Fresnel Zones
Visualize Fresnel zones between a transmitter and receiver. The first zone carries the most signal energy. Drag obstacles into the path and watch the signal attenuate as the zones are obstructed.
rₙ = √(n · λ · d₁ · d₂ / (d₁ + d₂))
About this lab
Fresnel zones describe the regions of space between a transmitter and receiver through which radio waves propagate. Named after Augustin-Jean Fresnel, who developed the wave theory of light in the early 19th century, these zones are concentric ellipsoids defined by the extra path length a wave travels compared to the direct line-of-sight path. The n-th Fresnel zone contains all points P where the extra path length TP + PR - TR equals nλ/2, where λ is the wavelength.
The radius of the n-th Fresnel zone at any point along the path is given by rₙ = √(n · λ · d₁ · d₂ / (d₁ + d₂)), where d₁ and d₂ are the distances from the point to the transmitter and receiver respectively. The zone is widest at the midpoint and tapers to zero at both endpoints. Lower frequencies (longer wavelengths) produce larger zones, which is why low-frequency links need more clearance.
The first Fresnel zone carries the vast majority of signal energy in free space. Waves arriving via paths within this zone add constructively at the receiver, while those in the second zone arrive with opposite phase and partially cancel the first zone’s contribution. Odd-numbered zones contribute constructively; even-numbered zones contribute destructively. The alternating constructive/destructive pattern converges such that the total received power in free space is about half what the first zone alone would deliver.
In RF engineering, the rule of thumb is that at least 60% of the first Fresnel zone must be clear of obstructions for a link to perform as if it had true line-of-sight. This is why cell towers and microwave relay stations are built taller than simple geometric line-of-sight would require. A hilltop or building that barely grazes the direct path can still cause significant signal loss if it intrudes into the first Fresnel zone. This principle also explains knife-edge diffraction: a signal can partially propagate over an obstacle by diffracting around it, but with substantial loss that increases as more of the first zone is blocked.