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BELL SYSTEM TECHNICAL JOURNAL 



where D is the time of delay in passing the network once. For a dis- 

 tortionless line 



D - VLC. (24) 



Hence, we can replace n by 



/ 



n = 



t 



2D 2VLC 



(25) 



Since D — > and 7i —^ », the time scale becomes continuous. In 

 equation (23) we insert the values given in (16) and (25), appropriate 

 to the limiting case considered here, namely 



P = 



R + ju>L 



R, 



t 



tR, 



Ro ' ' • 2^JLC 2L 



and note that 2P -> so that e^^p _^ i - 2P; then 



Ro 

 = E 



2(1 — g-tRalLl(R+joiL)lRo]\ 



1 - 1 + 2{R+joiL)IR^ 



- 1 



\ g-t(.RlL+joi) 



Ro 



But Rr 



R + jooL 

 °o and hence the solution is 



g-t(.RlL+ju) 



'i' 



R+jcoL 

 This is the symbolic or complex algebra solution of the equation 



(26) 



4,+ Ri = E. 



(27) 



In general it is desirable to obtain the current due to an applied 

 voltage of the form 



E = Eo cos {cot + 6). 



This solution can be obtained directly from the symbolic solution 

 given in (26) by taking the real part. The result is 



i" = £o 



cos (cct-\- e - <p) - COS (d - ip)e-~'^i^ 



(28) 



It will be found that (28) is a solution of (27) for an applied voltage 

 £o cos (o)/ + d). 



