Attenuation is the loss of signal strength in networking cables or connections. Any wave – water, sound or electromagnetic attenuates (dies away) with increasing distance from the source. Attenuation in wireless technology may look like a disadvantage but it actually has benefits.
Quantifying attenuation of an electromagnetic wave
Quantifying: express or measure the quantity of
The inverse square law
After travelling a distance of 1 unit, the power of the wave is spread out of one square. At two units or twice the distance, it is spread out over four times the area. At 3 units or 3 times the distance, it is spread out over 9 squares. So the receiving antenna at two units collects a 1/4 of the power it would at one unit. At three units, it would collect 1/9 of the power it would collect at one unit. This reduction in power in proportion to the square of the distance is called inverse square law.
Note: units of distance do not matter.
The inverse square law concerns relative power only. We cannot say what the actual relative power will be at 2km from the transmitter without further information. For example, if we knew that at 1km the power received by the antenna was 8nW, we could calculate that at 2km, the power would be 1/4 of 8nW or 2nW
the received power is proportional to 1/d²
So if the distance was 3km. the receiving power is (1/3)² or 1/9th of that collected at d=1
Q: A rambler with her mobile phone starts her walk at 1km from a mobile phone mast. By the time she is 6km from the mast, what fraction of signal power will her phone receive using reverse square law? If the power received was 0.5nW. What will the power be at 6km?
A: (1/6)² or 1/36 of the signal at 1km. If the power received was 0.5nW, the power at 6km will be 1/36 if that or 0.138 nW
If the rambler had an app, showing her signal strength received, and it was showing 0.125 nW, she would be 2km away from the mast. This is because the original signal strength at 1km was 0.5km, and 0.125 nW is a quarter of 0.5km, meaning she is double the distance away. Given the starting unit was 1km, she is now 2km away.
Inverse cube and inverse fourth power
There is additional attenuation introduced by atmosphere, weather conditions, topographical features such as natural terrain or buildings/traffic. Such situations are hard to model mathematically, but measurements have shown in urban environments, an inverse cube model (1/d)³ or inverse fourth power (1/d)4