Page 129 - Satellite Communications, Fourth Edition

Radio Wave Propagation 109

for El 10° a flat earth approximation may be used, and from Fig. 4.3
it is seen that

h h 0
L 5 (4.4)
R
S
sin El
The effective path length is given in terms of the slant length by
L L r (4.5)
S p
where r is a reduction factor which is a function of the percentage time
p
p and L , the horizontal projection of L . From Fig. 4.3 the horizontal
S
G
projection is seen to be
L L cosEl (4.6)
S
G
The reduction factors are given in Table 4.3.
With all these factors together into one equation, the rain attenuation
in decibels is given by
b
A aR p L r dB (4.7)
p
S p
Interpolation formulas which depend on the climatic zone being con-
sidered are available for values of p other than those quoted earlier
(see, e.g., Ippolito, 1986). Polarization shifts resulting from rain are
described in Sec. 5.6.

Example 4.1 Calculate, for a frequency of 12 GHz and for horizontal and verti-
cal polarizations, the rain attenuation which is exceeded for 0.01 percent of the
time in any year, for a point rain rate of 10 mm/h. The earth station altitude is
600 m, and the antenna elevation angle is 50°. The rain height is 3 km.

Solution The given data follows. Because the CCIR formula contains hidden
conversion factors, units will not be attached to the data, and it is understood
that all lengths and heights are in kilometers, and rain rate is in millimeters
per hour.

El 50°; h 0 0.6; h r 3; R 01 10
From Eq. (4.4):

L S 5 h R h 0
sin El
3 0.6

sin 50
3.133 km