Design of Broadband Doubly Asymmetrical Branch-Line Directional Couplers

An analytic broadband design method for four-port N-branch branch-line couplers with outputs terminated by arbitrary impedances is given. An alternative, more practical design method has also been included, which avoids impedance discontinuities in the branches and retrieves the outputs-in-quadrature property lost in the asymmetrization. The doubly asymmetrical couplers so obtained are then used in a proposed design methodology for three-way power dividers that can include, if desired, an impedance level transformation. This article relies on the analysis of a class of asymmetrical structures by means of the odd and even excitations. Therefore, the formalization of this analysis is also detailed.