ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 213 



Ir= -I (4) 



and from equations (2) and (3) we have: 



E r = + E (5) 



Reflection at the open end of a line is complete and it takes place 

 with reversal of current. 



Reflection from short-circuited end of line. The doubled 

 arrow in Fig. 149 represents a wave which has been turned back 



wire 



short-circuited 



wire end of line 



Fig. 149. 



Showing a rectangular wave pulse partly reflected from the ghort circuited end 



of a line. 



or reflected from the short-circuited end of a line. The necessary 

 condition which must be satisfied at the short-circuited end of a 

 line is that the actual voltage across the end be zero. Therefore 



we have: 



E + E r = o (6) 



whence 



Er = - E (7) 



and, since equations (2) and (3) always apply, we get: 



/,--+'/ (8) 



Reflection at a short-circuited end of a transmission line is com- 

 plete and it takes place with reversal of voltage. 



Reflection from a non-inductive circuit connected across the 

 end of a transmission line.* The doubled arrow in Fig. 150 

 represents a wave which has been turned back or reflected from 



* Reflection from inductive circuits is discussed in a paper by W. S. Franklin, 

 Proceedings American Institute of Electrical Engineers, April, 1914. 



