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Engineers at UCLA have combined engineering with the mathematical field of geometry to design smaller, more diverse antennas.

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 a machine.

While Gianvittorio considers the technology novel, he admits that fractals are just another means of achieving the same result.

“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 fundamental understanding.”

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,” Rahmat-Samii said.

“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.