How this instrument works
A radio signal travelling from one antenna to another doesn't stay confined to the straight line drawn between them. Huygens' principle says every point on a wavefront re-radiates in all directions, so energy also arrives along paths that bulge outward from the direct line before reconverging at the receiver. The first Fresnel zone is the region enclosing every such path that is no more than half a wavelength longer than the direct one — the paths whose contributions still add constructively rather than cancel. It forms a long, cigar-shaped ellipsoid with the two antennas as its foci, fattest at the midpoint and pinched to nothing at each end.
The formula folds a lot into one constant. The general relation for the nth zone is r = √(nλd₁d₂ ⁄ (d₁+d₂)), where λ is wavelength; here n = 1, and λ is replaced by c ⁄ f so frequency can be entered directly in gigahertz. Converting d₁ and d₂ from kilometres to metres and f from gigahertz to hertz collapses the unit conversions and the speed of light into a single number, √300 ≈ 17.3 — which is why the formula reads as a bare constant rather than a wall of scientific notation. The d₁d₂ ⁄ (d₁+d₂) term supplies the ellipsoid's shape: it is zero when either distance is zero, right at an antenna, and largest when d₁ equals d₂, at the geometric midpoint of the link.
The number this instrument returns is a geometric limit, not a guarantee of a clean link. A path can have unobstructed line of sight — you can see the far antenna through binoculars — and still perform poorly if a treeline, rooftop edge, or ridge intrudes into the first Fresnel zone, because that edge diffracts and scatters part of the signal even without ever blocking the view. Standard microwave-link practice treats the zone as an obstruction budget: keep terrain and foliage below roughly 60% of r₁ at every point along the path, not only at the midpoint, since a tower or treeline near either end can still poke into a zone that stays open enough there to matter.
- Enter the path length from the transmitter to the point you're checking as Distance from transmitter, km.
- Enter the remaining distance to the receiver as Distance from receiver, km — the two need not match; only their sum sets the total link length.
- Set the link's operating frequency in Frequency, GHz.
- Read First Fresnel zone radius — the minimum obstruction-free radius, in metres, required at that exact point along the path.
- Shift the split between the two distance fields toward either antenna to check clearance elsewhere along the link, not only at the midpoint.
Worked example — a 10 km link at 5 GHz, checked at midpoint
Take a 10 km wireless backhaul link and check clearance at its midpoint, 5 km from each end, running at 5 GHz: Distance from transmitter, km = 5, Distance from receiver, km = 5, Frequency, GHz = 5. The formula gives r₁ = 17.3 × √((5 × 5) ⁄ (5 × (5 + 5))) = 17.3 × √(25 ⁄ 50) = 17.3 × √0.5 = 17.3 × 0.70711 = 12.233 m. Anything intruding within 12.233 m of the direct line at that exact point — a stand of poplars, a warehouse roof edge, a low ridge — starts to diffract part of the signal.
Frequency changes that number fast, because r₁ scales as the inverse square root of f. Run the identical 10 km link at 10 GHz instead of 5 GHz and the radius shrinks to 17.3 × √(25 ⁄ 100) = 17.3 × 0.5 = 8.65 m — nearly a third less clearance for the same geometry, which is why crowded microwave bands push installers toward higher frequencies on tight rooftops. Applying the industry's 60% clearance guideline to the original 5 GHz figure gives a practical minimum of about 7.34 m (0.6 × 12.233 m) that should stay free of obstruction at the midpoint for the link to perform close to its free-space potential.
Questions
Why isn't a clear visual line of sight enough for a reliable link?
Because line of sight only confirms the direct path is unobstructed — it says nothing about the elliptical zone of air around that path where diffracting wavefronts still add constructively. An obstruction that never touches the line itself, like a treeline below eye level or a rooftop parapet off to the side, can still sit inside the first Fresnel zone and scatter enough signal to raise the link's measured path loss well above the free-space prediction.
What is the 60% Fresnel zone clearance rule?
It's the widely used engineering shortcut that keeping at least 60% of the first Fresnel zone radius free of obstruction, at every point along a path, keeps diffraction loss to roughly 1 dB or less — close enough to free-space performance for most links. For the 12.233 m radius in the worked example that means roughly 7.34 m of clearance; tighter margins are sometimes accepted deliberately, but they trade signal budget for that gap.
Why do both distances matter instead of just the total path length?
Because the d₁d₂ ⁄ (d₁+d₂) term describes an ellipsoid with the two antennas as its foci, and that shape isn't symmetric with respect to total length alone — a 2 km-and-8 km split of a 10 km path gives a smaller radius at that point than the 5 km-and-5 km midpoint split, even though the total distance is identical. The zone is always widest at the geometric midpoint and narrows to zero at each antenna, so where an obstruction sits along the path matters as much as how tall it is.
Does raising the frequency need more Fresnel clearance or less?
Less. The radius is proportional to 1 ⁄ √f, so doubling frequency shrinks it by a factor of √2. The worked example's 10 km link needs a 12.233 m radius clear at 5 GHz but only 8.65 m at 10 GHz — one reason licensed microwave backhaul increasingly moves to higher bands on sites where rooftop obstructions make full low-frequency clearance impossible.
What actually counts as an obstruction inside the Fresnel zone?
Anything with electrical properties different from air that intrudes into the ellipsoid: trees (wet foliage attenuates more than bare branches), building edges and parapets, terrain rises, and even other antenna structures. Loss increases gradually as the intrusion goes deeper into the zone rather than switching on all at once, which is why marginal links sometimes work fine in dry weather and degrade once wet leaves fill in the canopy.