382 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
the field can be obtained for intermediate points. 
There is a further possibility occurring with the 
transmitting antenna elevated, the receiver low and 
lying below the interference pattern, and the dis- 
tance short. In this event, none of the previous 
methods apply. However, the reciprocity principle 
(see Chapter 2) can be applied to find the radio 
gain at the receiver by interchanging the role of 
receiver and transmitter. Suppose the original 
transmitter height is 100 meters, the original re- 
ceiver height 15 meters, and the wavelength 1 meter. 
Now let the transmitter height be 15 meters. If the 
receiver height is low (ht: < 30 meters), values of 
the gain can be found ( page 405); if the receiver 
height is in the interference region, the gain can be 
found by the ray method. Now suppose a curve be 
drawn for these results, giving the attenuation 
versus receiver height. From this graph, the value 
of the gain factor A at h, = 100 meters can be read. 
This value of A by the principle of reciprocity is the 
gain factor for the original heights. 
4. Ultra-short waves in the diffraction region. 
Dielectric earth. For } < 10 meters (f > 30 mc) and 
for either polarization, land acts as a dielectric earth 
or absorbing earth in contradistinction to a conducting 
earth. Propagation over a dielectric earth is practi- 
=10-mhos/m 
© 10 20 30'40 50 60 70 80 90 100 
d IN KILOMETERS —> 
Ficure 5. Field strength ratio versus distance for 
vertical polarization over dry soil for h; = 100 meters 
and h, = 0. 
WA ATA A 
Hit KK 
Lian 
t) © 20 30 40 50 60 70 80 90 100 
____» d IN KILOMETERS 
Ficure 6. Field strength ratio versus distance for 
vertical polarization and heights h; = h2 = 100 meters. 
cally independent of earth constants. For a given 
type of polarization, the chief variables affecting 
gain are then the heights of the antennas, their 
distance apart, and the wavelength. Within the 
diffraction region, the effect of increasing wavelength 
is to increase the field strength. This is illustrated 
by the curves in Figures 5 and 6. The dielectric earth 
is characterized by a value of 6 > a 1. 6 is given 
by equation (193). 
While sea water has a relatively high conductivity, 
radio wave propagation over it is the same as that 
over a dielectric earth in the case of horizontal polar- 
ization for \ < 10 meters, and in the case of vertical 
polarization for \ < 1 meter. Consequently, verti- 
cally polarized radiation of wavelength range 1 to 10 
meters over sea water is given special treatment on 
pages 416-419. 
In the same range, 1 to 10 meters, for vertically 
polarized radiation and for distances less than those 
given in Table 3, propagation conditions over land 
also deviate slightly from those corresponding to a 
dielectric earth. 
5. Optical region. In the optical-interference 
region, the lobes for the shorter waves are more 
numerous, narrower, and lower, as can be seen from 
the oscillatory part of the field strength versus 
distance curves of Figure 6. 
The dependence of reflection coefficients upon 
polarization, wavelength, and ground constants is 
discussed on pp. 370-375. 
6. Horizontal versus vertical polarization. In the 
optical region, for rays at small grazing angles, there 
is not much difference between the two types of 
polarization. For larger grazing angles, the differ- 
ence is more marked (see the section on reflection 
coefficients. 
FIRST MAXIMUM 
vn 
OPTICAL REGION ——— 
SHADOW ZONE 
ELEVATED ANTENNA 
20 LoG(g,£h,)+ cae 
(APPLIES ONLY WELL 
BELOW LINE OF SIGHT) 
ae i 20 LOG g, 
ala / 
8 17 
a 
° Ve 
TRANSITION 
hg= 300° : 
B= RADIO GAIN AT ho= = 
FOR £,SEE TABLE 4 
ow he 
ho IN METERS 
Ficure 7. Gain versus height at distances beyond the 
radio horizon. 
