ELECTRIC CIRCUITS APPLIED TO COMMUNICATION 



which the solution must meet in the two fields of application that it 

 seems in the past not always to have been made clear to students that 

 the power line equations and the telephone line equations are simply 

 special solutions of the same general line formula. 



To illustrate this point it is desirable to refer to a few well-known 

 equations. The differential equations for what may be called the 

 classical transmission line theory are given in equation 1. Equation 

 2 is a solution of these differential equations for the steady state, for 

 the circuit indicated in Fig. 1. 



^Z = R+JX-> 



Vt 



(I-X) 



Y=G + iB 



Vr 



^°=V? 



lf=YzY 



Fig. 1 



^s+^i^ = 



^5+'^)'' = 



dx 

 A/ 



(1) 



/. = 



Zo+Z, 



1 + 



Zq -\- Zt Zq -\- Zr 



.-27* 



+ 



Zi Zfj Zr 



Zq -t Zt Zq -f- Zr 



Zo- z 



-yl _j_ 



-47* _|_ . . , 



Zq — Zt / Zq 



Zo -T Zr Zq -[- Zi\ Zq -f- Zr 



I I Zq — Zt\ / Zq Zr 



,-37* 



Zq -j- Zt / \ Zq -\- Zr 



57* 



+ 



(2) 



This equation indicates the current flowing at any point in the circuit 



for a given impressed voltage. The solution in this form seems to 



have special educational value because it gives a very clear physical 



picture of what is taking place in the transmission line. As was early 



pointed out by Heaviside, the current flowing in any simple circuit 



such as indicated can be considered to be built up from a directly 



transmitted wave which at the transmitting end has the magnitude of 



Et 

 y — 7 — ^ • This direct wave is attenuated as it is propagated along the 

 ^t "T ■^o 



