MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 51 



Subtracting the value of R/m/fL/m for frequency /i from the corre- 

 sponding value for frequency /2, and dividing by the frequency interval 



A/ = /2 - /i, gives 



A 



Rfm 

 JLfm 



A/ 



= eti,. 



1 - ^ (1 + 5X5„)(/,2 + j^. + j^j^) 



2 



- —2 gMoX5,„(l - 7X5,„)(/i + /2) • • • 

 ox 



(44) 



An approximate value for e is sufficient in obtaining the correction 

 terms in this equation. With the precise value of e/x„, thus obtained, 

 the eddy current term in eq. (43) can be calculated for any frequency 

 and permeability. Subtracting the proper eddy current term for each 

 value of Rfm/fLfm gives the hysteresis terms as remainders, which can 

 be further analyzed in their relation to magnetizing force, as in the 

 previous graphical loss separation. Loss separations, made thus pre- 

 cisely, reveal frequency variations of apparent resistivity and of the 

 residual loss constant. 



Capacitance, Leakance, and Eddy Current Loss 

 OF THE Winding 



In the discussion thus far, it has been assumed that the measured 

 inductance and resistance of a test coil depend solely upon the core 

 permeability and losses. This assumption must be modified under 

 some conditions, for it is found that the distributed capacitance and 

 leakance of the coil winding act as shunt impedances, which may 

 diminish sufficiently at high frequencies to miask the actual inductance 

 and resistance of the coil. Furthermore, the resistance of the test 

 coil includes an amount corresponding to the power expended by eddy 

 currents in the copper winding itself. It will be shown that such 

 disturbing factors can generally be eliminated, either by modifications 

 in the method of core loss separation, for materials in which eddy 

 current shielding is negligible; or by winding the test core to give an 

 inductance low enough to suppress such disturbing factors, for ma- 

 terials in which eddy current shielding is not negligible. 



If the distributed capacitance and leakance can be considered as 

 single lumps, C, and G, in parallel with the coil of inductance L and 

 resistance R, the observed inductance at a frequency corresponding to 

 CO = lirf is found to be 



J. _ L(l - co^LC) - CR^ 



(1 - co^LCy -f 2GR -f G'{R- + co2L2) + co^C^i?^ * 



