of fractal antenna designs were first published in 1995,[1] 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[9] and cell phones.[10] Fractals have been used commercially in antennas since the 2010s.[11] Their advantages are good multiband performance, wide bandwidth, and small area.[12] The gain with small size results from constructive interference with multiple current maxima, afforded by the electrically long structure in a small area.[13]
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".[14] Hansen & 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.[15] Balanis (2011) reported on several fractal antennas and found them equivalent in performance to the electrically small antennas they were compared to.[16] Log periodics, a form of fractal antenna, have their electromagnetic characteristics uniquely determined by geometry, via an opening angle.[17][18]
One different and useful attribute of some fractal element antennas is their self-scaling aspect. In 1957, V.H. Rumsey[18] presented results that angle-defined scaling was one of the underlying requirements to make antennas invariant (have same radiation properties) at a number, or range, of frequencies. Work by Y. Mushiake in Japan starting in 1948[19] demonstrated similar results of frequency independent antennas having self-complementarity.
It was believed that antennas had to be defined by angles for this to be true, but in 1999 it was discovered[20] that self-similarity was one of the underlying requirements to make antennas frequency and bandwidth invariant. In other words, the self-similar aspect was the underlying requirement, along with origin symmetry, for frequency independence. Angle-defined antennas are self-similar, but other self-similar antennas are frequency independent although not angle-defined.
This analysis, based on Maxwell's equations, showed fractal antennas offer a closed-form and unique insight into a key aspect of electromagnetic phenomena. To wit: the invariance property of Maxwell's equations. This is now known as the Hohlfeld-Cohen-Rumsey (HCR) Principle. Mushiake's earlier work on self complementarity was shown to be limited to impedance smoothness, as expected from Babinet's Principle, but not frequency invariance.
In addition to their use as antennas, fractals have also found application in other antenna system components, including loads, counterpoises, and ground planes.
Fractal inductors and fractal tuned circuits (fractal resonators) were also discovered and invented simultaneously with fractal element antennas.[3][21] An emerging example of such is in metamaterials. A recent invention demonstrates using close-packed fractal resonators to make the first wideband metamaterial invisibility cloak at microwave frequencies.[22][23]
Fractal filters (a type of tuned circuit) are another example where the superiority of the fractal approach for smaller size and better rejection has been proven.[24][25][26]
As fractals can be used as counterpoises, loads, ground planes, and filters, all parts that can be integrated with antennas, they are considered parts of some antenna systems and thus are discussed in the context of fractal antennas.
Researchers at Finland's Tampere University of Technology found that a fractal UHF RFID handheld reader antenna performed better than four traditional antenna designs.