6G4 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



If the coupling mechanism is non-directive (sending equal waves forward 

 and backward) and has the same value for all modes, then K = l^ and 

 M = 1.0. For simplicity these values are assumed in writing the remain- 

 der of the expressions. However, the theory is applicable if the coupling 

 mechanism is mode selective and/or directive provided that these proper- 

 ties do not change over the length of the coupling interval. 



The mode discriminating property of the coupled Unes is the ratio of 

 the forward current for Xi = X2 to the forward current for Xi 5^ X2 . This 

 ratio is 



Discrimination = 



// (Xi = X2) 

 // (Xi N X2) 





dx 



L 



(4) 



29 



dx 



where d = 7rL(l/Xi — I/X2) = L(^i — j82)/2 and the /3's are the phase 

 constants of the two transmission Imes. 



The directivity of the coupUng arrangement is defined as the ratio of 

 the forward current for Xi = X2 to the backward current; this ratio is also 

 given by equation (4) provided 



= -ttL 



i + ^ 

 Xi X. 



= -| (/3i + /32). 



Thus, in the loose coupling case, the critical performance characteristics 

 are given by the discrimination function, equation (4), for appropriate 

 values of the parameter d. 



Fig. 2 — Schematic of coupled transmission lines. 



