(30 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



the load fur\'o with the family of pull curves for ^'arious \'alues of A^I. 

 The just operate ampere turn value is that for the pull curve which just 

 exceeds the load curve at all points. For design purposes, estimated pull 

 and load characteristics must be used in this comparison, and conditions 

 determined for minimizing the ampere turns required to operate a speci- 

 fied load. 



The work V done against the load is represented by the area under the 

 load curve. Its maximum possible \'alue is equal to the work W done by 

 the magnet, represented by the area under the pull ciu've. Within the 

 region of substantially linear magnetization, the pull is given by (29), 

 which may be written in the form: 



I' = ., ^ ,., (31) 



(1 + u)- 



where: 



2Tr(NI)- 



and u = x/(A(Ro), or the ratio of the gap reluctance .r/.4 to the closed 

 gap reluctance (Ro . 



The work W done by the magnet in the travel from an initial gap xi 

 to a; = is the integral of F dx, or of ASio F du. From (31), this integral 

 is given by: 



TF=-^Tr„3x, (33) 



1 + Wl 



where Ui = a;i/(,4(Ro) and ir,„ax == AiSUF^ . For a large initial gap {ui 

 large), W approaches Wnv^^ , which therefore measures the upper limit 

 to the output for this ampere turn value; the total area under the pull 

 curve. In general, the difference between the force displacement charac- 

 teristics of the load and pull curves permits only a fraction of ir„K,x to 

 be used to operate the load. The potential output of the magnet, how- 

 ever, depends solely upon IFmax • From (32), in which A(RoFo ecjuals 

 IFmax , the ampere turn sensitivity, or potential output for a given ampere 

 turn value, is given by: 



'' max -J" /^Q 1 ^ 



Thus the ampere turn sensitivity depends solely upon the closed gap 

 reluctance (Ro throughout the region of linear magnetization. 



