A generalized broadband coupled-line based rat-race coupler with arbitrary power division ratios and free terminated impedances

A generalized broadband coupled-line based rat-race coupler with arbitrary power division ratios and free terminated impedances is proposed in this paper. Besides, rigorous closed-form equations with respect to electrical parameters are derived in the section of analysis. Furthermore, one shorted coupled-line section and two identical open-circuited stubs are employed to achieve the requirement of wideband and miniaturization. Owing to additional design freedom, the calculation of parameters becomes much more flexible. For demonstration, a prototype for 6-dB wideband rat-race coupler centered at 1 GHz with the fractional bandwidth of 51.69% and free terminated impedances is designed, fabricated, and measured. Good agreement between the simulated and measured results can be observed, which can verify the validity of the proposed design principle.