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BELL SYSTEM TECHNICAL JOURNAL 



since, as discussed in connection with Figs. 2C and 2D, the interaction 

 crosstalk involves the product of a near-end crosstalk path and a far- 

 end crosstalk path. This product is small since the coupling through 

 the far-end path is inherently small. Therefore, the interaction 

 crosstalk coefficient is much smaller for near-end crosstalk than for 

 far-end crosstalk, while for the transverse crosstalk coefficients the 

 reverse is true. 



As was indicated by the discussion of Fig. 8B, the transverse near- 

 end crosstalk between two long circuits may be computed by dividing 

 the parallel into short segments, each having the same transverse 

 crosstalk coupling. The coupling between circuit terminals for any 

 segment will be different from that at the segment terminals due to 

 propagation effects as explained in connection with Fig. 8B. There- 

 fore, the coupling at the circuit terminal for each segment must be 

 determined and, finally, the sum of the coupling values for all the 

 segments. 



The simplest case is that of two non-transposed circuits. The 

 problem is indicated by Fig. 13 which is like Fig. 8B except that 

 more segments are showm. 



.d^ 



Zb 



--f 



4 



-4 



j_. 



Fig. 13^ Method of computing near-end crosstalk between untransposed 

 circuits in length D. 



The near-end crosstalk coupling n at point A due to the first segment 

 is NKd, where N is the crosstalk coefficient and K is the frequency in 

 kilocycles. The crosstalk current from the second segment relative to 

 that from the first segment is attenuated by the factor e-("i+"!)'^, and 

 also retarded in phase by the angle e~''^^i+''2^'^. In other words, the 

 crosstalk current from the second segment is equal to the crosstalk 

 current from the first segment times the factor e~('''i+'^2''^, where 7x and 

 72 are the propagation constants for the two circuits and y equals 

 a -\-j^. Letting 7 be the average propagation constant, the coupling 



I 



