Complex Impedance Transformers Based on Branch-Line Hybrid Couplers

Abstract

A topology, equations and design methodology for complex impedance-transforming branch-line hybrid couplers are presented. This method also allows the realization of real impedancetransforming 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% bandwidth, 4 ± 0.9 dB amplitude balance and 93.22◦ ± 6.74◦ phase balance, while accomplishing a 25% size reduction.