54 BELL SYSTEM TECHNICAL JOURNAL 



BC and the important type of interaction crosstalk between length 



BC and length AB. The output-to-output crosstalk values only will 



be written for all these paths or, in other words, the effect of the 



propagation distance A C will not be considered in the expressions. 



The far-end crosstalk for either length AB or BC is given by the 



above expression. Since both circuits are transposed at point B the 



far-end crosstalk values in the two lengths will add directly and their 



sum will be 



1 _ e-'yD 



2FK 



27 



Transmission from ^ to C through the crosstalk path in length AB 

 is reversed in sign due to the transposition in circuit b at B. The 

 output current of circuit a is also reversed in sign. In general, the 

 output-to-output current ratio may or may not be reve''sed in sign 

 depending on the transposition arrangement. It is convenient, how- 

 ever, to consider the first path as a reference and assign a plus sign to 

 the crosstalk. Other paths are then assigned the proper relative 

 phase angles. 



As discussed in connection with Fig. 16, if the length D is very 

 short the interaction crosstalk between the two segments may be 

 written : 



- 2y FiKD^ = - 2yFKD^ approx. 



In practice the length D may be too long for this approximate ex- 

 pression in which case it is necessary to substitute for D in the above 

 expression the value derived in connection with the discussion of the 

 near-end crosstalk in a length D. In other words, D of the above 

 expression should be replaced by 



1 - e-^y" 



27 ' 



With this substitution the interaction crosstalk between the two 

 lengths becomes 



(1 - 6-2^^)2 



FK 



27 



Transmission from A to C through this crosstalk path involves two 

 transpositions and therefore the sign of the above expression is not 

 reversed. Relative to the reference path through the crosstalk in 

 length AB the sign should be reversed, however, and become plus. 

 The total crosstalk in the length 2D is, therefore, 



1 _ ^-2yD Cl _ -2yD\2 3 _ 4^-2yD I -47O 



2FK^^^ + FK^ — ^ ^ = FK- ' ^ • 



Z7 27 27 



