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Rise and fall of directed transient: Use of Mellin transformation in time domain problems


  • Hung-Mou Lee


The Mellin transform is utilized in the study of the time domain radiation from a circular disk. In the Mellin transformed space, the integrals over the source distribution for the frequency domain fields and the Fourier transform of the fields to the time domain can be carried out in closed form. The source is a uniform distribution of current which is switched on at t = 0 and varies as (t/T) for some positive T. It is found that δ must be positive when the source is assumed to be switched on at t = 0. Furthermore, in some finite volume of space, the transient pulse is plane wave-like and propagates along the axis of the disk. Its E and H field strengths decrease as R−2δ. Its energy decreases as R−1–4δ. A measure of the effectiveness of the current source in generating such a directed transient pulse is also provided.

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