High-frequency asymptotic formulation for prompt response of parabolic reflector antennas

A Time-Domain Uniform Asymptotic Theory Applied to the Analysis of Pulse-Excited PEC Wedges

“…(21) applies, and from (12) and the analytic Dirac delta properties, it follows that [8] ( 22) showing that the TD-UAT formulation for observation points far away from shadow boundaries reduces to a time-domain version of Keller's GTD, exactly as derived by Veruttipong [15] and obtained by Pathak [8] by applying appropriate limits to the TD-UTD formulation. The desired expression for the total field is then given by the real part of the analytical signal representation in (11) (23)…”

“…These singularities are compensated by the modified geometrical optics (GO) field. Performing the integration expressed in (1), we obtain the time-domain version of UAT (11) where the first term of (11) corresponds to the modified GO field and is expressed by (12) The vectors are respectively the direct [6] and reflected fields [8] (considering that only one of the wedge faces is illuminated). The signal denotes a time convolution, and the transition functions are (13) with (14) The diffracted field corresponding to the second term of (11) is expressed as (15) where the distances are shown in Fig.…”

“…These techniques sustain the simplicity of the physical optics currents and the simple ray picture of their frequency-domain counterparts. The TD-PO formulation, together with the development of time-domain-equivalent fringe wave currents (TD-FWCs) to correct the imperfections of the physical-optics induced currents near surface edges, has been implemented in a practical application within the framework of reflector antennas illuminated by pulsed sources [12], [13]. This letter deals with the canonical problem of the pulsed field diffraction by a perfectly electrically conducting wedge.…”

Closed-form solution for integral operators applied to the calculation of radiated fields from parabolic reflector antennas

“…The electric field radiated by sources bounded in a volume V' located at the free-space can be expressed as [2], [3] E(r,s) = -~r [M(r',s) x it c lVI + Zoj-t(r',s)] Go(r, r'; s)dV' +0 (~2)' (1) where s == (J" + jw is the complex frequency, c is the freespace velocity of light, Zo is the free-space impedance, and vectors rand r' locate the observation and source points, with (9) (10)…”

“…Numerical techniques such as the finite-difference time-domain method (FDTD) and method of moments are very time-consuming when applied to large scatterers, requiring large amounts of computer memory and/or use of very sophisticated algorithms to provide useful responses [1]. On the other hand, time-domain asymptotic techniques such as geometrical optics, physical optics, uniform theory of diffraction, and aperture method can be used to provide fast and very accurate tools to obtain transient response of reflector antennas [2].…”