232 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 

 and the complete tap voltage is 



e t =q\E\ sin [sin ut+faqs sin (3W/+03+TCO)) 

 P 



+595 sin (5o)/+6 5 +xw)+etc.] . (13) 



The root mean square tap voltage is then 



sn - 



t 



V2 P 



and the ratio of brush to tap voltage is 



_ _ w v t i-r-gfa3-r-6Va5-rT a 7-rc^. > t \ 



^ ~g~- ^r~ / . - . .- o .-r-o ^=^> V 1 ^-' 



/>' 



or 



(16) 



gi sin ^7 



when 



/_ii_ ii_ ii_ i _i_ \ 



d7) 



THREE-PART POLE 



With a normal flux distribution, or with a three-part pole sym- 

 metrical distortion, the q h 's are zero, q\ = i and gm = gam. The denomi- 

 nator of K Q is nearly unity, always a little greater. The numerator 

 may differ considerably from unity on either side, according as the 

 q,'s are positive or negative, slightly less than unity for undistorted 

 flux distribution. Thus K M will be slightly less than as given by the 

 usual approximate formula. Any variation in the g a 's, due to a sym- 

 metrical distortion, causes a variation in the voltage ratio, but also 

 in the harmonics of the tap E.M.F.'s. 



The relation between these two changes is shown in Fig. 32 for 

 the 180 E.M.F., and for the third, seventh, eleventh, and seventeenth 

 harmonics, each being taken separately. 



