1462 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



face and other air gaps, and (f) Decay of leakage field. It, therefore, also 

 has the nature of a mop-up factor in which is included other effects not 

 explicitly covered in the elementary analysis. 



The above discussion has been directed toward establishing an easily 

 determined core time constant having characteristics useful for rating 

 purposes, and demonstrating that the distributed nature of the core eddy 

 currents precludes an accurate representation of the core as a single 

 coupled turn. 



Open circuit flux decay measurements of round and rectangular solid 

 core electromagnets of magnetic iron, 1 per cent silicon iron, and 45 per 

 cent permalloy all are accurately represented by the measured flux decay 

 curve of Fig. 23, after establishing appropriate values for Ge and Li in 

 each case. 



DYNAMIC FLUX RISE 



Dynamic flux rise curves, measured with the relay armatures blocked 

 open, are shown in Fig. 24. A family of curves, is needed because of the 

 added variable of the winding. The value of te is determined by the 

 method just described, except that the armature is held open, resulting 

 primarily in a new and lower value of Li. The winding may be charac- 

 terized by its coil constant: 



Go = N^/R, 



where N = number of turns, and R = dc resistance of winding circuit. 

 These curves are a composite of measurements on many structures and 

 fit all data to within a few per cent. 



An empirical closed form expression has been determined which fits 

 these data, and in fact was used to compute these curves. However, 

 once the curves have been plotted there is no further need for the rather 

 complicated expression. Any particular rise curve desired can be inter- 

 polated from the drawing. 



These curves again show, with windings of relatively low coil constants, 

 a divergence of the dynamic flux rise from being a straight line. The 

 particular curve Gc/Ge = actually is a decay curve because such a rise 

 measurement would involve the use of both an infinite voltage battery 

 and an infinite resistance winding. Now for this case, as well as for all 

 the others, the rise and decay curves differ because of the shape of the 

 hysteresis loop, the decay curve persisting longer. This effect is most 

 evident for the last few per cent of the flux change. However, the differ- 

 ences are small on a full range basis. The curves shown near Gc = are 



