MAGNETIC DESIGN OF RELAYS 25 



To illustrate the objectives of majiiuMic (l(\si<iii, i-ct'efeiice may be 

 made to Fig. 1, which sliows the load characteristic of the recently de- 

 veloped general purpose wire spring relay for a particular contact ar- 

 rangement.. The figure is taken fi'om an article' desci'ibing tiiis relay, 

 which discusses the economic and other considerations which governed 

 its design. Included in the figure are curves showing tlu> pull exerted by 

 tliis relay's magnet for various values of coil ampere tiu'iis. These pull 

 curves determine the ampere turns required to operate a contact ar- 

 rangement having a specific load characteristic, such as that shown. Hy 

 means of the magnetization relations, these pull characteristics can be 

 related to the design of the electromagnet. 



The notation used in this article conforms to the list that is given 

 on page 257. 



1 THE COIL CONSTANT 



The relay coil characteristics of interest in its use as a circuit com- 

 ponent are its resistance and the current flow for operation. Subject to 

 some ciualifications as to available voltages and wire sizes, these may be 

 summarized in a statement of the steady state power I^R supplied in 

 operation. As illustrated in Fig. 1, the coil quantity determined jointly 

 l)y the load and the magnetic design is the ampere turn value NI. The 

 power and the ampere turn value are related by the coil constant Gc or 

 X'/R (which ecjuals {Nlf/{l'^R)). This quantity is the equivalent single 

 turn conductance of the coil, and is usually expressed in mhos. It is 

 determined by the coil dimensions, as can be shown as follows: 



Let A be the area of a cross-section of the coil as cut by a plane through 

 the coil axis. Let m be the mean length of turn, the arithmetic mean of 

 the lengths of the inner and outer turns. Then the coil volume S equals 

 Am. If a is the cross-section of the wire, the number of turns A'^ equals 

 eA/a, where e is the copper efficiency, or fraction of the coil volume 

 occupied by conductor. Substituting S/m ior A, N equals eS/(am). The 

 Avire length is Nm, and hence the resistance R equals pNm/a, where p 

 is the resistivity of the conductor. Hence N/R equals a/(mp), and the 

 coil constant is given by: 



Gc = ^ = —,. (1) 



The coil constant is thus independent of the wire size, except to the 

 minor ext(>nt that the copper efficiency c decieases as the wire is made 

 finer. With this qualification, and assuming copper wire to be used, the 



