OPEN-WIRE CROSSTALK 197 



calculated from the values of 5" for the individual transposition 

 sections, a given permissible value of R may be obtained with various 

 sets of values of S. It seems reasonable to determine individual 

 values of 5 on the principle that a transposition section of length Lg 

 should have the same probability of exceeding a given unbalanced 

 length as any other section of the same length and that a section of 

 length 2Ls should have the same probability as two sections of length 

 Lg, etc. On this basis, the value of S- for any transposition section 

 should be proportional to the section length Ls. This leads to the 

 rule used in practice that for any transposition section 5^ should not 

 exceed kL^. If Ls and 5 are expressed in feet, a value of three for k 

 is found suitable for practical use. The choice of a value for k will 

 depend, of course, upon the cost of locating and maintaining trans- 

 position poles with various degrees of accuracy and upon the effect 

 on the crosstalk of varying the value of k. 



The above rule permits a large deviation at one point in a trans- 

 position section if it is compensated by small deviations in the rest 

 of the segments. For example, with 128 segments and a mean 

 segment length of 260 feet, one long segment of 575 feet is permissible 

 if the rest of the segments are 258 feet. The expression for the total 

 unbalanced length in a succession of transposition sections assumed 

 that the deviations varied from segment to segment in a truly random 

 manner. The above example involves an unusual arrangement of 

 the deviations. When there are a number of transposition sections 

 in a line, such unusual arrangements of deviations in various sections 

 do not have much effect on the probability that the total unbalanced 

 length will exceed a given value. 



The computation of near-end crosstalk due to pole spacing irregu- 

 larities is a more complicated problem since the crosstalk elements 

 resulting from the various segments vary in their magnitudes and 

 phase relations because the various segments involve different propa- 

 gation distances. It may be concluded, however, that the r.m.s. 

 value of the total unbalanced length in all the sections may be ex- 

 pressed as follows: 



This differs from the expression for far-end crosstalk in that the 

 values of S"^ for the second and succeeding transposition sections are 

 multiplied by attenuation factors. The attenuation factor A^ cor- 

 responds to propagation through the first section to the second section 

 and back again. The other attenuation factors are similarly defined. 

 The above expression neglects attenuation within any particular 



