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telecommunications Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...
, the free-space path loss (FSPL) (also known as free-space loss, FSL) is the
attenuation In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a Transmission medium, medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and ...
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 A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
(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 In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cau ...
and decreases with the square of the
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
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.


Free-space path loss formula

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 P_r to the power transmitted P_t is: :\frac = D_t D_r \left( \frac \right)^2 where *\ D_t is the
directivity In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It is the ratio of the radiation intensity in a given direction f ...
of the transmitting antenna *\ D_r is the
directivity In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It is the ratio of the radiation intensity in a given direction f ...
of the receiving antenna *\ \lambda is the signal wavelength *\ d is the distance between the antennas The distance between the antennas d must be large enough that the antennas are in the far field of each other \ d\gg\lambda. 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 In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also ...
and have no directivity (D_t = D_r = 1): \begin \mbox = \left ( \frac \lambda \right )^2 \end Since the frequency of a radio wave f is equal to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
c divided by the wavelength, the path loss can also be written in terms of frequency: \begin \mbox = \left(\right)^2 \end 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 A Fresnel zone ( ), named after physicist Augustin-Jean Fresnel, is one of a series of confocal prolate ellipsoidal regions of space between and around a transmitter and a receiver. The size of the calculated Fresnel zone at any particular di ...
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.


Influence of distance and frequency

The free-space loss increases with the distance between the antennas and decreases with the wavelength of the radio waves due to these factors:, Section 1.8 *
Intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...
(I) – the
power density Power density, defined as the amount of power (the time rate of energy transfer) per unit volume, is a critical parameter used across a spectrum of scientific and engineering disciplines. This metric, typically denoted in watts per cubic meter ...
of the radio waves decreases with the square of distance from the transmitting antenna due to spreading of the electromagnetic energy in space according to the
inverse square law In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cau ...
* Antenna capture area (A_\text) – the amount of power the receiving antenna captures from the radiation field is proportional to a factor called the ''antenna aperture'' or antenna capture area, which increases with the square of wavelength. Since this factor is not related to the radio wave path but comes from the receiving antenna, the term "free-space path loss" is a little misleading. *Directivity of receiving antenna- while the above formulas are correct, the presence of Directivities Dt and Dr builds the wrong intuition in the FSPL Friis transmission formula. The formula seems to say that "free space path loss" increases with frequency in vacuum, which is misleading. The frequency dependence of path loss does not come from free space propagation, but rather from receiving antenna capture area frequency dependence. As frequency increases, the directivity of an antenna of a given physical size will increase. In order to keep receiver antenna directivity constant in the formula, the antenna size must be reduced, and a smaller size antenna results in less power being received as it is able to capture less power with a smaller area. In other words, the path loss increases with frequency because the antenna size is reduced to keep directivity constant in the formula, and has nothing to do with propagation in vacuum. *Directivity of transmitting antenna - the directivity of transmitting antenna does not have the same role as directivity of receiving antenna. The difference is that the receiving antenna is receiving the power from free space, and hence captures less power as it becomes smaller. The transmitting antenna does not transmit less power as it becomes smaller (for example half wave dipole), because it is receiving its RF power from a generator or source, and if the source is 1 Watt or Pt, the antenna will transmit all of it (assuming ideal efficiency and VSWR for simplicity). * System Loss Factor (L) : Miscellaneous loses or system loses (L=>1) are usually due to transmission line attenuation, filter loses, and antenna loses in communication system. A value of L = 1 indicates no loss in the system hardware.


Derivation

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 d is 4\pi d^2. Thus the intensity or power density of the radiation in any particular direction from the antenna is inversely proportional to the square of distance :I \propto (The term 4\pi d^2 means the surface of a sphere, which has a radius d. Please remember, that d here has a meaning of 'distance' between the two antennas, and does not mean the diameter of the sphere (as notation usually used in mathematics).) For an
isotropic antenna An isotropic radiator is a theoretical point source of waves that radiates the same intensity of radiation in all directions. It may be based on sound waves or electromagnetic waves, in which case it is also known as an isotropic antenna. It ...
which radiates equal power in all directions, the power density is evenly distributed over the surface of a sphere centered on the antenna :I = \qquad \qquad \qquad \text The amount of power the receiving antenna receives from this radiation field is :P_r = A_\textI \qquad \qquad \qquad \text The factor A_\text, called the ''effective area'' or ''aperture'' of the receiving antenna, which has the units of area, can be thought of as the amount of area perpendicular to the direction of the radio waves from which the receiving antenna captures energy. Since the linear dimensions of an antenna scale with the wavelength \lambda, the cross sectional area of an antenna and thus the aperture scales with the square of wavelength \lambda^2. The effective area of an isotropic antenna (for a derivation of this see
antenna aperture In electromagnetics and antenna theory, the aperture of an antenna is defined as "A surface, near or on an antenna, on which it is convenient to make assumptions regarding the field values for the purpose of computing fields at external points. ...
article) is :A_\text = Combining the above (1) and (2), for isotropic antennas :P_r = \Big(\Big)\Big(\Big) :\text = = \Big(\Big)^2


Free-space path loss in decibels

A convenient way to express FSPL is in terms of
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
s (dB): : \begin \operatorname(\text) &= 10\log_\left(\left(\frac\right)^2\right) \\ &= 20\log_\left(\frac\right) \\ &= 20\log_(d) + 20\log_(f) + 20\log_\left(\frac\right) \\ &= 20\log_(d) + 20\log_(f) -147.55, \end using
SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...
s of meters for d,
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...
(s−1) for f, and meters per second (m⋅s−1) for c, (where c=299 792 458 m/s in vacuum, ≈ 300 000 km/s) For typical radio applications, it is common to find d measured in
kilometers The kilometre ( SI symbol: km; or ), spelt kilometer in American and Philippine English, is a unit of length in the International System of Units (SI), equal to one thousand metres (kilo- being the SI prefix for ). It is the preferred measu ...
and f in
gigahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base un ...
, in which case the FSPL equation becomes :\operatorname(\text) = 20\log_(d_) + 20\log_(f_) + 92.45, an increase of 240 dB, because the units increase by factors of and respectively, so: :20\log_(10^) + 20\log_(10^) = 240. (The constants differ in the second decimal digit when the speed of light is approximated by 300 000 km/s. Whether one uses 92.4, 92.44 or 92.45 dB, the result will be OK as the average measurement instruments cannot provide more accurate results anyway. A logarithmic scale is introduced to see the important differences (i.e. order of magnitudes), so in engineering practice dB results are rounded)


See also

* Computation of radiowave attenuation in the atmosphere *
Friis transmission equation The Friis transmission formula is used in telecommunications engineering, equating the power at the terminals of a receive antenna as the product of power density of the incident wave and the effective aperture of the receiving antenna under i ...
*
Radio propagation model Radio propagation is the behavior of radio waves as they travel, or are propagated, from one point to another in vacuum, or into various parts of the atmosphere. As a form of electromagnetic radiation, like light waves, radio waves are affect ...
*
ITU-R P.525 ITU-R P.525 is the International Telecommunication Union radiocommunications standard for the calculation of free-space attenuation. See also * Free space loss References ITU-R recommendations {{Wireless-stub ...
* Link budget * Two-ray ground reflection model *
Free-space optical communication Free-space optical communication (FSO) is an optical communication technology that uses light propagating in free space to wirelessly transmit data for telecommunications or computer networking over long distances. "Free space" means air, oute ...


References


Further reading

*
Derivation of the dB version of the Path Loss EquationPath loss
Pages for free space and real world – includes free-space loss calculator *Hilt, A. “Throughput Estimation of K-zone Gbps Radio Links Operating in the E-band”'', Journal of Microelectronics, Electronic Components and Materials, Vol.52, No.1, pp.29-39'', 2022. DOI:10.33180/InfMIDEM2022.104

shows Fresnel zone and its calculation {{Radio frequency propagation models Telecommunications engineering Radio frequency propagation model