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TABLE 4.2
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Speci c Attenuation Coef cients ah 0.0000387 0.000154 0.00065 0.00175 0.00301 0.00454 0.0101 0.0188 0.0367 0.0751 0.124 0.187
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Ippolito, 1986, p. 46.
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Frequency, GHz 1 2 4 6 7 8 10 12 15 20 25 30
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Reduction Factors r0.001 5 r0.01 5 r0.1 5 r1 10 10 90 90 4LG LG 180 180 LG
For p For p For p For p
0.001% 0.01% 0.1% 1%
SOURCE:
Ippolito, 1986.
LS Rain hR El h0 LG
Path length through rain.
Rain height as a function of earth-station latitude for different climatic zones.
Radio Wave Propagation
for El 10 a flat earth approximation may be used, and from Fig. 4.3 it is seen that LS 5 hR h0 (4.4)
sin El
The effective path length is given in terms of the slant length by L LSrp (4.5)
where rp is a reduction factor which is a function of the percentage time p and LG, the horizontal projection of LS. From Fig. 4.3 the horizontal projection is seen to be LG LS cosEl (4.6)
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 Ap aRb LSrp dB p (4.7)
Interpolation formulas which depend on the climatic zone being considered 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 From Eq. (4.4): LS 5 hR h0 50 ; h0 0.6; hr 3; R01 10
sin El 3 0.6 sin 50 3.133 km
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From Eq. (4.6): LG LS cosEl 3.133 cos 50 2.014 km From Table 4.3, the reduction factor is r01 5 90 90 4LG
0.9178 For horizontal polarization, from Table 3.2 at f From Eq. (4.7): Ap ahR01h LSr01 0.0188 0.891 dB For vertical polarization, from Table 3.2 at f Ap avR01h LSr01 0.0168 0.766 dB 10
1.2 b b
12 GHz; ah
0.0188; bh
12 GHz; av
0.0168; bv
The corresponding equations for circular polarization are ac 5 bc 5 ah 2 ahbh 2ac av avbv (4.8a) (4.8b)
The attenuation for circular polarization is compared with that for linear polarization in the following example.
Example 4.2 Repeat Example 4.1 for circular polarization.
Solution
From Eq. (4.8a): ac 5 ah 2 0.0188 2 0.0178 0.0168 av
Radio Wave Propagation
From Eq. (4.8b): bc 5 ahbh 2ac 0.0188 1.209 From Eq. (4.7): Ap acR01c LSr01 0.0178 0.828 dB 101.209 3.133 0.9178
avbv 1.217 2 0.0168 1.2
4.5 Other Propagation Impairments Hail, ice, and snow have little effect on attenuation because of the low water content. Ice can cause depolarization, described briefly in Chap. 5. The attenuation resulting from clouds can be calculated as that for rain (Ippolito, 1986, p. 56), although the attenuation is generally much less. For example, at a frequency of 10 GHz and a water content of 0.25 g/m3, the specific attenuation is about 0.05 dB/km and about 0.2 dB/km for a water content of 2.5 g/m3.
4.6 Problems and Exercises
4.1. With reference to Table 4.1, identify the propagation impairments which most affect transmission in the C band. 4.2. Repeat Prob. 4.1 for Ku-band transmissions.
4.3. Calculate the approximate value of atmospheric attenuation for a satellite transmission at 14 GHz, for which the angle of elevation of the earth-station antenna is 15 . 4.4. Calculate the approximate value of atmospheric attenuation for a satellite transmission at 6 GHz, for which the angle of elevation of the earth-station antenna is 30 . 4.5. Describe the major effects the ionosphere has on the transmission of satellite signals at frequencies of (a) 4 GHz and (b) 12 GHz.
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4.6. Explain what is meant by rain rate and how this is related to specific attenuation. 4.7. Compare the specific attenuations for vertical and horizontal polarization at a frequency of 4 GHz and a point rain rate of 8 mm/h which is exceeded for 0.01 percent of the year. 4.8. Repeat Prob. 4.7 for a frequency of 12 GHz.
4.9. Explain what is meant by effective path length in connection with rain attenuation. 4.10. For a satellite transmission path, the angle of elevation of the earth station antenna is 35 , and the earth station is situated at mean sea level. The signal is vertically polarized at a frequency of 18 GHz. The rain height is 1 km, and a rain rate of 10 mm/h is exceeded for 0.001 percent of the year. Calculate the rain attenuation under these conditions. 4.11. Repeat Prob. 4.10 when the rain rate of 10 mm/h is exceeded (a) 0.01 percent and (b) 0.1 percent of the year. 4.12. Given that for a satellite transmission El 22 , R0.01 15 mm/h, h0 600 m, hR 1500 m, and horizontal polarization is used, calculate the rain attenuation for a signal frequency of 14 GHz. 4.13. Determine the specific attenuation for a circularly polarized satellite signal at a frequency of 4 GHz, where a point rain rate of 8 mm/h is exceeded for 0.01 percent of the year. 4.14. A circularly polarized wave at a frequency of 12 GHz is transmitted from a satellite. The point rain rate for the region is R0.01 13 mm/h. Calculate the specific attenuation. 4.15. Given that for Prob. 4.13 the earth station is situated at altitude 500 m and the rain height is 2 km, calculate the rain attenuation. The angle of elevation of the path is 35 . 4.16. Given that for Prob. 4.14 the earth station is situated at altitude 200 m and the rain height is 2 km, calculate the rain attenuation. The angle of elevation of the path is 25 .
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