50 BELL SYSTEM TECHNICAL JOURNAL 



annealed materials is also practically absent. For many materials, 

 however, the apparent resistivity falls to 50-75 per cent of the true 

 resistivity. The increase in eddy current loss thus observed is techni- 

 cally very undesirable since it necessitates rolling laminations con- 

 siderably thinner than otherwise required, in order to suppress eddy 

 current losses sufficiently. 



The cause of extra eddy current losses in laminated material is 

 definitely chargeable to the hard, low permeability surface of the 

 material. The eddy current losses are determined largely by the high 

 interior permeability, and the laminar thickness. The material near 

 the surface conducts large eddy currents induced by interior material 

 of high permeability, but it contributes very little to the average 

 permeability for the entire sheet. Removal of low permeability 

 surface material by etching ^^ lowers the eddy current losses and 

 increases the average permeability of the core, so that the apparent 

 resistivity approaches more closely the true d-c. value. Of course, 

 selection of material and proper mechanical working and heat treating 

 technique are most desirable in avoiding at the outset such inhomo- 

 geneities, with their resulting excessive losses. 



Analytical Separation of Losses 



For special investigations where the accuracy of the graphical 

 method of loss separation is not sufficient, it is necessary to return to 

 the unabridged form of eq. (36), and employ an analytical method. 

 For example with sheet material, 



e = —1 — and 0- = - g/xn/. 

 op T 



Rewriting eq. (36) with these substitutions and with an additional 

 term to provide for the residual loss, 



= anmUm 



JL 



fm 





+ eiJimf 



9eWP 

 1407 



1 - -t£v^ (1 + 5X5.) + 



+ CUm 



(43) 



It should be recalled that R/m and Lfm are the core resistance and 

 inductance measured at a definite current and frequency, while /i^ is 

 the permeability of the core measured at the same current, but at a 

 frequency low enough to make eddy current shielding negligible. 



"Legg, Peterson and Wrathall, U. S. Patent 1,998,840 (1934). 



