HARMONIC PRODUCTION IN MAGNETIC MATERIALS 771 



may be obtained with the aid oi AC bridge measurements under 

 appropriate conditions for which eddy currents and winding capacities 

 are unimportant. These measurements are of a higher order of 

 precision than those obtained by the ballistic method, and will be 

 treated in detail in the next section. 



Part 2. Alternating Magnetization 

 Sinusoidal Magnetizing Force. The same magnetic characteristics 

 which were the subject of the investigation of the last section are 

 involved in alternating magnetization when the applied field has but 

 one maximum and but one minimum per cycle, and when the eddy 

 losses are not great enough to introduce screening effects. As one of 

 the results of that investigation, we have arrived at equations for both 

 the upper and the lower branch families, so that to obtain an expression 

 for the flux density valid over the entire cycle, it is now necessary to 

 combine the two branches by a Fourier's series in the usual manner. 

 Before doing this, however, it is necessary to express the branch 

 equations for the flux density in terms of time, rather than as series of 

 powers of the independent variable, the magnetizing force. To do 

 this we substitute the equation for the magnetizing force ^ 



h = H cos pt (18) 



in the branch equations (4a) and (5a) of Part 1. The result of the 

 substitution is to give the upper and lower branch flux equations in 

 terms of powers of cos pt, which may be expressed in terms of multiple 

 angles. These two equations are then combined in a Fourier series 

 which is valid over the entire cycle: 



5 = ^ + ^ (6fc cos kpt + ak sin kpt), 



in which the coefficients are given by the usual expressions, equation 

 22a of Appendix 3. The coefficients &o, &2, • • • h-ih, ao, ao, • • • a-^k are 

 found to be identically zero on account of the symmetry of the loop 

 family about the origin, while the fundamental and third harmonic 

 coefficients are found to be as follows: 



hi = aioH + auH- + (an + fa3o)i^^ 



o 



^3 = - 7Y- (aooH- + aozIP), 



(25) 



63 = a3oi/V4. 



* The purely sinusoidal magnetizing force may be obtained, despite the varying 

 reaction of the iron core coil, by connecting a generator through a low pass or band 

 pass filter having a high impedance outside the pass band, or by connecting a pure 

 sine wave generator to the coil through a high impedance. 



