Field Guide · term

Also known as: FSPL, free-space path loss

Free-space path loss (FSPL) is the reduction in a signal’s power density as it spreads outward over a clear, unobstructed path between two isotropic antennas.1 It is the idealised baseline of path loss — no obstacles, no reflections, no atmosphere — and it falls off with the square of distance, the plain geometry of energy spreading over an ever-larger sphere.

TX power spreads over 4πr² distance →Prx
The transmitted power spreads over a sphere of area 4πr², so received power falls as 1/r² — a fourfold drop (6 dB) for every doubling of distance.

How it works

Imagine a transmitter radiating equally in all directions. At distance d its power is spread evenly over a sphere of surface area 4πd². A receiving antenna captures only the fraction of that sphere its effective aperture intercepts, so received power falls as 1/d². This is pure geometric spreading — no energy is absorbed, it is just diluted.

Two facts about the standard formula surprise newcomers:

  • The frequency term is about the antenna, not the wave. A wave loses no energy to frequency in free space. FSPL rises with frequency because the reference is the isotropic antenna, whose effective aperture shrinks with wavelength (∝ λ²). Hold the physical dish size fixed and higher frequencies actually capture more — the loss “penalty” is an artifact of the isotropic reference, which the Friis equation makes explicit.

  • It is a 20 log law. In decibels:

    FSPL(dB) = 20 log₁₀(d) + 20 log₁₀(f) + k

    where k folds in the constants and units (for d in km and f in MHz, k ≈ 32.4). Every doubling of distance or frequency adds 6 dB; every tenfold increase adds 20 dB.

FSPL is not the whole story of real links — multipath, atmospheric absorption, diffraction, and terrain all add to it — but it is the floor every other loss builds on, and over a clear line-of-sight path it is often the dominant term.

In practice

FSPL is the first line of any link budget: start with transmit power and antenna gain, subtract FSPL for the path, subtract extra margins, and compare the result against receiver sensitivity to see whether the link closes. The Friis transmission equation is FSPL written with real (non-isotropic) antenna gains folded in. Extreme cases make the 20 log law vivid: a satellite or a Moonbounce path can run to 200 dB or more, which is why those links demand huge antennas and low-noise front ends.

Relevance to SDR

For any SDR user, FSPL is the intuition behind “why can’t I hear it?” — doubling the distance to a transmitter costs 6 dB, and moving up a band costs more against a fixed whip. For a trunking scanner like GopherTrunk, FSPL underlies the coverage picture: a system’s usable range is set by transmit power minus path loss versus the receiver’s sensitivity and noise floor. GopherTrunk does not compute path loss — it decodes whatever arrives — but the term explains why antenna height, a clear path, and a low-noise front end so often matter more than raw radio quality, and why a distant hilltop site can outperform a closer, obstructed one.

Sources

  1. Free-space path loss — Wikipedia, on inverse-square spreading, the decibel formula, and the frequency term’s isotropic-aperture origin. ↩

See also