MAGNETIC DESIGN OF RELAYS 65 



Tliere is thus obtained: 



dxJa 



47r 



For saturation confined to the core, as in the series-parallel circuit of 

 Fig. 21, 01 = (Re + (Hb . On substituting this expression for (R in the pre- 

 ceding equation, (Re is independent of x and 6{b is independent of <p, so 

 that the expression becomes: 



Stt dx 

 or, for the series parallel circuit of Fig. 21 



F = 



8x^2 (Ro2 + (Rl2 + 





(30) 



As ' 



E\'idently this same expression should apply equally to the equivalent 

 circuit of Fig. 23. That this is the case can be shown by substitution of 

 the equivalence conditions of equations (25), giving an expression for the 

 pull identical with (30) except that the magnetic circuit constants (R02 , 

 (Rz.2 , and Ai are replaced by their equivalent values (Ro , (Rl , and A . 



Thus when saturation occurs in the core, as in most ordinary electro- 

 magnets, (30) gives the pull through the full range of magnetization, 

 and the expression is invariant to a change from the design constants of 

 Fig. 21 to the equivalent constants of Fig. 23. If (p is taken as (p , the 

 saturation flux, (30) gives the upper limit to the attainable pull. It is 

 also useful, as sho^^^l in the companion article on relay speed, in esti- 

 mating the pull effective in rapid operation, when (p may be nearly con- 

 stant during the latter stage of armature motion. 



In estimating the steady state pull characteristics, equation (29) is 

 applicable throughout the low density range. In the high density range, 

 the pull may be determined from (27), or, provided saturation occurs in 

 the core, from (30). In cases of armature saturation, the pull must be 

 determined from (27), the expression of most general application. 



8 SENSITIVITY AND WORK CAPACITY 



.4 nipcrc Turn Sensifin'tij 



Aside from any margin for rapid operation, the pull of the electro- 

 magnet must exceed the static mechanical load at all values of gap x. 

 As illustrated in Fig. 1, this maj^ be studied graphically by comparing 



