Also known as: knife-edge diffraction, edge diffraction
Knife-edge diffraction describes how a radio wave bends around the sharp top edge of an obstacle — a ridgeline, a rooftop, a hill — so that some energy reaches into the geometric shadow behind it.1 It is the reason signals are receivable just over the crest of a hill even with no line of sight, and it is modelled by treating the obstacle as an idealised opaque half-plane with a single sharp edge. The predicted loss depends on how deeply the edge cuts into the Fresnel zone.
How it works
The geometry is captured by the dimensionless Fresnel–Kirchhoff diffraction parameter
v = h · √(2/λ · (1/d₁ + 1/d₂)),
where h is the height of the edge above (positive) or below (negative) the direct ray,
λ is the wavelength, and d₁, d₂ are the distances from the
edge to each endpoint. The diffraction loss is then a smooth function of v:
- v ≪ 0 (edge well below the ray, first Fresnel zone clear): essentially no loss.
- v = 0 (edge exactly grazing the line of sight): about 6 dB of loss — half the wavefront is blocked.
- v > 0 (edge above the ray, receiver in shadow): loss grows steadily, roughly
20·log-scale with
v, reaching tens of dB deep in the shadow.
A curiosity of the model is the obstacle gain or “knife-edge gain”: for a narrow band
of slightly negative v, the edge can reflect and refocus energy so the received level is
marginally higher than the unobstructed free-space value.
Variants
A single sharp ridge is the ideal case. Real terrain often presents rounded hills or multiple successive edges, handled by extensions — rounded-obstacle corrections and multiple-knife-edge methods (Bullington, Epstein–Peterson, Deygout) that cascade several diffraction events along a path profile. These underpin the terrain-diffraction engines in propagation planning tools such as ITU-R P.526.
Relevance to SDR
Knife-edge diffraction is why VHF and UHF coverage extends somewhat beyond the optical
radio horizon and why a scanner can hear a repeater whose
tower is hidden behind a hill. The received strength in such a shadow follows the v
curve, so a modest change in geometry — moving over the crest, or raising the antenna to
reduce h — can swing the signal by many decibels. Because longer wavelengths diffract
more readily, low-VHF signals fill in behind terrain far better than microwave ones, a
reason land-mobile trunking favours VHF/UHF for wide-area coverage.
Combined with refraction, which slightly extends the horizon, diffraction explains most “impossible” over-the-hill receptions. GopherTrunk does no propagation modelling — it simply decodes whatever reaches the antenna — but the diffraction loss on a shadowed path is often the difference between a decodable and an undecodable trunking site, and it shows up directly as reduced SNR at the receiver.
Sources
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Knife-edge effect — Wikipedia, on obstacle diffraction, the Fresnel–Kirchhoff parameter, and diffraction loss. ↩