MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 55 



A good separation of losses requires measurements at four or more 

 frequencies, up to a point where the eddy current resistance is several 

 times the hysteresis resistance, and at four or more values of measuring 

 current in the useful range. The maximum frequency necessary to 

 make the eddy current resistance mount to p times the hysteresis 

 resistance is 



ph 

 fm = ^—' where h = {aB,„ + c), (55) 



and the total core loss resistance at this frequency is 



R,. = ""^"'''^'^ + ') . (56) 



e 



At this maximum frequency, the observed resistance is 



i?obs. = {Re + e,.LaP + R„. + ^iv'CUfj;Q){\ + Sir'-LCfJ). (57) 



Since it is desired that the observed resistance indicate directly the 

 d-c. copper and core loss resistance, all other terms in eq. (57) may be 

 considered as errors, to be suppressed to a small fraction q of the core 

 resistance. Setting the total error equal to gRm, and rejecting errors 

 of higher orders gives 



qR^ = e^LaU' + Sir'-LCfJiRe + Rm + ttL^'Q). (58) 



Substituting the above values for fm and R,n at the maximum 

 measuring frequency gives a quadratic equation in L (neglecting air 

 inductance), which solves quite accurately to require, 



^ ^ e[_eqtim(P + 1) - Sw^CRcp'] ecLgp , . 



STr'Cp%l7r'Q-^fxJl{p-\-l)^ eqfi^ip + 1) - Stt'CRcP' ^^ 



Since it is desirable to use a large inductance for ease in resistance 

 determination, it appears that the copper resistance Re, the copper 

 eddy current coefficient Cc, and the distributed capacitance C should 

 be made as small as possible, while Q should be large. 



As an illustrative example, assume a core material of permeability 

 iu„, = 100, to be measured up to a frequency such that p = 5, with an 

 error of not more than 1 per cent at the maximum frequency, i.e., 

 q = 0.01. Assume also, g - 25 X 10-^ h = 0.5 X \0-\ C = 25 X IQ-^^, 

 Q = 20, ecLa = 10-", Re = 2. 



The maximum frequency for measurement will then be/m= 10,000 ~. 

 The core should be wound to give an inductance of 5.30 mh. At the 



