784 BELL SYSTEM TECHNICAL JOURNAL 



magnetizing force 



Hnet = — 2 — Yo ' ^ -^ 



in which the reduction factor appHed to the force due to the primary 

 alone is seen to be the ratio of resistance to reactance in the secondary 

 circuit. 



This equation with the aid of (56) may now be put in terms of the 

 primary voltage — a fixed quantity — rather than in terms of the 

 primary current which is variable according to the circuit resistances 

 used. Applying the assumptions (59) and (61), Equation (56) may 

 be written 



ii = E/iR, + Ro/K'-), (56a 



which may be put in (60a) to express the net force explicitly in terms 

 of the circuit constants: 



^ OAn^E / 1 \ (.^. 



^^"'" dX, V 1 + K'Ri/Ro I ^ ^^ 



In view of (58). When the transformer is terminated in its normal 

 resistances the expression within parentheses reduces to the value one- 

 half. It is of interest in this connection to compare the field here with 

 that produced with the secondary open ; in the latter case it is clearly 



OAniE/dXi, 



which is twice as great as the field in the properly terminated trans- 

 former. This result is otherwise evident, for in the properly termi- 

 nated transformer but half the generator voltage is applied across 

 the primary. 



Third Harmonic. According to Equation (28) the amplitude of 

 third harmonic voltage generated in a coil of n turns encircling a core 

 subjected to a magnetizing force of Hnet gilberts/cm is 



£3 = A \0-^ao2pnAH\,t (63) 



and the generated primary or secondary voltage is obtained by attach- 

 ing appropriate subscripts to n. Because of the coupling, the two 

 circuits leact on one another at the third harmonic frequency as they 

 did at the fundamental frequency, and to find the two third harmonic 

 currents we must go through a procedure analogous to that followed 

 for the fundamentals except that here we have an independent 

 generator voltage effective in each of the two windings. 



Indicating quantities referring to the third harmonic frequency 



