128 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



The force factor diminishes with increasing frequency, and is largely 

 dependent upon the alternating component of flux in the field of the air-gap. 

 The presence of eddy currents produces a component of flux there also, 

 which is usually in opposition to that produced by the current in the coil 

 winding. The net amount of flux is thus diminished with increasing fre- 

 quency as the effect of eddy currents becomes greater. It has been shown^^ 

 that, for a single eddy current path, the locus of the vector plot such as that 

 of Fig. 15(a) would be a semicircle with its center on the horizontal axis. 

 The fact that the center of the circular locus shown here is somewhat below 

 the horizontal axis indicates a departure from the simple theory. It seems 

 likely, however, that if two or more eddy current paths exist having sub- 

 stantially different time constants, the departure shown here might be 

 explained. 



The values of force factor are obtained from a circle diagram analysis with 

 the diaphragm resonated at different frequencies in the middle and upper 

 frequency range. For very low frequencies, the mechanical impedance of the 

 receiver is determined by the stiffnesses of the system, provided the hole 

 in the diaphragm is closed, and a simple expression for the force factor at 

 low frequencies can be derived in terms of the pressure generated by the 

 receiver in a closed coupler for a given current in the receiver. This expres- 

 sion is 



TO = Y¥\ ' -^~~^ — ^ ' ^ dynes per abampere. 



where Tq is the low frequency force factor, po is the low frequency pressure 

 generated in a closed coupler for current I in the winding, Sr is the total 

 mechanical stiffness of the diaphragm and acoustic chambers back of the 

 diaphragm referred to the effective diaphragm area A , and Sf is the mechani- 

 cal stiffness of the closed coupling chamber in which po is measured. 



Since the force per unit current will depend on the number of turns in the 

 coil, force factor is not independent of receiver impedance. Thus, when 

 comparing the force factors of receivers, it is necessary to refer the measured 

 values of force factor to a common value of impedance by introducing a 

 factor based on the ratio of the square roots of the impedances of the re- 

 ceivers being compared. Such comparisons between the ring armature re- 

 ceiver and its bipolar predecessor show approximately equal values of force 

 factor at low frequencies, with the ring armature receiver force factor falling 

 off more rapidly at higher frequencies. 



Limits of Receiver Efficiency and Distribution of Losses 

 AT Low Frequencies 

 In the design of this receiver, an object has been to make the efficiency 

 as high as practicable over the frequency range from 350 to 3500 cps. Since 



