190 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



slow release case. In this same article it is shown that, under these condi- 

 tions, the relation between the changing values of '3- and (p in (1) is sub- 

 stantially identical with that given by static magnetization measure- 

 ments. 



The static magnetization relation between ff and (p may therefore be 

 substituted in (1), which may then be integrated to give the relation 

 between (p and /. For linear magnetization, or constant reluctance 

 (R = 3/(p, integration of (1) gives the equation. 



^ _ ^-«/«o 



where ^i is the value of <p for t = 0, and to = 4:tG/6{, the time constant 

 for this simple exponential decay. For release, however, the magnetiza- 

 tion relation is not linear, but has the character shown in Fig. 1. The 

 <p versus 5 relation is asymptotic to the saturation flux <p", and has an 

 intercept ^o at 3^ = 0, resulting from the remanence of the magnetic 

 material. The relation between ^ and t in release is given by (1) with the 

 relation between tp and CF that of the decreasing magnetization curve 

 illustrated in Fig. 1. 



Graphical Determination of Release Time 



Writing 4:TrNi for JF in (1), the integral form of this equation is: 



t_ r' dip 



G 



=/:i' 



where t is the time for the field to decay from an initial value ^i to a 

 final value ip. If experimental data for the decreasing magnetization 

 curve are available, the integral of (2) may be evaluated graphically as 

 is indicated in Fig. 2. 



For purposes of illustration, the left hand plot shows two decreasing 

 magnetization curves, such as might be obtained with two models of 

 the same relay. The dashed curve 1 corresponds to a higher value of (^o 

 and a lower reluctance than apply to the solid curve 2. To evaluate the 

 integral of equation (2), the curves are replotted as at the right to give 

 (p versus \/{Ni). Then the integral of equation (2) is given by the area 

 between the curve and the axis of ^. For curve 1, for example, the area 

 o-d-a' measures the value of t/G for the flux to decay from ipi to the value 

 of <p at a. 



If the areas are evaluated for a series of points, such as a and c, the 

 resulting values of t/G can be plotted, either against the correspond- 



