HARMONIC PRODUCTION IN MAGNETIC MATERIALS 783 



The transformer circuit equations from which the currents may be 

 evaluated are the famiHar ones 



E = Ziii + jpMi2, , . 



= Z2i2+jpMiu ^^^^ 



in which we assume the transformer to be an icleaHzed structure — the 

 capacity and leakage effects of actual transformers will be assumed 

 combined with the connected impedances for simplicity — they will 

 therefore not be dealt with explicitly. From the second of (54) is 

 obtained the relation between the two currents 



^'2 = - jpMii/Z2 (55) 



which may be substituted in the first of (54) to give the usual expression 

 for the primary current 



-/ 



R,+P^R,+jfx,-i^X.. 



(56) 



An expression for the net magnetizing force in terms of ii may be 

 had putting (55) and (56) in (53) 



ff„..=5:i^(l_i£|5), (57) 



in which K represents the turns ratio: 



X=^^ = #. (58) 



If we make the convenient assumption, which is closely approximated 

 under working conditions, that the coupling is perfect (no leakage) we 

 have 



pM = ^[]cJcl (59) 



and (57) may be simplified to the form 



-«net = ^ -^ • (OO) 



This equation shows that the net magnetizing force may be obtained 

 from that of the primary alone by applying the reduction factor R2/Z2. 

 Now in well designed transformers the winding reactances are much 

 greater than the resistances to which they are connected, and in this 

 case 



X\2»R\.2. (61) 



Applying this further simplification to (60) we have finally foi the net 

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