A rigorous design methodology for compact planar branch-line and rat-race couplers with asymmetrical T-structures

In this paper, a rigorous design methodology is developed to design compact planar branch-line and rat-race couplers using asymmetrical T-structures. The quarter-wave transmission line, namely the basic element for realizing the coupler, can be replaced by the asymmetrical T-structure, which is composed of a low-impedance shunt stub and two series high-impedance lines with unequal electrical lengths. As compared with the use of the conventional symmetrical T-structure, employing the asymmetrical one to implement the coupler not only has the advantage of flexibly interleaving the shunt stubs to achieve a more compact circuit size, but also provides a wider return loss bandwidth. Based on the proposed designed methodology, the asymmetrical T-structure can be exactly synthesized and then applied to implement the compact planar couplers. The developed planar branch-line coupler occupies 12.2% of the conventional structure and has a 35.5% 10-dB return loss bandwidth. On the other hand, the rat-race coupler is miniaturized to a 5% circuit size and developed with a 29.5% 20-dB return loss bandwidth.