HARMONIC PRODUCTION IN MAGNETIC MATERIALS 779 



This equation may be solved for <p by identifying coefficients when we 

 substitute the solution 



T S '' 



which is equivalent to 



Biji, II) = Y^HaJIfll^ (41) 



T S 



Carrying out the operations, the primed coefficients are determined 

 in terms of the original coefficients and the core structure as follows: 



aid' = aio I 1 +Ta]o j, 



ao2 = — a2o = ao2 /( 1 +7-aio ) , (42) 



a-u' = flu / ( 1 +Taio j • 



It is clear that the effect of an air-gap is to diminish the higher 

 order coefficients to a greater extent than those of lower order; no 

 new coefficients are introduced. If we refer to a constant flux density, 

 then the impressed force is 



H' = Il(l+jaro) (43) 



and the modulation voltage becomes proportional to 



ao2lI^ 



0-02 H 



1 a_^ 



1 +T-aio 



so that the harmbnic e.m.f. has been reduced in the ratio of 1 + v flio 



to unity, which is precisely the ratio of initial permeabilities. 



Dilution. If the magnetic material is diluted with a non-magnetic 

 substance (insulation) so that the effective air-gap length is X, the 

 above equations for the flux density still hold. The effective cross- 

 sectional area, however, is reduced to 



A' = A(^-^y, (44) 



which is ordinarily of small account compared to the other factors 

 involved. 



Choice of Core Material. The ideal characteristics for a core ma- 



