Science + Technology

Fractals Help UCLA Researchers Design Antennas for New Wireless Devices


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

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

"Manufacturers of wireless equipment, and particularlythose in the automotive industry, are interested in developing a single,compact antenna that can perform all the functions necessary to operate AM andFM radios, cellular communications and navigation systems," said YahyaRahmat-Samii.

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

Fractals, short for "fractional dimension," aremathematical models originally used to measure jagged contours such ascoastlines. Like a mountain range whose profile appears equally craggy whenobserved from both far and near, fractals are used to define curves andsurfaces, 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 behindthe repetition of these geometrical structures with similar shapes could beapplied to a methodology for developing antenna designs.

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

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

Because fractal designs are self-symmetrical (repeatthemselves), they are effective in developing antennas that operate at severaldifferent frequencies. "One portion of the antenna can resonate at onefrequency while another portion resonates at another frequency," Rahmat-Samiisaid.

UCLA, where much of the early research on internalantennas was conducted in the mid 1990s, is today "one of the leading researchinstitutions exploring the use of fractals in developing antenna design,"Rahmat-Samii said.

Thesubject of fractals came into vogue during the last decade as new-age gurusclaimed fractals were capable of all manner of feats. Serious use inengineering, however, has developed over the last five years, Rahmat-Samiisaid.

This is not the first time Rahmat-Samii has borrowedfrom other disciplines. He has experimented with using "genetic algorithms" —the Darwinian notion of natural selection and evolution — as a means ofdeveloping 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 iscomplete when it has produced a design that meets the experimenter'sobjectives.

Although the method produces unanticipated results, italso provides few clues about the next iteration of the design, Rahmat-Samiisaid. Using fractals, however, makes the process more predictable, givingresearchers more control over the results.



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