152 BELL SYSTEM TECHNICAL JOURNAL 



intermediate circuit with an impedance Z3 and propagation constant 

 per unit lengtli 73. Let the disturbing voltage E be appHed at the A 

 end of circuit (1). Then the current in the section kl is given by the 

 expression similar to (3) 



iki=^^e-yi^dx. (20) 



ZZ1Z.3 



The current in the section pq is 



ipg = ikte-''', (21) 



where 



s = \y - x\. (22) 



The total current in the generic element of the intermediate trans- 

 mission line due to coupling with circuit (1) is, then, 



ly = Cip, = ^^ r e-y^^e-yi^dx. (23) 



In carrying out the process of integration, we must keep in mind that 

 from to y, s = y — X and from y to I, s = x — y. 

 Hence, we have 



e~yz^e~y^Hx = e'^^y \ e^-y^-yO^dx + ey^^ | e~'-y3+yi'>''dx, 



, „ Jo Jv 



and 



^ _ EZ 13 

 ^~2ZiZ3 



73 - Ti 73 + Ti 



(24) 



The elementary electromotive force induced in the second coaxial 



conductor by the current ly is 



f 



Ey = Znlydy. (25) 



The contribution of this electromotive force to the voltage across the 

 near-end of the second coaxial pair will be then 



dVn=\ Eye-y^y = ^ Iye~y^ydy. (26) 



The total induced near-end voltage will be given by the expression 



F„=^ r Zs.Iye-y^ydy. (27) 



