Library / Communications / COM-01
Communications
Free-space link budget
Received power on a line-of-sight radio link from transmit power, antenna gains and free-space path loss.
- Ref
- COM-01
- Rev
- v1
- Field
- Communications
- Result
- Pr [dBm]
with d in metres and f in hertz. With d in km and f in GHz this becomes Lfs = 92.45 + 20 log10 f + 20 log10 d, which is what the calculator uses.
Start with the power you send, add what the antennas gain by focusing it, then subtract what is lost as the wave spreads over the distance. Every term is in decibels, so the whole calculation is addition and subtraction.
Calculator
- Path loss Lfs120.1 dB
- Received power, linear4.952×10−11 W
- Wavelength λ12.49 cm
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.
- Every doubling of distance costs 6 dB (20 log10 2 ≈ 6.02 dB). Doubling the frequency also costs 6 dB when both antenna gains are held fixed.
- One dB gained anywhere on the link (transmit power or either antenna) is worth exactly one dB at the receiver.
- Path loss dominates the budget. At 10 km and 2.4 GHz it is about 120 dB, far more than the gains you can usually add, which is why antenna directivity matters so much.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (dBm) | Local step | Change in result |
|---|---|---|---|---|---|---|
| d Distance | 0.1 to 1,000 km | −113.1 | −33.05 | 80 | +10% | −0.828 dBm |
| Pt Transmit power | 10 to 60 dBm | −93.05 | −43.05 | 50 | +1 dBm | +1 dBm |
| f Frequency | 0.1 to 30 GHz | −94.99 | −45.45 | 49.54 | +10% | −0.828 dBm |
| Gt Transmit antenna gain | 0 to 30 dBi | −83.05 | −53.05 | 30 | +1 dBi | +1 dBm |
| Gr Receive antenna gain | 0 to 30 dBi | −83.05 | −53.05 | 30 | +1 dBi | +1 dBm |
| Lsys System losses | 0 to 10 dB | −80.05 | −70.05 | 10 | +1 dB | −1 dBm |
Sweep of Distance
| Distance (km) | Received power (dBm) |
|---|---|
| 0.1 | −33.05 |
| 0.3162 | −43.05 |
| 1 | −53.05 |
| 3.162 | −63.05 |
| 10 | −73.05 |
| 31.62 | −83.05 |
| 100 | −93.05 |
| 316.2 | −103.1 |
| 1,000 | −113.1 |
Sweep one variable
Variables and how each one contributes
Received power
What the equation gives you. Everything else feeds it.
Transmit power
Power fed to the transmit antenna. 30 dBm is 1 W. Adds dB for dB at the receiver.
Transmit antenna gain
Focusing of the transmit antenna relative to an isotropic radiator. Adds dB for dB, exactly like transmit power.
Receive antenna gain
Gain of the receive antenna toward the transmitter. Adds dB for dB. A better receive antenna is as good as more transmit power.
Frequency
Carrier frequency. Path loss rises 6 dB for every doubling of frequency when both antenna gains are held fixed.
Distance
Straight-line distance between the antennas. Path loss rises 6 dB for every doubling of distance (inverse-square law, in dB).
System losses
Cable, connector, pointing and polarisation losses lumped together. Subtracts dB for dB. Easy to underestimate.
Worked example with the values above
- Path loss: Lfs = 92.45 + 20 log10(2.4) + 20 log10(10) = 92.45 + 7.604 + 20 = 120.1 dB.
- Pr = Pt + Gt + Gr − Lfs − Lsys = 30 + 10 + 10 − 120.1 − 3 = −73.05 dBm.
Assumptions and limits
- Free space, line of sight, far-field distance.
- No rain, gas or foliage absorption, no ground reflection or multipath.
- Antennas aligned and polarisation matched.
- The constant 92.45 applies with d in km and f in GHz.
Common mistakes
- Mixing dBm and dBW. They differ by 30 dB.
- Using the wrong constant for the unit pair: 92.45 for km and GHz, 32.44 for km and MHz, −147.55 for m and Hz.
- Reading the 20 log f term as absorption. It arises because an antenna’s capture area shrinks with wavelength; it is not a loss in the medium.
- Adding gains in linear units, or multiplying dB values.
Statistics and uncertainty
Real links fade, so designers add margin. Link margin is received power minus receiver sensitivity. The fade margin needed for a target availability (for example 99.9%) comes from the statistics of the fading, such as Rayleigh or Rician models, not from this equation.
Where it is used
- Line-of-sight communication, datalink and telemetry budgets.
- Checking a link has enough margin before adding a fade margin.
- Comparing an antenna upgrade against a transmit power increase.
Maths you need
- Decibels: dB, dBm and dBi, and why products become sums
- Logarithms: log10 of a ratio; why distance enters as 20 log
- Wavelength: λ = c / f