f.I.F.CTRlC CIRCllT TIJr.ORY 3.19 



terminal due to the terminal irregularity which exists there. The 

 third term is a reflected \va\e from the sending end terminal, etc. 

 The solution is therefore a wave solution and is expanded in a form 

 which corresponds exactU' with the scriuence of phenomena, which it 

 represents. 



The solution takes a particular!}- instructi\e form when Zi = k[K 

 and Z'i = k-iK where ki and k'^ are numerics. Then 



1 + ^1 



1 l-k. 



(249) 



and 



1 l-ko l^ki 



1 I «-vW+f^;«2.-.v(/) I. 





J 



If ^1 = 0, ^2 = 1 we ha\'e the case of the e.m.f . impressed directly on the 

 sending end of the line and the distant end closed through its char- 

 acteristic impedance; the solution reduces to 



^1 ,-(/)= a v(0 



as, of course, it should be by definition. 



If ^1 = and ^2= "^ , we have the case of the line open-circuited at 

 the distant end, and the solution reduces to 



A,{t) = ■ a,{t)-a2s-x{t) -a2s+x{t) +a,s-.y(t) +...';. (251) 



Finally, if both ^i and ^2 are zero, the line is shorted and 



^.v(/) = ■) «.v(/) -\-a2s-,{t) +a25+.r(/) -\-ais-x{t) -\- ■ ■ .\- (252) 



The operational equations (247) admit of further interesting and 

 instructi\-e physical interpretation without computation. Consider 

 a circuit consisting of an impedance Zi in series with an impedance 

 K. Let a unit e.m.f. be applied to this circuit and let Vo be the re- 



