Practical_Antenna_Handbook_0071639586

26 p a r t I I : F u n d a m e n t a l s
⎛ ⎞
R M N D1 D2
n
= ⎜ ⎟
F ⎝ D + D ⎠
1 2
(2.11)
where R n = radius of nth Fresnel zone
F = frequency in gigahertz
D 1 = distance from source to plane B 1 -B 2
D 2 = distance from destination to plane B 1 -B 2
N = an integer (1, 2, 3 . . .)
M = constant of proportionality equal to:
17.3 if R m is in meters and D 1 , D 2 are in kilometers
72.1 if R m is in feet and D 1 , D 2 are in statute miles
If you first calculate the radius (R 1 ) of the critical first Fresnel zone, you can calculate the
nth Fresnel zone from
Rn = R1 n
(2.12)
Example 2.1 Calculate the radius of the first Fresnel zone for a 2.5-GHz signal at a
point that is 12 km from the source and 18 km from the destination.
Solution
R M N ⎛ D D ⎞
1 2
1
=
F ⎝
⎜ D + D ⎠
⎟
1 2
1 ⎛ 12 × 18⎞
= (17.3)
2.5 ⎝
⎜
12 + 18⎠
⎟
= (17.3) (0.4)(7.2)
= (17.3)(2.88)
= 29.4 m
For most terrestrial microwave systems an obstacle clearance of 0.6 R 1 is required to
prevent diffraction attenuation under most normal conditions. However, there are conditions
in which the clearance zone should be more than one Fresnel zone.
Propagation Paths
There are four major propagation paths for a radio wave emanating from a terrestrial
source: surface wave, space wave, tropospheric, and ionospheric. The ionospheric path is a
major factor in medium-wave (MW) and HF propagation, but serves primarily only as
a potential source of loss for VHF, UHF, or microwave propagation to/from spacebased
antennas. Ionization and recombination phenomena in the ionosphere add to the
noise level experienced at VHF, UHF, and microwave frequencies. In satellite communications,
there are some additional trans-ionospheric effects.