172 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



The particular vertical N'^/R to be used is the one passing through the 

 higher of the two given times, which lies at the minimum point on a 

 watts curve. Satisfying the smaller wattage relay assures sufficient 

 ampere-turns for both winchngs, and also gives a smaller time loss com- 

 pared to optimum for the other higher speed relay, as the higher power 

 curves are flatter for coil constants above the optimum. Thus the speci- 

 fied times determine eciuivalent watts for each coil, and the actual total 

 circuit watts are exactly the sum of the equivalent watts. Hence: 



Jti\ -f- tti 



This sets the total resistance {Ri + R'l). Also, knowing the current is 

 the same through the two coils, and that the actual division of the dc 

 resistance has no effect on time, the ratio of the two resistances can 

 initially be chosen the same as the ratio of the two effective powers: 



1^^ = ^. (35) 



W2 R'l 



Finally, knowing that the effective coil constants for the two relays 

 are equal, the desired turns are determined using the already selected 

 coil constant, Gc • Solving these three equations, the individual relays 

 are: 



R, = Ei^ , R, = ^ , N, = Vm'c, N, = VR^c (36) 



W^total ^total 



The resistance values Ri and R2 can be used as shown above or divided 

 in any other way as long as the total is unchanged. The numbers of 

 turns, however have to be kept fixed. 



A particularly simple relationship exists when it is desired to have 

 equal times. In this case the turns on the two coils are equal. 



One Winding Known 



As is often the case in actual use, a winding must be chosen to be 

 used in series with another known winding and have best operate times. 

 The method described here can be applied to any relay structure, but 

 the numerical values in the analysis are applicable to the wire spring 

 relays only. The first step is to choose the desired resistance for the coil. 

 This is usually set by the heating and power limits, knowing that the 

 higher the total power is, the less the operate time. Then the choice of 

 turns for the coil depends on which of the two coils needs speed the most. 



