Free-space path loss

Free-space path loss

In telecommunication, free-space path loss (FSPL) is the loss in signal strength of an electromagnetic wave that would result from a line-of-sight path through free space, with no obstacles nearby to cause reflection or diffraction. It does not include factors such as the gain of the antennas used at the transmitter and receiver, nor any loss associated with hardware imperfections. A discussion of these losses may be found in the article on link budget.

Free-space path loss formula

Free-space path loss is proportional to the square of the distance between the transmitter and receiver, and also proportional to the square of the frequency of the radio signal.

The equation for FSPL is

:egin{align} mbox{FSPL} &= left ( frac{4pi d}{lambda} ight )^2 \ &= left ( frac{4pi d f}{c} ight )^2end{align}

* lambda is the signal wavelength (in metres),
* f is the signal frequency (in hertz),
* d is the distance from the transmitter (in metres),
* c is the speed of light in a vacuum, 2.99792458 × 108 metres per second.

This equation is only accurate in the far field; it does not hold close to the transmitter.

Free-space path loss in Wireless Communication

This formula applies to Wireless Communications as shown below.In highways and in rural areas where there are at most 2 multipaths ( the LOS-Line of Sight and/or the ground reflected ), this is part of the 2-ray path loss model

As depicted in the figure above, it assumes that the distance between transmitting and receiving antennas 'd' is much greater than the wavelength of the EM ( Electromagnetic ) waves and the wavefronts impinging the receiving antenna are planar and not spherical and this distance is large enough to neglect the curvature of earth.The relation between the transmitted and the received power ( Pu and Pr ) in Watts is given as :

:egin{align} P_{r} &= P_{u}left ( frac{G_{l}lambda}{4pi d} ight )^2end{align}

* Gl is the product of transmit and receive antenna radiation patterns

Derivation of the formula can be found in [C.A. Balanis "Advanced Engineering Electromagnetics", 1989, John Wiley and Sons, Inc.]

Free-space path loss in decibels

A convenient way to express FSPL is in terms of dB:

:egin{align}mbox{FSPL(dB)} &= 10log_{10}left(left(frac{4pi}{c}df ight)^2 ight) \ &= 20log_{10}left(frac{4pi}{c}df ight) \ &= 20log_{10}(d) + 20log_{10}(f) + 20log_{10}left(frac{4pi}{c} ight) \ &= 20log_{10}(d) + 20log_{10}(f) - 147.56end{align}

where the units are as before.

For typical radio applications, it is common to find f measured in units of MHz and d in km, in which case the FSPL equation becomes

: mbox{FSPL(dB)} = 20log_{10}(d) + 20log_{10}(f) + 32.44

For d in statute miles, the constant becomes 36.6 .

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.

: S = P_t frac{1}{4 pi d^2}

* S is the power per unit area (in watts per metre-squared) at distance d,
* P_t 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

: P_r = S frac{lambda^2}{4 pi}

where P_r 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

: mathrm{FSPL} = frac{P_t}{P_r}

which can be found by combining the previous two expressions.

ee also

*Friis transmission equation
*Link budget

Further Reading

*C.A. Balanis, "Antenna Theory", 2003, John Wiley and Sons Inc.
* [ Andrea J. Goldsmith, PhD Thesis]

External references

* [ Derivation of the dB version of the Path Loss Equation]
* [ Propagation Models] Chapter on Free Space Propagation
* [ Radio propagation primer] A more in-depth explanation of the relationship between path loss, the inverse square law, and antenna aperture

Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Path loss — (or path attenuation) is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is a major component in the analysis and design of the link budget of a telecommunication system.This term… …   Wikipedia

  • Free space optical communication — In telecommunications, Free Space Optics (FSO) is an optical communication technology that uses light propagating in free space to transmit data between two points. The technology is useful where the physical connection by the means of fibre… …   Wikipedia

  • Loss — may refer to:*A negative difference between retail price and cost of production *An event in which the team or individual in question did not win. *Loss (baseball), a pitching statistic in baseball *Attenuation, a reduction in amplitude and… …   Wikipedia

  • Space colonization — Artist Les Bossinas 1989 concept of Mars mission Space colonization (also called space settlement, space humanization, or space habitation) is the concept of permanent human habitation outside of Earth. Although hypothetical at the present time,… …   Wikipedia

  • Space debris — populations seen from outside geosynchronous orbit (GEO). Note the two primary debris fields, the ring of objects in GEO, and the cloud of objects in low earth orbit (LEO) …   Wikipedia

  • Space Shuttle — STS redirects here. For other uses, see STS (disambiguation). This article is about the NASA Space Transportation System vehicle. For the associated NASA STS program, see Space Shuttle program. For other shuttles and aerospace vehicles, see… …   Wikipedia

  • space exploration — Investigation of the universe beyond Earth s atmosphere by means of manned and unmanned spacecraft. Study of the use of rockets for spaceflight began early in the 20th century. Germany s research on rocket propulsion in the 1930s led to… …   Universalium

  • Space Shuttle Columbia disaster — For further information about Columbia s mission and crew, see STS 107. STS 107 mission patch The Space Shuttle Columbia disaster occurred on February 1, 2003, when shortly before it was scheduled to conclude its 28th mission, STS 107, the Space… …   Wikipedia

  • Space Shuttle external tank — A Space Shuttle External Tank (ET) is the component of the Space Shuttle launch vehicle that contains the liquid hydrogen fuel and liquid oxygen oxidizer. During lift off and ascent it supplies the fuel and oxidizer under pressure to the three… …   Wikipedia

  • Okumura Model — The Okumura model for Urban Areas is a Radio propagation model that was built using the data collected in the city of Tokyo, Japan. The model is ideal for using in cities with many urban structures but not many tall blocking structures. The model …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”