80 



BELL SYSTEM TECIIMC.IL JOURNAL 



works are due to Kennelly " and fur their generalized form, as illus- 

 trated in Fig. 18, arc as follows: 



Za = ^^ 



Za'Zb 



Za'+Zb' + Zc" 

 ZaZc 



ZB = yr-, 



Zb'Zc 



Za'+Zb'+Zc 



y Zc=. 



Za 'Zc 



-n (65) 



/:^'=Z,+Zc+^,ZB'=Z.i+ZB+'?^,Z'c = ZB+Zc+^^f^. (66) 



ZA'^-Z^^Zd 

 ZbZc 

 Za 



We shall discuss here only two of the principal reactance meshes of 

 the T and ir form, namch', those employing solely inductances and 



La Le Lb' 



-o o 



-o o 



Fij;. !*> — Ktiuivalent rand t Inductance Networks and Equivalent Tand ir Capacity 

 Networks 



solely capacities. It is to he understood that where\er an intluctance 

 or a capacity mesh of an\- of the following types occurs, its variant 

 network may be subslitutwl for it without change in the electrical 

 characteristics of the circuit excluding those conditions within the 

 mesh or its variant. Fig. 19 illustrates equivalent T and it networks 

 of inductance and capacity." The formulae relaling ihc iiidiictance 

 and capacity meshes of Fig. 19 are as follows: 



La'Lb' t Lb'Lc r _ La'Lc 



La = 



La'+Lb'+U" 



Lb = 



La' + Lh' + U" 



Lc = 



La'+Lb'+Lc 



-,- (67) 



" Kennelly, A. K., "The lu|iiivalence of TrianRJes and Tliree-I'oinlc<l Stars in 

 (cindiictinK .Networks," ElfftrUal World mid Engineer, New York, Vol. XXXIV, 

 No. \1, |>|i. 41.i 41-J, S-|>t. 1(1, IX'W. Also, ".Xpiilication of Hyperbolic Functions to 

 Elitlrical KngineeriiiK" (I'M 1 1 (.\p|>endix K). 



" These meshes arc rJKorously couivalent, even when resistance is present if the 

 ratio d i» the same for all of the inductances and if the ratio d' is the same for all of 

 the ca|>acitiea. 



