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BELL SYSTEM TECHNICAL JOURNAL 



distortionless line can be made to approach as a limit, all three of the 

 electrical elements, resistance, inductance, and capacity, and that the 

 complete solution for the current in a distortionless line can be 

 obtained by adding the incident current and the sum of the reflected 

 currents which can occur up to the time of interest. That is the dis- 

 tortionless line has a true velocity of propagation, and hence the 

 current at any time will be the initial current and the sum of the 

 reflections which can occur up to the time of interest. All of the 

 three electrical elements, resistance, inductance, and capacity, can be 

 considered as limiting cases of the distortionless line. Hence the 

 process of solution consists in solving for the current in the distortion- 

 less line, and then proceeding to the limiting value of the line which 

 coincides with the element of interest. 



r 



r 



T 



r 



Fig. 1-A. 



I 



r 



L 



r 



T 



Fig. 1-B. 

 Diagrammatic representations of lines. 



A . The Distortionless Line 



Since the distortionless line is the tool by means of which problems 

 are solved by this method, a brief discussion of lines ^ is given here. 

 If a voltage is suddenly applied to a transmission line, the current 

 at any point in the line is zero for a certain time and then begins to 

 build up to its final or steady state value. If there is no distributed 

 inductance in the line, the current begins to build up immediately. 



For a distortionless line, however, the current is zero for the time 

 required to propagate the wave to the point of interest and then 

 instantaneously reaches its steady state value. To show this let us 

 consider the equations for a transmission line. A line has distributed 



^ For a more complete discussion of lines see "Transmission Circuits for Telephone 

 Communication," K. S. Johnson, page 144. 



