HARMONIC PRODUCTION IN MAGNETIC MATERIALS 785 



by the subscripts p, s for primary and secondary circuits, respectively, 

 we have the circuit equations for the third harmonic currents: 



ep = Zpip +j3pMi„ 

 Kep = Zds -i-j3pMij„ ^^^^ 



and by equating the two expressions for Cp we obtain a relation between 

 the two currents: 



_ KZp-j3pM 

 "" ~ Zs - jSpMK'"" ^^^^ 



Putting ip in terms of ep, and using (59) and (61) we find 



is = epKRp/RsXpil + K^Rp/Rs). (66) 



Suppose now that we are dealing with pure resistance loads so that 



Ri = Rp, R2 = Rs- 



We may then substitute (63) for ep in (66) to obtain the third harmonic 

 current in the secondary. 

 From (63) 



8 in R . .0.16ni2£2 / 1 \2 



ep = ^^ lO-^a..pn.A -^^^ [ , ^ k^r^,rJ ' (67) 



and by substitution in (66) 



E^KRia 



3X,R2( 1 +^'1;^' 



(68) 



If we consider the factor containing the resistances, 



R2 a-\-K'Ri/R2y 



(69) 



it is zero for R1/R2 zero or infinite, and reaches a maximum under the 

 condition 



The third harmonic secondary current is maximum when 



K'=§_. (71) 



Now K^ is fixed by the turns ratio (58), so that we may say the 

 secondary third harmonic current is maximum when the primary 

 resistance is made half its nominal value, or when the secondary 



