HARMONIC PRODUCTION IN MAGNETIC MATERIALS 773 



effective fundamental current multiplied by the hysteresis resistance, or 



w/^7r^lO-7 = PRhl2. 



Here d is the diameter in cm, I is the peak value of the fundamental 

 current, / is the frequency, and Rh is the hysteresis resistance. This 

 may be solved for the hysteresis resistance in terms of the r.m.s. 

 value of fundamental current /, which is at low fields, 



Rh = l.2-10-^nUfIao2/d\ 



(27) 



The hysteresis resistance at small fields thus varies linearly with the 

 applied current. 



It is easy to derive the relation between the hysteresis resistance 

 and the generated third harmonic voltage at low fields since they 

 involve the same constants ao2 and aos; from (26a) and (25) we have 

 for the r.m.s. third harmonic voltage 



£3 = SpnAlO-^as/^Jl = 0.72-lO-Jn^AI''ao2!d\ 



Comparison with (27) shows that 



£3 = 0.6RJ. (28) 



This simple relation is valuable in obtaining an idea of the harmonic 

 production in a specific coil through resistance measurements, and 

 more than that, it enables us to determine the coefficients significant 

 in the distorting process for the material under test, so that the har- 

 monic production in a coil of any dimensions enclosing the same core 

 material may be calculated. The degree of precision ordinarily attain- 



.1 I _ 10 100 



e3in millivolts 

 Fig. 3 



able is brought out for two materials in Fig. 3, and the agreement is 

 observed to be within the experimental error in those two representa- 

 tive cases. 



