ELECTRIC CIRCUIT THEORY 65 



CHAPTER VII 



The Propagation of Current and Voltage Along the 

 Transmission Line 



We now take up the more important and difficult problem of 

 investigating the propagation phenomena in the transmission line. 

 The transmission line has distributed series resistance R and in- 

 ductance L, and distributed shunt capacity C and leakage conductance 

 G. It is the addition of the series inductance L which makes our 

 problem more difficult and at the same time introduces the phenomena 

 of true propagation with finite velocity, as distinguished from the 

 diffusion phenomena of the cable problem. The cable theory serves 

 very well for the problems of trans-oceanic telegraphy * but is quite 

 inadequate in the problems of telephonic transmission. 



If / denotes the current and V the voltage at point x on the line, the 

 well known differential equations of the problem are: — 



Replacing d/dt by p, these become 



{Lp+R)I= -i-V, 



(195) 



{Cp-\-G)V= -i-I. 



h 



dx 



(196) 



From the second of these equations 



dx Cp+Gdx' 



and substitution in the first gives 



I 



{Lp+R){Cp+G)I = ^L (197) 



Similarly if we eliminate I, we get 



{Lp+R){Cp+G)V=^V. (198) 



8 With the installation of the new submarine cable, continuously loaded with per- 

 malloy, this statement must be modified. In this cable, the inductance plays a very 

 important part, and is responsible for the greatly increased speed of signaling ob- 

 tainable. 



