370 BELL SYSTEM TECHNICAL JOURNAL 



crosstalk in length 21 will be simply twice that in length / since the 

 interaction crosstalk between lengths / is proportional to l^ and there- 

 fore is negligibly small. 



The view of the mechanism of far-end crosstalk summation as de- 

 veloped above is illustrated by measurements to be presented in 

 Part II. It may be pointed out here that the measurement of far-end 

 and interaction crosstalk in phase and magnitude on short lengths 

 where equations (15) and (16) hold gives the far-end and interaction 

 crosstalk coefhcients from which the crosstalk in any length of line 

 may be computed provided the propagation constants and impedances 

 of the coaxial and the tertiary circuits are known. 



A practical difficulty may arise from the fact that the application of 

 this method involves equations (12) or (5) where the first bracketed 

 term consists of the difference of two quantities each of which is very 

 large compared with this difference. Thus, a considerable error may 

 be introduced in the computation of this term because of small errors 

 in the measurement of its components. For some cases it is, therefore, 

 better to use a method based on certain crosstalk measurements in a 

 short length of cable with the tertiary circuits open and shorted.^" 

 There are cases, however, where the controlling crosstalk in a five-mile 

 section is predominantly due to the second term of equation (5). 

 One such case is for the crosstalk between diagonally opposite coaxials 

 in a four-coaxial cable. In this case tests have shown that the cancel- 

 lation of components in the first term is so complete that the second 

 term is controlling in five miles. For such a case the more accurate 

 method may be to determine the interaction coefficient from equa- 

 tion (16). 



Near-End Crosstalk 



It will be sufficient here to give simply the final equations for the two 

 crosstalk components for any length /. 



For the component which would exist for two contacting coaxials 

 in free space we have 



--¥-£(^^) 



and for that component due to the presence of the sheath 

 Z„«2 1 r 74^ 1 - e-^yi 



N,= - 



1 r 74^ 1 



-2^44 L 74^ — 7^ 



2Z 4:Zu |_ 74^ — 7^ 27 



74^ 1 - 2€-(T'«+T)' -f t-^y^ 



742 — 72 274 



^° The method described in a companion paper by K. E. Gould. 



(19) 



