270 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



Eliminating N from (5) and (7) 



and 



^'^' ~ V^ ^^^ 



Dae = vis (9) 



V'fif 



where k2 , k^ , k^ are constants. 

 From (1) and (2) it is seen that 



De = k,nf (10) 



1 3/2 7-1/2. 



Dh = k^Bmii = — ^ — (11) 



Dr = W (12) 



in which the flux density, 



H is the field strength due to the r.m.s. current, i, and k^ to A;io are 

 constants. 



Combining (9) through (12) 



7 3/2x1/2- 



For a specified inductance at a given frequency and current the op- 

 timum permeability can be found from (14) by inserting the numerical 

 values and solving graphically. It is very unUkely, however, that this 

 cumbersome procedure would be necessary in practical work. Usually, 

 depending on the design requirements, one or another of the core loss 

 factors will be comparatively large and the others can be neglected. We 

 will examine separately the three cases where residual, hysteresis and 

 eddy current loss, respectively, predominate over the other core losses, 

 and show how the permeability can be adjusted to minimize the dis- 

 sipation factor. 



1. DC Resistance and Residual Loss Predominate 



This condition, which formerly was very seldom encountered, is be- 

 coming of increasing practical importance for two reasons. First, the eddy 



