342 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
where F,, = overall noise figure, 
F,, = noise figure of the kth element, 
9, = gain of the kth element. 
In using this equation it is understood that the suc- 
cessive stages are matched. 
It is clear from equation (38) that most of tne 
noise comes from the early stages of reception; in 
high-frequency radar sets, it comes from the crystal 
mixer and the first intermediate-frequency (i-f) 
stage. This means of course that noise picked up at 
later stages is much less amplified by the system 
than the noise from the early stages. 
In equipment specifications, the noise figure is 
usually expressed in the decibel scale as decibels 
above thermal noise. Actual noise figures vary from 
a few decibels above thermal noise in the very high- 
frequency [VHF] region (receivers built a few years 
ago often have appreciably higher noise figures) to 
larger values for microwave receivers. 
Sensitivity of Radar Receivers 
It is by no means true for radar receivers that 
Prin= Pao} 28 a matter of fact, Prin >>Pro. That 
is, the minimum discernible power considerably 
exceeds the noise level. 
The largest single additional loss in radar recep- 
tion is scanning loss which is related to the rotation 
of the antenna (one or several revolutions per 
minute). As an example, for one particular radar 
which has a bandwidth Af = 2 me, this loss is from 
10 db to 12 db. 
In case the antenna does not rotate, there is no 
scanning loss. This fact would seem to be of limited 
operational importance, since it would usually be 
necessary to locate the target (a plane, for example) 
by scanning. 
Another loss, closely connected with scanning 
loss, is sweep-speed loss. This loss is due to the fact 
that practical targets, such as airplanes, reflect 
rapidly varying amounts of power to the radar 
receiver, these amounts depending on the precise 
orientation of the target at the moment when the 
radar beam sweeps over it. Consequently, sweep- 
speed loss will depend on the speed of rotation of the 
antenna, on the distance of the target from the 
antenna, and, to some extent, on the beamwidth 
and the nature of the target. The overall figure 
for this loss on the same radar used to illustrate 
scanning loss is about 4 db for targets 200 miles 
from the radar. 
In addition to these losses, careful experiments 
with the radar used as an example above have 
indicated that there is an operator loss of about 
4 db for even experienced operators. This might be 
thought of as a loss due to the difference between 
laboratory and field conditions. 
Statistical consideration about the extent of noise 
fluctuation and about the fact that a target need 
not be seen on every sweep lead to further small 
losses which total, for the radar under discussion, 
2 db. : 
Summarizing for the case of the radar of the above 
example, the minimum detectable power is about 
34 db above kTAf or about 8 X 1071"* watt, not 
12 db above kTAf or 8 X 10°12* watt, as would be 
indicated from the noise level alone. This amounts 
to 22 db or a factor of 166; that is, the actual min- 
imum discernible power is 166 times that calculated 
‘rom noise alone. It will be seen in the results of 
the next section that the maximum range of a radar 
set varies with the inverse fourth root of the min- 
imum discernible power. Consequently, a calcula- 
tion of the maximum range of the radar of the 
example, which assumed that the minimum dis- 
cernible power was equal to the noise power, would 
give a range too great by a factor of 166 = 3.59. 
Since this would be a serious error, it shows the 
importance of a very careful consideration of radar 
receiver sensitivity in calculations of this type. 
RADAR CROSS SECTION AND GAIN 
Radar Cross Section 
The total scattering of a target may be described 
by the use of a parameter (having the dimensions 
of an area) called a scattering cross section. This 
concept has already been presented in subject mat- 
ter on page 338, where both scattering and absorp- 
tion cross sections of doublets were discussed. 
It should be noted in passing that the cross sections 
introduced here should not be confused with the 
radar cross section discussed before 
The scattering cross section S is defined by 
S = =, (39) 
where P, is the total power scattered by the target 
irrespective of its angular distribution and W; is 
the incident power per unit area. 
The scattering cross section S, which gives in- 
formation about the total scattered energy, is not 
directly useful in radar work because in such applica- 
tions one. is interested only in that fraction of the 
total scattered power which is scattered in the direc- 
tion of the radar; that is, one wants a parameter 
involving the scattered power per unit area at the 
receiver instead of the total scattered power. If 
the target is an isotropic scatterer, 
Ps 
W, = —, 
4nd? 
where W, is the scattered power per unit area at the 
