Both branch-line and rat-race couplers are easily realized using planar circuit technology as they employ only transmission lines without additional components. However, as the electrical lengths of the transmission line elements are either 90 or 270 , such couplers consume a significant amount of circuit area. This paper shows the development of branch-line and rat-race couplers that use artificial transmission lines (ATLs) in place of conventional transmission lines resulting in significant

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... ze reduction. As the ATLs are constructed entirely from microstriplines, the couplers are easily fabricated using conventional printed-circuit processes. The design formulas developed for the ATLs are explicit. Full-wave simulation and experimental results were used to confirm the design approach for hybrids operating at 1.8 GHz. The frequency response of the proposed hybrids is similar to conventional hybrids. Index Terms-Artificial transmission lines (ATLs), branch-line coupler, periodically loaded transmission lines, rat-race coupler.