Improvement of the Diffraction Coefficient of GTD by Using Multiplicative Calculus

The diffraction coefficient of the geometrical theory of diffraction is expressed in terms of contour integrals that are of the same form. A series of approximations are made for the evaluation of those integrals by employing a multiplicative calculus. Finally, two different expressions are derived for the evaluation of the diffraction coefficient: one is for a case where the field observation angle is away from the reflection/shadow boundaries (RSB) of a conducting surface, and the other is for a case where the field observation angle is close to the RSB. The derived expressions are seen to be relatively simple when compared with those existing in the literature and they can be used in place of them. The given approximation techniques for the contour integrals can be extended to other high-frequency techniques in electromagnetics.