CROSSTALK IN COAXIAL CABLES 343 



impedance per unit length between any coaxial line (in the presence of 

 the other coaxial lines) and the tertiary circuit consisting of all of 

 the coaxial outer conductors with return by way of the sheath or other 

 tertiary conductors, we will designate by Z13. 



If we consider the crosstalk between two coaxial lines of length, I, 

 such that the coaxial lines and the tertiary are electrically short, each 

 coaxial line being terminated in its characteristic impedance Z and the 

 tertiary open at each end, the crosstalk (near-end and far-end being 

 identical for such a length) is given by 



IZ ' 



If, now, we consider a case similar except that the tertiary is short- 

 circuited at each end, the crosstalk is the above term plus the effect 

 of the tertiary current /a, which, for unit current in the disturbing 

 coaxial line, is given by 



T — ^^^ 

 -tS — 1^ , 



where Z33 is the series impedance of the tertiary circuit per unit length. 



/ Z"^ I \ 

 This tertiary current will produce a current ( — -„3,^ ■ j in the dis- 

 turbed coaxial line and the total crosstalk will be 



Z12I Z'lzl 



IZ 2ZZ3 



Z12 



If we designate -pr^ by X and -^ — ^— by ^, then, for an electrically 

 2.Z Z12Z33 



short length, X will represent the crosstalk per unit length between 



two coaxial lines with the tertiary open, and X{\ — ^) the crosstalk 



per unit length with the tertiary short-circuited. In the formulas 



developed below these quantities will be found to be of fundamental 



importance. 



Tertiary Terminated in its Characteristic Impedance 

 Far-End Crosstalk 



From the Schelkunoff-Odarenko paper, the sum of the direct far-end 

 crosstalk (eq. 19) and the indirect far-end crosstalk (eq. 40) for any 

 length under these conditions gives the total far-end crosstalk Ft, as 



F, = ^''^ 



lysl 1 - e-(T3-7)i 1 _ e-(r,+7)« 



2Z 4ZZ3 L 73' - y (73 - 7)' (73 + 7)"' J 



;i) 



