222 



BELL SYSTEM TECHNICAL JOURNAL 



Further information on hysteresis loss is obtained from measure- 

 ments of harmonic voltages generated in the coil winding when there is 

 current /i of frequency /. It has been shown ^ that the third harmonic 

 voltage for materials with Rayleigh hysteresis loops is 



£3 = 0.6 aB„iiJLmL,„fIi, 



from which the hysteresis coefficient is 



a = 



25 Es Ad X 10-3 





3//i2\ IfiJLJ 



Measurements of third harmonic voltages have been made on the coil 

 described in this paper by P. A. Reiling and the results are shown in 

 Table II. 



TABLE II 



The values of a thus obtained show no consistent variation with current 

 or frequency. They give an average value of 2.5 X 10~^, which is in 

 close agreement with the ballistic and a.-c. bridge results. It therefore 

 appears that that part of the effective resistance which is proportional 

 to current is identifiable with hysteresis loss as obtained by ballistic 

 means, and with that which generates harmonic voltages. 



The intercepts for / = in Fig. 5 are therefore due to eddy current 

 and any residual losses. They have been plotted against frequency in 

 Fig. 6. The line through these points is generally assumed to be 

 straight, and the eddy current and residual loss coefficients are derived 

 from its slope and intercept. It appears, however, that this line is not 

 strictly straight, but has a somewhat steeper slope at lower frequencies, 

 so that the ordinary graphical method of loss separation fails. 



An analytical separation of losses can be made for any frequency 

 interval by returning to the values of Rf/nofLf as obtained from Fig. 5, 



« E. Peterson, Bell Syst. Tech. Jour., 7, 762 (1928). 



