Short note: Fresnel zones

Fresnel zones are a series of ellipsoids around the direct line between a transmitter and receiver, such that a path via any point on the boundary of the nth zone is longer than the direct path by nλ/2.

          _..--~~~~~~~~--.._     1st Fresnel zone
   Tx o<-------- d1 --->|<--- d2 ------->o Rx
          ~~--..______..--~~
                        ^ radius r1 here

Radius of the nth zone

At a point that is d1 from the transmitter and d2 from the receiver:

rn = √( n·λ·d1·d2 / (d1 + d2) )

The first zone is largest at mid-path: r1(max) = ½√(λd), where d = d1 + d2.

Significance

• Secondary wavelets from adjacent zones arrive with a phase difference of 180°, so odd zones add and even zones subtract. Most of the energy reaching the receiver travels inside the first Fresnel zone.
• If an obstacle blocks part of the first zone, diffraction loss appears even when the optical LOS is clear. At grazing (obstacle touching LOS) the loss is about 6 dB.
• Design rule: keep at least 60% of the first Fresnel zone (0.6r1) clear of terrain and buildings. This sets tower heights for microwave links, with earth bulge (k = 4/3) also included.

Example: For d = 20 km at 6 GHz (λ = 0.05 m), r1 at mid-path = ½√(0.05 × 20000) = 15.8 m.