DISTORTION CORRECTION 471 



characteristics for no distortion. Let us obtain the steady-state 

 characteristics of each network and of the composite one; then con- 

 sider transient conditions and obtain the indicial voltages of the 

 corresponding networks to verify again by this illuminating example 

 that the steady-state characteristics laid down for no distortion are 

 quite sufficient when transient conditions exist. 



The first section is Network 2a, Appendix IV, wherein Zw is parallel 

 resistance Ru and inductance L12, with Rn less than 2R and the 

 characteristic 1. Let us put m = RujlR, and n = L12I2R. 

 Then 



Zii imni)} 



2R m -\- inco 

 and the propagation constant formula becomes from (13) 



(53) 



rj ^ m + i(l -\- m)no} ^ , . 



m + i{l — m)nij} 



To obtain a complementary second section let us assume that the 

 total attenuation constant, Ac napiers, of the composite structure is 

 to equal the maximum of the first section which occurs at infinite 

 frequency. Then from the above 



,Ac = 



1 + w 

 1 — w 



and tanh (^c/2) = m, giving as the correcting section by (44) one of 

 Network lb, Appendix IV, with characteristic 1 in which 



Rn = 2mR, as in (53), 

 and 



(1 — m?)n 



^'' ~ 2m'R 

 For this second section then 



2ll 



?^1 -1 



Rn 



Li2 



IR' 



(55) 



2R m -\- i{l — m'^)no} 

 and 



1 -\- 7n\ / m -}- i{l — m)nu 



1 — mj \m -\- i{l + rn)nw 

 Obviously, from (54) and (56), 



(56) 



1 — m ' 



as was assumed. 

 31 



