![6452553 Vicsek Fractal Antenna](https://upload.wikimedia.org/wikipedia/commons/4/4e/6452553_Vicsek_Fractal_Antenna.png)
A fractal antenna is an
antenna
Antenna ( antennas or antennae) may refer to:
Science and engineering
* Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves
* Antennae Galaxies, the name of two collid ...
that uses a
fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
,
self-similar
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In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...
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
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
within a given total surface area or volume.
Such fractal antennas are also referred to as multilevel and
space filling curves
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, spac ...
, but the key aspect lies in their repetition of a motif over two or more scale sizes,
[Nathan Cohen (2002) "Fractal antennas and fractal resonators" ] 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 and fractals
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. Some authors (for instance Cohen) 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
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...
that exceeds their
topological dimension
In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a
topological invariant, topologically invariant way.
Informal discussion
F ...
– which is one way of defining fractals. More typically, (for instance Pandey) authors treat them as a separate, but related, class of antenna.
Fractal element antennas and performance
![Antenna flat panel](https://upload.wikimedia.org/wikipedia/commons/6/63/Antenna_flat_panel.png)
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 then a professor at
Boston University
Boston University (BU) is a private research university in Boston, Massachusetts. The university is nonsectarian, but has a historical affiliation with the United Methodist Church. It was founded in 1839 by Methodists with its original campu ...
, starting in 1988.
Cohen's efforts with a variety of fractal antenna designs were first published in 1995.
[ Cohen's publication marked the inaugural scientific publication on fractal antennas.
Many fractal element antennas use the fractal structure as a virtual combination of ]capacitors
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a ...
and inductors
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a ...
. 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
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...
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.
Studies during the 2000s showed advantages of the fractal element technology in real-life applications, such as RFID and cell phones. Fractals have been used commercially in antennas since the 2010s. Their advantages are good multiband performance, wide bandwidth, and small area. The gain with small size results from constructive interference with multiple current maxima, afforded by the electrically long structure in a small area.
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". 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. Balanis reported on several fractal antennas and found them equivalent in performance to the electrically small antennas they were compared to. Log periodics, a form of fractal antenna, have their electromagnetic characteristics uniquely determined by geometry, via an opening angle.[Rumsey, V.H. "Frequency Independent Antennas", IRE International Convention Record, Vol. 5, Part 1, pp.114-118, 1957]
Fractal antennas, frequency invariance, and Maxwell's equations
One different, and useful, attribute of some fractal element antennas is their self-scaling aspect. In 1957, V.H. Rumsey 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 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 that ''self-similarity
__NOTOC__
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...
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.
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.
Fractal inductors and fractal tuned circuits (fractal resonators) were also discovered and invented simultaneously with fractal element antennas.[ An emerging example of such is in ]metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
s. A recent invention demonstrates using close-packed fractal resonators to make the first wideband metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
invisibility cloak at microwave frequencies.
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.
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.
See also
* Waveguide (electromagnetism)
In radio-frequency engineering and communications engineering, waveguide is a hollow metal pipe used to carry radio waves. This type of waveguide is used as a transmission line mostly at microwave frequencies, for such purposes as connecting m ...
References
External links
How to make a fractal antenna for HDTV or DTV
CPW-fed H-tree fractal antenna for WLAN, WIMAX, RFID, C-band, HiperLAN, and UWB applications
Video of a fractal antenna monopole using fractal metamaterials
{{Antenna Types
Radio frequency antenna types
Antennas (radio)
Fractals