Miniaturization of Rat-Race Coupler With Dual-Band Arbitrary Power Divisions Based on Stepped-Impedance Double-Sided Parallel-Strip Line

Generalized equations are presented for the design of a rat-race coupler with a phase inverter and an arbitrary power division, where its four arms are built by symmetric reciprocal lossless two-port networks. According to these equations, uniform- and stepped-impedance rat-race couplers are analyzed and synthesized with dual-band arbitrary power divisions. The relationships between the geometries and the design specifications of proposed dual-band rat-race couplers are completely determined. Under such circumstances, the most compact configuration of the stepped-impedance rat-race coupler is achieved when the maximum allowable impedance ratio is applied for all its arms. Several prototypes are realized with double-sided parallel-strip lines (DSPSLs) and DSPSL phase inverters. As the stepped-impedance arms are not limited to simulate 90^° sections and the phase inverters are implemented into our proposed dual-band couplers, the component circumferences are reduced significantly by 65%-70%, in comparison with their conventional 540^° counterpart. Their good performances are demonstrated by the simulated and measured results.