This paper treats a band-broadening design technique of a dual-band branch-line coupler with matching networks composed of an impedance step and a short-circuited stub based on the equivalent admittance approach. By replacing each right-handed transmission line (RH-TL) with a composite right/left-handed transmission line (CRLH-TL), very flat couplings over a relative bandwidth of about 10% can be obtained at two arbitrary operating frequencies in comparison with previous CRLH-TLs branch-line couplers. Furthermore, by adding periodical open-circuited stubs into RH-TLs of the designed CRLH-TLs branch-line coupler with matching networks, the entire size of the coupler can be reduced to about 50%. Verification of these band-broadening and size-reduction design techniques can be also shown by an electromagnetic simulation and experiment.

This paper presents a design procedure of a directional coupler consisting of a twofold symmetric four-port circuit with four identical matching networks at each port. The intrinsic power-split ratio and the equivalent admittance of the directional coupler are formularized in terms of the eigenadmittances of the original four-port without the matching networks. These formulas are useful for judgment on the realizability of a directional coupler in a given circuit structure and for design of the matching networks. Actually, the present procedure is applied to designing various quadrature hybrids and directional couplers, and its practical usefulness as well as several new circuit structures are demonstrated.