l's diffraction formula is still one of the most useful tools for prediction of the loss over a hilly terrain. A rigorous analysis for a path obstructed by many edges involves a multiple integral but, because this is difficult to solve, attempts have been made to get acceptable results from a sum of single integrals. It is now well established that a method originally devised by Deygout (1966) gives the best results in most cases. It consists of taking each hill as if it alone existed on the path to establish which one gives the largest predicted loss. This hill is then taken as a terminal to divide the path into two subpaths, and the process is repeated. Further subdivisions can then be made. The total diffraction loss is taken as the sum, in decibels, of the primary loss and the losses on each subpath. This process is illustrated by the profile drawn in Figure 7.18, which is stylized into the construction shown in Figure 7.19. From this, three Fresnel limit parameters can be derived, of the type introduced in equation 7.24, as in equations 7.67 to 7.69. (7.67) The Space Wave Virtual Edge Giving Loss A1 Edge Giving Loss A'2 Edge Giving Loss A'3 Fig. 7.18 Example of a path Transmitter profile with multiple obstructions. Receiver Fig. 7.19 Construction for the Deygout method. (7.68) (7.69) Let us assume that V1 is the largest of these SO that we then get equations 7.70 and 7.71. (7.70) (7.71) To avoid the complication of evaluating the Fresnel integral, it is possible to go directly from the above parameters to the required losses in dB via a graph of the type shown in Figure 7.20. The diffraction attenuation assumed for the path is as in equation 7.72. Ak=Aj+A2+A3 (7.72) As stated, this method is generally the most accurate of the approximations. However, it is liable to overestimate the loss by up to 6 dB if either A2 or A3 is nearly equal to A1. Chapter 7 Electromagnetic Waves Diffraction Loss (dB) Fig. 7.20 Fresnel diffraction loss chart. Surface Diffraction The rounded nature of hilltops, and reflections from