844 
In this expression, t is the time in seconds and all other quantitiesare 
the same as previously defined. This expression is a general one for the 
step-transient response of the network of Plate 1. It covers the special 
cases considered in reference (a)*. 
In Eq. (4) the time required for a signal applied to the input 
of the cable to travel the length of the cable is given by the transit 
time RC. Hence the value of the response at the output of the cable is 
zero for all values of time from t = 0 to t = RC. The first term of Eq. (4) 
represents the direct signel at the output after one trip along the cable. 
The second term of Eq. (4) represents the reflected signal at the output 
after it has been reflected from the output end and again from the input 
end of the cable and has therefore made three trips along the cable. Thus 
for values of time between RC and 3RC the transient response is calculated 
by using only the first term of Eq. (4), and fo: values of time between 
3RC (h) 5RC the transient response is calculated by using both terms of 
Eq. (4). 
In the ideal case, the perfect response to an applied step 
voltage V, would be a constant response equal to the final value of the 
response for all values of time greater than t = RC. In the actual case 
of the network of Plate 1 a high-impedance gaugs represented by V, and Cy 
is connected to a low-impedance cable and the transient response will 
oscillate about the final value and will be attenuated because of the 
cable losses. The magnitude of the initial response at time t = RC and 
the magnitude of the oscillations can be varied by proper selection of the 
terminating resistance and capacity. 
The final value of the transient response can not be obtained 
from the two terms of Eq. (4). However, since the final value of the step- 
transient response after a long time has elapsed if equal to the steady- 
Ytate response as the frequency approaches zero, it can be found from Eq. (2) 
Hence the relative amplitude of the step-transient response was 
obtained by dividing the calculated values of Eq. (4) by Ea. (2). Calculated 
values of the relative amplitude of the step-transient cable response are 
plotted in Plates 7, &, 9 and 10 for time values from zero to 5RC and for the 
geme ranges of values of terminating resistance and capacity as were used for 
the calculated values of the steady-state response. 
* It is to be noted that several errors occur in the numerical constants 
in Eq. (8) of reference (a) as published, for the special case 
considered there. The correct values of these numerical constants are 
given by Eq. (4) of this report. 
-6-<- NOIM 10467 
