156 BELL SYSTEM TECHNICAL JOURNAL 



where Z — Z373 is the distributed series impedance of the intermediate 

 transmission line. 



Comparison between Direct Crosstalk and Crosstalk via 



Intermediate Circuit for Two Parallel 



Coaxial Conductors 



We have already seen that two parallel coaxial conductors in free 

 space form actually three transmission circuits, the third circuit being 

 formed by two outer shells of the coaxial conductors. When this 

 third line is shorted by direct electrical contact or by frequent straps 

 only direct crosstalk is present. When the third circuit is terminated 

 in its characteristic impedance we have crosstalk via the third circuit. 

 In this last case, however, the crosstalk via the third circuit is also the 

 total crosstalk, since the only available path for the transfer of inter- 

 fering energy is via the third circuit. Thus, we can directly compare 

 the values of crosstalk for the system for both conditions. 



We have shown that for sufficiently short lengths of the crosstalk 

 exposure the direct type of crosstalk is given by (12) or (19), namely, 



F=N = ^l. . (47) 



We have also found that the crosstalk via an intermediate circuit is 

 given by (34) or (41) provided that the length of conductors is small 

 enough. Thus 



F' = N' =-^^P. (48) 



4Z0Z3 



Consequently 



In seeking an experimental verification of equation (49) a series of 

 measurements were taken on a pair of coaxial conductors of varying 

 lengths, separations, and different terminating conditions of the third 

 circuit. The results agreed fully with the theory. 



Mutual Impedance 



Like the other constants of transmission lines the distributed mutual 

 impedance can be measured. In certain cases, however, it is possible 

 to obtain simple formulae for this impedance. For details of such 

 calculations the reader is referred to a paper by one of the authors.^ 



In this paper the mutual impedance is expressed in terms of surface 



