Free-space path loss formula

Free-space path loss describes how signal power spreads as an unobstructed radio wave travels farther. At the same frequency, doubling the distance adds about 6 dB of loss.

Use consistent distance and frequency units

For distance in kilometres and frequency in megahertz, the free-space loss in dB is approximately 32.45 + 20 log₁₀(distance) + 20 log₁₀(frequency). The wavelength form is 20 log₁₀(4πd/λ), using the same distance units for d and λ.

See the ITU-R recommendation on free-space attenuation.

Work through a 2.4 GHz, one-kilometre example

At 2,400 MHz and 1 km, the ideal path loss is approximately 100.05 dB. Suppose the radio transmits at 20 dBm, each antenna gain is 12 dBi, and each cable loses 1 dB. The estimated receive power is 20 + 12 − 1 − 100.05 + 12 − 1, or about −58.05 dBm.

For a receiver threshold of −92 dBm at the intended data rate, that leaves about 33.95 dB between estimated power and sensitivity. If your design target is 10 dB of margin, approximately 23.95 dB remains above that target under these assumptions.

Estimate midpoint clearance

For a direct link, the approximate radius of the first Fresnel zone at the midpoint is √(λd/4), with wavelength and path length in the same units. At 2.4 GHz over one kilometre, that radius is about 5.6 m. Use it to judge which obstacles to investigate along the path.

See ITU-R’s recommendation on propagation by diffraction.

Compare scenarios before a site survey

Start with fixed gains and losses, then change one variable at a time. Compare the effects of distance, frequency, cable losses, and a higher receiver threshold. A real path may introduce obstruction, multipath fading, interference, or weather losses. Use equipment specifications and field measurements to validate the design.