RECTIFYING DEVICES 369 



be, on the brushes, a uni-directional e.m.f. If a load circuit 

 is connected to the brushes, c-c. power will be supplied to 

 this load. As the amount of c-c. power output increases, 

 the a-c. power input will correspondingly increase in 

 fact, the input on the a-c. end must always equal the c-c. 

 output plus the losses in the machine. The speed remains 

 constant (at synchronous speed for the machine considered 

 as a synchronous motor) irrespective of the load. 



Continuous Voltage Independent of Load. The value 

 of the continuous voltage is nearly independent of the 

 load provided the alternating voltage is maintained constant; 

 this point is covered more completely by saying that, for 

 any converter, the ratio of the alternating voltage to the 

 continuous voltage is a constant. Moreover, this ratio 

 is independent of the field current, the frequency of the 

 a-c. supply, and the size of the machine; it depends only 

 on the number of phases for which the winding is tapped 

 on the a-c. end. 



A three-phase converter has one ratio and a single- 

 phase converter has another, but the ratio for all three- 

 phase converters is the same, independent .of size or fre- 

 quency. The value of this ratio for different phases will 

 now be derived. 



113. Voltage Ratio and Its Dependence upon the 

 Number of Phases. Suppose a converter winding con- 

 sists of only twelve coils in a bipolar field, as shown in Fig. 

 241, and that each coil has the same number of turns and 

 each is spaced from its neighbor by t l 2-X360 = 30 . The 

 derivation of the voltage ratio depends upon the assumption 

 that each coil generates a sine wave e.m.f. and hence, that 

 the e.m.f. of each coil may be represented by a rotating 

 vector. 



Vector Diagram for the E.M.Fs. of Different Coils. The 

 vector diagram for the e.m.f. generated by each coil is given 

 in Fig. 242; all the vectors are of the same length and each 

 is spaced from its neighbor by 30. Now we know that 



