268 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



been achieved. In the discussion that follows, however, it will be more 

 convenient to use the reciprocal of Q as the measure of quality. This per- 

 mits combining the loss components in a simple additive manner. Thus 



Dissipation Factor = D = - = _rf_l f_! 'L-L ! i_! f (2) 



where Rdc = dc resistance of the winding 



Re = eddy current loss 



Rh = hysteresis loss 



Rr = residual loss 



Re = increment of measured resistance due to distributed ca- 

 pacitance 



Rg = ac loss in wire of the winding. 



or 



D = D,c + De + Dh + Dr -h D, -\- D, (3) 



r) 



where Dn = -^ {n being any of the above subscripts). 



Having been given the inductance, and the operating frequency and 

 current, for a desired inductor, and having chosen the core material 

 that will be used, each of the D's above will be functions of the following 

 variables: Permeability, Volume and Proportions of the core structure. 

 We will now investigate how each of these factors can be manipulated 

 to yield the highest Q (or lowest D) coil. 



EFFECT OF PERMEABILITY ON DISSIPATION FACTOR 



The permeability of a permalloy powder core is determined by the 

 fineness of the powder and the amount of insulation with which it is 

 mixed before firing. Obviously it is commercially impracticable to manu- 

 facture cores having a great variety of permeabihties, and it has hap- 

 pened that four values have been standardized for commercial use; 

 125, 60, 26 and 14. The coil designer working with permalloy powder, 

 beyond choosing the most appropriate of these four values, seldom finds 

 it practicable to control the permeability. This is due to the difficulty of 

 pressing shapes suitable for use with air gaps, and the fragility of the 

 parts. With ferrite, on the other hand, the parts can readily be adapted 

 to the control of permeability by insertion of air gaps, and thus establish- 



