34d 



BELL SYSTEM TECHNICAL JOURNAL 



termined by the impedances, Z' and Z" , of the tertiary as seen in the 

 two directions from this point, these impedances being 



and 



Z' = Zz tanh y^x 

 Z" = Zz tanh 73(/ - x) 



(9) 



(10) 



respectively toward and away from the sending end. 



At any other point at a distance y from the sending end, the tertiary 

 current due to the voltage Z\ze~''''dx will be given, for y > x, by 



• ( \ _ Zne~'*''dx cosh ys{l — y) 

 *3W - z' + Z" cosh 73(/ - x) 



(11) 



From this the transfer admittance A{x, y) between these two points 

 is obtained as 



A (x, y) = 



1 



cosh yzil — y) 



Zstanh jzx cosh jz^l — x) -\- sinh yz(l — x) 

 Similarly, for y < x, this transfer admittance is obtained as 



A(x,y) =—-, ^Qs^^ y^y 



Zz sinh jzx + cosh jzx tanh 73 (/ — x) 



The tertiary current, iz{x), is given by 



'I 



izix) = I 

 Jo 



Zize-^«A(x, y)dy 



(12) 



(13) 



(14) 



from which we obtain 

 Z13 



iz{x) = 



2Z3 sinh 73/ 



X 



73 + 



+ 7L 



73 - 7 L 



cosh 73(/ — :t) + e""^' sinh 73/ 



— e~T' cosh 73.r 



cosh 73(/ — x) — e~y'' sinh 73/ 



— e~i'' cosh 73.r 



(15) 



Far-End Crosstalk 



The indirect far-end crosstalk F/ due to this tertiary current (eq. 15) 

 is given by 



F/ = ey^f^^^^ e-y^^-^Ux (16a) 



_ Z'^iz r hz^ 2737" cosh 73/ — cosh 7/ 



2ZZ33 L 73^ — -) 



(73^ - 7^) 



sinh 73/ 



. (16b) 



