A topology, equations and design methodology for complex impedance-transforming branch-line hybrid couplers are presented. This method also allows the realization of real impedance-transforming to higher impedances. Limitations for real, imaginary and complex impedances are discussed. Test results are shown for a 3 dB 50 to 450 Ω hybrid coupler, at a 2 GHz center frequency, with a 21% bandwidth, an amplitude balance of 4.35±1 dB and a phase balance of 92.16°±8.8°. To showcase the complex impedance scenario, two 3 dB 50 Ω to 70-200j Ω are measured at a 2 GHz center frequency. One of these couplers uses a technique for reducing the chip size, yielding a 22.5% bandwith, 4-0.9 dB amplitude balance and 93.22°-6.74° phase balance, while acomplishing a 25% size reduction.
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