330 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
Depending upon the-strength and the thickness 
of the duct, there is a limiting frequency below 
which the duct cannot trap the wave energy. 
Though trapping does at times occur at 200 me, 
it is more likely to occur at the higher frequencies 
such as 3,000 me. 
Ability to calculate performance under standard 
conditions is necessary if performance under non- 
standard conditions is to be evaluated. 
Radio Gain 
The basic problem to be solved is that, of com- 
puting the radig gain of a transmitting-receiving 
system. 
The radio gain of a transmitting-receiving system 
is defined as the ratio of received power Pe, delivered 
to a load matched to the receiving antenna, to 
power P,, supplied to the transmitting antenna, with 
both antennas adjusted for maximum power transfer. 
Thus 
Radio gain = a, (5) 
1 
which is equal, in the decibel scale, to 
10 logio < = radio gain in decibels. (6) 
1 
The attenuation is the reciprocal of the gain. Since 
P2/P, < 1, the gain in decibels is necessarily a nega- 
tive quantity. The attenuation in decibels is a 
positive quantity equal in magnitude to the gain in 
decibels. 
The radio gain can be taken as the product of 
physically significant factors. Among these are the 
gains G, and G3 of the transmitting and receiving 
antennas respectively; and A? which accounts for all 
other influences modifying the transmission of power. 
A is called the gain factor. 
Radio gain = fav 
P: 
1 
= G,G,A2. (7a) 
The radar problem involves double transmission 
over the path as well as the reradiating properties of 
the target, 1620/92. 
; P, 1610 
Radar gain = — = (GA! 5 (ad 
SEC OPM ie ee) oO 
1 
Fronts 
Radiation 
ie 
au 
Tronemitter Circuit 
where o is the radar cross section of the target and \ 
is the wavelength. 
The gain factor, 4, may also be split into two 
factors, so that 
A = AvA». (8) 
Here Apo is the free-space gain factor for doublet 
antennas (see next Section and pp.338, 339 ,379 ) 
adjusted for maximum power transfer. Ao = 3A/87d 
where d is the distance between doublets. A, is the 
path gain factor which includes all additional influ- 
ences modifying the transmission of power. 
These factors may also be related to the field 
strength, #, at any point in space by 
E = EWNGA, (9) 
and 
eae (10) 
Ao E.\VG, 
Here Zp is the free-space field at a point in space 
set up by a doublet transmitter and HoVG is the 
free-space field of a transmitter with antenna 
gain G). 
The primary function of this book is to show how 
the factors A and A, may be caleulated, taking into 
account all contributory influences which modify 
their magnitudes. 
Radio Gain of Doublet Antennas 
in Free Space 
This is the fundamental and simplest case of 
transmission of radiant energy, against which other 
transmitting combinations may be compared. Two 
doublet antennas (for which the gains, by definition, 
are unity) are set up in free space in a manner whieh 
insures the maximum transfer of power to the re- 
ceiver circuit, i.e., the doublets are parallel to each 
other, have a common equatorial plane, and the 
receiver circuit impedance is matched to that of the 
receiving antenna (see Figure 3). Then for free 
space, 
ral 9 » 2 
Free-space gain = = = Aj? = =) , (1) 
and the free-space field strength at distance d from 
Renrpcoticn 
0 
—d 
To 
Recelver Circuit 
Medes 
Figure 3. Doublet antennas in free space. 
