A LADDER NETWORK THEOREM 



311 



impedances of legs 1 and 4 and of the crossbar. The current expression 

 follows from equation (2) with I2 = Is = 0; — Ii = I4 = E/Zq. 



For multiple generating points (or for multiple points of short 



A . Short Circuit Between Generator Points 



_[<5>- 



KS>L 



j<I>^ 



Z|'3':i'4' = Z'+v2(Z|'2':i'2.-Z|'2':3'4')-v (l-v)(Z3.4':3.4'-Z,'2':3'4') 



_cd>j> 



B. Short Circuit Beyond Generator Points 



_E7a>-| 



A4' 



^(Z34:34~Z|2:34) 



El 



j-a> 



1 Z|3:i4 



(l-l')Z34:34+l^Z|2:34 



yZ,'2':l'2'+0-l')Zi'2':3'4' 

 Zr4':2'4' 4' 



(l-v)(Z|'2':i'2'-Z|'2':3'4') 



"1 



Z|'4':2'4' = Z'-v(l-v)(z,'2':i'2'-Z|'2':3'4') + ('-v)^ (ZsU': 3'4' -Z,'2': 3'4') 

 Fig. 3 — Equivalent networks for electrified railways; two-wire system, two sources. 



circuit) the theorem may be used to represent portions of the network. 

 Examples for the case of two generators are shown on Fig. 3 ; on Fig. diA 

 the short circuit is located between generator points, on Fig. SB beyond 

 them. On Fig. ZA the network is supplied with duplicate pairs of 

 terminals at the short-circuit point, separated by an infinitesimal 



