CALCULATION OF RADIO GAIN 
419 
20LOG H. 
Ficure 47. Height-gain function Hz versus lh, for low antenna heights. [See equation (152.)] 
a relation between A, dy, and hz, and Figures 48, 49, 
and 50 for \ = 1, 3, 6 meters are in terms of these 
coordinates. The height-gain function of the trans- 
mitter g; can be found from Figure 41. 
7. Illustrative example: Communication. A com- 
munication set used in ship-to-ship work has a wave- 
length of 1 meter, a receiver sensitivity of 10 micro- 
volts with a resistance of 50 ohms across the input 
terminals and a transmitter power output of 100 
watts. The transmitter and receiver antennas are 
vertical half-wave dipoles at anelevation of 30 meters. 
The range is to be found. 
To produce a voltage of 10 microvolts across 
50 ohms, a power of 
Ws USO: 
watt = 2 X 10” watt, 
R 50 
P, = 
so that this is the minimum detectable power. The 
value of P2/P; for the given power output of 100 
watts is 
21057 
=2x 10%, 
100 
and 
10 log #2 =3-+ (—140) = —137. 
Py 
This is to be changed to 20 log A by equation (3). The 
gain of a half-wave dipole over a doublet is 1.09 
so that G, = Gz = 1.09 , or 0.4 db, 
20log A = —137 —0.8 = —138 db. 
In changing from 20 log A to 20 log A it must be 
determined which of the relations in equation (186) 
is required by comparing the transmitter height of 
30 meters with 4/1. The value of 1 as given by 
Figure 46 is 0.4. Hence the value of 4/1 is 10, which 
is less than 30. Then 
20 log A = 20 log A — 20 log 30 — 20 log gq’, 
= — 138 — 30-0, 
= — 168. 
Referring to the chart for \ = 1, Figure 48, we 
find that for h, = 30 meters and 20 log A = — 168, 
the distance d is 53 kilometers. This then is the 
maximum theoretical range between the two sets. 
Radio Gain Near the Line of Sight 
For @ much greater than dz, the first mode is 
sufficient, as given in the last two sections. For 
d nearly equal to dz, i.e., the receiver near the line of 
sight, a formula [equation (190)] can be given which 
takes into account several modes and still permits 
the use of graphical aids. This formula is valid only 
when the elevated antenna is very high, ie., 
h > 1,200d7/* and the other antenna is low, i.e., 
h < 30d72. (Otherwise the transition curve near 
the line of sight must be sketched in graphically, as 
indicated by the broken portion in Figure 7.) 
Denoting by H;, the height-gain of the low antenna 
at height hi, 
(sd)? 
A = 2A )Hy, M(s) Eis 
190 
2Qehe ( ) 
where fis and Fo(A) refer to the clevated antenna. 
1. sd and eh are given in Figures 40 and 41. 6 is 
givenon page 422. 
a = Ae) (oh = Baa). 
3. g(6) = 1, except for the VHF range, vertical 
polarization, over sea water. The values are given in 
Table 9. 
