597 
27 
large as the period of time which is of interest. Thus if the time of in- 
terest is 20 milliseconds, the time constant must exceed 250 milliseconds. 
DISTORTIONS DUE TO FREQUENCY RESPONSE OF AMPLIFIERS 
Thus far distortions associated with the cable and those due to in- 
adequate time constant have been discussed. Another kind of signal distor- 
tion arises from inadequate frequency response of the amplifiers. There are 
several ways of describing this frequency response. The following are three 
methods in common use. 
Let E, sinwt represent a standard sinusoidal signal going to the 
input of the amplifier. Then the output will have the form 
E sin(wt — 6) 
E is the amplitude of the output. If it is a function of the fre- 
quency w, i.e., E = E(w), then the amplifier has amplitude distortion. 96 is 
the change in phase introduced by the amplifier. If 6 is either a constant 
or a linear function of the frequency, i.e., 6 = 0(w) = aw+ B, where @ and B 
are constant, then there is no phase distortion. If 9 is a nonlinear func- 
tion of w, then the amplifier has intrqduced phase distortion. In the case 
of the properly terminated cable treated in an earlier section, see Equation 
[5], 
E(w) — which is independent of signal frequency w; 
6(w) = jLVLC w, which is a linear function of w. 
Thus the properly terminated cable is an example of a distortionless system. 
When E(w) and 6(w) are determined experimentally, the frequency response is 
completely known. 
A second method involves obtaining the response of the amplifier to 
a periodic square wave. 
A third method is to ob- 
tain the response of the amplifier 
to a unit pulse; see Figure 16. 
These modes of descrip- 
tion are essentially equivalent, 
and any one may be derived from 
any other (23). Each may be useful 
for some specific purpose. Thus, 
for example, if it is desired to Oo ] Sen 3 4 5 
t/t. in radians 
learn the effect of some parameter, Figure 16 - Types of Response of 
such as the value of a resistance Amplifiers to a Unit Pulse 
