ESTIMATION AND COXTKOL OF OPERATE TIME OF RELAYS 155 



always is used which completely fills the winding volume. Hence an.y 

 winding which can ho designed also can he simulated. 



The conditions wiiich must be I'ulfillcd for perfect simulation dcrixe 

 from Lenz's Law. It is essentially an imjjedance ti'ansformation technicjue 

 keeping the magnetic flux invariant, with the assumption that a winding 

 can be considered as a hniiped ratiier than a distributed network. Tiiis is 

 equivalent to stating that at any instant the cui'i'ent flow is the same in 

 every turn and there is no propagation time in\'olved. This is true for 

 times in\()l\(Hl in electro-magnets. 



Fig. 5 siiows a cii'cuit to be simulated, in which all the components 

 witii subscripts 1 have been given. The simulating circuit has only the 

 numbei' of turns.Y2 , of the test winding, given. The other four elements 

 must be determined. After switch closure, the exact differential equa- 

 tions appl3'ing are 



= r.i — nm , 



t = 0; ii = 12 = 0. (6) 



at 



dt 



Xow for equality of magnetic flux, the two rates of flux change must be 

 identical at all times including the first instant. Inserting the initial 

 boundary conditions and equating the two rates, we have 



-^ = -^ (7) 



Ni N2 



At infinite time, the same magnetomotive force must apply to both 

 circuits for equality of final flux. Eciuating these, and cancelling the 4Tr 

 factor, 



Nih = N2I2. (8) 



Noting that 



and (9) 



T E2 



we have, after using (7) and rearranging, 



