Compute Fresnel zone radii, minimum obstacle clearance, earth bulge, and free-space path loss for any point-to-point RF link — from Wi-Fi bridges to microwave backhaul.
Fresnel zones are a series of concentric ellipsoidal regions surrounding the direct line-of-sight (LOS) path between a transmitter and receiver. They arise from the wave nature of radio propagation — diffraction and reflection from objects in and around the path affect the received signal, sometimes constructively and sometimes destructively. Understanding and clearing the first Fresnel zone is the single most important step in designing any point-to-point wireless link.
The zones are numbered outward from the direct path. Signals arriving via odd-numbered zones (1st, 3rd, 5th…) combine constructively with the direct ray. Signals via even-numbered zones cancel it. The first Fresnel zone carries the majority of the transmitted power, so ensuring it is clear of obstructions is the standard design target.
Full theoretical free-space path loss is achieved when the first Fresnel zone is completely clear. In practice, 60% clearance of the first zone (no obstruction penetrates deeper than 40% of r₁) provides near-free-space conditions, adding less than 0.5 dB of diffraction loss. This is the minimum acceptable clearance for most links. Below 60%, diffraction loss increases rapidly.
For paths longer than a few kilometres, the curvature of the earth raises the ground between the two antennas above the straight line connecting them. This earth bulge must be added to the required Fresnel zone clearance when calculating minimum antenna height. The standard atmosphere is represented by an effective earth radius factor k = 4/3:
With clear Fresnel zones, the propagation follows the free-space inverse-square law. FSPL is the minimum possible path loss between isotropic antennas:
First Fresnel zone radius at the midpoint of the path for common link scenarios:
| Application | Frequency | Path | r₁ at midpoint | 60% clearance | Earth bulge |
|---|---|---|---|---|---|
| Wi-Fi outdoor bridge | 2.4 GHz | 500 m | 2.50 m | 1.50 m | < 1 mm |
| Wi-Fi outdoor bridge | 5.8 GHz | 500 m | 1.61 m | 0.96 m | < 1 mm |
| Campus wireless link | 5.8 GHz | 2 km | 3.21 m | 1.93 m | 0.07 m |
| ISP last-mile link | 5.8 GHz | 10 km | 7.18 m | 4.31 m | 1.85 m |
| Microwave backhaul | 11 GHz | 15 km | 6.37 m | 3.82 m | 4.16 m |
| Microwave backhaul | 24 GHz | 5 km | 2.50 m | 1.50 m | 0.46 m |
| LoRa IoT gateway | 868 MHz | 5 km | 14.7 m | 8.82 m | 0.46 m |
| 60 GHz mmWave link | 60 GHz | 200 m | 0.50 m | 0.30 m | < 1 mm |
The Fresnel zone radius scales with √λ — halving the wavelength (doubling frequency) reduces the zone radius by √2 ≈ 1.41×. This is why 60 GHz mmWave links are far less sensitive to vegetation and minor obstructions than 900 MHz IoT links. However, shorter links and smaller Fresnel zones don't eliminate the clearance requirement — they just make it easier to achieve with lower antenna heights.
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