Free Space Path Loss and Formula or Equation
- summary, tutorial or overview about the free space path loss, FSPL, and how to calculate the loss using the RF path loss formula or equation.
Radio path loss and link budget tutorial includes:
The free space path loss is used in many areas for predicting radio signal strengths that may be expected in a radio system. Although it does not hold for most terrestrial situations as there are several situations in which it can be used and it is also useful as the basis for understanding many real life radio propagation situations.
Despite this, the free space path loss is an essential basic parameter for many RF calculations. It can often be used as a first approximation for many short range calculations. Alternatively it can be used as a first approximation for a number of areas where there are few obstructions. As such it is a valuable tool for many people dealing with radio communications systems.
In addition to this, these calculations can be used in wireless survey tools. With the growing requirements to be able to analyse wireless or radio coverage, wireless survey tools are being sued increasingly to enable coverage to be predicted at the early stages of design. Accordingly these wireless survey tools are being used increasingly in the development and installation of radio and wireless systems.
Free space path loss basics
The free space path loss, also known as FSPL is the loss in signal strength that occurs when an electromagnetic wave travels over a line of sight path in free space. In these circumstances there are no obstacles that might cause the signal to be reflected refracted, or that might cause additional attenuation.
The free space path loss calculations only look at the loss of the path itself and do not contain any factors relating to the transmitter power, antenna gains or the receiver sensitivity levels. These factors are normally address when calculating a link budget and these will also be used within radio and wireless survey tools and software.
To understand the reasons for the free space path loss, it is possible to imagine a signal spreading out from a transmitter. It will move away from the source spreading out in the form of a sphere. As it does so, the surface area of the sphere increases. As this will follow the law of the conservation of energy, as the surface area of the sphere increases, so the intensity of the signal must decrease.
As a result of this it is found that the signal decreases in a way that is inversely proportional to the square of the distance from the source of the radio signal.
Free space path loss formula
The free space path loss formula or free space path loss equation is quite simple to use. Not only is the path loss proportional to the square of the distance between the transmitter and receiver, but the signal level is also proportional to the square of the frequency in use for other reasons explained in a section below.
|FSPL =|| ( 4 π d / λ ) ^2
|=|| ( 4 π d f / c ) ^2
FSPL is the Free space path loss
d is the distance of the receiver from the transmitter (metres)
λ is the signal wavelength (metres)
f is the signal frequency (Hertz)
c is the speed of light in a vacuum (metres per second)
The speed of light is 2.99792458 x 10^8 metres per second, although for most practical purposes, this is taken to be 3 x 10^8 metres per second.
The free space path loss formula is applicable to situations where only the electromagnetic wave is present, i.e. for far field situations. It does not hold true for near field situations.
Free space loss formula frequency dependency
Although the free space loss equation given above seems to indicate that the loss is frequency dependent. The attenuation provided by the distance travelled in space is not dependent upon the frequency. This is constant.
The reason for the frequency dependence is that the equation contains two effects:
- The first results from the spreading out of the energy as the sphere over which the energy is spread increases in area. This is described by the inverse square law.
- The second effect results from the antenna aperture change. This affects the way in which any antenna can pick up signals and this term is frequency dependent.
As one constituent of the path loss equation is frequency dependent, this means that there is a frequency dependency within the complete equation.
Decibel version of free space path loss equation
Most RF comparisons and measurements are performed in decibels. This gives an easy and consistent method to compare the signal levels present at various points. Accordingly it is very convenient to express the free space path loss formula, FSPL, in terms of decibels. It is easy to take the basic free space path loss equation and manipulate into a form that can be expressed in a logarithmic format.
d is the distance of the receiver from the transmitter (km)
f is the signal frequency (MHz)
Affect of antenna gain on path loss equation
The equation above does not include any component for antenna gains. It is assumed that the antenna gain is unity for both the transmitter. In reality, though, all antennas will have a certain amount of gain and this will affect the overall affect. Any antenna gain will reduce the "loss" when compared to a unity gain system. The figures for antenna gain are relative to an isotropic source, i.e. an antenna that radiates equally in all directions.
Gtx is the gain of the transmitter antenna relative to an isotropic source (dBi)
Grx is the gain of the receiver antenna relative to an isotropic source (dBi)
The free space path loss equation or formula given above, is an essential tool that is required when making calculations for radio and wireless systems either manually or within applications such as wireless survey tools, etc. By using the free space path loss equation, it is possible to determine the signal strengths that may be expected in many scenarios. While the free space path loss formula is not fully applicable where there are other interactions, e.g. reflection, refraction, etc as are present in most real life applications, the equation can nevertheless be used to give an indication of what may be expected. It is obviously fully applicable to satellite systems where the paths conform closely to the totally free space scenarios. .......
By Ian Poole
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