A novel compact dual-band branch-line coupler with cross-shaped stubs

A cross-shaped branch-line coupler for dual-band applications is presented in this letter. The new structure uses a cross-shaped stub instead of one transmission line in the conventional branch-line coupler to work at two arbitrary frequencies. The two degrees of freedom have been introduced to have the flexible adjustment of the frequency ratio ranging from 2 to 7. The design equations are obtained by using ABCD-matrix. A new mathematical analysis has been used to discuss this structure. For verification, a dual-band branch-line coupler operating at 1 and 3.5 GHz has been designed and measured on a Rogers' RO4003 board which has a compact size of 0.022λ
0
²
.