Analytical Modeling of Conventional and Miniaturization Three-Section Branch-Line Couplers

Analytical modeling equations are proposed for the conventional and modified three-section branch-line couplers. The analytical equations are explicit and capable of determining the characteristic impedance of each branch line for the coupler at desired coupling level as well as the suitability of broadband S-parameters analysis. In addition, a bandwidth extension and miniaturization of three-section branch-line coupler using slow-wave and meandering line structures were designed. The modified coupler, which is able to operate within frequencies from 1.5 to 3.32 GHz has been fabricated, tested and compared. A bandwidth extension of 600 MHz and 53% reduced size of the modified coupler have been achieved compared to a conventional coupler. The modified coupler has roughly insertion loss and coupling of -4 dB and -3.2 dB, while the isolation and return loss, respectively less than -14 dB with fractional bandwidth of 77 %, as well as phase imbalances less than $2^{\circ}$ over the operating bandwidth. Overall, the derived analytical model, simulation and measurement results demonstrated a good agreement.