212 ADVANCED ELECTRICITY AND MAGNETISM. 



118. Reflection. For the sake of brevity and clearness we 

 will discuss only the reflection of rectangular wave pulses, and 

 such a wave pulse will be represented by a single heavy hori- 

 zontal arrow. When such a wave is turned back or reflected 

 at the end of a line, the heavy arrow will be shown as turned 

 back as in Figs. 148, 149 and 150. The voltage and current 

 in the original wave are represented by E and / and the 

 voltage and current in the reflected wave are represented by 

 E r and I r as shown. 



Reflection from open end of line. The doubled arrow in Fig. 

 148 represents a wave which has been turned back or reflected 



wire 



open end 

 wire <> f line 



Fig. 148. 

 ; Showing a rectangular wave pulse partly reflected from the open end of a line. 



at the open end of a transmission line. The necessary condition 

 which must be satisfied at the open end of a line is that the actual 

 current there be zero. Therefore we have: 



/ + I r = o (i) 



In addition to this we must have: 



E 



and 



f = - >/i (3) 



Now the voltage and current in the original wave are supposed 

 to be given and the voltage and current in the original wave do, 

 as a matter of course, satisfy equation (2). From equation (i) 

 we have: 



