Fresnel Zone and Path Clearance: Why a Clear Line Is Not Enough

The Fresnel zone explains a puzzle that many VHF and UHF operators meet. You can see the other antenna from yours. There is no hill, no building and no wall between them, and the line drawn on the map is clear. Yet the signal on 23 centimetres is 10 dB weaker than the calculation promised, and it changes when the wind moves the trees. The explanation lies in a fact that is easy to forget when we think of radio waves as rays: a wave does not travel along a line as thin as a thread. It occupies a volume of space around the line, and objects inside this volume can reduce the signal even when they do not block the view. The volume is the Fresnel zone, and understanding it is the difference between a link that works in all weather and one that works only on some days. This guide shows how to calculate the size of the zone, how much of it must be clear and what happens to the signal when it is not.

Why Radio Waves Need More Than a Line

A radio wave spreads as it travels, and the energy that arrives at the receiver comes from a region around the straight path, not from the path alone. The parts of the wave that take slightly longer routes arrive a little later, and their phase differs from the direct wave. If the extra path is half a wavelength, the delayed part arrives in opposite phase and cancels some of the direct signal; if it is a full wavelength, it adds. The surfaces on which the extra path is exactly half a wavelength, a full wavelength and so on form a series of nested ellipsoids with the two antennas at the foci. These are the Fresnel zones, and the Wikipedia article on the Fresnel zone illustrates them.

The first zone is the most important. The energy in it adds to the direct wave, and the later zones alternate between adding and cancelling, so their net effect is small if they are partly blocked. An obstruction that cuts into the first zone removes part of the energy that contributes to the signal, and the loss increases with the amount of the zone that is blocked. A path that is clear to the eye may therefore lose several decibels when the ground, the trees or the roofs reach into the first zone.

Calculating the Radius

The radius of the first Fresnel zone at any point along the path is given by a short formula. With the distances d1 and d2 from the point to the two ends in kilometres, the frequency f in gigahertz and the total length D = d1 + d2 in kilometres, the radius in metres is approximately

r = 17.3 × square root of (d1 × d2 / (f × D))

The radius is largest in the middle of the path, where d1 and d2 are equal, and it shrinks to zero at the antennas. It becomes smaller as the frequency increases, which is the reason why microwave links tolerate closer obstacles than a link on 2 meters. The table gives the radius at the midpoint of a 20 km path, together with the 60 percent figure that is used as the target for clearance.

The numbers may surprise you. On 2 meters, a path of 20 km needs about 60 metres of clear space around the middle of the line to be undisturbed. That is more than the height of most masts, and it shows why the long VHF links need height at both ends, or at one end when the other is on a hill. On the microwave bands a few metres are enough, which is why a dish on a roof can serve a path where a 2 meter antenna would struggle.

The 60 Percent Rule

In practice a link designer does not demand that the whole first zone is clear. The usual target is that at least 60 percent of the first zone radius is free of obstacles. At this clearance the signal is within a decibel or so of the free space value, as the knife-edge diffraction theory in the Wikipedia article on the knife-edge effect indicates. The remaining 40 percent may touch the ground or the tops of the trees without a significant effect.

The rule is easy to use. Find the height of the line of sight at the critical point, usually the highest obstacle or the ground bulge in the middle, subtract 60 percent of the radius and check that the result clears the obstacle. If it does not, raise the antenna, move to another site or accept some loss. Our article on the radio horizon explains how the curve of the Earth takes a share of the available height on a long path.

The Earth Bulge Takes Its Share

On a long path the surface of the Earth rises between the two ends, and the bulge can fill a large part of the first zone. Radio waves are bent slightly by the atmosphere, so the effective curvature is smaller than the geometric one, and radio engineers use a factor of 4/3 to describe the average effect. With this factor the bulge in metres at a point is roughly d1 × d2 / 12.75 × (3/4), where the distances are in kilometres. On a path of 20 km the bulge at the midpoint is about 6 metres, which is small compared with the 61 metres of clearance needed on 2 meters, but on a path of 50 km it grows to about 37 metres.

Let us combine the two. A 50 km path on 144 MHz has a first zone radius of about 160 metres at the midpoint, so 60 percent means about 97 metres, plus 37 metres of bulge, which gives 134 metres of height above the ground that the line must have in the middle. If the antennas are 30 metres above flat terrain, there is not enough clearance; the path will work, but with a loss, unless an elevated ridge raises the line. The calculation tells you where a hill is of use and where it is a disadvantage.

What an Obstacle Costs

When an obstacle enters the zone, the loss can be estimated with the knife-edge model. In this model the obstacle is a thin sharp ridge, and the loss depends on how far the edge is above or below the line of sight, measured in fractions of the first zone radius. The values below are approximate figures from the standard diffraction curve.

• Clearance of 60 percent of the radius or more: loss of about 0 dB, the path behaves like free space.
• Clearance of 30 percent: loss of about 2.5 dB.
• Edge exactly on the line: loss of about 6 dB, which is half of the amplitude.
• Edge above the line by half the radius: loss of about 12 dB.
• Edge above the line by a full radius: loss of about 16 dB.

A real obstacle is not a knife edge. A rounded hill or a block of houses typically gives a greater loss, and trees add absorption on top of the diffraction, particularly in the summer when the leaves are wet. The knife-edge figure should be seen as the best case for the shadow. It also shows why a slightly obstructed path still works on VHF, where the loss of 6 to 15 dB is within the margin of a strong station, and why the same path is hopeless on 10 GHz with weak equipment.

An Example on 70 Centimetres

Suppose that two stations on 432 MHz want to build a permanent link of 12 km between two hills, and the line passes over a village in the middle. The midpoint radius of the first zone is 17.3 times the square root of 6 times 6 divided by 0.432 times 12, which is about 45 metres, and 60 percent of it is 27 metres. The earth bulge at the midpoint of 12 km is only about 2 metres. If the roofs of the village stand 10 metres above the ground and the line of sight is 40 metres above the ground at that point, the clearance is 30 metres, which is more than 60 percent of the radius, and the link should work without a measurable loss. If the line were only 25 metres above the ground, the clearance would be 15 metres, about one third of the radius, and a loss of 2 to 3 dB would be expected. Such a simple check takes five minutes and can save a trip up the mast.

Reflections and Fading

There is another effect, which is the reason for the changes that you may observe over a path that seems clear. If the ground or a water surface below the path reflects the wave, the reflected wave arrives with a different phase and combines with the direct wave. When the reflection point is inside the first zone, the sum changes as the atmosphere changes the path lengths, and the signal fades up and down by several decibels. Water paths are famous for this, and an amateur who works a lake or a bay on 23 centimetres will often see deep fades in the morning and in the evening. The remedy is to move the path so that the reflection point is outside the first zone, to use antennas with some directivity in the vertical plane or to use diversity with two antennas at different heights.

The loss over a path is also affected by the atmosphere beyond the simple geometry. In stable conditions with a temperature inversion, a duct can carry signals over distances far beyond the horizon, as described in our guide to tropospheric ducting. This is the opposite of the case discussed above, and it explains why the same link can be weaker than predicted on a day with a strong gradient and much stronger on another.

Using the Zone When You Plan a Station

• Check the path profile. A map tool or a terrain profile gives the heights along the path, and you can mark the line, the zone and the highest obstacle.
• Give priority to height at the end with the worse terrain. Raising an antenna near an obstacle changes the clearance faster than raising the other end.
• Remember the vegetation. The height of the trees grows, and the wet leaves add loss.
• Allow for seasons. Snow, leaves and water levels change the reflection and the obstruction.
• Use the zone also for fixed links. Links for repeaters, mesh networks and linked stations benefit from the 60 percent rule because it prevents a link that works in the summer but fails in the winter.

The planning applies to the bands described in our articles on 2 meters and 23 centimetres, and to the microwave bands where small zones allow narrow beams and small dishes.

The Bottom Line

A clear line of sight is not enough, because a radio wave needs a volume of space around the line, described by the Fresnel zones. The radius of the first zone is about 17.3 times the square root of d1 times d2 divided by f times D, and it is 102 metres at the midpoint of a 20 km path on 144 MHz but only 12 metres on 10 GHz. Keep at least 60 percent of the first zone free of obstacles, remember the Earth bulge on long paths and expect a loss of about 6 dB when an edge touches the line and more when it rises into the path. Plan antenna heights with the zone in mind, and a link that works on a dry day will work in all seasons.

Frequently Asked Questions

What is the Fresnel zone?

It is the elliptical volume around the line between two antennas in which objects can add or cancel part of the signal. The first zone contains the paths that are within half a wavelength longer than the direct path.

How much of the Fresnel zone must be clear?

Aim for at least 60 percent of the radius of the first zone. At that clearance the loss compared with free space is small.

Does the Fresnel zone matter on HF?

Not in the same way. HF signals travel by reflection from the ionosphere, and the zones would be enormous, so the concept is used mainly for VHF, UHF and microwave links.

Why does my UHF link fade in the morning?

Reflections from the ground or water inside the first zone combine with the direct wave, and changing atmospheric conditions shift the phase, which causes fading.

Why is the zone smaller at higher frequencies?

The radius is proportional to the wavelength, so as the frequency rises the zone shrinks, and a microwave link needs much less clear space than a link on 2 meters.

Can trees inside the zone be ignored?

No. Trees add both diffraction loss and absorption, and wet leaves absorb more. Treat them as obstacles when they reach into the first zone.