CROSSTALK BETWEEN COAXIAL CONDUCTORS 



369 



wherein the second term in equation (10) is cancelled completely by 

 the third term of equation (11). This equation (12) is exactly what 

 we would get by substituting 2/ for / in the general equation (5). The 

 only reason for deriving it in terms of 2Fi plus interaction between the 

 sections is to present a better physical picture of the mechanism of 

 far-end crosstalk summation with length, that is, to show how the 

 interaction crosstalk between two sections alters what otherwise would 

 be a direct summation with length. 



In lengths where the tertiary circuit is electrically long equation 

 (12) for total crosstalk in length 2/ becomes 



^2; = 2Fl + Fnn + Fff = 



Zal 



2Z 





7r 



21 



4Z44 74^ — 7^ 



+ 



74 



4Z4 



74^ + 7^ 



(13) 



which differs from equation (6) for total crosstalk in length / only by 

 the factor of 2 in the first bracketed term. Thus, as mentioned before, 

 there is a range of lengths wherein the crosstalk will be constant at 

 a level determined by the second term of (6) or (12) until the length 

 becomes sufhcient for the first term to become controlling. 



In lengths where the tertiary circuit is electrically short equation 

 (11) becomes 



2Fi = 



which reduces simply to 



Z^ 

 2Z 



21 

 Z33 



4Z44 



2Fi = 



(14) 



(15) 



when the length is sufficiently short. The interaction crosstalk between 

 two electrically short lengths becomes, from equation (10), 



Fnn + Fff = 



2Z 



4Z4 



/2 



P, 



(16) 



one-half of which is due to component Fnn and the other half to com- 

 ponent Fff. The sum of (14) and (16) is 



F2I = 2Fl + Fnn + F, 



// 



Z^ 

 2Z 



2l_ 



Zz3 



74 

 4Z4- 



2/2 



(17) 



which is exactly equal to equation (7) if 21 is substituted for / therein. 

 From (15) and (16) it is apparent that for very short lengths the total 



