Synthesis of an ideal phase ratio for a coupled-line coupler with a given type of directionality
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 contra-directional 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 co-directional and trans-directional couplers.