136 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



Where ^i = M.m.f. of lower cylindrical part of magnet 

 fFi = M.m.f. of flanged portion of magnet 

 G(mi = Reluctance of lower cylindrical part of magnet 

 9^2 = Reluctance of flanged portion of magnet 

 9igi — Reluctance of main air gap (a variable modulating reluctance) 

 9ig2 = Reluctance of auxiliary air gap 

 9ld = Diaphragm reluctance 



The above relationship can be derived by placing the flux through the 

 diaphragm reluctance did equal to zero in the circuit shown. Under these 

 conditions, the armature carries no d-c. flux over its middle portion and will 

 be operating at maximum permeability to a-c. flux. Moreover, the d-c. air 

 gap flux density in the lower air gap where most of the field of force resides 

 can be made higher before saturation begins to degrade the permeability of 

 the inner marginal portion of the armature, than if all of the armature had 

 to carry d-c. flux. The above factors tend to increase the a-c. and d-c. flux, 

 and, since the force factor is a function of the product of these two quanti- 

 ties, a higher force factor will result from the addition of the overlying 

 portion of the magnet. ^ 



In order to maintain the position of the freely supported diaphragm on its 

 seat at the outer periphery, it has been found desirable to have only a partial 

 balance of the circuit. This is accomplished by making the upper air gap 

 approximately five times larger than the lower one. Thus the field in the 

 upper air gap is weaker, so that a 25 to 50% unbalance in flux exists. Under 

 these conditions, the flux component in the diaphragm due to the upper 

 portion of the magnet only partially cancels that due to the lower portion. 

 However, the resulting flux density in the diaphragm is such that the per- 

 meability will be only slightly below the maximum permeability which 

 obtains for the perfectly balanced condition. The reluctance of the upper 

 mesh to a-c. flux is so high, that the a-c. flux flowing in this branch can be 

 neglected, hence the lower mesh carries substantially all of the a-c. flux, as 

 shown in the figures. Thus, a partial separation of the a-c. and d-c. flux paths 

 is accomplished. 



The magnetic materials which comprise this structure include a remalloy 

 magnet, a vanadium permendur diaphragm, and a 45% permalloy pole- 

 piece. Some of the considerations which led to the choice of these materials 

 are indicated below. The remalloy magnet can be formed from sheet material 

 while at elevated temperatures, is machinable prior to the final heat treat- 

 ment, and has good magnet properties. Although Alnico could be used as 

 magnet material, it would not lend itself to forming, and the result would be 

 a more expensive magnet. The vanadium permendur diaphragm has a 

 higher permeability at the higher flux densities than other materials, and 



