Free-Space Path Loss and Link Budgets for VHF, UHF and Satellites
How much signal is left when a radio wave arrives at a receiver 100 kilometres away, or at a satellite 36,000 kilometres above the equator? The answer is not a mystery, and you do not need a computer to find it. The reduction in signal strength between two antennas in clear space is called free space path loss, and it follows a formula that fits on one line. Add the transmitter power, the gain of both antennas, the losses in the cables and the sensitivity of the receiver, and you have a link budget that tells you whether a contact is possible and how much margin you have. This guide gives the formula, works through examples from a 2 meter handheld to the Moon, and shows how to read the result. The numbers are the basis for every VHF, UHF, microwave and satellite station you may want to build.
Why a Radio Wave Gets Weaker With Distance
The word “loss” is misleading, because in free space no energy is absorbed. The transmitter radiates power into a growing sphere, and the same power spreads over a larger and larger area. If the distance doubles, the area becomes four times as large, and the power that falls on a receiving antenna of a fixed size drops to a quarter, which is a change of 6 dB. The Wikipedia article on free-space path loss describes this as the inverse square law, and it explains why the loss depends on the distance in a straightforward way.
There is a second factor that surprises many beginners: the loss rises with frequency. This is not a property of space but of the receiving antenna. A given antenna design becomes smaller as the frequency rises, since its size is measured in wavelengths, and a smaller antenna collects less power from the same wave. If you keep the gain of the antennas constant, the loss increases by 6 dB every time the frequency doubles. When you use larger antennas at the higher frequencies, as satellite and microwave stations do, you can win this loss back.
The Formula You Can Do in Your Head
With the distance in kilometres and the frequency in megahertz, the loss in decibels is
FSPL (dB) = 32.44 + 20 log10(distance in km) + 20 log10(frequency in MHz)
The constant 32.44 covers the units. Because of the logarithms you can break the calculation into steps: every tenfold increase in distance adds 20 dB, and every doubling adds 6 dB. The same applies to the frequency. A calculator with a logarithm button is all that is needed, and the table below shows the results for typical amateur paths.
| Path | Frequency | Distance | Free space path loss |
|---|---|---|---|
| Local FM contact | 145 MHz | 10 km | 95.7 dB |
| Long line-of-sight link | 145 MHz | 100 km | 115.7 dB |
| UHF tropo opening | 432 MHz | 300 km | 134.7 dB |
| Microwave link | 10 GHz | 50 km | 146.4 dB |
| Low orbit satellite overhead | 145.8 MHz | 400 km | 127.8 dB |
| Geostationary satellite | 10.489 GHz | 35,786 km | 203.9 dB |
| Moon, one way | 144 MHz | 384,400 km | 187.3 dB |
Look at how the figures grow. The ham who works 10 km on 2 meters has to overcome about 96 dB, while the Moon station deals with nearly 190 dB in each direction. The difference of 90 dB is a factor of a billion in power. This is the reason why EME stations need big antennas, a quiet receiver and a mode as sensitive as the one described in our beginner’s guide to EME with Q65.
Building a Link Budget Step by Step
A link budget is a simple addition of gains and losses, all in decibels, from the transmitter to the receiver. You start with the power of the transmitter, add the antenna gain at the sending end, subtract the loss in the feedline and the path loss, add the gain of the receiving antenna and subtract the loss in the receiving feedline. The result is the signal power at the receiver input, and you compare it with the sensitivity of the receiver. The difference is the link margin: the number of decibels you have in reserve for fading, mismatch, rain, a poor antenna alignment and everything else that you did not calculate.
Take a handheld with 5 watts on 145 MHz. Five watts is 37 dBm. A rubber duck antenna has a gain of about 0 dBi at best, and the cable loss is zero. The receiving station is a similar handheld 10 km away. The signal at the input is 37 – 95.7 = -58.7 dBm, which is a strong signal that is far above the level at which an FM receiver needs a good quality signal, usually about -120 dBm. The margin is more than 60 dB. In practice the path is not free space because of buildings, hills and trees, and the real loss is much higher, but the margin shows that the radio itself is not the limit.
Now try a path of 100 km with the same handhelds. The loss rises by 20 dB, and the signal drops to -78.7 dBm. The margin is still 40 dB in the textbook case, but a path of 100 km at low height is blocked by the curvature of the Earth, as our guide to the radio horizon explains. The calculation tells you that power is not the problem; the obstacle is. That is a useful lesson, because it saves you from buying an amplifier when a taller mast is what you need.
A Low Orbit Satellite Example
A pass of an amateur satellite shows how the budget is used in a real situation. The ISS orbits at about 400 km, and when it is directly overhead the free space path loss on 145.8 MHz is about 127.8 dB. Near the horizon the distance grows to over 2,000 km, and the loss climbs to about 142 dB, which is roughly 14 dB more. A handheld with a small directional antenna such as a three-element Yagi, 5 watts and a decent receiver is enough for FM satellites, and the extra loss at low elevation is the reason why the signal fades at the beginning and at the end of a pass. The figures help to explain the experience described in our introduction to amateur radio satellites, where an antenna with a modest gain makes such a difference.
A second example shows the other end of the scale. A geostationary satellite downlink on 10.489 GHz arrives after a loss of about 204 dB. If the satellite radiates a few watts toward the whole of the visible Earth, the signal that reaches a small dish is extremely weak, and the budget works only because the dish has a gain of 30 dB or more and the low-noise converter at its focus adds very little noise. Remove the dish and use a simple antenna instead, and the margin disappears by about 30 dB. This is the kind of reasoning that tells you in advance which equipment is needed, before a single part has been bought.
Beyond Free Space: What the Formula Leaves Out
The free space value is the minimum loss. A real path has extra terms, and it is useful to know the main ones so that you can add a margin to the budget.
- Obstructions and diffraction. A hill or a building on the path adds loss that can be 10 to 30 dB or more. The size of the clear zone around the line of sight is the subject of the Fresnel zone, which determines how much clearance a path needs.
- Ground reflections. A wave that reflects from the ground can add to the direct wave or cancel it, so the signal changes by several decibels for a small change in the antenna height.
- Atmospheric absorption. Oxygen and water vapour matter above about 10 GHz, and rain is a serious factor on the microwave bands. Below 1 GHz the effect is negligible.
- Polarisation mismatch. A vertical antenna that talks to a horizontal one loses a large part of the signal, and the case of circular polarisation has a fixed 3 dB penalty against a linear antenna.
- Feedline loss. At VHF and UHF the coax can eat several decibels, and every decibel counts. The effect grows with the frequency, as our article on coaxial cable types shows.
Troposphere effects can also help. A temperature inversion can bend the signal and carry it far beyond the horizon, with a loss that is less than the free space value would predict at that distance. The phenomenon is covered in our article on tropospheric ducting.
Antenna Gain and Receiver Sensitivity Win Back the Loss
The budget shows where to put your effort. A 10 dB gain antenna at each end improves the margin by 20 dB, and you can obtain it with a Yagi, which is cheaper than a 100 times more powerful amplifier. A low-noise preamplifier at the antenna can improve the sensitivity of the system, but only if the receiver was the weak link, and that is a question of noise figure. The comparison between gain and power is simple: 3 dB of antenna gain on each side equals 6 dB of margin, which is the same as four times the transmitter power. An antenna works in both directions, so a larger antenna helps the station when it transmits and when it receives.
The same arithmetic is the reason for the choice of modes. A weak-signal mode that decodes at a signal to noise ratio 15 dB lower than SSB gives the same advantage as an increase of the power by a factor of 30, and it costs nothing. If you work through a few budgets, you will find that many problems that look like needs for more power are really problems of the antenna, of the height or of the mode.
Common Mistakes
Several errors appear again and again in station planning. The first is to mix the units: the formula above wants kilometres and megahertz, and a value in metres or in gigahertz gives a wrong constant. The second is to forget that dBm and dBW differ by 30 dB, so the transmitter power must be expressed in the same unit as the sensitivity. The third is to treat the margin as certain; a link with a margin of 3 dB is a link that fails when the weather changes. A good design keeps at least 10 dB for terrestrial paths and more for the paths that are affected by rain or that depend on pointing a narrow beam. The fourth mistake is to measure the distance along the surface of the Earth when the path is a satellite pass; the slant range is longer than the distance on the ground, and the elevation of the satellite decides the loss.
The Bottom Line
Free space path loss equals 32.44 + 20 log(km) + 20 log(MHz) in decibels, which means 6 dB more for every doubling of the distance or of the frequency. A local 2 meter contact has about 96 dB to overcome, a geostationary satellite on 10 GHz about 204 dB and the Moon on 144 MHz about 187 dB in each direction. A link budget adds transmitter power and antenna gains and subtracts the path loss and the cable losses to give the signal at the receiver input, and the difference to the sensitivity is your margin. Use it to see whether a better antenna, a taller mast, a sensitive mode or a clearer path is the cheapest improvement.
Frequently Asked Questions
What is free space path loss?
It is the reduction in signal strength between two antennas in empty space with a clear line of sight. It grows by 6 dB each time the distance or the frequency doubles.
Does path loss mean that the signal is absorbed?
No. In free space the power is spread over a larger area, and a receiving antenna captures only a small part of it. The energy is not converted to heat.
How do I convert watts to dBm for a link budget?
Take ten times the logarithm of the power in milliwatts. One watt is 30 dBm, 5 watts is about 37 dBm, and 100 watts is 50 dBm.
How much margin should I plan for?
For a terrestrial VHF or UHF path, a margin of 10 dB is a reasonable minimum. For links that fade, such as satellite passes at low elevation or microwave paths in rain, plan for more.
Why is the loss to a geostationary satellite so high?
The satellite is about 36,000 km away, and the frequency is high. Both increase the free space loss. Ground stations compensate with large dish antennas and low-noise receivers.
Is the formula valid on HF?
Not directly. HF signals travel by ionospheric reflection and ground wave, so the path is not free space, and the loss depends on propagation conditions more than on distance.