Free-space Path Loss - Physical Explanation

Physical Explanation

The FSPL expression above often leads to the erroneous belief that free space attenuates an electromagnetic wave according to its frequency. This is not the case, as there is no physical mechanism that could cause this.

The expression for FSPL actually encapsulates two effects. Firstly, the spreading out of electromagnetic energy in free space is determined by the inverse square law, i.e.

where:

• is the power per unit area or power spatial density (in watts per metre-squared) at distance ,
• is the total power transmitted (in watts).

Note that this is not a frequency-dependent effect.

The second effect is that of the receiving antenna's aperture, which describes how well an antenna can pick up power from an incoming electromagnetic wave. For an isotropic antenna, this is given by

where is the received power. Note that this is entirely dependent on wavelength, which is how the frequency-dependent behaviour arises.

The total loss is given by the ratio

which can be found by combining the previous two expressions.