or ae 
PROPAGATION ASPECTS OF EQUIPMENT OPERATION 455 
tal data, shown by small circles, illustrate the increase 
in detection range at 0 degree while at 5 degrees 
elevation angle there is little gain over free space. 
The roll of a ship, by varying the beam tilt, results 
in a shift in coverage, as can be seen from Figure 1. 
Signal-to-Noise Ratio 
The visibility of a signal on a scope depends on its 
relation to the noise. In early work with radar, the 
maximum range was defined by a ratio of signal 
voltage S to noise voltage N of unity, ie., 
S 
—=1. 1 
y (1) 
However, as pointed out in Chapter 2 , the min- 
imum detectable signal is greater than N. Since the 
pip on a scope includes noise, equation (1) is equiva- 
lent to 
= 2. (2) 
The relation of receiver power, P2, to noise power, 
NP, and the signal-to-noise ratio, S/N, is given by 
1 S 
10 log —= = 20 log —. 3 
GNP Ey (3) 
On an A scope, this relation signifies that the height 
of the signal is twice that of the noise grass. 
Since the visual signal in a set functioning properly 
varies linearly with the signal voltage, the size of 
targets can be estimated by means of the size of the 
visual signal. The ratio S/N gives a means of meas- 
uring a signal in terms of the noise. To change 
(S + N)/N to S/N, the value of (S+N)/N is 
expressed with unity as denominator. For example, 
if (S + N)/N is estimated to be 8/2 from the scope, 
the equivalent fraction is 4/1. The value of S/N is 
(4 — 1)/1 = 3/1. 
Calibration of an A Scope 
On an A scope, the ratio (S + N)/N can be 
estimated roughly by eye. To improve upon this, a 
calibration is employed. One method is to mark the 
A scope to facilitate the reading of heights. Another 
method goes beyond this and calibrates the gain 
control. A turn of 5 db is equivalent to a raito of 
1.8/1. A datum line 1 cm above the time line and 
another at 1.8 cm are drawn on the A scope. The 
noise is brought up to the datum line by means of 
the gain control. The position is marked 0 on the 
gain control (see Figure 2). A steady signal is found 
(permanent echo, large boat, or signal generator) 
which produces a signal height of 1.8 em above the 
time line. The gain control is then turned until the 
signal is reduced to the datum line. The position 
on the gain control is marked 5 db (see dotted lines 
in Figure 3). 
Keeping the 5-db position on the gain control, 
another signal is obtained which comes up to 
1.8-cm line. The gain control is turned until the 
signal is brought down to the-datum line. The new 
setting is marked 10 db. This is repeated until 
markings up to about 70 db are obtained. 
This calibration of (S + N)/N must be corrected 
to S/N (Figure 3) which can be done by means of 
Table 1. For 25 db and above, the values of 
(S + N)/N can be taken as equal to S/N. Any 
signal voltage can then be measured in decibels 
above the noise voltage (NV) by turning the gain 
control until the signal height is 1 em. By equation 
(3) this is also the signal power received, in decibels, 
above the noise power which is discussed in Chapter 
9 
ae 
TasLE 1. Correction of (S + N)/N to S/N. 
Corrected Uncorrected 
(4) db pe N ) db 
N N 
0 6 
5 9 
10 12.5 
15 16.5 
20 21 
In the calibration just described, the pip on the 
scope is supposed to be proportional to the received 
signal strength. In a set functioning normally, this 
is justified, but occasionally defects in the set may 
destroy the linearity. The existence of a linear rela- 
tion can be tested by means of a signal generator. 
10 OB LINE 
5 DB LINE 
1g'cm DATUM LINE 
4¢mTiME BASE 
o 10 20 30 70 80 90 100 
RANGE SCALE 
Ficure 2. Method of calibrating an A scope. 
Ficure 3. Calibration of gain control of an A scope. 
(Dotted lines are uncorrected calibration.) 
