INDICIA L RESPONSE OF TELEPHONE RECEIVERS 141 



The amplifier must be compensated at low frequencies in order to main- 

 tain a strictly square-wave output. The entire system characteristic is 

 shown in Fig. 5 and covers a range of 1 to 10,000 cps with a substantially 

 uniform frequency response. The indicial response of the system is also 

 shown to be reasonably free from irregularities. Such irregularities as do 

 exist are due largely to the sharp cut-off of the s\'stem at 10 kc which was 

 necessitated by the limitations of the string oscillograph. 



Indicial vs. Frequency Response 



The calculated pairs of curves for telephone receivers in Fig. 6 show the 

 relations between the frequency response and the indicial response. Since 

 the characteristics of receivers measured on a closed coupler of known volume 

 are readily amenable to calculation if the constants of the receiver are known, 

 such a procedure is often useful in predetermining the design of a receiver. 



The upper three curves, Fig. 6, are the characteristics of a moving coil 

 receiver calculated for three different frequency ranges, being otherwise 

 similar in shape, the curve being shifted in frequency by an arbitrary factor 

 K. The effect on the indicial admittance is to shift it in time by the same 

 factor without change of shape, if the plot is logarithmic as shown. In gen- 

 eral, if the cut-off frequency is divided by the factor K, the corresponding 

 time delay will be increased by the factor K. This is an application of a 

 theorem by Carson'^ that: 



where p = jui is proportional to frequency, and / is the time, , , is the 



L{kp) 



frequency response, and A (t/k) is the indicial response. In other words, the 



curve may be shifted in frequency by a simple transformation and the effect 



on the indicial admittance curve is very similar except that the shift is in 



a direction opposite to the change in frequency, and is inversely proportional 



to the change in frequency scale. 



The second group of curves. Fig. 6, relates to the effect of damping on an 



early magnetic type of receiver, showing the freely resonant condition, a 



moderately damped, and a highly damped receiver. The curves of indicial 



response show the effects of free resonance to be very detrimental, and the 



ringing of the diaphragm is sustained over such a long period that any speech 



waves would have superposed on them a continual train of sine waves. If 



the rate of decay of these waves is increased, as shown by the damped curves, 



a noticeable improvement results. By using critical damping as in the 



highly damped curve, all oscillations can be eliminated, but the time of 



pickup is degraded and the departure from a square wave is somewhat greater 



than for the moderately damped condition. 



