Last Updated on March 28, 2025 by John Berry
The loss in signal as a wave propagates in an environment between two antennas is termed the path loss. The path can propagate through, for example, the troposphere alone, or up to the ionosphere and back, or out into space and reflected by the moon, or scattered by rain.
Path loss is made up of free space loss plus additional losses. Those additional losses describe, for example, diffraction over an obstacle. Those additional losses are expressed as losses ‘over free space’.
in a free space loss calculation, the antennas at either end of the link must be stated. There are two options: dipoles, or isotropic antennas. This standard antennas are signified by the suffix dBd for dipoles and dBi for isotropic antennas. Isotropic antennas are point sources which radiate equally in all directions. Polarisation of the antennas must be specified.
Dipoles have the classic dumbbell radiation pattern, with maximum radiation orthogonal to the driven element. The assumption is that the dipoles are in free space – free, that is, of ground and other environmental influence.
When in free space, a dipole has a small gain of 2.15dB over an isotropic antenna.
Free space path loss
When mounted in free space and transmitting through the normal atmosphere near to the surface of the earth, the path loss is given by a simple equation:
FSL(dBi) = 32.4 + 20logd + 20logf
FSL is the free space path loss. d is the distance in kilometres, and f is the frequency in megahertz. The answer is given relative to isotropic antennas and denoted by the suffix dBi.
If dipoles are used as reference, the equation becomes:
FSL(dBi) = 28.1 + 20logd + 20logf
Note that the gain term is applied at both ends, changing the constant to 28.1, and reducing the path loss by 4.3dB.
Free space loss is expressed by an empirical formula that accounts for normal spreading (diffusion) and absorption.
Free space loss application
There is, in principle, no limit to the use of the free space loss equation. The caveat is that the antenna must be defined relative to a dipole or an isotropic radiator.
That’s difficult below about 30MHz where the ground forms part of the antenna itself. Modern modelling software does allow antenna definitions below 30MHz, and to express antenna gains in terms of dBd or dBi, but there are many errors made. For example, it can’t be assumed that a horizontal half-wave dipole resonant around 3.6MHz has a gain of 0dBd if it’s only ten metres above the ground. This antenna will have a plethora of lobes, and it would be far from certain that its gain would be unity in the direction of interest.
Likewise, it would be false to convert this to dBi by adding 2.15dB.
Whenever antenna gain is discussed at HF, gain must be determined by modelling, not by assumption.
Diffraction loss
Loss due to diffraction varies from a few dBs for some trees in the foreground to maybe 50dB for the blocking of a path by the curvature or bulge of the Earth. It’s complicated to model diffraction and needs software and a digital elevation model that includes land use.
Diffraction loss is calculated considering obstruction of the first Fresnel zone. The narrower the obstruction (towards a perfect knife edge), the lower the excess loss. The broader and more rounded the obstruction (or collection of obstructions) the greater the loss.
Diffraction loss can be estimated from knowledge of the path profile and obstructions. It increases with frequency – trees in the foreground will be of little consequence at 144MHz, but at 10GHz vegetation losses may be catastrophic.
Reflection loss
Radio waves reflect from surfaces like the sea, the ground, and the Moon. Strictly reflection is the case where the reflecting surface is smooth relative to the wavelength. Snells Law would also be obeyed. If there are a plethora of disparate reflections, it can perhaps be more accurately described as scattering, and the loss described as scattering loss.
Reflection loss is described by the reflection coefficient, typically a fraction. It can of course be expressed as a dB loss over free space from the equation:
Reflection loss (dB) = 10logρ
Where ρ is the scalar reflection coefficient. As an example, the reflection coefficient of the moon has been measured as about 6.5% or 0.065. As a reflection loss, that’s 12dB.
Typically, reflection loss from the ground and sea during multi-hop HF communications, and from meteor trails is considered equal to zero.
Refraction and absorption losses
In the same sense, there can be additional losses as the wave refracts through a medium like the ionosphere.
Typically, it’s assumed that refraction though the ionosphere as the wave returns toward Earth is small. Losses must be added for each entry and exit from the ionosphere.
Absorption occurs when a wave propagates a dense medium such as a rain cloud. Often the distance for which the wave is in the cloud is low compared to the path length and absorption is typically ignored.
Aggregating path loss
Typically, a path loss value can be aggregated by summing all the losses (and gains if there are any) in this sort of sum:
Total loss (dBi or dBd) = free space loss (dBi or dBd) + diffraction loss (dB) + reflection loss (dB) etc.
The total loss is expressed in dBi or dBd, set by the reference antennas used in the free space loss calculation. All the additional losses must be included and there may be many.
The total loss is used to determine if a path will work – for example the total path loss to the Moon and back is:
Total loss = free space loss up + reflection loss + free space loss down
As a value, that’s about 197dBi + 12dB + 197dBi, or about 406dBi at 432MHz. Other losses or gains then need to be added, and the Moon’s ‘billboard’ gain subtracted to give a final path loss value on the day.