Synthesis of an ideal phase ratio for a coupled-line coupler with a given type of directionality

Authors: Sychev A. N., Struchkov S. M., Rudyy N. Yu.

Annotation: For the first time, an ideal phase ratio formula is obtained that expresses the ratio of the electrical lengths of normal modes in coupled lines through three integers – the directivity code, the number of proximity and the number of the difference. The ideal phase ratio function forms three two-dimensional sequences whose values are represented by rational numbers. From the obtained formula it follows that the contradirectional operation mode of coupled lines is possible not only in a homogeneous dielectric medium, but also in an inhomogeneous medium. The formula is also convenient for the synthesis of codirectional and trans-directional couplers.

Keywords: directional coupler, coupled lines, ideal phase ratio, contra-directional coupler, co-directional coupler, transdirectional coupler