Analysis of Metallic Antennas and Scatterers
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Most antennas are assembled from conducting surfaces and wires. The usual approach to numerical analysis of such structures is to approximate them by small surface or wire elements, with simple current approximation over the elements (the socalled subdomain approach), which requires a large amount of computer storage. This book describes a novel general entiredomain method for the analysis of metallic antennas and scatterers which enables the solution of a very wide class of problems to be obtained using computers of relatively modest capability. Antennadesign engineers, scientists and graduate students interested in the analysis and design of electrically small and mediumsized metallic antennas and scatterers will find in this book a selfcontained and extremely powerful tool that circumvents most difficulties encountered in other available methods.
Inspec keywords: numerical analysis; antennas; electromagnetic wave scattering; wires (electric)
Other keywords: metallic antenna analysis; scatterer analysis; conducting surfaces; numerical analysis; wire elements; subdomain approach; general entiredomain method; electrically smallandmediumsized metallic antennas; current approximation; computer storage
Subjects: Single antennas; Wires and cables; Antenna theory; Other topics in statistics; Electromagnetic wave propagation
 Book DOI: 10.1049/PBEW038E
 Chapter DOI: 10.1049/PBEW038E
 ISBN: 9780852968079
 eISBN: 9781849193948
 Page count: 208
 Format: PDF

Front Matter
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1 Introduction
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This book is aimed at presenting a general computeroriented method for the analysis of electrically small and mediumsized metallic objects. The objects are assumed to be situated in a lossless homogeneous dielectric medium in an arbitrary incident monochromatic electromagnetic field. The term 'electrically small objects' refers to objects the maximum dimension of which is much smaller than the freespace wavelength, and 'electrically mediumsized objects' to those the maximum dimension of which does not exceed a few wavelengths. The method is not intended for the analysis of electrically large objects, i.e. those the maximum dimension of which is many wavelengths. However, the limitation is due not to the method itself, but rather to the speed and storage capabilities of available digital computers. The principal aim of the analysis is to determine the surfacecurrent distribution on the objects. Once this has been determined with sufficient accuracy, all the quantities of interest, such as the scattered (or radiated) field, the near field, the impedance of generators driving the system etc. can be obtained with relative ease.
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2 Modelling of geometry of metallic antennas and scatterers
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This chapter discusses modelling of geometry of metallic antennas and scatterers. Although this Chapter is devoted to modelling of the structure geometry, it is pointed out that the modelling should be carried out bearing in mind the type of approximation of currents over conductor surfaces. In particular, it is very useful to define both the (approximate) surface elements and surface currents over them in the same local coordinate system.
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3 Approximation of current along generalised wires and over generalised quadrilaterals
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This chapter is aimed at deriving general entiredomain, or almost entire domain, current expansions (in the above sense), following to some extent the method described in References 66 and 67, but also at explaining some subdomain current expansions. It is shown that basis functions can be defined over the surface of arbitrary generalised quadrilateral surface elements that automatically satisfy the continuity equation along the element interconnections and free edges. This is a very important step, which makes most of the methods proposed so far for the analysis of similar structures special, frequently less accurate, cases of the general method proposed here. Specific polynomial expansions will also be elaborated, and their relative advantages with respect to other possible expansions will be discussed.
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4 Treatment of excitation
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This chapter was aimed at introducing convenient models of excitation for antennas. The distributed excitation, that of a uniform plane wave, was introduced first. The localised excitation was considered next. It was concluded that practical reasons dictate the use of a few simple models of localised excitation, which can be used in most cases; the deltafunction generator is one such possibility, and the TEM magneticcurrent frill (usually changed to an approximately equivalent distribution of impressed electric field) is the other. An important addition to the standard treatment of excitation relates to relatively thick monopole antennas connected to metal plates of finite size and driven at the junction by a magneticcurrent frill approximating the coaxialline excitation. By a simple theorem the frill excitation is transferred to the wire, which enables the plate and the monopole to be analysed in the same manner as if the excitation were by a deltafunction generator or a plane wave, i.e. an additional attachment mode or finer partitioning of the plate is avoided.
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5 Electromagnetic field of currents over generalised surface elements
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This chapter is devoted to derivation of expressions for the electromagnetic fields due to known distributions of currents over arbitrary curvilinear rectangles, over bilinear surfaces, and along generalised wires and truncated cones. The first step is determination of the Lorentz potentials, from which the electric and magneticfield vectors in the near and far zones are then evaluated.
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6 Solution of equations for current distribution
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In the preceding chapters methods have been explained for approximation of the geometry of surfaces or wires and of current distributions over these surfaces or along these wires. Some approximations of the actual excitation of the structures have been proposed which permit relatively simple treatment of real excitation regions. The general expressions for the potentials and the electric and magneticfield vectors have also been derived. Determination of the unknown coefficients in the expression for current distribution therefore represents the only remaining step in the analysis of metallic antennas and scatterers. As already mentioned, this can be achieved by solving numerically any of a number of known integral or integrodifferential equations that can be formulated for the unknown current distribution, some of which were outlined in Section 1.3. This chapter is devoted to discussing these equations in more detail, to justifying the adoption of one of them, and to explaining the reasons for adopting a specific procedure (the Galerkin method) for solving this equation for the unknown currentdistribution coefficients. Finally, explicit expressions for the elements of the socalled impedance matrix in the Galerkin method are derived.
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7 Numerical examples illustrating the choice of optimum elements of the method
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This and the next, final, chapter are aimed at illustrating numerically the method for the analysis of metallic antennas and scatterers elaborated in the preceding chapters. In this chapter several groups of examples are presented which are intended to justify various choices made in the method adopted for the analysis. The first group consists of examples illustrating the choice of the method for modelling of the structure geometry of both metallic bodies and wires. The second group contains examples which illustrate the reasons that have led to the choice of the method for the approximation of currents over generalised quadrilaterals and along generalised wires. These are followed by a group of examples illustrating modelling of excitation. A final group of examples is intended to assist understanding of the reasons for the particular choice of the test procedure adopted in the book.
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8 Numerical examples illustrating possibilities of the method
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In this chapter various examples are presented intended to illustrate some possibilities of the method proposed in the book for the analysis of metallic antennas and scatterers. The method being quite general, it was possible to choose only a limited number of examples, but it is hoped that they will indicate the advantages and possible shortcomings of the proposed method when compared with other methods. If not stated otherwise, the results presented in this chapter were obtained by the polynomial approximation, satisfying the continuity equation at interconnections and the quasistatic condition at conical ends which was termed conditionally as the optimum set of conditions, and the Galerkin method. Symmetry was used whenever possible to reduce the number of unknowns. Also, if not stated otherwise, the general localisedjunction model was used for the treatment of wiretoplate junctions.
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Appendix 1: Evaluation of line integrals of potentials and field vectors
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This appendix discusses reduction to canonical form of line integrals of potentials and field vectors due to currents along a truncated cone and the evaluation of line integrals of potentials and field vectors given in canonical form.
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Appendix 2: Evaluation of the integrals of potentials and field vectors due to polynomial distribution of current over bilinear surfaces
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This method of evaluating the integrals should also be used if the point is close to the bilinear surface, and not only when it is on it. A similar process is used to evaluate the integrals Q,y.However, with the integrals Q,y we have additional problems. For a field point at the bilinear surface, in the general case these integrals have infinite values. In numerical evaluation of the electric and magnetic field vectors, only appropriate combinations of these integrals yield finite values which correspond to the tangential component of the electricfield vector and the normal component of the magneticfield vector. This problem can be circumvented in several ways. The simplest is probably to position the field point close to the bilinear surface, on either side of it, instead of actually at the surface.
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Back Matter
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