152 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



"- 0.80 



z 

 o 



O 0.70 



60 



260 



Fig. 3 



80 100 120 140 160 180 200 220 240 



AMPERE TURNS REQUIRED (CRITICAL LOAD POINT) 



Correction of computed operate time for magnetic saturation. 



large load at the critical load point and the ampere turns needed are in 

 the saturation region for the core or armature. In the saturation region 

 the current builds up faster than the linear time constants indicate, and, 

 therefore, the indicated operate times are too large. Correction factors 

 are determined by graphical integration of the integral form of the flux 

 rise equation expressed as a ratio to the linear relationship: 



Saturation Correction Factor = 



i 



d(p 



NI - Ni 



(5) 



- Li In (1 - Nh/NI) 



These corrections are plotted as a function of the just operate ampere 

 turns iV7o, with the final NI as a parameter for each curve. Actually, 

 because the correction factor is only of the order of 20 per cent maximum, 

 assuming the final winding ampere turns are well into the saturation 

 region, it is found that a single curve for any one type of relay fits all 

 the computed points to an accuracy of a few per cent, and generally 

 is used. Such composite curves are shown in Fig. 3 for the three types of 

 wire spring relays. 



A method has now been established for determination of the operate 

 time of a relay with two restrictions (1) that the final ampere turns 

 will operate the relay and (2) that the relay is in the load controlled 

 class. An indication of the latter is whether the operate time determined 

 is in the time region where the q curves are decreasing in curvature. For 

 Fig. 2, 10 milliseconds is taken as the lower bound for load controlled 

 relays. 



Now the determination of an optimum winding for a particular 



