Rat-Race Circuits with Loose Coupling Using Parallel Ring-Lines

This paper treats a rat-race circuit with loose coupling using parallel ring-lines. The minimum coupling factor of a conventional rat-race circuit is limited by the highest impedance of ring-lines that can be manufactured. The proposed rat-race circuits with parallel ring-lines can be realized couplers with loose coupling factors of less than -10 dB by reducing the difference between two admittances of parallel ring-lines. The circuit with a coupling factor of -20 dB can be successfully designed. Finally, verification of this design method can be also shown by using electromagnetic simulator and experiment.