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There are many online Fresnel Zone calculators. Most do the basic calculation for the maximum radius of the Fresnel Zone for a given frequency and separation between antennas. Some allow you to enter an obstacle's distance from one of the antennas, and its height, then lets you know if the obstacle falls within the Fresnel Zone. Very few plot the shape of the Fresnel Zone, and even less include an obstacle positioned on the plot. Most rare are calculators which take the curvature of the Earth into account. RF Cafe's Espresso Engineering Workbook includes a Fresnel Zone calculator incorporating all those features - and more.

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...where r is the radius of the zone in meters, d1 and d2 are distances from the obstacle to the link end points in meters, d is the total link distance in meters, and f is the frequency in MHz.

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Taking this approach you find that when the reflected path is less than half a wavelength longer than the direct path, the reflections will add to the received signal. Conversely, when the reflected path length exceeds the direct path by more than one half wavelength, its contribution will decrease the received power. Figure RP 11: The Fresnel zone is partially blocked on this link, although the visual line of sight appears clear.

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"The overall goal of this book is to help you build affordable communication technology in your local community by making best use of whatever resources are available." - The Authors

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For example, let's calculate the size of the first Fresnel zone in the middle of a 2 km link, transmitting at 2.437 GHz (802.11b channel 6):

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This is normally acceptable, but to improve the situation we would need to position our antennas higher up, or change the direction of the link to avoid the obstacle.

Subtracting the result from 10 meters, we can see that a structure 5.3 meters tall at the center of the link would block up to 40% of the first Fresnel zone.

If the first Fresnel zone is partially blocked by an obstruction, e.g. a tree or a building, the signal arriving at the far end would be diminished. When building wireless links, we therefore need to be sure that the first zone is kept free of obstructions. In practice, it is not strictly necessary that the whole of this zone is clear, in wireless networking we aim to clear about 60 percent of the radius of the first Fresnel zone.

Many thanks to the authors for making this very informative works available per the Creative Commons ShareAlike license.

Assuming both of our towers were ten meters tall, the first Fresnel zone would pass just 2.16 meters above ground level in the middle of the link. But how tall could a structure at that point be to block no more than 60% of the first zone?

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Note that there are many possible Fresnel zones, but we are chiefly concerned with the first zone, because the contributions from the second zone are negative. The contributions from the third zone are positive again, but there is no practical way to take advantage of those without the penalty incurred in going through the second Fresnel Zone.

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The exact theory of Fresnel (pronounced "Fray-nell") zones is quite complicated. However, the concept is quite easy to understand: we know from the Huygens principle that at each point of a wavefront new circular waves start, we know that microwave beams widen as they leave the antenna, we know that waves of one frequency can interfere with each other. Fresnel zone theory simply looks at a line from A to B, and then at the space around that line that contributes to what is arriving at point B. Some waves travel directly from A to B, while others travel on paths off axis and reach the receiver by reflection.

To calculate the height above ground, you need to subtract the result from a line drawn directly between the tops of the two towers.

It is apparent that the maximum value of the first Fresnel zone happens exactly in the middle of the trajectory and its value can be found setting d1=d2=d/2 in the preceding formulas. Note that the formulae give you the radius of the zone, not the height above ground.