The Bell System Technical Journal 



Vol. XXI H April, 1944 No. 2 



Indicial Response of Telephone Receivers 



Ey E. E. MOTT 



A method of analyzing telephone receiver characteristics by indicial response is 

 discussed and illustrated by oscillograms. The indicial response of a telephone 

 receiver is the instantaneous response of the receiver to a suddenly applied electro- 

 motive force. This type of response is of particular fundamental interest 

 because it furnishes a key to the solution of transient problems such as are 

 involved in the response to speech waves. 



Oscillograms of indicial response, together with the more familiar steady-state 

 frequency response characteristics, are shown for different types of receivers. 

 The relationships existing between the two types of measurements are discussed. 



From the standpoint of most faithfully reproducing transients, indicial 

 response data indicate that a receiver having a limited range of frequency response 

 should have a frequency response characteristic which droops gradually rather 

 than abruptly near the upper end of the range. 



Introduction 



THE use of indicial response analysis as an outgrowth of the Heaviside 

 operational calculus' has been extended to a number of different fields. 

 The indicial admittance as defined by J. R. Carson^ in his analysis of the sub- 

 marine cable and other transmission problems has been an efifective tool in 

 the study of transients. More recently, a similar type of measurement has 

 been used as an indication of performance of amplifiers^, television equip- 

 ment\ and audio frequency transformers^. 



In the field of telephone receivers^ an analysis by means of impressed 

 square waves has been found useful as a measure of transient response. In 

 the transmission of speech, so much emphasis has been placed upon steady- 

 state frequency response as an indication of performance, that it seems in 

 order to consider the possible advantages of a transient method of analysis, 

 as obtained by measuring the indicial response. Only recently has the 

 technique of such measurement been made feasible by the improvement at 

 low frequencies of amplifiers and related apparatus. 



The Indicial Response 



The indicial response of a telephone receiver may be defined as the in- 

 stantaneous sound pressure generated by the receiver in a closed air chamber 

 due to a suddenly-applied unit voltage. This term differs from Carson's 

 indicial admittance only in that sound pressure rather than current response 

 is used. The sound pressure in an air chamber of pure stiffness is a measure 



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