Analysis of Asymmetrical Inhomogeneous Coupled-Line Directional Coupler

The scattering matrix of asymmetrical coupled two-line structure in an inhomogeneous medium, terminated in a set of impedances which are equal to the characteristic impedances of the individual, uncoupled lines, has been derived in terms of the coupled-mode parameters. It has been proved that the structure can compose an ideal, backward-coupling directional coupler, perfectly matched and isolated at all frequencies, if the inductive kL and capacitive kC coupling coefficients of the coupled lines are equal each other. The effect of the non-ideal equalization of the coupling coefficients on the coupler critical parameters is then investigated. The normal-mode parameters (mode numbers and mode impedances) in the proximity of the point when kL = kC and at that point are also examined. The numerical results presented confirm the validity of the developed analysis and prove the possibility of a very high directivity asymmetrical coupler design.