Campbell Scientific RF401-series and RF430-series Spread Spectrum Data Radios/Modems - Manual (Page 87)

Appendix H. Distance vs. Antenna Gain, Terrain, and Other Factors
Here is a table showing the free space path loss (in dB). Note the effect of
frequency.
Frequency Distance
1 mi. 2 mi. 4 mi. 8 mi. 10 mi. 16 mi. 22 mi. 26 mi. 30 mi.
400 MHz 89 95 101 107 109 113 115 117 118
915 MHz 96 102 108 114 116 120 123 124 125
2.4 GHz 104 110 116 122 124 128 131 133 134
Notice the relationship between path loss and distance: each time you double
the distance, you lose 6 dB of signal under free space conditions. Or, put
another way, if you add 6 dB of gain (for example with 6 dB of additional
antenna gain, or 6 dB less cable loss), you can double the distance for free
space conditions.
As mentioned before, free space conditions are the ideal, but seldom actually
seen. The higher the antenna height relative to the terrain in the line of sight
path, the closer to free space conditions. Antenna height is everything!
Here are some additional propagation effects that increase the path losses:
Diffraction
This is caused by objects close to the line of sight path. Real world examples
of this would be hills, buildings, or trees. The object may not be in the direct
line-of-sight, but if it is close enough, it will cause the RF to diffract around the
object, giving additional path loss. “Close enough” is a function of frequency,
path length, and position of the obstacle along the path.
An example at 900 MHz: a 10 mile path length with an obstacle halfway along
the path will see diffraction “losses” from an obstacle within ~70 ft. of line-of
sight. The amount of loss would be from 6 dB to 20 dB, depending on the
obstacle surface. A sharp edge (like a rock cliff) would give the minimum loss
(6 dB), while a rounded hill would give the maximum loss (20 dB).
Ground Reflections
These are caused by the RF signal being reflected from the ground (or water),
and undergoing a phase shift so that it destructively interferes with the line of
sight signal. The conditions that cause this the most are propagation over
water, or over a low-lying fogbank. The reflected signal suffers little
attenuation, gets out of phase, and interferes with the main signal. If antennas
need to be sited near water, they should be positioned away from the water’s
edge so that the ground vegetation attenuates the reflected RF.
The result of the reflection and interference (worst case) is that the path loss
increases as the 4 th power of the distance, instead of the 2 nd power. This
changes the distance term in the path loss equation to: 40 x log ( d ) dB.
Then, with each doubling of distance, the path loss increases by 12 dB, instead
of 6 dB.
Vegetation
Losses due to vegetation (trees, bushes, etc) cause the path loss to increase by
the 3 rd to 4 th power of the distance, instead of the 2 nd power. This is just like in
the severe ground reflection case above.
H-5