Analysis and Design of Branch-Line Hybrids with Coupled Lines

Abstract

The scattering parameters of four-ports consisting of coupled lines with coupled or uncoupled connecting branches are derived in terms of the even- and odd-mode impedances and the lengths of the lines. These are used to analyze and formulate basic design procedures for the application of these structures as directional couplers including 0° and 90° 3-dB hybrids. The proposed new structures are quite compact at lower frequencies as compared to conventional uncoupled branch-line and rat-race hybrids. The results for the case of the coupled-line four-port with uncoupled branch lines also lead to closed-form expressions for the lengths and impedances of the lines required to nullify the effect of coupling between the main lines of a conventional branch-line coupler for use at higher frequencies. The measured response of the fabricated couplers is in good agreement with the theoretical predictions.