VOLTAGE RATIO IN CONVERTERS 237 



rotary UfiiiL; raised to a high voltage by means of a step-up trans- 

 loniu T, and at tho far end transformed down and fed into another 

 rotary converter. 



The general principles underlying the construction of a rotary 

 converter have already been briefly considered in 39. We shall 

 now study it somewhat more in detail, and shall, in the first place, 

 investigate the voltage relations on the alternating- and continuous- 

 current sides. 



. Voltage Ratio in Converters 



If we assume the space distribution of the magnetic flux to follow 

 the sine law, then the e.m.f. induced in each coil of the armature 

 winding will be a sine function of the time. The sine wave e.m.f.'s 

 induced in the consecutive coils will differ in phase by a constant 



amount, represented by the phase angle -, c being the number of 



c 



coils per pole-pitch. These e.m.f.'s may, in a vector diagram, be 

 represented, as in Fig. 147, by a series of radial vectors of equal 

 length and spaced at equal angular intervals apart, eacli angular 



interval amounting to-. In order to find the resultant alternating 



C 



e.m.f. between any two points of the winding, 

 we have to add vectorially the e.m.f.'s of all 

 the coils included between those two points, 

 using the construction known as the polygon 

 of vectors. Thus, taking two points which 

 correspond to a span equal to the pole-pitch, 

 and thus embrace all the coils whose e.m.f. 

 vectors in Fig. 147 are included between A and 

 B, we get the open polygon OQP of Fig. 148, 

 the closing side OP of which is the resultant 



,. , ., ., , Tr rlG. 14/. \ectorDiagrnm 



e.m.i. ot the group of coils considered. If O f e.m.f.'s in Consccu- 

 cach of the vectors be taken to represent the tive Coils. 

 maximum value of the alternating e.m.f., then 

 the vector OP in Fig. 148 will represent the maximum value of the 

 e.m.f. in a group of coils included within a pole-pitch ; but this is 

 evidently equal to the continuous e.m.f. between two brushes. For 

 any smaller group of coils, such as that represented by the vectors 

 included between A and C in Fig. 147, we get for the maximum 

 value of the e.m.f. a vector OQ (Fig. 148). 



Now if as is generally the case the number of coils between 

 two brushes is considerable, the regular polygon (OQP in Fig. 148), 



