HARMONIC PRODUCTION IN MAGNETIC MATERIALS 



781 



than the circuit resistance at the fundamental frequency, and consider 

 the case of an input transformer in which the secondary is practically 

 open-circuited. 



Case 4 — ^Input Transformer. In accordance with the above assump- 

 tion the fundamental current through the coil is determined by the 

 coil reactance x or 



d 



Putting this in (45), we find 



17 . 1 «02 



(50) 



which is identical with Equation (49). 



In the four cases treated above it has appeared that there are three 

 quantities which characterize the modulating properties of a ferromag- 

 netic coil under different conditions — a^ily., 002/^^'^, do^/iJr- The values 

 of these ratios have been determined for a number of materials and are 

 tabulated below. 



These results apply only when eddy currents are negligible; as the 

 frequency is raised eddy currents effectively screen the core and the 

 harmonic flux is reduced to a greater extent than is the fundamental. 

 This effect, as is well known, depends upon the specific resistivity of 

 the core material and will not be evaluated here. 



It has been pointed out that under different circuit conditions an 

 index of the modulation is given by the ratios Gos/mi ^02/^^'", 002/^^, 

 depending upon specific conditions. For diluted materials, these ratios 

 referred to the undiluted material become 



a 02 



^02 



X \2 



fllO ( 1+^^10 



aio ( 1 -|- 7-flio 



3/2 



02 



aw 



1 +7«io 



and the utility of air-gaps toward the reduction of harmonic is made 

 evident quantitatively in every case. 



In order to test these relations a comparison was made of the 



" Laboratory specimens. 



