98 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



ties, it follows from (12) that F' /F is equal to ipu/fph , where (po is the 

 actual value, and ipo the fictitious value that would obtain if the mag- 

 netic circuit reluctances remained constant at all values of J. For the 

 case of core saturation, to which the magnetic circuit of Fig. 5 applies, 

 the ratio (pa/^p is constant for a given value of x, and hence in this case 

 F'/F eciuals <p /(p" where ip is the actual \-alue and tp the fictitious \'alue 

 that would obtain if the reluctance were (R'. Thus for core satura- 

 tion, 



F V ^^\ 

 and hence: 



F' /6{ 



As values of (R' and (R can be read directly from magnetization curves, 

 this relation provides a simple means of computing the high density pull 

 for specific values of x and fF, provided the low density pull has been 

 measured or estimated from (13), using the values of (Ro and .4 deter- 

 mined from the low density magnetization relations. 



An approximate expression for the right-hand side of (14) can be ob- 

 tained in a convenient form from the two limiting conditions: (R = cR' 

 for jy = (R'(p', and (R approaches 5 V'' as J becomes yery large. A simple 

 expression satisfying these conditions is: 



rR^ = crii -(HYWi. 



Aside from meeting the limiting conditions, this, like the Frohlich- 

 Kennelly relation used previously, is a purely empirical expression. 

 Assuming it to apply, the high density pull in the case of core saturation 

 is, from (14), given by: 



F' . /cp'V . ( iT 



As F' is given by (13), this expression gives the high density pull in 

 terms of the magnetomotive force 5, or explicitly: 



F = — ^ 



8..M^Ho + ^Yfl-fa+^^V\' (15A) 



.4 / \ \p / \(Vi ^ 



where (s\' is given by (3), so that the constant terms in this expression 

 are confined to <p , ip" , and the eciuivalent magnetic circuit constants 

 .4 , (Ro , and cR^ . 



