764 



BELL SYSTEM TECHNICAL JOURNAL 



a function of its previous history as manifested in the phenomenon 

 of hysteresis. This comphcates matters to an extent far greater than 

 is the case with other circuit elements, and some analysis has been 

 carried out in which the hysteresis loop has been replaced by the 

 normal magnetization curve, or by some such single valued relation 

 between the variables. For some purposes this convenient simplifica- 

 tion — it cannot be called a close approximation for our present pur- 

 poses — is satisfactory, while for others it does not begin to tell the story. 

 Inasmuch as our aim here is to deal with the actual phenomena 

 involved rather than to arrive at some arbitrary procedure for repre- 

 senting the facts, we shall in the following base considerations upon 

 the hysteresis loop. 



Fig. 1 will serve to illustrate the effect of previous history upon 

 flux density. The main loop there, which extends between the two 



Fig. 1 



limits of magnetizing force — // and //, is obtained when the magne- 

 tizing force is varied cyclically between those two values in such a 

 way that the magnetizing force has but one maximum and one mini- 

 mum per cycle. In that case the B-H loop is traversed in the direction 

 shown by the arrow. It is independent of frequency when the eddy- 

 current losses in the iron are small, as we shall suppose them to be, 

 and it is independent of the wave form of the magnetizing force so 

 long as that wave form satisfies the condition we have laid down above. 

 A sinusoidal magnetizing force, for example, satisfies that condition. 

 When the magnetizing force contains components of such magnitude 

 and phase that the wave form has multiple maxima or minima, the 

 simple B-II loop no longer suffices to represent that relation, but 

 auxiliary loops shown in the figure are involved. 



