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BELL SYSTEM TECHNICAL JOURNAL 



to so-called transient effects. That is, the currents, after arriving at 

 the distant end of the communication circuit, require an appreciable 

 time, varying with the impressed frequency, to build up and, under 

 certain conditions, may never build up to anything remotely resembling 

 the transmitted currents in the short interval during which the latter 

 exist. This effect, moreover, may produce serious impairment in the 

 quality of the received speech or signal even when the line is so 

 designed that the steady state attenuation of all currents in the 

 essential range is substantially constant. 



0.1 0.2 03 



TIME IN SECONDS 



Fig. 1 — Building-up of current on 1500 mile telegraph cable 



As an illustration of the transient distortion on a transmission line, 

 consider the indicial admittance, A{t), of the cable of length / miles, 

 and of resistance R and capacity C per mile; that is, the received 

 current in response to a unit d.c. voltage applied at the sending end 

 at time / = 0. This is given by ^ 



A{t) = 



2_ e^ 

 Rl -yjy ' 



where 



4/ 

 RCP 



Curve (1) of Fig. 1 represents relative values of A{t) on a cable 1,500 

 miles long. (This is the same cable whose phase characteristic is 

 shown in Fig. 5, the inductance being ignorable in determining the 

 indicial admittance.) The departure of the received current from 

 the abrupt wave front of the impressed d.c. voltage is clear. 



^ See reference 3. 



