HARMONIC PRODUCTION IN MAGNETIC MATERIALS 789 



amplitude and phase angle in their relation to the fundamentals 

 producing the distortion. 



A situation somewhat analogous to the one under discussion which 

 is less involved, however, is found in the diffraction of light, in which 

 the illumination at a point proceeds from a number of coherent sources 

 at various distances from the point. An important difference in the 

 two cases is the attenuation of the transmitting medium which is 

 ordinarily small in the optical case, so that the results of the optical 

 investigations cannot be taken over directly. 



In the following we propose to calculate the third harmonic output 

 currents with the aid of our previously established relations. The law 

 of harmonic production has been quite definitely established in the 

 low frequency-low flux density range. The driving third harmonic 

 voltage of frequency 3/ produced by a fundamental current of rms 

 value / is given by (25) and (26a) as 



£3 = 0.72 X \Q-^aJ-^JP = MP, (75) 



while the phase angle of the third harmonic generated potential is 

 related to that of the fundamental current by the expression 



^3 = 3^1. (76) 



The above data are sufficient for a solution of the problem of distortion 

 in continuously loaded lines when the propagation constant is known 

 as a function of frequency. 



The fundamental current at any point distant x from the sending 

 end of the continuously loaded, properly terminated line is 



/ = /o6-^-, (77) 



where 



P = a+i/3. 



The third harmonic driving e.m.f. dEz generated in a length dx of 

 the line may be written with the aid of (75), (76), and (77) as 



dEz = MIo~e-^-"+''^^^. (78) 



Writing the line impedance as Zo, the resulting current at x is 



dh =m^e-^<^+flP^\ (79) 



With the line parameters a function of frequency we may write for the 

 propagation of third harmonic current 



iz = Ize-^-'+i^^'. (80) 



