CALCULATION OF RADIO GAIN 397 
power output under the given conditions would be 
P, = P, x 10%’ 
= 10-'° x 10°7= 107! watts. 
RapDaR 
Suppose that, instead of a receiver, there is a target 
at the same position with a radar cross section of 
o = 50 square meters. The value of P2/P; at the 
radar receiver can be found from equation (5) using 
the value of A found above and the given values 
of o and X. If the radar uses the same antenna for 
transmitting and receiving, G; = Gz, which in this 
case is 100 or 20 db, and the radar gain 
10log = SONEGne 10 log = + 10loge 
1 
+40 log A — 20 logy}, 
= 40+ 7.5 + 17 — 254 — 0, 
— 189.5 db 
This gives P; = 10®° watts, which obviously is unat- 
etainable. 
Errect oF VERTICAL POLARIZATION 
The general value for K in equation (108), when 
the reflection coefficient p differs from — 1 and 
F. 2/, F. i= 1 is 
K = pD. (128) 
© im equation (108) is no longer given by equation 
(116) but is the sum of two phase shifts, one caused 
by path difference, (R/r)x = nz, while the other is 
’ = > — 7, the difference between the phase of the 
reflection coefficient and that for perfect reflection. 
Hence 
Oe Eg Hon. (129) 
r 
The lobe variable (for imperfect reflection) is 
now N, defined by 
Q = Nr (130) 
rather than n = R/r. The relation between N and n 
is derivable from equation (129), giving 
Wey ace OP (131) 
vis 
The propagation is assumed to take place over 
sea water. The angle between the reflected wave 
and the earth is given by equation (107) or Figure 24, 
and is 
W = 0.582°. 
From Figures 14 and 15 in Chapter 4, 
od = 168°, p = 0.76. 
The lobe variable N, in terms of the old lobe variable 
(for p = 1,¢ = 180°), by equation (131), is 
N = 1.88 — ace 1.81, 
180 
The fact thet N <7 signifies that the lobe for 
vertical polarization (other things being equal) has a 
greater angle of elevation than the lobe for hori- 
zontal polarization. 
K = pD = 0.76 X 0.95 = 0.722 
The value of 10 log [« — K)? + 4K sin? | 
= 10 log 0.322 = —5. 
Therefore, for vertical polarization, 
20 log A = —118 — 5 = —123, 
which may be compared with the value 20 log A 
= —127, obtained for horizontal polarization with 
p=1. 
° Type II. Radio Gain Versus 
Receiver Height for Given Distance 
Radio gain versus receiver antenna height are 
to be found, while transmitter antenna height, 
wavelength, and distance are given. 
Suppose that a radar set has an antenna height 
of 30 meters, and an antenna gain of 13.5 db. Polari- 
zation is horizontal and the wavelength is 1.5 meters. 
Assume also a receiver with a gain of G2 = 1 (or 0 db) 
at a distance of 100 km. 
The following calculations are made: 
1. The variation of the radio gain P2/P;, with 
receiver antenna height hz is to be found. 
2. Instead of a receiver assume a target with 
cross section of 50 square meters. The value of the 
radar gain P2/P, at the radar receiver is to be found 
as a function of target height ho. 
The diffraction part of the calculation is given on 
pp.413-416 ; the optical part in this section. The 
results are represented in Figure 25, the two partial 
curves for one-way transmission having been com- 
bined into a smooth overall curve which makes pos- 
sible the estimation of 10 log P:/P, in the transition 
region near the line of sight. The radar gain varies as 
40 log A [equation (5)] rather than as 20 log A and 
contains a constant shift 10 log [G2(1670/9n2)] 
rather than 10 log GGo. 
Ravio Garin: ONE-Way TRANSMISSION 
The calculation is most readily performed by using 
p = d;/dr as the independent variable and then 
finding the corresponding values of he, the receiver 
height, and A. 
1. From Figure 15 in Chapter 6 or equation (115), 
r = 9,403. 
