Ni, 



170 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



Table I — Equation 30 



Turns „ ■, „ 



Relay N Resistance Re Voltage Ee Power W e Coil Constant 



R1 + R2 E, El A'l' r, , £2 {Nf 



"* ■+i-;(i;y '^t(m <-+->D + r;(S'] "^"^ '■^'"' 



2 of A''2 turns, a 1 turn inductance L-2 and a resistance R2 . What are the 

 two equivalent relays, each in a local circuit and what are their virtual 

 applied voltages? The first step is to reassign the total resistance to 

 obtain two equivalent windings having the same time constant N Li/R. 

 Then determine the two virtual voltages by division of the total in 

 proportion to the impedances. These and their dependent power and 

 coil constant relationships for the case of two relaj^s are tabulated in 

 Table I. The procedure can be extended to any number of dissimilar 

 series structures. 



For the case of all identical magnetic structures, the 1 turn inductances 

 Li , L2 , etc., are all equal and their ratios become unity, simplifying the 

 expressions. Note that the coil constants are not equal unless the struc- 

 tures are the same magnetically, but that the time constants always are 

 equal. Further, the total power is constant and equal to that of the origi- 

 nal circuit. 



After determining the effective powers and coil constants, the operate 

 time for each can be read from the applicable single relay charts such 

 as Fig. 6. 



Tivo Like Parallel Relays in Series with a Third Relay, Identical Structures 



The equivalent relay method can be extended to include the case of 

 two like parallel relays in series with a third relay, as shown in Fig. 10. 

 The first observation to make is that, because of symmetry, the current 

 flow in the two parallel relays is identical. No winding current change 

 would be made if, for instance, all the dc resistance of the two parallel 

 relays were removed and half of either were connected in series with 

 the single relay. Thus again, the resistances can be assigned as neces- 

 sary to result in equal winding constants and total power. The same net 

 dc resistance gives a second condition : 



Nl ^ Ni 



H\E RiE 



(31) 

 ft + f -ft. + 'l'. 



