666 ELECTRICAL MEASUREMENTS 



To combine the sine and cosine terms, 



[/? T 

 kwt + tan- 1 -p 



C k sin k orf + 



* 

 tan ^ = ^ 



^ is positive if the ascending portion of the component curve 

 first cuts the axis at the left of the origin. 



Harmonic Analyzers. There are other methods of harmonic 

 analysis, 18 but it is evident that the labor involved in such 

 work is very considerable and becomes formidable if an in- 

 vestigation is in hand which requires the treatment of many 

 curves. Cases arise where curves other than those of e.m.f. and 

 current must be analyzed and it is necessary to be able to include 

 both the odd and the even harmonics. Hence the need in 

 practical work of machines by which the analysis may be 

 effected. References to descriptions of a number of these 

 harmonic analyzers are given at the end of this chapter. 



A simple form of harmonic analyzer, particularly designed 

 for electrical engineering work has been described by Chubb. 11 

 Its action may be explained as follows. 



On page 650 attention was called to the fact that the exact 

 expressions for Ak and Bk are 



A k = - I /(0) sin k0 dO 

 ir Jo 



and 



Bt = i f 7, 



7T JO 



I /(0) cos kO dO. 



7T Jo 



Referring to Fig. 415, if the point P be given a displacement 

 along the horizontal axis always equal to /(0), and if at the same 

 time it experiences a perpendicular displacement always propor- 

 tional to sin (kO), then 

 x=fO 



y = R sin kO, where R is the maximum displace- 

 ment along y, 



dy = kR cos kO dO 



