Fresnel Zone

The First Fresnel Zone is the locus of points where, if a reflecting surface is introduced, the direct wave and reflected wave reinforce. Effects alternate for other orders of Fresnel Zone (1st, 2nd, 3rd…). Reflected waves from odd Fresnel zones reinforce, reflection from even Fresnel zones weaken though cancellation. Effects differ for reflection from other points.

This idea of reflection from the Fresnel zones is shown below related to path loss. This graph shows two zones – the interference zone described above, and the obstruction zone. The interference zone shows this reinforcement and cancellation against Fresnel zone number. Reinforcement is illustrated by a gain of up to 6dB over Free Space. Cancellations are illustrated by up to 3dB loss over Free Space (in theory infinite loss for perfect cancellation at reflection coefficient R=1). This a classic interference pattern.

The obstruction zone is important in radio propagation because path loss between any two stations relates to obstruction in the First Fresnel Zone. Any obstruction that impinges the First Fresnel zone causes obstruction loss. Few paths between amateur radio stations offer Free Space Loss (unless both are on hilltops). Most are heavily obstructed in a normal atmosphere.

Looking at the effect more closely, and coming left on the graph from the 1st Fresnel Zone, we see that the zero dB point occurs at 0.6 times the First Fresnel Zone. This gives rise to the definition of a Free Space path where clearance is available for 0.6 times the First Fresnel Zone. If that condition is met, Free Space path loss is then said to be available between the two stations. Obstructed path losses are related to this as a loss in dB over Free Space.

Radio amateurs have little control over the path loss (calculated as the Free Space loss plus obstruction loss) between their station and others’. The first they’ll know about obstruction loss is if they can communicate. If communication is possible over a path, that means that the system value is greater than the sum of all the losses and gains in the system – including, crucially, the path loss.

But radio amateurs do have control over their Fresnel Zone clearance in the foreground of their station. So, what does the Fresnel Zone look like?

The first Fresnel Zone is an ellipsoid whose radius at any point between transmitter and receiver of the two radio amateurs wishing to communicate is given by:

Where f is the frequency (MHz) and d1 and d2 are the distances (km) between transmitter and receiver at the point where the ellipsoid radius (R) is calculated. Insert n=0.6 for 0.6FFZ.

Consider then the geometry of a 300km path. The Fresnel radius at 144MHz at 300m from the transmitter is about 20m.  But as I noted above, a path of that length is going to be heavily obstructed anyway, thereby reducing the effect of any obstruction out at 300m. And short of moving house, there’s little either radio amateurs can do about the mid-path.

Measuring closer to the transmitter (or receiver) at say 30m out, the Fresnel zone radius is about 6m. And at 10m out, it’s about 1m. The situation is shown below.

On this simplified path profile between the two amateur stations, there are two obstructions into the 0.6First Fresnel Zone – a broad rounded obstruction mid path and a narrow, sharp obstruction in the foreground (within the first 1km) of the left-hand station. The mid-path obstruction could exhibit say 40dB loss but with Earth bulge impinging on a long path, this might be higher. This mid-path is, of course, unavoidable.

A foreground obstruction obscuring the bottom half of the 0.6 First Fresnel Zone might exhibit 6dB, and 12dB if the whole of the ellipse is intruded. This foreground obstruction loss is, to a large extent, often avoidable. As a reference, 12dB loss negates the gain afforded by a decent sized Yagi!

So, what does this analysis tell us?

Simply, make sure that your foreground is as clear as you can make it at all azimuths round your station. Often the single variable here is antenna height. Increasing the antenna height to avoid foreground obstruction is much better than increasing transmitter power or antenna gain. But remember, the 0.6FFZ must be clear – not just the optical line of sight.

NB, this analysis was at 144MHz. At 50MHz and 10m out from the antenna, the 0.6FFZ radius is 6m. So even higher antennas are needed at lower frequencies in order to clear the foreground and avoid foreground obstruction loss.

1. From Bullington, K (1957) Radio Propagation Fundamentals, Bell Systems Tech Journal, Vol. 36, no. 3. In Van Valkenburg ME & Middleton WM (eds.) (2002) Reference Data For Radio Engineers, 9th edn.: Woburn MA: Newnes.
2. See RECOMMENDATION ITU-R P.526-10, Propagation by diffraction, available at https://www.itu.int/en/ITU-R/Pages/default.aspx.