Fresnel Zone Clearance & Earth Curvature in Point-to-Point Wireless Links

1. What is a Fresnel Zone?

In point-to-point wireless link engineering (such as microwave backhaul, 5G fixed wireless access, and long-range Wi-Fi bridges), an optical line-of-sight (LOS) between transmitter and receiver is not sufficient to guarantee full signal strength. Even if a technician can visually see the distant tower through a telescope, the link can suffer 10 dB to 30 dB of catastrophic signal attenuation if terrain, trees, or buildings encroach into the electromagnetic wavefront.

This phenomenon is explained by French physicist Augustin-Jean Fresnel's wave optics. Radio energy travels in concentric, three-dimensional prolate ellipsoidal regions around the direct line-of-sight path. These regions are called Fresnel Zones.

The boundaries of the n-th Fresnel zone represent points in space where an indirect reflected path is exactly n × (λ/2) longer than the direct boresight path.

2. Mathematical Formula for the n-th Fresnel Zone Radius

For any arbitrary point along a wireless link of total path length D, located at distance d₁ from the transmitter and d₂ from the receiver (such that D = d₁ + d₂), the radius r_n of the n-th Fresnel zone ellipsoid is:

For the critical First Fresnel Zone (n = 1), where carrier frequency f is expressed in Gigahertz (GHz) and distances d₁, d₂, and D are in kilometers (km), the formula simplifies into the standard telecommunications planning equation:

The maximum radius occurs exactly at the path midpoint (d₁ = d₂ = D/2):

3. The 60% Clearance Rule of Thumb

Electromagnetic wave theory proves that signals reflecting from obstacles within the First Fresnel Zone arrive at the receiving antenna with a phase difference between 0° and 180°. When clearance drops below 60%, destructive phase interference begins to cancel the primary direct wave.

Therefore, international telecommunications standards mandate that at least 60% of the First Fresnel Zone radius (0.6 F₁) must remain completely unobstructed by trees, terrain, or man-made structures under all atmospheric conditions.

4. Earth Curvature Bulge and Atmospheric Refraction (k-Factor)

On links exceeding 5 to 10 kilometers, the spherical curvature of the Earth creates a substantial virtual "bulge" in the terrain profile. The apparent height of this Earth bulge h (in meters) at distance d₁ and d₂ (km) is:

Where k is the equivalent Earth radius factor resulting from atmospheric refraction. Under standard standard atmosphere conditions, air density decreases with altitude, bending radio rays downward and making the Earth appear flatter (k = 4/3 ≈ 1.33).

However, during hot, humid nights or sub-refractive weather, k can drop to 2/3 (0.67), causing the Earth bulge to double in height and block previously clear microwave links.