Library / Communications / COM-02
Communications
Free-space path loss
Signal loss over a clear path, in decibels.
- Ref
- COM-02
- Rev
- v1
- Field
- Communications
- Result
- L [dB]
d is the distance between the antennas in kilometres and f the frequency in GHz. L is the loss between two ideal isotropic antennas in free space, in decibels. Antenna gains are added separately in the link budget. Each tenfold increase in distance or frequency adds 20 dB.
Signal loss over a clear path, in decibels. Loss rises by 6 dB each time the distance or the frequency doubles.
Calculator
- Loss at twice the distance126.1 dB
- Ratio of transmitted to received power, 10L/101.012×1012
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 2.4 GHz link over 10 km loses 120 dB: a 1 W transmitter gives only about 1 pW at an isotropic receiver. Antenna gain and a sensitive receiver make up the difference.
- The frequency term is not a loss in the air. It arises because a fixed antenna size collects less power at a higher frequency, so using a larger dish at the high end recovers it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (dB) | Local step | Change in result |
|---|---|---|---|---|---|---|
| d Distance | 0.01 to 10,000 km | 60.05 | 180.1 | 120 | +10% | +0.828 dB |
| f Frequency | 0.01 to 100 GHz | 72.45 | 152.4 | 80 | +10% | +0.828 dB |
Sweep of Distance
| Distance (km) | Path loss (dB) |
|---|---|
| 0.01 | 60.05 |
| 0.05623 | 75.05 |
| 0.3162 | 90.05 |
| 1.778 | 105.1 |
| 10 | 120.1 |
| 56.23 | 135.1 |
| 316.2 | 150.1 |
| 1,778 | 165.1 |
| 10,000 | 180.1 |
Sweep one variable
Variables and how each one contributes
Path loss
What the equation gives you. Everything else feeds it.
Distance
The distance between transmitter and receiver, in km. Logarithmic: every doubling of the distance adds 6 dB. A 10 % rise in d adds only 0.83 dB.
Frequency
The radio frequency, in GHz. Logarithmic, the same as distance: every doubling of the frequency adds 6 dB, since a smaller wavelength means a smaller antenna aperture. A 10 % rise in f adds 0.83 dB.
Worked example with the values above
- Distance term: 20 log₁₀(10,000 m) = 80 dB.
- Frequency term: 20 log₁₀(2.4×109 Hz) = 187.6 dB; constant 20 log₁₀(4π/c) = −147.6 dB.
- L = 80 + 187.6 − 147.6 = 120.1 dB.
Assumptions and limits
- Free space with a clear line of sight and the first Fresnel zone free of obstacles.
- Far field (distance much greater than the wavelength and the antenna size) and ideal isotropic antennas.
Common mistakes
- Forgetting the antenna gains, which are added to the link budget separately.
- Using the formula with the distance in miles or the frequency in MHz without converting.
Statistics and uncertainty
Because L is on a logarithmic scale, errors in d and f are heavily compressed: a 10 % error in distance is only 0.8 dB. The real uncertainty is in what the formula leaves out (rain, foliage, multipath, ground reflection), which can add tens of decibels, so the free-space figure is a best case.
Where it is used
- Radio link budgets and jammer-to-signal calculations.
- Estimating the range of a communications or telemetry link.
Maths you need
- Decibels: 10 log₁₀ of a power ratio
- Logarithms: log₁₀ of products