Fractals used to optimize antennas
By David Zisser
Nov. 19, 2002 9:00 p.m.
Engineers at UCLA have combined engineering with the
mathematical field of geometry to design smaller, more diverse
UCLA electrical engineering chairman, Yahya Rahmat-Samii, and
Ph.D. student John Gianvittorio are using fractals, mathematical
models normally used to define curves and surfaces, and applying
them to the design of antennas.
Rahmat-Samii found that using fractals in designing antennas
conserves space and allows antennas to operate simultaneously at
several different frequencies.
“Fractals enable the users to put a long length in a small
area,” Rahmat-Samii said. “(Using) the same size, we
can (have) a lot larger perimeter.”
It works like this: starting with a line, a small fold is made
in the line. Another bend is made in that line, and a bend is added
to each additional bend.
“You have an infinite number of little kinks, but your
endpoints are fixed,” Gianvittorio said.
In other words, a fractal can be a line which approaches the
shape of a sheet. The line can meander in such a way as to fill
almost the entire sheet, meaning that the curves are electrically
very long but fit into a compact physical space.
Fitting such a large amount of information in a small space has
allowed the researchers to miniaturize antennas by up to 30 percent
so far, while maintaining the same performance.
“Miniaturization means you’ll be able to put an
antenna on more things,” Gianvittorio said.
Potential applications could include watches, appliances and
laptop computers, according to Gianvittorio.
Because of the “iterative,” or repeated bending,
process available in geometry, a number of different
“scales” of different lengths are achieved.
The process of designing and creating a fractal starts with
understanding each unique application.
Using their understanding of fundamental antennas, Gianvittorio
and Rahmat-Samii first develop an idea of what they want the
fractal antenna to do. They then analyze different fractal
geometries and visualize a design.
Rahmat-Samii and Gianvittorio then simulate the potential design
on a computer before making a physical antenna. Once they have what
looks like a design which fits their hypothesis, they build the
antenna in their research lab by hand or by using a process called
etching, where the antenna is etched out of a sheet of copper using
While Gianvittorio considers the technology novel, he admits
that fractals are just another means of achieving the same
“It’s definitely been a well-received tool, but (it
is) basically just a tool,” he said.
Rahmat-Samii and Gianvittorio have also designed fractals to
model the complex shapes found in nature, including mountain
ranges, trees, clouds and even waves.
“It’s a very broad field, so there’s a lot of
geometry that’s possible,” Gianvittorio said.
“This is an area that is just kind of under way. … By
pursuing various geometries, we’ll try to get a more
A better understanding of the efficiencies of fractal antennas
can also lead to many different applications.
“I would say two fronts we’re very excited about are
… (the) interaction of antennas with the human head for
communications application and also for implanted devices,”
“The medical community has a lot of interest in implanting
devices in the body.”
Rahmat-Samii is also excited about nature-based optimization
techniques with fractal antennas using genetic algorithms.
Following the Darwinian theory of evolution for antenna
optimization, Rahmat-Samii and Gianvittorio are using evolutionary
processes to cross “species” of antennas, and letting
them grow to the “fittest” design.
Rahmat-Samii and Gianvittorio started working with fractals in
1998 in conjunction with a colleague from Barcelona, Spain.