by Tom Vernon — copied from Radio World, September 1, 1999

Since they were first described by the French mathematician Benoit Mandelbrot in the mid-1970s, repeating geometric figures known as fractals have fascinated computer scientists, mathematicians and graphic artists.

These "broken curves" have been used to explain naturally-occurring phenomenon such as lightning, galactic clusters and clouds. Many computer-image compression schemes are based on fractals. Until recently, however, there have been few hardware applications of fractal geometry.

Fractal antennas and fractal arrays are notable exceptions.

A fractal element antenna, or FEA, is one that has been shaped in a fractal
fashion, either through bending or shaping a volume, or introducing holes.
They are based on fractal shapes such as the Sierpinski triangle.
Mandelbrot tree, Koch curve, and Koch island. The advantage of FEAs, when
compared to conventional antenna designs, center around size and bandwidth.

Size can be shrunk from two to four times with surprising good performance. Multiband performance is at non-harmonic frequencies, and at higher frequencies the FEA is naturally broadband. Polarization and phasing of FEAs also are possible.

The theory of fractal antenna operation is steeped in mathematics, but in its most basic form, it comes down to this: In order for an antenna to work equally well at all frequencies, it must satisfy two criteria: it must be symmetrical about a point, and it must be self-similar, having the same basic appearance at every scale: that is, it has to be fractal.

In many cases, the use of fractal element antennas can simplify circuit design, reduce construction costs and improve reliability. Because FEAs are self-loading, no antenna tuning coils or capacitors are necessary. Often they do not require any matching components to achieve multiband or broadband performance.

Much of the manufacturing and research on fractal antennas is being done by Fractal Antenna Systems Inc., a privately-held company with manufacturing facilities in Ft. Lauderdale, Fla., and research and development labs in Belmont, Mass.

The company holds key patent pending positions on the technology. Its founder, Dr. Nathan Cohen, is a professor of Applied Science and Telecommunications at Boston University.

While much of the current reserch and development work has centered on the 900 MHz, PCS and S-band applications, fractal antenna design techniques can be applied to any frequency and any type of antenna, such as dipoles, monopoles, and helices. Replacing the spring stubby on cell phones with a fractal design results in a more efficient antenna, one that is cheaper to manufacture, and broad-band enough that designers are considering including a GPS receiver in future cell phones.
"We have been able to use a fractalized helix to shrink the height to
one-third normal with the same gain," Cohen said. The trade-off with
this reduction in size is a decrease in bandwidth to slightly less
than 25 percent."

While the company does not actively manufactuire antennas for broadcasters, Fractal Antenna Systems does a lot of custom work, and welcomes all inquiries. The most promising pplications would seem to be in the 450 MHz RPU and 950 MHz STL arenas. In addition to the increased bandwidth that FEAs afford, the reduced size may be an important consideration for broadcasters when aesthetics or wind loading are important considerations.

Fractal antennas have existed for a long time, although they were not consciously designed as such. Log periodic antennas are fractal in nature. While they have been around for more than 40 years, their behavior was not completely understood until fractal techniques were applied.Another type of aerial, the randomly bent antenna, is really based on random fractals.

A radio amateur and Boston apartment dweller with space limitations, Cohen assembled the first true FEA in 1988 to work the 2-meter amateur band. He later built a 10-meter dipole and worked dozens of stations in Europe with 1 watt. Cohen initially reported his findings at an ARRL convention in 1994, and published the first article on FEAs in 1995.

Universitity researchers confirmed his findings, and investigations into FEAs continue at Penn State, UCLA and UPC in Spain.

Research on the related field of fractal arrays is under way at the University of Pennsylvania in Philadelphia. Antenna arrays traditionally have been constructed with elements either ramdomly scattered or regularly spaced. By using a fractal arrangement, efficient arrays can be constructed with a quarter of the number of elements used in a conventional design.

To learn more about fractal element antennas, including constuction plans for a 10-meter fractal dipole, visit the company Web page.

Some interesting 3D fractal antenna student projects are on display at http://www.antlab.ee.ucla.edu/~johng/fractal.html

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