VEKXIER RESOLVER 1493 



To obtain the voltage induced in the output coils, the flux amplitude 

 for each pole-shoe must be established. Defining the electrical angle of 

 the rotor, de , as its mechanical angle multiplied by its number of teeth 

 and choosing de to be zero when the center of a rotor tooth lines up with 

 the center of pole-shoe No. 0, one can write for the flux amplitudes 

 00 through 09 of pole-shoes No. through No. 9: 



00 = .4u + Ai cos de + A2 COS 26 e A- ■ • • 



01 = Ac + Ai cos (de - ae) + ■•• 



(8) 



09 = .4o + Ai cos {de - 9oie) + 



where Ao , Ai , A2 ,. . . . are the Fourier Components of 0. 



The amplitude, Ec , of the voltage induced in the cosme winding is 

 the sum of the products of the pole-shoe flux, 0^ , measured in [volt sec] 

 and the coil turns, tc^ , multiplied by the exciting current frequency in 

 radians per second, w: 



9 

 Ec = 0)^ (i>vtcv . (9) 



Substituting the \'alues of 1,.^ and 0;, from (6) and (7) and neglecting all 

 higher order Fourier components of 0, one obtains 



Eo ^ — wAi cos de . (10) 



Similarl}'- one obtains for the amplitude E^ of the sine voltage : 



Es = wAi sin de . (11) 



As required, the two induced secondary voltages are proportional to 

 the cosine and sine of the electrical rotor angle. 



As shown in the appendix, an analysis which takes into account the 

 higher order Fourier components of the pole-shoe flux shows that a 

 sinusoidally distributed Avinding is sensitive solely to the so-called slot- 

 harmonics. The order "m" of these harmonics is given by the expression 



m = A-g ± 1 (12) 



where "/c" is any integral positive nvnnber and q is the number of pole- 

 shoes divided b}^ the largest integral factor common to the number of 

 pole-shoes and the number of rotor teeth. For instance, in the case of a 



