154 BELL SYSTEM TECHNICAL JOURNAL 



near-end crosstalk is given by the expression 



which is proportional to the second power of length. 



For 7/ very large we can rewrite expression (32) as follows: 



4ZoZ3t(73 + 7) ^ ^^ 



Thus, for a system sufficiently long the near-end crosstalk via an 

 intermediate line is independent of length. 



If the intermediate transmission line is short-circuited a large 

 number of times per wave-length, its propagation constant 73 becomes 

 very large on the average and we have approximately 



2[1 - ^-(1^2+.!)^] 

 On = 7 J- X ' (36) 



(Ti + 72)73 

 ^^^ - £ - 2Z.Z373 7X + 72 ^^^^ 



and 



But Z373 = Z, the distributed series impedance of the intermediate 

 transmission line. Hence the "indirect" cross-talk becomes direct 

 with the mutual impedance given by 



Y Z13Z23 



^12 — 79 • 



Indirect Far-End Crosstalk 



Using the method outlined in the previous section we arrive at the 

 following expression for the far-end crosstalk from circuit (1) into 

 circuit (2) via the intermediate circuit (3) ; see Fig. 3. 



The crosstalk from circuit (2) into circuit (1) will be given by a similar 

 expression with Z2 replacing Zi in the denominator, namely 



F.^'^j^Sf. (386) 



