36 BELL SYSTEM TECHNICAL JOURNAL 



at B must also be propagated a distance d in order to reach A. As 

 indicated by this vector diagram the total crosstalk current due to the 

 two short segments is a little less than the arithmetic sum of the 

 individual crosstalk currents. 



Figure 8C is like Fig. 8B except that a transposition is inserted in 

 the middle of circuit a at point B. This reverses the phase of the 

 transmission current at the right of B and also reverses any crosstalk 

 current due to current in circuit a between B and C. As a result the 

 crosstalk current in of Fig. 8B is reversed and the resultant of the two 

 crosstalk currents is very much reduced as indicated by the vector 

 diagram of Fig. 8C. The angle between i„ and in is proportional to 

 the length 2d which equals A C. The tendency for the two currents to 

 cancel may, therefore, be increased by reducing the length AC which, 

 in a long line, would mean increasing the number of transpositions. 



Figure 8D is like Fig. 8B except that the far-end transverse crosstalk 

 coupling / in each of the two short segments is considered. The 

 coupling in the left-hand segment results in a crosstalk current at 

 point B of circuit h, w^hich is propagated to point C as indicated by if. 

 The far-end crosstalk coupling in the right-hand segment produces a 

 crosstalk current i/ at point C. Since the total propagation distance 

 is from ^ to C for both of these crosstalk currents, they must be equal 

 in magnitude and in phase if circuits a and h are similar. This is 

 indicated by the vector diagram of Fig. 8D. A transposition at point 

 B in either circuit would reverse one of these crosstalk currents and, 

 therefore, the resultant crosstalk current would be nil. 



From consideration of Figs. 8C and 8D, it may be seen that if both 

 circuits were transposed at point B, the sum of the crosstalk currents 

 for the two segments would be the same as if neither circuit were 

 transposed. Transposing one circuit reverses the phase of one of 

 the component crosstalk currents, but if the second circuit is also 

 transposed the original phase relations between the two currents are 

 restored. 



The foregoing discussion applies only to transverse crosstalk as 

 discussed in connection with Fig. 2. When interaction crosstalk must 

 be considered, a different principle is involved. 



In connection with Fig. 8D, it w^as shown that the transverse far-end 

 crosstalk between similar circuits could be readily annulled by trans- 

 posing one of the circuits at the center of their paralleling length. 

 Far-end crosstalk of the interaction type is not so readily annulled. 

 The effect of transpositions on this type of crosstalk is indicated by 

 Fig. 9. 



This figure shows four short segments in a parallel between two 



