246 



BELL SYSTEM TECHNICAL JOURNAL 



Substitute these values in (15.60) and (15.61) to obtain the coordinates of 

 the center of the circle, PFo, and the radius, <y. 



T^o = 



[(- 



^" +2 

 Co + Cx R 



0-«( 



4 _|_ Co + Cx I tXc3 . M, vxu 



C3 r7^ '^Y^^ 



m 



[} "^ \rJ + Co + C. rJ 



M 



Co 



Co + Cx 



[' - fe) 



^ + 



ilfCo 



(15.80) 

 (15.81) 



Co + Cx Rl. 



From the above expressions, a is not exactly equal to the real component 



T MCo 



of PFo . If however, 2 — - <<C ;:; — , — rr , then the above equations reduce to 



M 



R, 



Co 



Wo 



Co + Cx 



Co + Ca 



C3 



■^i-Cs/ J 



[K-c^.^J] 



(15.82) 



and 



Co "l" Cx Rl 



r MCo "I 



LCo + CxJ 



[ 



2 1 + 



MCo 



Co + Cx R 



fj 



(15.83) 



Now the radius, a, equals the real component of TFo . The per cent error 

 of P.I. resulting from tuning to minimum impedance rather than unity 

 power-factor in terms of Fig. 15.10 is given as, 



Per Cent Error of P.I. = 100 1 



L - pj 



= 100 



/R51 



y-ay 



(15.84) 



Now since 17 represents the imaginary component of (15.82) then 



2a 



= P2 = 



M 



(-l:X 



C3 ^ R, 



:) 



(15.85) 



