HARMONIC PRODUCTION IN MAGNETIC MATERIALS 



765 



Thus suppose a subsidiary maximum to exist at hu as the magnetiz- 

 ing force decreases, the flux density no longer follows the main loop 

 but branches off on a subsidiary loop as indicated by the arrows. 

 When the subsidiary minimum at h^ is reached a new branch is started 

 which completes the subsidiary loop, and which brings the magnetizing 

 force back to the main loop at the point from which it originally 

 diverged, and the main loop is thereafter followed until another 

 maximum (or minimum as the case may be) of the magnetizing force 

 wave is reached. For simplicity in the following we are going to deal 

 solely with a sinusoidal wave of magnetizing force so that subsidiary 

 loops are never called into play. With this understood, the relation 

 between B and H is described by the simple loops of Fig. 2 over a 



Fig. 2 



certain range of magnetizing force, each loop being defined by a 

 particular value of maximum magnetizing force. Each loop may be 

 considered as constituted by two branches which join at the maximum 

 field of the loop. 



It is clear, therefore, that with a periodic magnetizing force having 

 but one maximum and one minimum per cycle, the flux density depends 

 upon three properties of the magnetizing force — the maximum value, 

 the instantaneous value, and the sign of dhjdt, being located on the 

 lower branch when dhjdt is positive, and on the upper when it is 

 negative. Now it is of course evident that when a definite loop form 

 is available, a numerical solution by graphical or step-by-step methods 

 may be had. It is further evident that, in the case of a definite im- 

 pressed magnetizing force, the B-H loop may be broken up into its 



