Introduction
For communications systems to operate reliably a good signal needs to be received. Too weak a signal will cause loss of data and too strong a signal can result in overloading of the receiver or interference to other communications systems. Environmental factors will (normally) reduce the received signal below the level resulting from a simple line of sight computation. Note that this posting only considers propagation in the far field – antennas more than a few wavelengths apart and in an uncluttered environment.
The transmitting isotropic antenna
This is an antenna which radiates equally in all directions, in effect distributing the power over the surface of a sphere with the antenna at the centre. This is an important definition because all antennas are characterised in comparison with an isotropic antenna. A high gain antenna concentrates the power in a preferred direction at the expense of power being radiated in other directions. A useful analogy is squeezing a balloon where it shrinks where it is squeezed and pops out further in other areas.
Antenna gains are usually expressed in dB referenced to an isotropic antenna and these figures are denoted as dBi (dB relative to an isotropic antenna). An example of this is a dipole antenna which shows a gain of 2.2dBi in its preferred radiation directions.
An isotropic antenna is defined as being 100% efficient. This means all the power which is put into the antenna is transmitted onto its coverage area. This is known as radiation efficiency and all antennas are less than 100% efficient. Factors which can impact radiation efficiency include the impedance matching to the signal source (mismatches result in power being reflected to the source) and resistive losses of the surfaces of the antenna.
As the surface area of a sphere is equal to
the power density at a distance r from the antenna can be computed as
where Pt is the transmitted power.
From this it can be seen that the power density reduces by the square of the distance.
The receiving isotropic antenna.
Antennas receive as well as transmit and the amount of power they receive is a function of the area of the signal they intercept. The effective area of an isotropic antenna is defined as
where Λ is the wavelength of the signal being received.
Isotropic antennas receive equally well in all directions and are defined as being 100% efficient. Real world antennas have efficiency losses and can increase their sensitivity in some directions at the expense of others. This figure is exactly the same as the transmit case as antennas are reciprocal in nature.
Path loss
Knowing the power density of a transmitting isotropic antenna and the effective area of a receiving antenna it is possible to work out the power transferred by two antennas.
and the path loss is
As wavelength isn’t normally used we convert to frequency
where c is the speed of light (300,000,000 m/s)
Converting everything to dB and separating the terms we end up with
As antenna gains are expressed in dBi and we can easily add the effect of them to the pathloss computation:
This is a useful result as it allows us to quickly work out the loss between two antennas under optimal conditions. If you only have the natural logs rather than base 10 then you can convert the base using the substitution below:
