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In telecommunication, the free-space path loss (FSPL) is the attenuation of radio energy between the feedpoints of two antennas that results from the combination of the receiving antenna's capture area plus the obstacle free, line-of-sight path through free space (usually air). The "Standard Definitions of Terms for Antennas", IEEE Std 145-1993, defines "free-space loss" as "The loss between two isotropic radiators in free space, expressed as a power ratio." It does not include any power loss in the antennas themselves due to imperfections such as resistance. Free space loss increases with the square of distance between the antennas because the radio waves spread out due the inverse square law and decreases with the square of the wavelength of the radio waves. The FSPL is rarely used standalone, but rather as a part of the Friis transmission formula, which includes the gain of antennas. It is a factor that must be included in the power link budget of a radio communication system, to ensure that sufficient radio power reaches the receiver that the transmitted signal is received intelligibly.
The free-space path loss (FSPL) formula derives from the Friis transmission formula.[1] This states that in a radio system consisting of a transmitting antenna transmitting radio waves to a receiving antenna, the ratio of radio wave power received
where
The distance between the antennas
Since the frequency of a radio wave
Beside the assumption that the antennas are lossless, this formula assumes that the polarization of the antennas is the same, that there are no multipath effects, and that the radio wave path is sufficiently far away from obstructions that it acts as if it is in free space. This last restriction requires an ellipsoidal area around the line of sight out to 0.6 of the Fresnel zone be clear of obstructions. The Fresnel zone increases in diameter with the wavelength of the radio waves. Often the concept of free space path loss is applied to radio systems that don't completely meet these requirements, but these imperfections can be accounted for by small constant power loss factors that can be included in the link budget.
The free space loss increases with the distance between the antennas and decreases with the wavelength of the radio waves due to these factors[4]
The radio waves from the transmitting antenna spread out in a spherical wavefront. The amount of power passing through any sphere centered on the transmitting antenna is equal. The surface area of a sphere of radius
For an isotropic antenna which radiates equal power in all directions, the power density is evenly distributed over the surface of a sphere centered on the antenna
The amount of power the receiving antenna receives from this radiation field is
The factor
Combining the above (1) and (2), for isotropic antennas
A convenient way to express FSPL is in terms of decibels (dB)
where the units are as before.
For typical radio applications, it is common to find
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