CHAPTER XII. 

 THE ANALYSIS OF ALTERNATOR CURVES. 



Composition of Curves. All curves of current or electro- 

 motive force may be considered to consist of a principal 

 sine wave (called the fundamental], which is the regular 

 curve to which the actual curve approximates, together 

 with other sine waves of smaller amplitude and having 

 frequencies differing from that of the fundamental. 



The frequency of these minor waves will always be 

 some multiple of the frequency of the fundamental, i.e., 

 of the periodicity of the supply. Further, there will be only 

 one sine curve having a given frequency, since two sine 



/ PERIOD 



FIG. 199. EVEN HARMONIC. 



waves of equal period may always be added together to 

 give a single resultant sine wave. These small waves, 

 which have each a periodicity which is a multiple of that 

 of the fundamental, are called harmonics. 



The general expression for a simple harmonic electro- 

 motive force may be written in the form 



e - E sin (2-n-nt + 6) 

 where e = instantaneous value of the electromotive force. 



n = frequency of the alternator. 



t = time counted from any given moment. 



= phase of the voltage at moment from which 

 time is counted. 



E - maximum value of the voltage. 



