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An efficient method for the calculation of the radiation pattern of an electric line source placed on a semi-infinite grounded dielectric structure is presented. An expansion wave concept is used to determine electric and magnetic fields at the edge. The diffraction effects caused by the truncation are taken into consideration by the application of general theory of diffraction (GTD) postulates, which link the diffracted fields with the incident expansion waves at the edge via diffraction coefficients. The diffraction coefficients for these waves are calculated numerically using integral equations techniques. Application of the method is shown for different grounded dielectric slabs, including the situation when the surface wave is close to cut-off. Numerical results are in good agreement with those that have been obtained by alternative approaches, based on the method of integral equations.