132 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



loss, because it adds a diaphragm stiffness Sr , in series with the load stiff- 

 ness, Sf . Curve (4) includes the coupling factor, K/1 -{- K^ which depends on 

 the force factor that can be developed in relation to the inductance and stiff- 



ness of the system. This factor contains the term K — r— — — -— - which is a 



sort of coefficient of coupling, analogous to the electrical coupling coeffi- 

 cient of a transformer, except that it may exceed unity. The whole factor, 

 however, K/l+K, can never exceed unity, and we may call it k^, defining k 

 as the "coupling f actor.'' Thus each term of this equation may be associated 

 with some physical part of the receiver, which contributes to the losses. 



A fifth term will now be developed, which may be called the resistance 

 loss, due to the electrical resistance of the receiver. If the receiver has a 



RoX 

 resistance R, the last term of equation (8) may be written as /„" ^24!' ya 



where R and X are taken as the measured low-frequency resistance and 

 reactance of the receiver. 



In equation (9) however, the term "" /.//.no was factored out of this 



expression and included as part of the first term. To take account of this, 

 the remaining term for the resistance loss becomes 



Resistance Loss — ~ 



{Ro + RY + X' JIU 



If this remaining factor is included, the expression for the response of the 

 receiver with resistance becomes 



10 log r? = 10 log 



2tPc 10^ \ / Fe \ I ^s \ 



A-^A'i ^ ^_±fll^ (10) 



This is the equation of the curve (5) shown in Fig. 16a. This curve checks 

 quite closely with the measured response of the actual receiver, shown by 

 the dashed curve (5). The close coincidence of the solid and dashed curves 

 constitutes a check on the accuracy of both the theoretical and measured 

 response of the receiver. The slight divergence of these curves in the range 

 from 300 to 500 cps is due to the effect of the mass of the diaphragm, which 

 was neglected in the calculations. 



While the above analysis is limited to low frequencies, it gives one an 

 indication of the magnitudes of the various types of losses. It shows that, of 



