A fractal antenna
is an antenna that uses a fractal
design to maximize the length, or increase the perimeter (on inside sections or the outer structure), of material that can receive or transmit electromagnetic signals
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, or 'iterations'. For this reason, fractal antennas are very compact, are 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 Here, each line of copper is just 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.
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.
Fractal element antennas and superior performance
Antenna elements (as opposed to antenna arrays) made from self-similar shapes were first done by Nathan Cohen, 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 (see list in references, for example). 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. Note that such resonances may not be related to a particular scale size of the fractal structure: the scaling of the structure does not lead to a one-to-one scaling of resonances. 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, fractal element antennas are 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, much as not all conventional antennas are suitable for a given need. Computer search methods in simulation are commonly used to identify which fractal antenna designs best meet the need.
Although the first validation of the technology was published as early as 1995 (see ref.1) recent independent studies continue to show the superiority of the fractal element technology in real-life applications, such as RFID.
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 (see reference 5) 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.
Fractal tuned circuits, fractal inductors, fractal loads, fractal counterpoises; fractal ground planes
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 were also discovered and invented simultaneously with fractal element antennas (see reference 1 and reference 2-- patent 7256751). In the near future, fractals will have applications as inductors and tuned circuits. Fractal filters (a type of tuned circuit) are just one example where the superiority of the approach has been proven (see reference 6).
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.
- 1. Cohen, N., "Fractal Antennas", Communications Quarterly, Summer,1995, p.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
- 5. Hohlfeld, R., and Cohen, N., "Self-Similarity and the Geometric Requirements for Frequency Independence in Antennae", Fractals, Vol. 7, No. 1 (1999) 79-84.
- 6. Hong, J., and Lancaster, M., "Microstrip Filters for RF/Microwave Applications", J. Wiley, New York (2001) p.410-411.