Free-space path loss

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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).[1] 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."[2] Despite this name and definition, the FSPL includes a receiving antenna aperture component in the total attenuation.[1] It does not include any path loss associated with hardware imperfections, or the effects of any antenna gains. A discussion of these losses may be found in the article on link budget. The FSPL is rarely used standalone, but rather as a part of the Friis transmission formula, which includes the gain of antennas.[3]

Free-space path loss formula[edit]

The free-space path loss (FSPL) formula derives from the Friis transmission formula[3] that states power gain of an antenna system thus...

The FSPL formula expresses a loss value that is the reciprocal of gain and assumes the directivity for the transmit and receive antennas are isotropic and therefore unity. Both modifications simplify the equation to...


  • is the signal wavelength,
  • is the distance between the antennas,
  • and are in the same unit of length,
  • such that both antennas are in the far field of each other.[4]

Substitute for to calculate from frequency where:

  • is the speed of light (in metres/s),
  • is frequency (in Hz).

Antenna effective aperture and free space loss[edit]

Despite the misleading name, the free-space path loss formula inherits two important effects from the Friis transmission formula:

  • Intensity () – the power density due to path loss by spreading of the electromagnetic energy yielding loss proportional to the square of distance;[1]
  • Antenna capture area () – the capability of the receiving antenna to capture electromagnetic energy yielding loss inversely proportional to the square of wavelength or proportional to the square of frequency.[1]

Hence the equation for FSPL is:

Friis implied the antennas are isotropic.[3] Hence the power density from the isotropic transmit antenna vs. distance from the antenna is...

The effective area of the isotropic antenna is...

Combining the two yields...

Free-space path loss in decibels[edit]

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

where the units are as before.

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

For in meters and kilohertz, respectively, the constant becomes .

For in meters and megahertz, respectively, the constant becomes .

For in kilometers and megahertz, respectively, the constant becomes . [5]

See also[edit]


  1. ^ a b c d Islam, Syad Kamrul; Haider, Mohammad Rafiqul. Sensors and Low Power Signal Processing (2010 ed.). p. 49. ISBN 978-0387793917.
  2. ^ IEEE Std 145-1993(R2004), IEEE Standard Definitions of Terms for Antennas. New York, NY: The Institute of Electrical and Electronics Engineers, Inc. 1993. p. 14. ISBN 1-55937-317-2.
  3. ^ a b c Friis, H.T. (May 1946). "A Note on a Simple Transmission Formula". IRE Proc.: 254–256.
  4. ^ Johnson, Richard (1984). Antenna Engineering Handbook (2nd ed.). New York, NY: McGraw-Hill, Inc. pp. 1–12. ISBN 0-07-032291-0.
  5. ^ Poole, Ian. "Free Space Path Loss: Details, Formula, Calculator". Adrio Communications Ltd. Retrieved 17 July 2017.

Further reading[edit]