# Radio Propagation by Diffraction Over an Obstruction

Author: R.J.Edwards G4FGQ © 20th August 2001Propagation ordinarily can occur by groundwave between two or more radio antennas located on or near the Earth's surface. Even if an obstruction such as a hill, mountain, or building intervenes, propagation still can occur via slant paths over the top edge of the obstruction. This depends on diffraction over the edge. So, in addition to the basic or spreading loss along the sum of the slant paths, D1+D2, there is an additional loss due to diffraction.

For zero diffraction loss the direct line of sight path between a transmitter and a receiver must clear the obstruction by several wavelengths. When the direct path just grazes the obstruction diffraction loss is exactly 6 dB. This program does not compute the small loss or gain as a direct path becomes well clear of an obstruction.

The least diffraction loss occurs when the top of an obstruction is sharp, a condition which is termed "knife edge" diffraction. If the top of an obstruction is more rounded, i.e., if the radius of curvature increases relative to a wavelength, additional diffraction loss occurs.

When the radius of curvature exceeds the height of an obstruction, or when a ridge has an irregular top edge, the uncertainty of predictions increases.

When the radius of obstruction curvature is not small, the waves pass over a curved top via groundwave. So there also is a ground loss over this relatively short distance. However, the program does not ask for ground conductivity and the small loss in the ground, probably less than 1 dB, is ignored.

It may occur that path loss due to diffraction is less than the groundwave loss which would occur if the obstacle was removed, depending on type of terrain. To make such comparisons use the program *GrndWave3* by the same author.

Earth curvature is taken into account in the calculations. A warning is given if the height of an obstacle, such as a mountain range, is too low to appear above the horizon as seen from either end of the path. This program must not be used to predict loss on long sea paths where the horizon itself is the obstruction. Use the *GrndWave3* program instead. However, the computed loss of the sum of the two direct slant paths, D1+D2, is always correct.

This program cannot take into account changes in antenna gain which result from different elevation angles needed to clear high obstacles. This must be taken into account by the program user when entering antenna gains. It matters most when the antennas are simple verticals for which the power gain relative to an isotrope radiator along the horizontal is three, but falls to zero at an elevation angle of 90 degrees. However, this predicting error will not occur when the elevation angle of a beam antenna can be adjusted to clear the height of an obstacle.

The program's frequency range extends from LF to GHz provided an obstacle's height is greater than about four wavelengths and its width is greater than 20 wavelengths. The possibility of propagation around the sides of an obstacle or via sky waves is ignored.

Slant path lengths may be from a few metres to 100Km provided the height of an obstruction is sufficient to clear the bulge in the earth's surface due to the Earth's curvature. The program assumes both antennas and the base of an obstruction are at the same height above sea level. It is not worth the inconvenience of making precise adjustments to input values to improve accuracy. Note that ground and slant path distances are approximately equal at low elevation angles.

At a slant path distance of 25Km (*15 miles*) from the transmitter an obstruction must be at least 55m (*180 ft*) high to come into view. At 100Km (*62 miles*) it must be at least 850m (*2800 ft*) high. At these low heights very low-angle direct waves may not clear undulating ground local to the antennas. They may become indistinguishable from the groundwave and therefore suffer the same type of loss.

A simplification which will cause little error is to assume that the height of an obstruction is that above a straight line drawn between the two antennas. This need be considered only when transmitting and receiving antennas are at greatly different heights above sea level.

When an antenna is known to be inefficient, the inefficiency can be allowed for by entering a power gain less than unity. The smallest power gain accepted is 0.1 (*-10 dBi*).

If antenna power gain is not known enter 1. Computed results are then average values disregarding directivity in both the vertical and horizontal radiation planes.

A "matched receiver" is one with its input resistance matched to the antenna's radiation resistance such that maximum power is transferred. Maximum receiver power is 50-percent of the total power available to the antenna. The other 50-percent is re-radiated.

*Use program Diffrac2 where there are two obstructions, one behind the other. Both obstructions are assumed to have knife-edges.*

Run this Program from the Web or Download and Run it from Your Computer

This program is self-contained and ready to use. It does not require installation. Click this link Diffrac1 then click *Open* to run from the web or *Save* to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer *(Right-click Start then left-click Explore to start Windows Explorer)* and it will run.

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