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Abstract Although miniaturized and fractal‐shaped branch‐line couplers have been reported by many researchers, their operating bandwidth are narrowed and shifted greatly, thus the application of these techniques were limited. In this article, we presented an exact design technique to obtain compact and fractal‐shaped branch‐line couplers for a given frequency. As an example, novel fractal‐shaped branch‐line couplers operated at 2.4 GHz using Koch fractal shapes of different iteration orders have been designed successfully, and the designed couplers all operated at the designed frequency and achieved a maximal 81.8% size reduction. And furthermore, the operating frequency and its bandwidth are virtually unaltered. The proposed method is verified by the measurement results. ? 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1198–1201, 2008; Published online in Wiley InterScience （www.interscience.wiley.com）. DOI 10.1002/mop.23316
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