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BELL SYSTEM TECHNICAL JOURNAL 



where 



Zz — characteristic impedance of tertiary circuit, 

 7, 73 = propagation constants of coaxial Hnes and tertiary 

 circuit respectively. 



This may be rearranged and written (since Z373 = Z33) 



Ft = 



IZ 



X 



2ZZ3 



r It 



2ZZ3 



= X^/(1 - 



^) -l^ 



73 / 1 — e-(T3-7)^ ^ 1 - g-^T- 

 2 \ (73 - 7)- 

 7^ , ^73 



(73 + 7) 



3+7)' \ 1 



73^ 



X 



7'^ 2 

 1 — e-(T3 



-1)1 1 _ p-(T3+7)' 



+ 



(2a) 



(2b) 



(73 — 7)^ ' (73 + 7)^ 



This formula has been found to be applicable, with good accuracy, to 

 the types of coaxial cable which have been studied so far. The quan- 

 tities X and X{\ — ^) are determined from crosstalk measurements on 

 a short length, and the propagation constants are of course readily 

 determined. 



Near-End Crosstalk 



A similar approach to the problem of the near-end crosstalk Nt with 

 the tertiary terminated in its characteristic impedance, using equations 

 (10) and (32) of the Schelkunoff-Odarenko paper, gives 



1 - ^ ^7 



Ni = X 



(1 - e-2>i) 



27 

 + 



2(73^ - 7^) 

 ^73 



(1 + e-2>' - 2e-(^a+^)') 



(3) 



2(73' - y) 



Here, as in the case of equation (2b) above, the crosstalk may be 

 computed readily from crosstalk and impedance measurements on a 

 short sample. 



Interaction Crosstalk 



Far-End Far-End and Far-End Near-End 



We will consider the interaction crosstalk between two adjoining 

 sections of lengths / and /', respectively, the tertiary being connected 

 through at the junction, with no discontinuity. The tertiary current 

 iz{r) at the far end of a section of length /, for unit sending-end current, 

 with the tertiary terminated in its characteristic impedance, is readily 

 formulated as 



Ul) = 77 ^ _ ^ • (4) 



/Z3 73 7 



