MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 53 



determination of the core loss is possible. The eddy current resistance 

 of the copper winding is of the form 



Rce = ecLaP, (49) 



where La is the total air inductance of the winding, and Cc is the 

 copper eddy current coefficient. 



This eddy current coefficient is inversely proportional to the number 

 of strands in the wire, so that it can be minimized by using wire 

 consisting of many insulated strands. It increases somewhat with the 

 number of layers in the winding. The coefficient may be determined 

 for any type of winding by resistance measurements on an air core 

 coil of dimensions and winding details similar to those of the magnetic 

 core to be tested. Subtracting the eddy current resistance Rce so 

 computed, and the d-c. copper resistance Re, from eq. (48) gives as 

 the residual resistance 



AR = ^ r -Re- e.LaP 



1 ^2^^^ — - 



= UmLmliaBr, + c)f + 6f ] + Gco'L\ (50) 



This residual resistance consists of the core loss resistance, and an 

 increment due to leakance. The latter can be largely suppressed by 

 the use of low leakance insulating materials, by insuring that the 

 winding is free from moisture, and by making the distributed capaci- 

 tance as small as possible. Furthermore, it is known from experiments 

 on the electrical conductance of insulating materials at elevated 

 frequencies that the "quality" Q = wC/G is practically a constant 

 (C is the capacitance associated with G, — in this case the distributed 

 capacitance). Inserting this value of G in eq. (50) gives 



AR = (XmL^liaBm + c)f + eP^ + Sir'CUP/Q. (51) 



Theoretically, the coefficients in this equation can be obtained 

 from resistance measurements taken at three different frequencies. 

 Unavoidable errors in the measurements render such an analysis 

 unreliable, so that it is generally preferable to obtain a larger number 

 of observations, and to determine the coefficients graphically. Di- 

 viding by iJLmLmf, and neglecting the air inductance of the coil, the 

 equation becomes 



(aB^ + c)+ef + ^^^^. (52) 



