Free-space path loss
Encyclopedia
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 (usually air), 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
.
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
where:
This equation is only accurate in the far field where spherical spreading can be assumed; it does not hold close to the transmitter.
:
where the units are as before.
For typical radio applications, it is common to find
measured in units of MHz and 
in km, in which case the FSPL equation becomes
For
in meters and megahertz, respectively, the constant becomes 
.
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.
where:
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
where
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
which can be found by combining the previous two expressions.
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
, free-space path loss (FSPL) is the loss in signal strength
Signal strength
In telecommunications, particularly in radio, signal strength refers to the magnitude of the electric field at a reference point that is a significant distance from the transmitting antenna. It may also be referred to as received signal level or field strength. Typically, it is expressed in...
of an electromagnetic wave that would result from a line-of-sight
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...
path through free space (usually air), with no obstacles nearby to cause reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
or diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
. It does not include factors such as the gain
Antenna gain
In electromagnetics, an antenna's power gain or simply gain is a key performance figure which combines the antenna's directivity and electrical efficiency. As a transmitting antenna, the figure describes how well the antenna converts input power into radio waves headed in a specified direction...
of the antennas
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
used at the transmitter
Transmitter
In electronics and telecommunications a transmitter or radio transmitter is an electronic device which, with the aid of an antenna, produces radio waves. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating...
and receiver
Receiver (radio)
A radio receiver converts signals from a radio antenna to a usable form. It uses electronic filters to separate a wanted radio frequency signal from all other signals, the electronic amplifier increases the level suitable for further processing, and finally recovers the desired information through...
, nor any loss associated with hardware imperfections. A discussion of these losses may be found in the article on link budget
Link budget
A link budget is the accounting of all of the gains and losses from the transmitter, through the medium to the receiver in a telecommunication system. It accounts for the attenuation of...
.
Free-space path loss formula
Free-space path loss is proportionalProportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
to the square of the distance between the transmitter and receiver, and also proportional to the square of the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of the radio signal.
The equation for FSPL is
where:
is the signal wavelength (in metres),
is the signal frequency (in hertzHertzThe hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
),
is the distance from the transmitter (in metres),
is the speed of light in a vacuumSpeed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, 2.99792458 × 108 metres per second.
This equation is only accurate in the far field where spherical spreading can be assumed; it does not hold close to the transmitter.
Free-space path loss in decibels
A convenient way to express FSPL is in terms of dBDecibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
:
where the units are as before.
For typical radio applications, it is common to find
measured in units of MHz and in km, in which case the FSPL equation becomesFor
in meters and megahertz, respectively, the constant becomes .Physical explanation
The FSPL expression above often leads to the erroneous belief that free space attenuatesAttenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
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.
where:
-
is the power per unit area or power spatial density (in wattWattThe watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s per metre-squared) at distance
, -
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
Antenna aperture
In electromagnetics and antenna theory, antenna aperture or effective area is a measure of how effective an antenna is at receiving the power of radio waves. The aperture is defined as the area, oriented perpendicular to the direction of an incoming radio wave, which would intercept the same...
, which describes how well an antenna can pick up power from an incoming electromagnetic wave. For an isotropic antenna, this is given by
where
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
which can be found by combining the previous two expressions.
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