387 
7 
Thus the prescribed maximum variation of 4 per cent in E,will occur if 
coswZ,C,1is allowed to deviate from unity by 0.03, and sinwZ,C,/wZ,C, by 
0.01. Then 
2 
j eS wioLoe 
and therefore 
wZ,C, _ 0.245 
Let Z, = 55 ohms and C = 40 x 107” farad per foot. Then 
This is the maximum length of line that may be used under the 
stated conditions. 
Similarly the effect of C, in causing distortion may be estimated. 
Let the deviation of 1 - w°C,Z/C, from unity be 3 per cent for the range of 
frequencies up to 3 x 10° cycles per second. Let C, = 30 x 107 YF farad, and 
Z, = 55 ohms. Then 
@ UC, 2, Cs <.0-08 
Therefore 
C, < 0.11 x 10° farad 
A 0.1-microfarad terminating capacitor is thus the largest that 
could be employed under the given conditions. 
This is not a serious limitation on the attenuation of signal volt- 
age. Capacitors larger than 0.1 microfarad may be employed to obtain greater 
attenuation by using two capacitors in series on the end of the line. If one 
capacitor is kept below the limit of 0.1 microfarad, the other capacitor may 
be as large as needed to secure the desired attenuation. The signal would 
then be taken from the larger capacitor. The combination would be an equiv- 
alent capacitor whose capacitance is less than the smaller of the pair and 
hence less than 0.1 microfarad. 
It is more difficult to compensate for the use of a very long line 
to avoid distortion of the signal. There are two methods of dealing with 
this problem. One method is to use a preamplifier on the end of a line; for 
example, in the case just discussed the line was less than 59 feet long. The 
preamplifier is so designed that its output impedance is low enough to match 
the surge impedance of the cable. A line of any length can then be used from 
the output of the preamplifier to the input of the next amplifier. Such a 
preamplifier has been designed and tested in conjunction with 500 feet of 
