150 THE BELL .SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



which states that the coil constants must be equal. After steady state 

 has been reached and the switches opened, the two differential equa- 

 tions are: 



E, = ii{Rn + Ri) -^ n/-^ + ^ f n dt, 



at Ci Jo 



E2 = i2{R22 + R2) + ^2 '^' + i / i2 dt, (11) 



r\ • -^1 • E2 r^ r^ r\ 



at t = 0, ti = -- , %2 = ~ , Qi ^ Q2 = 0. 



Ri K2 



Multiplying the first equation by A^iCi and the second by N2C2 , and 

 equating term by term for equality at all times and equal magnetomotive 

 forces, two additional equations result: 



(/?n + Ri) Ci = {R22 + R2) C2 , 



(12) 

 N,'C\ = N2C2 . 



The four defining equations, with some further rearrangements using 

 (10), are shown in Fig. 5 as the relations applying for equality of mag- 

 netic flux in the two circuits. As the mechanical beha\-ior of a magnetic 

 structure is completely determined by the magnetic flux, it follows that 

 the mechanical performances will be identical and timing measurements 

 made with the simulating circuit will represent the actual circuit. This 

 is true whether the relay is mass or load controlled. It includes eddy 

 current effects and w^iether or not there is motion of the armature. 



Local Circuit I\Iass Controlled, Operation 



Typical mass controlled operate time curves are shown in Fig. 6. 

 These are for two different armature travels, indicated as short and 

 intermediate. The curves are characterized by the circuit power used 

 for each, with the coil constant plotted along the abscissa and the 

 corresponding operate time as the ordinate. As mentioned earlier, these 

 curves are substantially independent of contact spring load, and are 

 plotted for average conditions, including an averaging of the time for the 

 first and the last contact to be actuated. 



It will l)e noted that the best coil constant is not independent of tlie 

 circuit power, decreasing continuously as the power is increased. Also 

 by increasing the circuit power from 2.3 to 23 watts, the operate time is 

 decreased by a factor of a little less than 3, which is nearer the square 



