The electromagnetic radiation of antennas in an environment (e.g. fixed to a mast or surrounded by buildings) is influenced by reflections of surrounding structures and by diffraction at the edges of these structures. This edge diffraction can be calculated with asymptotic methods (like Uniform geometrical Theory of Diffraction (UTD) or Geometrical Theory of Diffraction (GTD)) which assume that the observer is located many wavelengths away from the edge. When the observer and the source are situated within a few wavelengths of the edge, the accuracy of the asymptotics is unclear. Because of the fact that antennas are placed in the neighbourhood of other objects, the first aim of this contribution is to get a quantitative idea of this accuracy by studying the simplified problem of a dipole near a perfectly conducting wedge for which an expression is available in closed form. The closed-form expression is quite involved. Hence, a second aim is to find ways for succesfully handling the complicated closed-form expression nummerically, which is far from trival. This closed-form expression is derived from the Maxwell equations using the formalism of Green's functions. This expression consists of an infinite integral over a summation over a product of Bessel, Hankel and complex exponential functions, see [1]. The expression has been evaluated using numerical integration techniques and is compared to the one obtained with asymptotic methods. The numerical solution of the electric field has been checked for the case of an axial dipole near a ground plane, which can be calculated using the image theory [2]. The numerical integration method has been used parallel with the Uniform geometrical Theory of Diffraction (UTD), see [3], for different parameter configurations. These parameter configurations consist of the angle of the wedge, the wavelength and the position of the source and the observer in cylindrical coordinates. The results were used to appraise the UTD in the parameter configurations where the UTD is expected to deviate from the exact solution. The most striking difference occurs when the angle of the wedge is sharp and both the source and observer are located within one or two wavelengths of the point of the wedge.

[1] Tai, C.T., Dyadic Green's Functions in Electromagnetic Theory, second edition, IEEE Press, Piscataway, N.J., 1994.
[2] Balanis, C.A., Antenna Theory, Harper and Row, New York, 1982.
[3] Kouyoumjian, R.G. and Pathak, P.H., A Uniform Geometrical Theory of Diffraction for an Edge in a Perfectly Conducting Surface, Proc. IEEE, vol. 62, No. 11, pp. 1448-1461, 1974.