FERRITE CORE INDUCTORS 279 



Putting in the values, from (27) to (30), for X, I, W and A: 



D ^ ^ A/ (Vl - P' + P)(SVl - P^ - 1 + 2i/) (3g) 

 R y P\Vl - P'- P)i2Vl - P'- 2 +H) 



Since the volume of the coil, given in (31), is assumed to be con- 

 stant, we can eliminate R from the above equation: 



D = k^^ Y 



r2/3 



(Vl - P' + P)(3V1 - p2 _ 1 _|, 2H)H' (37) 



PWi - P^ - P)(2\/l - P"" - 2 + ^) 



where fcis = 



2ir"'k 



12 



Fi/3 



We now have an expression for the dissipation factor in terms of the 

 two variables, P and H, which determine the proportions of the coil 

 structure. The effects of these proportions on the dissipation factor are 

 shown in Fig. 6. It will be seen that best results are achieved when the 

 radius of the post is approximately 0.45 of the outside radius and the 

 axial height is about 1.2 times this radius. Fig. 5 is drawn to this scale, 

 and the 1509 type coil shown in Fig. 4 approximates these proportions. 



2. DC Resistance and Hysteresis Loss Predominate 



We have noted that for this case optimum permeability is that which 

 results in the following relationship between the dc and hysteresis 

 dissipations : 



Wh = 2Ddc (38) 



From (11) and (13) 



7 7 3/27-1/2- 



D. = hB^, = ^^9^* (39) 



Putting the values from (32) and (39) in (38), we can eliminate fx 

 and express Ddc in terms of the dimensional variables of the coil: 



>3/5^2/5 



where ku = {^k^kghn^^L^ ^if ^ 

 The total dissipation factor is 



^^3/5,2/6 



D = D,e-\- Dh = iD,c = iku ppTsjiTi (^1) 



