Fractal antenna
A fractal antenna is an antenna that uses a fractal, self-similar design to maximize the 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,[1] or "iterations". For this reason, fractal antennas are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications.
A good example of a fractal antenna as a spacefilling curve is in the form of a shrunken fractal helix.[2] Here, each line of copper is just a small fraction of a wavelength.
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. This makes the fractal antenna an excellent design for wideband and multiband applications.
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[edit] Log periodic antennas and fractals
The first fractal "antennas" were, in fact, fractal "arrays", with fractal arrangements of antenna elements, and not recognized initially as having self-similarity as their attribute. Log-periodic antennas are arrays, around since the 1950s (invented by Isbell and DuHamel), that are such fractal arrays. They are a common form used in TV antennas, and are arrow-head in shape.
[edit] Fractal element antennas and performance
Antenna elements (as opposed to antenna arrays) made from self-similar shapes were first created by Nathan Cohen,[3] then a professor at Boston University, starting in 1988. Cohen's efforts with a variety of fractal antenna designs were first published in 1995 (thus the first scientific publication on fractal antennas), and a number of patents have been issued from the 1995 filing priority of invention. Most allusions to fractal antennas make reference to these "fractal element 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. Electrical resonances may not be directly related to a particular scale size of the fractal antenna structure. The physical size of the antenna is unrelated to its resonant or broadband performance. The general rule of antenna length being near target frequency wavelength does not apply itself in the same way with fractal antennas.
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.
Fractal element antennas are shrunken compared to conventional designs, and do not need additional components. 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.
Although the first validation of the technology was published as early as 1995 (see ref.1), recent independent studies show advantages of the fractal element technology in real-life applications, such as RFID[4] and cell phones.[5]
One researcher has stated to the contrary that fractals do not perform any better than "meandering line" (essentially, fractals with only one size scale, repeating in translation) antennas. Specifically quoting researcher Steven Best: "Differing antenna geometries, fractal or otherwise, do not, in a manner different than other geometries, uniquely determine the EM behavior of the antenna."[6][7] However, in the last few years, dozens of studies have shown superior performance with fractals,[8] and the below reference of frequency invariance conclusively demonstrates that geometry is a key aspect in uniquely determining the EM behavior of frequency independent antennas.
[edit] Fractal antennas, frequency invariance, and Maxwell's equations
A different and also useful attribute of some fractal element antennas is their self-scaling aspect. In 1999, it was discovered[9] that self-similarity was one of the underlying requirements to make antennas "invariant" (same radiation properties) at a number or range of frequencies. Previously, under Rumsey's Principle, it was believed that antennas had to be defined by angles for this to be true; the 1999 analysis, based on Maxwell's equations, showed this to be a subset of the more general set of self-similar conditions. Hence 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 property being in keeping with the fundamental nature of Maxwell’s derivation and mathematical treatment of electromagnetic phenomena, and is further demonstrated by its complete harmony and integration with Einstein’s special theory of relativity.
[edit] Antenna tuning units
Antenna tuning units are typically not required on fractal antennas due to their wide bandwidth and complex resonance. However, if a transmitting antenna has deep nulls in its response or has electromagnetic structural issues that require equalization then an antenna tuning unit should be used[citation needed], per the definition of required.
[edit] Other uses
In addition to their use as antennas, fractals have also found application in other antenna system components including loads, counterpoises, and ground planes. Confusion by those who claim "grain of rice"-sized fractal antennas arises, because such fractal structures serve the purpose of loads and counterpoises, rather than bona fide antennas.
Fractal inductors and fractal tuned circuits (fractal resonators) were also discovered and invented simultaneously with fractal element antennas.[1][10] An emerging example of such is in metamaterials. A recent report demonstrates using close-packed fractal resonators to make the first wideband metamaterial invisibility cloak,[dubious ] at microwave frequencies.[11][citation needed] Fractal filters (a type of tuned circuit) are another example where the superiority[clarification needed] of the approach has been proven.[12][13][14]
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.
[edit] See also
- Waveguide antenna.
[edit] Notes
- ^ a b Nathan Cohen (2002) "Fractal antennas and fractal resonators" U.S. Patent 6,452,553
- ^ image used by permission
- ^ Fractal Antenna Systems, Inc
- ^ Ukkonen L, Sydanheimo L, Kivikoski M (26–28 March 2007). "Read Range Performance Comparison of Compact Reader Antennas for a Handheld UHF RFID Reader". IEEE International Conference on RFID, 2007. pp. 63–70. doi:10.1109/RFID.2007.346151. ISBN 1-4244-1013-4. http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4143512. [In an Academic Study, RFID Fractal Antenna Wins Out Lay summary].
- ^ N. A. Saidatul, A. A. H. Azremi, R. B. Ahmad, P. J. Soh, and F. Malek (2009). "Multiband Fractal Planar Inverted F Antenna (F-Pifa) for Mobile Phone Application". Progress In Electromagnetics Research B 14: 127–148. doi:10.2528/PIERB0903080. http://ceta.mit.edu/pierb/pier.php?paper=09030802.
- ^ Best,S, (2003). "A Comparison of the Resonant Properties of Small Space-Filling Fractal Antennas". IEEE Antennas and Wireless Propagation Letters 2 (1): 197–200. http://www.physics.princeton.edu/~mcdonald/examples/EM/best_ieeeawpl_2_197_03.pdf.
- ^ Best,S, (2002). "On the Resonant Properties of the Koch Fractal and other Wire Monopole Antennas". IEEE Antennas and Wireless Propagation Letters 1 (1): 74–76. http://www.physics.princeton.edu/~mcdonald/examples/EM/best_ieeeawpl_1_74_02.pdf.
- ^ [1]
- ^ Hohlfeld R, Cohen N (1999). "Self-similarity and the geometric requirements for frequency independence in Antennae". Fractals 7 (1): 79–84. doi:10.1142/S0218348X99000098.
- ^ Nathan Cohen (2007) "Fractal antennas and fractal resonators" U.S. Patent 7,256,751
- ^ Metamaterial Fractal Wideband Invisibility Cloak
- ^ Lancaster, M.; Hong, Jia-Sheng (2001). Microstrip filters for RF/microwave applications. New York: Wiley. pp. 410–1. ISBN 0-471-38877-7. http://books.google.com/books?id=vj0hz1KUAXoC&pg=PA410.
- ^ Pourahmadazar, J.; Ghobadi, C.; Nourinia, J.; Shirzad, H. (2010). Mutiband Ring Fractal Monopole Antennas For Mobile Devices. New York: IEEE. pp. 863–866. doi:10.1109/LAWP.2010.2071372. http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F7727%2F4357943%2F05560718.pdf%3Farnumber%3D5560718&authDecision=-203.
- ^ Pourahmadazar, J.; Ghobadi, C.; Nourinia, J.; (2011). Novel Modified Pythagorean Tree Fractal Monopole Antennas for UWB Applications. New York: IEEE. doi:10.1109/LAWP.2011.2154354. http://ieeexplore.ieee.org/search/freesrchabstract.jsp?tp=&arnumber=5766703&queryText%3Dpourahmadazar%26openedRefinements%3D*%26searchField%3DSearch+All.
[edit] References
- 1. Cohen, N. (Summer 1995). "Fractal Antennas". Communications Quarterly: 9.
- 2. US Patents: 6104349; 6127977; 6140975; 6445352; 6452553; 6476766; 6985122; 7019695; 7126537; 7145513; 7190318;7215290; 7256751.
- 3. A description of the first fractal element antenna, created in 1988, was given in reference 1, and is reproduced at: 4
- 4. Cohen, N.,"NEC Analysis of a Fractalized Monofilar Helix in the Axial Mode", ACES Conference Proceedings, April 1998, p. 1051
