2 TECHNICAL SURVEY 
1 10 
-60 
-70 5 
4 
3 
-80 
4 
2 
-90 
fo} 
q 
10 8 1 
at pa 
loo 5 
N 
il 
cal 
— —20 -110 ak 0.5 
fo) rt) 
ui 9 0,4 
Fi 30 5 
3 -120 N 0.3 
= 40 
= ”n 
2° -350 = O2E- = 
oa a 
-130-- ¥ bd 
8 : 
z = 
100 Z 0.1 
-140F- 2 
200 -150 0.05 
0.04 
pee 0.03 
-160 
400 
500 0.02 
-170 
1000 0.01 
-180 
Ficure 1. Nomogram for free space transmission between 
parallel doublets. 
where GG» are the antenna gains of the transmitting 
and receiving systems, respectively, and A, is the 
‘Hath factor.”” The nomogram, Figure 1, gives this 
relation for G,=G,=A,=1. Often the electric field 
at the position of the receiver is desired. It is given by 
E = iv V P,G,A,, (3) 
where E is in volts per meter, P; in watts. If EZ is 
known, the power delivered by the receiving antenna 
to a matched load is 
B2 3X2 
7 sce (4) 
The combination of equations (3) and (4) gives again 
the general transmission formula (2). 
The lower limit of possible receiver sensitivity is 
set by the thermal noise in the receiving system. At 
ordinary temperatures the thermal noise power in 
watts is very approximately 
Teroise =4.- 10-P Af, (5) 
where Af is the radio-frequency bandwidth of the 
receiver in megacycles. 
The minimum power P,,,, required for intelligible 
reception being usually in excess of the thermal noise 
power, it is customary to use the ratio Prin/Protse 
expressed in decibels as a measure of the receiver 
sensitivity Ten times the logarithm of this ratio 
(to the base 10) is the sensitivity of the receiver in 
decibels above thermal noise. 
As may be seen from this brief outline, the problem 
of transmission in free space is a very simple one from 
the engineering viewpoint. There are certain ques- 
tions regarding noise limit, receiver sensitivity, and 
matching of the load which constitute refinemerts of 
the above procedure. They are of interest primarily 
for those concerned with receiver design; apart from 
these the problem of power transmission may be con- 
sidered solved by these formulas. The most impor- 
tant and difficult part of ultra short wave propagation 
then becomes the quantitative determination of the 
path factor A, as a function of the geometry of the 
transmission path, electromagnetic properties of the 
ground, refractive properties of the atmosphere, etc 
P2 
OPTICAL PROPERTIES OF THE 
EARTH’S SURFACE AND ATMOSPHERE 
REFLECTION COEFFICIENTS 
In dealing with standard propagation it is usually 
assumed that the ground has electromagnetic prop- 
erties which are constant over the length of the 
transmission path. Deviations from this idealized 
behavior are treated below as diffraction phenomena. 
The electromagnetic properties of the ground 
are completely described by its complex dielectric 
constant, 
€ = € — je; = €, — J60oA, (6) 
where e, is the relative dielectric constant, ¢ the con- 
ductivity in mhos per meter, and d the wavelength 
in meters. In general, and especially in the micro- 
wave region, e, and e; are themselves functions of 
the frequency. Figure 2 shows the variation of the 
real and imaginary parts of the complex dielectric 
constant of sea water at 17 C for ultra-high fre- 
quencies according to the best available experi- 
mental data. 
