52 BELL SYSTEM TECHNICAL JOURNAL 



This simplifies at frequencies well below resonance to 



Lobs. = L{\ + a^^LC). (45) 



Thus the observed inductance tends to increase at higher frequencies 

 on account of distributed capacitance, in contrast to its tendency to 

 decrease on account of magnetic shielding in the core according to 

 eq. (33). If the inductance L is known from low frequency measure- 

 ments, and if computations from eq. {i2)) show that it does not decline 

 appreciably because of eddy current shielding at the measuring 

 frequency, the capacitance can be calculated from the relation 



^i>^^^ Lobs.^-L ^ (46) 



Similar complications arise in measuring the resistance of a coil at 

 high frequencies. Under the same assumptions as above, the observed 

 resistance is 



^ ^ R + GjR' + ^'U) 



^ob3. (1 _ JlLCy + 2GR + G2(i?2 _^ ^2^2) _|_ ^2(^2^2 ' 



At moderate frequencies, this reduces to 



i?obs. = {R + Gco2L2)(l + 2co2LC), (47) 



from which it appears that leakance enters as an important part, 

 and that the capacitance gives twice as large an increment for the 

 resistance as for the inductance. The effect of distributed capacitance 

 can be eliminated by dividing the observed value of resistance by 

 (1 + loi^LC), where the correction factor is obtained from eq. (46). 

 Thus 



= R + Goi'^U. (48) 



Roh6. 



1 _J_ 9 Lpba. Li 



^ "^^ L 



The leakance term GuP-U- can be eliminated as will be shown below. 



The resistance term R includes the desired magnetic core resistance, 

 but it also contains the resistance of the copper coil, which may have 

 a considerable eddy current loss of its own. The copper eddy current 

 loss occurs principally in the lower layers of the winding, which are 

 cut by the alternating magnetic flux set up by the current in the 

 winding. It is similar to the eddy current loss in the core material 

 itself, varying with the square of the frequency, to a first approxi- 

 mation.^* This loss must, therefore, be eliminated before accurate 



>8Cf. M. Wien, Ann. d. Phys. [4] 14, 1 (1904); S. Butterworth, Exp. Wireless 6, 

 13 (1929). 



