Double knife-edge diffraction in field-strength predictions

The loss in signal strength by diffraction over two knife-edges in succession is solved, with the usual approximations, by a double application of Huyghens´ principle expressed in terms of simple Fresnel theory. The solution is shown to depend on a Fresnel surface integral which will be discussed in a companion paper. Some typical curves of decibel loss as a function of knife-edge heights and position are given which illustrate the physical properties of the solution. In particular, a notable obstacle-gain phenomenon is revealed which shows that the simple treatment of a hilly ground profile as a single equivalent knife-edge can lead to considerable errors in field-strength predictions. The formal extension to three or more knife-edges is indicated, though the detailed development would be very laborious. An approximate treatment in terms of the loss at each edge in succession, treated as a single knife-edge between neighbouring points, is shown to agree well with the accurate method, provided that it is used with judgment gained by experience. It affords a practical method for the engineer who has many ground profiles to assess in predicting the service area of a broadcasting transmitter.