CROSSTALK IN COAXIAL CABLES 345 



In the adjoining section, with the tertiary terminated in its char- 

 acteristic impedance, the tertiary current ^3(3') will be given by 

 i3{l)e~'*^y, where y is the distance measured from the junction of the two 

 sections. 



This tertiary current H{y) will produce a far-end current in the 

 disturbed coaxial of 



Z\, e-y' - e-y^' f ,,, -J 



Tw- e-T3Ve-7(i'-!/)(^3,. 



4ZZ3 73 - T Jo 



The equal-level far end-far end interaction crosstalk FF, being this 

 far-end current divided by e~'i'^'+''\ may be obtained as 



PP = o/^^^' N2 (1 - e-^^'-^^0(l - e-^y^-y^^'). (5) 



2(73 - 7)^ 



The near-end current in the disturbed coaxial due to the current 

 iziy) is given by 



4ZZ3 73 — 7 Jo 



e—^^ve—ivdy. 



From this the equal-level far end-near end interaction crosstalk FN , 

 being this near-end current divided by e~y^, may be obtained as 



'P^ = 0/ ^^^' 2^ (1 - e-^^'-^^0(l - e-(T3+>)^'). (6) 



2(73^ — 7 ) 



Near-End Near-End 



The near-end tertiary current in the section of length / is similarly 

 formulated as 



iz{^)=f^- -T (7) 



2Z3 73 + 7 



The near-end near-end interaction crosstalk NN is readily obtained, in 

 a fashion similar to that outlined above for the far-end near-end inter- 

 action crosstalk, as 



^^ = ^^7^T^(1 - e-^y^-^y^'){\ - g-(>»+7)^'). (8) 



2(73 + 7) 



Tertiary Short-Circuited 

 The general case of the crosstalk between coaxial lines of length / 

 with the tertiary short-circuited at each end may be attacked as follows. 

 At any point at a distance x from the sending end, the voltage gradient 

 along the outer surface of the outer coaxial conductors, for unit sending- 

 end current, will be Zue^y". Each differential element, Zi^e-y'dx, of 

 this voltage drop will produce a current in the tertiary circuit de- 



