Exact Synthesis of Full- and Half-Symmetric Rat-Race Ring Hybrids With or Without Impedance Transforming Characteristics

Novel full- and half-symmetric rat-race ring hybrid structures are proposed, in which the impedance transforming property can be implemented. Impedance transformation implies that the impedances of the input and output ports can be different. The conventional even- and odd-mode partition and analysis method cannot be applied to the proposed half-symmetric circuits; therefore, an analysis method is developed. The rat-race ring is exactly synthesized on the basis of a newly deduced high-pass prototype that is based on Richards theorem, which allows the user-defined specifications to be satisfied. Three hybrids are synthesized as examples - a sixth-order full-symmetric hybrid with a bandwidth of 116% and a return loss of 20 dB, a fifth-order half-symmetric hybrid with a 100% bandwidth and 25-dB return loss, and a fifth-order impedance-transforming half-symmetric hybrid with an output port impedance of 70 Ω, a 100% bandwidth, and 20-dB return loss. The first and second hybrids are implemented to verify the method. A comparison of the measured and simulation results indicates good agreement.