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BELL SYSTEM TECHNICAL JOURNAL 



The attenuation and phase constants of each of these two sections 

 and the combined structure are shown in Fig. 9, as a function of 

 Li2i^l2R, where Ru = R. It will be seen that Ai and A2 are comple- 

 mentary while Bi and B2 are equal but opposite. For the composite 

 network Ac = constant and Be = 0; thus the latter phase constant 



I 



Fig. 9 — Propagation constants in distortionless network. 



has a zero slope with frequency. Whatever steady periodic voltage 

 exists at one end would appear across the terminating resistance R 

 in the same phase but attenuated by an amount Ac napiers. Since 

 these conditions hold for the composite network at all frequencies, we 

 should expect to obtain for it an indicial voltage and time-of-trans- 

 mission, respectively, 



g,{t) = e-^", 

 and (57) 



_Br _ dB, 

 CO dio 



0. 



Let us next determine the indicial voltages of the individual sections 

 when each is closed by a resistance R. Substitute the operator p for 

 icj and obtain symbolically from (54) and (56) 



