Fractals help UCLA researchers design antennas for new wireless devices

Antennas for the next generation of cellphones and other wireless communications devices may bear a striking resemblance to the Santa Monica Mountains or possibly the California coastline.

That is because UCLA researchers are using fractals — mathematical models of mountains, trees and coastlines — to develop antennas that meet the challenging requirements presented by the more sophisticated technology in new cellphones, automobiles and mobile communications devices. These antennas must be miniature and they must be able to operate at different frequencies, simultaneously.

“Manufacturers of wireless equipment, and particularly those in the automotive industry, are interested in developing a single, compact antenna that can perform all the functions necessary to operate AM and FM radios, cellular communications and navigation systems,” said Yahya Rahmat-Samii.

Rahmat-Samii, who chairs the electrical engineering department at UCLA’s Henry Samueli School of Engineering and Applied Science, leads the research in this area. His findings were reported in a recent issue of the Institute of Electrical and Electronics Engineers’ Antennas and Propagation Magazine.

Fractals, short for “fractional dimension,” are mathematical models originally used to measure jagged contours such as coastlines. Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale. Any portion of the curve, when enlarged, appears identical to the whole curve — a property known as “self-symmetry.”

Rahmat-Samii found the mathematical principles behind the repetition of these geometrical structures with similar shapes could be applied to a methodology for developing antenna designs.

Using this method, he has developed antennas that meet two important challenges presented by the new generation of wireless devices. They conserve space and can operate simultaneously at several different frequencies.

His fractal methodology allows Rahmat-Samii to pack more electrical length into smaller spaces, he said. Increased electrical length means the antennas can resonate at lower frequencies.

Because fractal designs are self-symmetrical (repeat themselves), they are effective in developing antennas that operate at several different frequencies. “One portion of the antenna can resonate at one frequency while another portion resonates at another frequency,” Rahmat-Samii said.

UCLA, where much of the early research on internal antennas was conducted in the mid 1990s, is today “one of the leading research institutions exploring the use of fractals in developing antenna design,” Rahmat-Samii said.

The subject of fractals came into vogue during the last decade as new-age gurus claimed fractals were capable of all manner of feats. Serious use in engineering, however, has developed over the last five years, Rahmat-Samii said.

This is not the first time Rahmat-Samii has borrowed from other disciplines. He has experimented with using “genetic algorithms” — the Darwinian notion of natural selection and evolution — as a means of developing alternative antenna designs. In keeping with the evolutionary model, a computer program “mates” various antenna components to produce new designs. Just as nature does, the algorithm selects the “fittest” design. The process is complete when it has produced a design that meets the experimenter’s objectives.

Although the method produces unanticipated results, it also provides few clues about the next iteration of the design, Rahmat-Samii said. Using fractals, however, makes the process more predictable, giving researchers more control over the results.

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