ANALYSIS OF PULL AXD ^L\GX1:TI/ATI0N MEASURKMEXTS 87 



lluMi ^■al■ies with x, the miiiiiiiuni miIucs of (t{ do iiol li(> on a coniinoii 

 \-ahie of (p in this case. 



In Fig. ()(iO, ^A may be taken as <2;iven hy an expression of tlie same 

 form as ((>), with ^p' and ip" rephiced by the minimum and saturation 

 \ahies of ip_i , and ol'c rephiced by the minimum \-ahie of 6\a . (Kc may be 

 taken either as given by (6), or as a constant if the variation in (Ha is 

 dominant. The other parameters of Fig. 6(a) are constants. The expres- 

 sion for (U applying to Fig. r)(a) may be obtained in the same manner as 

 those given for the circuits of Figs. 4 and o. 



The magnetic circuits of Figs, o and 6 are called "design" circuits, 

 liecause their constants may be estimated from the dimensions and 

 material constants of the design, as discussed m the companion article. 

 Estimates of the corresponding \^alues of the equivalent magnetic circuit 

 constants of Fig. 4 are obtained from these design constant estimates by 

 the eciuivalence equations given below. 



Conditions of Equivalence 



Whatever magnetic circuit is taken as apphdng, the component re- 

 luctances are independent of ^p in the low density region, tp < (p', and 

 are therefore constants except for the gap reluctance. If this \'aries 

 directly as x, as assumed in the schematics shown, the reluctance for 

 any circuit reduces to an expression of the form of (3), applying to the 

 circuit of Fig. 4. As shown in the companion article, the reluctance of 

 the circuit of Fig. 5 when (Re is constant is given by (3) when the param- 

 eters of this eciuation are given by: 



A = ^^-, (7) 



p- 



(Ro = p'^Mri + }M\c , 



where : 



p = 1 + — . 



(Rl2 



These relations are the conditions of e(|ui valence, for which the reluc- 

 tances of Figs. 4 and 5 are identical for all \'alues of x. With them, the 

 I'chictance gixcn l)y (4) can be reduced to the simpler form of (3) when 

 (Sic is a constant, as throughout the low density region. 



Similar relations apply to the magnetic cii'cuit of Fig. ()(aj. In particu- 



