# GTD analysis of the near-field patterns of a prime-focus symmetric paraboloidal reflector antenna

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TL;DR: A summary of various high-frequency techniques for analyzing the electromagnetic radiation from antennas in the presence of their host environment is presented in this paper, where numerical results are compared with those based on other independent methods or with measurements.

Abstract: A summary of various high-frequency techniques is presented for analyzing the electromagnetic radiation from antennas in the presence of their host environment. These techniques provide physical insight into antenna radiation mechanisms and are found to be highly efficient and accurate for treating a variety of practical antenna configurations. Examples to which these techniques have been applied include open-ended waveguide antennas, horn and reflector antennas, and antennas on aircraft and spacecraft. The accuracy of these techniques is established via numerical results which are compared with those based on other independent methods or with measurements. These high frequency methods can be combined with other techniques, through a hybrid scheme, to solve an even greater class of problems than those which can be solved in an efficient and tractable manner by any one technique alone. >

127 citations

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TL;DR: In this paper, the authors discuss the application of the geometrical theory of diffraction (GTD) for solving problems of electromagnetic (EM) radiation and scattering at high frequencies.

Abstract: Keller's geometrical theory of diffraction (GTD) [1,2] constitutes a major breakthrough for solving problems of electromagnetic (EM) radiation and scattering at high frequencies. The GTD can also be applied to solving acoustic and elastic wave problems; however, only the EM case is discussed here.
Recently, the development of fast solvers for signifi-cantly increasing the efficiency of numerical methods in solving large problems has met with some success. However, for truly large problems, asymptotic high-frequency methods in general, and especially ray methods such as the GTD and its uniform version, still remain the most useful analysis tools.
Keywords:
Keller's geometrical theory of diffraction;
electromagnetic radiation;
geometrical optics;
uniform theory of diffraction;
diffracted ray field

30 citations

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TL;DR: The spherical near field geometrical theory of diffraction (SNFGTD) method as discussed by the authors is an extended aperture method by which the near field from an antenna is computed on a spherical surface enclosing the antenna using the Geometrical Theory of Diffraction.

Abstract: The spherical near-field geometrical theory of diffraction (SNFGTD) method is an extended aperture method by which the near field from an antenna is computed on a spherical surface enclosing the antenna using the geometrical theory of diffraction. The far field is subsequently found by means of a spherical near-field to far-field transformation based on a spherical wave expansion of the near field. Due to the properties of the SNF-transformation, the total far field may be obtained as a sum of transformed contributions which facilitates analysis of collimated beams. It is demonstrated that the method possesses some advantages Over traditional methods of pattern prediction, but also that the accuracy of the method is determined by the quasioptical methods used to calculate the near field.

12 citations

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TL;DR: An analytical technique for predicting accurately the near (electric and magnetic) fields as well as the far fields of a reflector antenna with a pencil beam is presented in this article, which involves the near field geometrical theory of diffraction (GTD) analysis of reflector antennas developed earlier and spherical vector mode functions.

Abstract: An analytical technique for predicting accurately the near (electric and magnetic) fields as well as the far fields of a reflector antenna with a pencil beam is presented. The technique proposed involves the near-field geometrical theory of diffraction (GTD) analysis of reflector antennas developed earlier and spherical vector mode functions. The proposed technique does not place any restriction on the range of polar angles or radial distances of the observation point. It is demonstrated that the technique proposed can predict the fields radiated by the reflector with greater accuracy by comparing the calculated results with the available measured results. A few important applications of the analysis proposed are also highlighted.

9 citations

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TL;DR: In this paper, the authors used the field correlation theorem to determine the power coupled by a prime focus feed associated with a paraboloid which is being illuminated by a uniform plane wave, and computed the front-to-back ratio of unflanged and flanged paraboloids.

Abstract: An analysis is presented which uses the uniform geometrical theory of diffraction for determining the near fields diffracted by a paraboloid either with or without a conical flange attached to its circular rim when an axially propagated plane wave is incident on the concave or convex portion of the paraboloidal reflector. The field correlation theorem is used to determine the power coupled by a prime focus feed associated with the paraboloid which is being illuminated by a uniform plane wave. Based on this analysis, the front-to-back ratio of unflanged and flanged paraboloids is computed. Computed results show satisfactory agreement with the available measured as well as computed results based on alternative procedures. The variation in the on-axis gain on a prime-focus reflector when the feed is displaced from the focus is studied. Typical computed results are presented and compared with the available measured data. Computed results on the front-to-back ratio of paraboloids (flanged or unflanged) illuminated by a PFF whose radiated field exhibits phase variation over a constant radius are also presented. >

5 citations

##### References

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TL;DR: In this article, a compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved plane surfaces is obtained, which is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by cylindrical, conical, and spherical waves.

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

2,478 citations

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TL;DR: In this paper, the authors used the geometrical theory of diffraction to obtain the backscattered field for plane-wave incidence on a target with particular emphasis on those regions that are usually avoided, namely, the caustic region and its immediate vicinity.

Abstract: The fields diffracted by a body made up of finite axially symmetric cone frustums are obtained using the concepts of the geometrical theory of diffraction. The backscattered field for plane-wave incidence on such a target is obtained with particular emphasis on those regions that are usually avoided, namely, the caustic region and its immediate vicinity. The method makes use of equivalent electric and magnetic current sources which are incorporated in the geometrical theory of diffraction. This solution is such that it is readily incorporated in a general computer program, rather than requiring that a new program be written for each shape. Several results, such as the cone, the cylinder and the conically capped cylinder, are given. In addition, the method is readily applied to antenna problems. An example which is reported consists of the radiation by a stub over a circular ground plane. This present theory yields quite good agreement with experimental results reported by Lopez, whereas the original theory given by Lopez is in error by as much as 10 dB.

190 citations

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TL;DR: In this paper, the radiated far field is determined from a rapidly convergent series representation of the radiation integral, where the coefficients of the series are independent of the observation angles, and the field may be determined very rapidly at large numbers of points.

Abstract: Given the true or any approximate current on a reflector, the radiated far-field is determined from a rapidly convergent series representation of the radiation integral. The leading term is a well-shaped J_{1}(x)/x beam pointing in a desired direction. Higher order terms provide perturbations to the leading term. The coefficients of the series are independent of the observation angles. Hence, once they are computed, the field may be determined very rapidly at large numbers of points. Initially, a suitable small angle approximation is made that places the radiation integral in the form of a Fourier transform on a circular disk. The theory is then extended such that the results are valid in both the near and the wide angle regions. Application to a rotationally symmetric paraboloid is presented herein. Other applications include the offset and dual reflectors and near- to far-field integrations. A modified form of the series can also be used for Fresnel zone computations.

108 citations

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TL;DR: In this paper, a general computer program has been developed for the transverse electric case, where the computation of radiation and scattering of electromagnetic fields by electrically large convex conducting cylinders, using the geometrical theory of diffraction (GTD), is considered.

Abstract: The computation of radiation and scattering of electromagnetic fields by electrically large convex conducting cylinders, using the geometrical theory of diffraction (GTD) is considered. A general computer program has been developed for the transverse electric case. Illustrative computations are made for examples of radiation from a line source of magnetic current in the vicinity of a polygonal cylinder, scattering of plane waves, radiation from slots, and radiation from electric dipoles. Also given are examples of computations for conducting strips, grazing incidence on polygonal cylinders, and scattering from small cylinders. The computational accuracy is checked by comparing the results to corresponding ones computed by a moment solution to the H -field integral equation.

20 citations

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TL;DR: In this article, a multipole expansion technique to study radiation from aperture antennas in the form of an open-ended waveguidehorn is presented, and the far-zone fields of an axially-symmetric aperture-fed paraboloid are obtained in closed form.

Abstract: A multipole expansion technique to study radiation from aperture antennas in the form of an open-ended waveguide-horn is presented. Particular attention is paid to dual-mode and corrugated circular horns. The radiation pattern of these feeds, derived in terms of multipole moments, is in the form of an algebraic series which converges very rapidly. Further, based on the multipole-expansion technique presented, the far-zone fields of an axially-symmetric aperture-fed paraboloid are obtained in closed form. It is demonstrated that there is a drastic reduction in computer time by using this technique instead of the conventional numerical integration procedure for calculating the far-zone fields of the paraboloid.

4 citations

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