458 BELL SYSTEM TECHNICAL JOURNAL 



and 



„ XadRbc XadXbc /rjN 



y^cD = ■ — B ~ — V ■ ^^^ 



For this type it follows from equations (8) and (9) that the com- 

 ponents of ZcD are balanced by components of Zad of the same phase, 

 that is Rad will balance Rcd, and Xad will balance Xcd- 



2. Ratio Arm Type — Ratio Imaginary 

 If Zbc/Zab is imaginary, then 



e = Obc - Bab - ± 90°. 



That is 



Zbc/Zab = JXbcIRab = -JRbc/Xab. (10) 



Substituting equation (10) in equation (5) and separating, 



and 



XadXbc _ XadRbc /■■,.,\ 



KcD = 5 ~" — V ^^^^ 



i<-AB y^AB 



RadXbC _ RadRbC (^rf. 



yi-cD = — n — V ^ ^ 



Kab y^AB 



For this type it follows from equations (11) and (12) that the com- 

 ponents of ZcD are balanced by components of Zad 90° out of phase, 

 that is Xad will balance Rcd and Rad will balance Xcd- 



3. Product Arm Type — Product Real 

 If {ZbcZad) is real, then 



= 05C + Gad = 0° or 180°. 

 That is 



ZbcZad — Zbc/Yad = RbcJGad = — XbcIBad- (13) 



Substituting equation (13) in equation (6) 



and 



GabRbC _ Gab XbC (4 a, 



KcD — — 7^ — B y'-^) 



Ltad -Dad 



BabRbC _ B abXbC (4 c\ 



AcD — ~ — 7=i — n \^^J 



Ltad -Dad 



For this type the components of Zcd are balanced by components 

 of Yab of the same phase, that is Gab will balance Rcd and Bab will 

 balance Xcd- 



