842 
as would be the case if frequency were plotted along.the axis of abscissas. 
Thus if the cable has a characteristic impedance of 50 ohms, a capacity of 
30 micromicrofarads per foot, a length of 1000 feet, and if the frequency of 
interest is 100 kc, the numerical value of ROW is 0.942. Then for m = 2 
the curves of Plate 3 are used, and for k = 1 a value of 1.16 is obtained 
for the relative amplitude corresponding to the value of 0.942 for ROW. 
The calculated steady-state cable response as given by the 
relative amplitude from Eq. (3) is plotted in Plate 2 forms 1, and for 
k= 0,1, 1.5, 2, 3 and 4. Similar curves are plotted in Plates 3, 4, and 
5 for m = 2, 4, and 6 respectively. 
he From Eq. (2) it can be seen that greater sensitivity of the 
overall recording system can be achieved by using smaller values of the 
terminating capacity Coe This corresponds to the use of smaller values of 
mand hence greater output voltage V, in Eq. (2). A value of m = 2 has 
been used successfully in field work and the use of m = 1 will give even 
ereater gignal response. It is to be noted that after the value of m has 
been chosen, the corresponding value of k to be used will be determined by 
both the steady-state and transient responses desired. For example, for 
m= 2, from Plate 3, the use of k # 1 will give a steady-state relative ampli- 
tude of 1.62 for RCW= 2, but from Plate 8, the initial overshoot of the 
transient response will be on the order of 50 percent. As shown by Plate 8, 
this initial overshoot can be eliminated entirely by using k = 2 with m = 2, 
but the corresponding steady-state relative response from Plate 3, will be 
reduced from 1.62 to 0.82 for RCW = 2. 
5. From Plates 2, 3, 4 and 5 it can be seen that if resonances are 
to be avoided in the steady-state response, the value of RCW must not be 
appreciably greater than 2. Since C is proportional to the cable length and 
since W s 217f, this condition places upper limits on the length of cable 
which may be used with a recording system capable of transmitting a given 
range of frequencies. For example a special Simplex twin coaxial cable has 
a capacity of 30.5 micromicrofarads per foot and a characteristic impedance 
of 50.4 ohms for one of the twin coaxial lines. For an upper frequency of 
200 ke, the value of C is 31,600 micromicrofarads; hence the cable length 
should not exceed 1037 feet. 
6. From Plates 2, 3, 4 and 5 it can also be seen that various 
desired degrees of steady-state compensation can be realized by suitable 
choices of m and k, after the length of cable to be used has been specified. 
For example, using 700 feet of the same special Simplex twin coaxial cable, 
and for an upper frequency of 200 kc, a value of 1.35 is obtained for RCW. 
Then for this value of RCW and for m = 2, the curves of Plate 3 indicate 
a relative amplitude of 1.32 for k = 1, and by interpolation a relative ampli- 
tude of 1.14 for k = 1.25. The particular degree of compensation desired, 
and hence the relative amplitude desired, will of course be determined by the 
mig it NOL 10467 
