es 
a 
Chapter 5 
CALCULATION OF RADIO GAIN 
INTRODUCTION 
Objectives 
HIS CHAPTER is devoted to the definition and 
calculation of the various factors which enter 
into a computation of the field strength of radio 
waves propagated in the standard atmosphere above 
the earth. 
In Chapter 2, particularly in text on pp.336-340, 
are given the basic definitions of path-gain factor 
and radio gain for transmission between doublets 
and other antenna types in free space. The present 
chapter shows how these quantities must be modified 
to account for the influences introduced by the 
curvature and electrical properties of the earth. 
The methods of computation are presented in 
considerable detail to enable the interested reader to 
apply them to his particular problem, and sample 
calculations are given which should assist in reducing 
to a minimum the time required for obtaining the 
answers in a given case. 
Definitions Relative to Radio Gain 
The radio gain is defined as the ratio of received 
power P>, delivered to a load matched to the receiver 
antenna, to transmitted power Pi, with both an- 
tennas adjusted for maximum power transfer. For 
doublet antennas in free space this ratio is given by 
(8d/87d)?.and is denoted by A¢?, that is, 
Po ya ( sry 
Py a (2) (1) 
and the free-space gain factor is given by 
Ay =— (2) 
in which d denotes the distance from the transmitter 
to the receiver measured in the same units as the 
wavelength i. 
When the radiation is emitted and received by 
directive antennas and the propagation takes place 
through a refracting and absorbing atmosphere, and 
reflection and diffraction effects of the ground are 
taken into account, the expression for the radio gain 
becomes a very complicated affair. 
For the general case of one-way transmission, the 
radio gain is given by 
5B = GGA’, (3) 
377 
where G; and G» are the gains of the transmitting and 
receiving antennas, respectively, and A, the gain 
factor, is equal to 
A=A,A, (4) 
with A, equal to the path-gain factor. [See equation 
(27) in Chapter 2.] 
For radar or two-way transmission, the radar gain 
is decreased because the energy traverses the path 
both ways and is influenced by the radiating proper- 
ties of the target as given by the radar cross section o. 
Combining equations (46) in Chapter 2 and (2) in 
this chapter, the radar gain equals 
P, SS Ge) 
— = GG. Ao'A,4| = GiG2| —— } A+. (5 
Te ee pe) al Ce) EE) 
Comparing equations (8) and (5), it is seen that the 
gain factor A may be used also for two-way trans- 
mission, provided the additional term 1670/9)? is 
included in the formula. 
Later on it will be shown how to split up A and A, 
into a product of various factors, represented by 
graphs which make it possible to carry out computa- 
tions in specific cases. 
The gain factor A may also be expressed in terms 
of the field strength H and free-space field strength of 
a doublet transmitter Ho. From equation (28) in 
Chapter 2, 
E = Ey VG; Ay. (6) 
Combining this equation with equation (4) 
Wh eS SO (7) 
where EoVG, is the free-space field of the trans- 
mitting antenna with gain G. 
The free-space field, in terms of the transmitted 
power P), is given by 
VGEy = 3V5 VP; 8) 
d 
for a point in the direction of maximum radiation. 
In terms of the power P; delivered to the load circuit 
of a receiving antenna, with matched load and 
oriented for maximum pickup, the field at any point in 
space is equal, from equation (17) in Chapter 2, to 
7p ND (9) 
d VG 
It is sometimes convenient to express # in terms of 
the (radiation) field at one meter from the trans- 
