This paper presents an insight into the transient behavior of a vertical log‐periodic dipole antenna (LPDA) above a lossy ground and over a perfectly conducting half space. Mathematically, the problem is formulated in the Laplace domain by a singularity expansion representation of the solution of an electric field integral equation using a Sommerfeld integral kernel. The influence of the feeding network and of the mutual coupling of the elements as well as the influence of the element thickness on the natural resonances of the LPDA is studied. The modes of the antenna elements are presented and the current in frequency and time domain is computed for free space. Dependent on the ground parameters and the antenna height, we show the resonance migration in the complex frequency plane and determine the appropriate modes. Starting with the free space current distribution, we compute the transient far fields of the vertical LPDA over ground for various ground parameters and antenna heights.

The evaporation duct model used is that of Kahan and Eckart and consists of a discontinuous drop of the otherwise constant relative permittivity at the upper duct boundary. The earth is assumed to be a perfect conductor and ideally plane. We determine the electrical field strength exactly at some fixed point within the duct layer, having chosen a certain polarization of the primary source whose moment is allowed to vary arbitrarily in time. The method used for solution is essentially based on the application of two functional transforms and Cagniard's method for their inversion. Physically, the applicability of Cagniard's idea is based on the evaluation of the field in a series of image sources of the primary source. The field strengths of the image sources combine to the total field strength with different signs for the two polarizations apart from the fact that they are of different mathematical structure. Hence we can give a physically intuitive description of the polarization dependence of the time history of the electrical field strength. Furthermore, a number of numerical examples clearly show the different effects of the evaporation duct on differently polarized carrier‐modulated pulses. It turns out that for certain values of the carrier frequency the evaporation duct causes different arrival times for TE and TM polarized pulses, which is explained by their different modal cutoff frequencies.

The present diffraction problem is solved by means of a perturbation calculus in the transition conditions and by repeated application of the method of steepest descent to two-dimensional Fourier integrals. We obtain a reflection coefficient for the rough surface resulting in a geometrical-optics approximation for the space wave field strength. In the case of a periodic roughness profile the application of the method of steepest descent in the transform space can be avoided and we get the electromagnetic field through differentiation of the Bromwich potentials. The numerical results of the two methods are discussed in the case of a one-dimensional cosine profile. We show that the influence of the earth's roughness increases with increasing receiver heights and fixed receiver distance. On the other hand, we point out that the geometric optical approach is a rather good approximation for the space wave field strength.