52 BELL SYSTEM TECHNICAL JOURNAL 



Figure 16 indicates with a solid line the important type of interaction 

 crosstalk between the first two segments by way of a representative 

 tertiary circuit c. As discussed in the section on crosstalk coefficients 

 and in Appendix A, the far-end crosstalk (output-to-output) of this 

 interaction type will be 



NacNchKHn^)-'' = - 2yFiK<P approximately. 



The interaction crosstalk as well as the transverse crosstalk is about 

 proportional to the indirect coefficient Fi. 



Each segment of the disturbing circuit will have a similar interaction 

 crosstalk coupling with each preceding segment of the disturbed 

 circuit. The interaction crosstalk between segment EF and segment 

 BC \?> indicated on Fig. 16. The expression for this differs from the 

 above expression in that the additional propagation distance from E 

 to C and back must be allowed for. To get the total output-to-output 

 far-end crosstalk it is necessary to sum up all these interaction crosstalk 

 couplings between segments and to this sum add the total transverse 

 crosstalk in length D. 



This clumsy summation process may be avoided by letting d be an 

 infinitesimal length and integrating between points A and G. This 

 results in the following approximate expression for the output-to- 

 output far-end crosstalk in the length D. 



FjKD + FiKD + FiK 



27 



-2yD 



- D 



This assumes the same propagation constant for the disturbing, 

 disturbed and tertiary circuits. This approximation is justified for 

 short lengths of, say, 10 miles or less. 



The last term represents the interaction crosstalk and this term is 

 negligible for small values of D. For larger values of D interaction 

 crosstalk must be considered and it is convenient to rewrite the 

 expression as follows: 



1 _ e-270 

 FaKD + FiK ^ 



The first term representing the direct crosstalk is negligible for values 

 of D corresponding to a line angle of 90 degrees or less since Fd is 

 ordinarily small compared with Fi and D is not large compared with 

 (1 — e~2T^/27). Therefore, direct crosstalk ordinarily may be neg- 

 lected in computing far-end type unbalance. Another reason for 

 neglecting direct crosstalk is that it is readily cancelled by a few 

 relative transpositions while the remaining far-end crosstalk depends 



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