106 DRIVING SYSTEMS 



The sum of the forces, in dynes, at the points 1, 2, 3 and 4, acting upon 

 the armature due to a current in the coil is 



6.22 



or 



6.23 



In the case of the simple reed driving system a second harmonic term 

 appeared in the force when a sinusoidal current was passed through the 

 coil. It is interesting to note that in the case of the balanced armature 

 the second harmonic term cancels out due to the push-pull arrangement. 



The motional impedance oi this system will now be considered. Let 

 the armature be deflected a distance of Ax from the poles 2 and 3. The 

 flux, in maxwells, through the path 1 and 4, assuming that the entire re- 

 luctance exists in the air gap, is 



2{a — Ax) 



where M = magnetomotive force, in gilberts, of the steady field, 



a = spacing between the armature and pole, in centimeters, and 

 A = effective area of a pole piece, in square centimeters. 

 The flux through the path 2 and 3 is 



MJ . - , 



2{a + Ax) 



The flux through the armature is the difference between 6.24 and 6.25, 



MJAx _ MA Ax 



Act> = <l>u - 023 = ^, _ ^^^y ^ -J-. 6.26 



The change in flux with respect to the time is 



d(b MAdx MA, ^ ^_ 



— = — = X b.ll 



dt a? dt a^ 



The electromotive force, in abvolts, generated in the coil is 



d<^ NMA . 



e = N—- = -—X 6.2g 



dt a^ 



