Link Budget Part 5. How to Calculate the Path Loss Using Plane Earth Model (Ground Reflected Wave).
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Plane Earth Model
Propagation over a Plane Earth
If we consider the effect of the earth surface, the expressions for the received signal become more complicated than in case of free space propagation. The main effect is that signals reflected off the earth surface may (partially) cancel the line-of-sight wave.
Generally, the two antenna each have different height. The received signal having two components, the LOS component and the reflection component formed predominantly by a single ground reflected wave.
We assume that the earth is treated as a flat surface.
VHF, UHF and microwave signals normally propagate by space wave. Space wave consists of the direct wave and the ground reflected wave. Reflection from the ground will cause energy loss such that its attenuation will be higher than the free space loss.
At UHF and above, ground-reflection losses are greatly reduced by using highly directive antennas.
Path loss is given:
L (dB) = 120 + 40 log dkm - 20 log [hr(m) ht(m)]
where
d = distance in km
ht, hr = antenna hts in m
The plane earth propagation loss is independent of frequency.
Plane Earth Model (Example)
An aircraft is now approaching landing at a height of 1000m and is transmitting 5W to a control tower 10km away. The height of the control tower is 90m. Assume that there is a ground reflected signal to the control tower. Determine the received power in dBm at the control tower.
Since there is a ground reflected wave, we use the Plane earth model.
L (dB) = 120 + 40 log dkm - 20 log[hr(m) ht(m)]
= 120 + 40log10 – 20log(1000x90)
= 60.9dB
PT = 5W = 37dBm.
PR (dBm) = PT(dBm) – L(dB)
= 37 – 60.9
= -23.9dBm
In considering reflections introduced by the environment (Earth), the most significant source of reflections in terrestrial links is the earth’s surface.
Note that there are two paths from the transmitter (TX) to the receiver (RX): 1) a line-of-sight (LOS) path and 2) a reflected path.
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