368 



BELL SYSTEM TECHNICAL JOURNAL 



section and propagated along this circuit into the next section and 

 thence into the disturbed coaxial. Except for interaction crosstalk 

 between sections the total crosstalk in 21 would simply be twice that in 

 length /, that is, the crosstalk would be directly proportional to length. 

 Now, the expressions for far-end crosstalk due to such interactions 

 between two sections each of length I are 



F = 



74 



4Z 4Z44 



Zgg^ 74 



4Z ■4Z44 



r 1 _ f.-(y,+y)l 1 



L 74 + 7 J 



r 1 - e-(7,-7)n i 



L 74-7 J 



(8) 

 (9) 



Since the coefficients ^ outside of the brackets are the same for Fnn 

 and Fff the terms may be combined to give the total interaction cross- 

 talk between the two sections, namely. 



Fnn -\- Fff 



IZ 



74 / 74^ + 7^ 



L 4Z44 \ (74^ - 7')' 



74 



4Z44 



+ 



+ 



(74 - 7) 



74 / e 



(74 + 7)- 



-2(74-7)i e-2(74+7)i 



+ 



4Z44\2(74 - 7)- 2(74 + 7)=^ 



(10) 



As mentioned before, the crosstalk in length 21 exclusive of interactions 

 between the two sections is equal to 2Fi or equation (5) multiplied by 2, 

 namely, 



2Ft 



(11) 



The total crosstalk in length 21 is then the sum of (10) and (11), 

 namely, 



F21 = 2Fi + F„n + Fff = 



+ 



74 / 74^ + 7^ 



4Z44V(74='-V)2 



2Z 



74 

 4Z44 



21 



Z33 



74'' 



2/ 



4Z44 74^ — 7^ 



p-2(74-7)' 



2(7. 



7)'^ ^2(7 



Hyt+y)l \1 



(12) 



• These near-end near-end and far-end far-end coefificients are equal because the 

 coupling through a coaxial is of a series voltage character. In open wire and non- 

 shielded cables where there is also present coupling due to shunt admittances the 

 coefficients for Fnn and Fff are difTerent in magnitude and their effects must be 

 considered^separately. See paper by A. G. Chapman in Bell Sys. Tech. Jour, for 

 January and April, 1934. 



