THE RING ARMATURE TELEPHONE RECEIVER 129 



there are theoretical limits to the level of efficiency which cannot be sur- 

 passed even in the ideal case where there are no losses, it becomes of interest 

 to determine the magnitude of these upper limits. It is also of interest to 

 determine the amount and origin of the various types of losses that occur, 

 and to what extent they can be minimized. 



In the case of a telephone receiver, the character of the ear load is pre- 

 dominantly a reactance, corresponding to the stiffness reactance of an ear 

 cavity of about 6 cc. volume. The power transfer to such a load is not ordi- 

 narily used to denote the efficiency, as may be done for a resistance termi- 

 nated device such as a loudspeaker for example. Instead, the available 

 power response is taken as a measure of relative efficiency of receivers, and 

 it is defined as follows:* 



1 'b\^ 

 Response = 10 log 77 = 10 log ^^ (1) 



Where 



10 log T) = available power response in db referred to (1 dyne/cm^)^ per 

 watt. 

 p = pressure developed in the ear cavity in dynes/cm^, 

 E = voltage of source in volts. 



Ro = source resistance in ohms; chosen in this discussion to be equal 



to the receiver impedance at the midband frequency /« , 1000 cps. 



In this expression, the numerator 1^1^ is proportional to the acoustic 



power output, while the denominator E^I^Ro is the available power input. 



Low Frequency Loss Analysis 



It will now be shown that the available power response approaches a 

 theoretical limit which is about 17 db higher than the response level of this 

 receiver at low frequencies, and that this expression may be arranged to give 

 five loss factors, each of which has an important physical significance. 



For this purpose we need to consider only the stiffness, force factor, and 

 inductance of the receiver working into a closed chamber representing the 

 ear load. It is well known that in this instance for frequencies below 500 cps, 

 with the receiver working out of a source of constant voltage E, and resist- 

 ance Ro , the equations of motion are: 



{Ro + R+joiL) I +jo)T .10-7 ^ = £ 



- r/ + (^r + Sf)x = (2) 



where L = low frequency inductance of receiver winding in henries 

 R = low frequency resistance of receiver winding in ohms 

 r = transduction coefficient or force factor in dynes per ampere 

 Sr = Stiffness of receiver diaphragm, including the rear chamber, 

 negative field stiffness, etc. in dynes per cm. 



