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Concept
Free-space path loss
Summary
In telecommunication, the free-space path loss (FSPL) (also known as free-space loss, FSL) 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 (LoS) 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 by 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 such that the transmitted signal is received intelligibly.
The free-space path loss (FSPL) formula derives from the Friis transmission formula. 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 to the power transmitted is:
where
is the directivity of the transmitting antenna
is the directivity of the receiving antenna
is the signal wavelength
is the distance between the antennas
The distance between the antennas must be large enough that the antennas are in the far field of each other .
The free-space path loss is the loss factor in this equation that is due to distance and wavelength, or in other words, the ratio of power transmitted to power received assuming the antennas are isotropic and have no directivity ():
Since the frequency of a radio wave is equal to the speed of light divided by the wavelength, the path loss can also be written in terms of frequency:
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.
Official source
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