TD-UTD Solutions for the Transient Radiation and Surface Fields of Pulsed Antennas Placed on PEC Smooth Convex Surfaces
ABSTRACT A time-domain formulation of the uniform geometrical theory of diffraction (TD-UTD) is developed for predicting the transient radiation and surface fields of elemental pulsed antennas placed directly on a smooth perfectly conducting, arbitrary convex surface. The TD-UTD solution is obtained by employing an analytic time transform (ATT) for inverting into time the corresponding frequency domain UTD (FD-UTD) solution. An elemental antenna on the convex surface is excited by a step function in time and a TD-UTD solution is obtained first. The TD-UTD response to a more general pulsed excitation of the elemental current is then found via an efficient convolution of the TD-UTD solution for the step function excitation with the time derivative of the general pulsed excitation. In particular, this convolution integral is essentially evaluated in closed form after representing the time derivative of the general pulsed excitation by a small sum of simple signals whose frequency domain description is a sum of complex exponential functions. Some numerical examples are presented to illustrate the utility of these TD-UTD solutions for pulsed antennas on a convex body.
- IEEE Transactions on Antennas & Propagation. 01/1991; 39:355-361.
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ABSTRACT: Dispersive effects in transient propagation and scattering are usually negligible over the high frequency portion of the signal spectrum, and for certain configurations, they may be neglected altogether. The source-excited field may then be expressed as a continuous spatial spectrum of nondispersive time-harmonic local plane waves, which can be inverted in closed form into the time domain to yield a fundamental field representation in terms of a spatial spectrum of transient local plane waves. By exploiting its analytic properties, one may evaluate the basic spectral integral in terms of its singularities-real and complex, time dependent and time independent-in the complex spectral plane. These singularities describe distinct features of the propagation and scattering process appropriate to a given environment. The theory is developed in detail for the generic local plane wave spectra representative of a broad class of two-dimensional propagation and diffraction problems, with emphasis on physical interpretation of the various spectral contributions. Moreover, the theory is compared with a similar approach that restricts all spectra to be real, thereby forcing certain wave processes into a spectral mold less natural than that admitting complex spectra. Finally, application of the theory is illustrated by specific examples. The presentation is divided into three parts. Part I, in this paper, deals with the formulation of the theory and the classification of the singularities. Parts II and III, to appear subsequently, contain the evaluation and interpretation of the spectral integral and the applications, respectively.IEEE Transactions on Antennas and Propagation 02/1987; · 2.33 Impact Factor
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ABSTRACT: A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a smooth convex surface excited by a general time impulsive astigmatic ray field. This TD-UTD impulse response is obtained by employing an analytic time transform (ATT) for the inversion in time of an available and accurate corresponding frequency domain UTD (FD-UTD) solution. The ATT is employed because it overcomes the difficulties that occur when inverting FD-UTD fields associated with rays that traverse line or smooth caustics. Furthermore, the TD-UTD response to a general pulsed astigmatic wave excitation may be found by a convolution of the general excitation with the TD-UTD impulse response which can be performed in closed form. Some numerical examples illustrating the utility of this TD-UTD are presented.IEEE Transactions on Antennas and Propagation 07/2007; · 2.33 Impact Factor