Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The o set Gregorian dual re ector antenna is eminently well suited to a radio telescope antenna application as it o ers a narrow beam width pattern (i.e high gain) and good e ciency. The focus of this work is on the analysis of characteristics of such a Gregorian antenna. The design of the class of re ector antennas is normally based on the use of ray-optics, with this simpli ed approach being able to predict antenna performance based on approximate formulas for example the beam width against aperture size. However for compound antennas such as the Gregorian re ector there are several interdependent parameters that can be varied and this reduces the applicability of the simple ray-optic approach. It was decided that, if a fast enough analysis of a con guration can be found, the technique of design through interactive analysis would be viable. To implement a fast analysis of the main beam performance of such a Gregorian antenna, a solution algorithm has been implemented using a plane wave spectrum approach combined with a custom aperture integration formulation. As this is able to predict the beam performance within about a second on a PC, it is suitable for iterative design. To implement the iterative design in a practical manner a user interface has been generated that allows the user to interactively modify the geometry, see the physical layout, and then nd the antenna pattern. A complete working system has been realised with results comparing well to a reference solution. The limitations of the technique, such as its inaccuracy in predicting the side lobe structure, are also discussed. / AFRIKAANSE OPSOMMING: Die afset Gregoriaanse dubbelweerkaatser antenna is uiters gepas vir radioteleskoop toepassings aangesien dit 'n nou bundelwydte (ho e aanwins) en 'n goeie benuttingsgraad bied. Die fokus van hierdie werk is op die analise van die eienskappe van so 'n Gregoriaanse antenna. Die ontwerp van die klas van weerkaatsantennas is normaalweg gebaseer op straal-optika, waar hierdie vereenvoudigde tegniek, deur benaderde formules, gebruik kan word om antennawerkverrigting af te skat soos bv. die bundelwydte teen stralingsvlakgrootte. Vir saamgestelde antennas soos die Gregoriaanse weerkaatser is daar egter verskeie onafhanklike parameters wat verstel kan word en die toepaslikheid van die eenvoudige straal-optiese benadering verminder. Dit was besluit dat, indien die analise van die kon gurasie vinnig genoeg uitgevoer kon word, die tegniek van ontwerp deur interaktiewe analise werkbaar kan wees. Om 'n vinnige analise van die hoofbundelwerkverrigting van so 'n Gregoriaanse antenna te bewerkstellig, is 'n oplossingsalgoritme gemplementeer wat gebruik maak van 'n platvlakgolfspektrum benadering in kombinasie met 'n doelgemaakte stralingsvlakintegrasieformulering. Aangesien hierdie strategie die hoofbundel binne ongeveer 'n sekonde op 'n persoonlike rekenaar kan voorspel, is dit gepas vir iteratiewe ontwerp. Om die iteratiewe ontwerp op 'n praktiese wyse te implementeer is 'n gebruikerskoppelvlak geskep wat die gebruiker toelaat om, op 'n interaktiewe wyse, die geometrie aan te pas, die siese uitleg te sien en dan die stralingspatroon te bereken. 'n Volledige werkende stelsel is gerealiseer met resultate wat goed ooreenstem met 'n verwysingsoplossing. Die tekortkominge van die tegniek, soos die onakkuraatheid in die voorspelling van die sylobstruktuur, word ook bespreek.

[pt] Estuda-se o espalhamento de ondas eletromagnéticas por condutores elétricos perfeitos com simetria de revolução. A formulação envolve a solução da Equação Integral para o Campo Elétrico (EFIE), aplicável a superfícies fechadas ou abertas, utilizado-se o Método dos Momentos com funções teste iguais às funções base (alternativa de Galerkin). São empregadas três diferentes classes de funções base: locais (triângulos e retângulos), globais (senos e cossenos) e limitadas em banda (funções sampling-like). Os resultados da análise (determinação da densidade de corrente elétrica induzida por uma onda plana axialmente incidente) de diversos tipos de objetos canônicos (esferas, discos e cone-esferas) ao utilizar-se as duas primeiras classes são comparados com aqueles encontráveis na literatura. Em seguida, analisa-se (determinação da corrente induzida, do campo espalhado e do campo irradiado com uma fonte esférica pontual situada no foco) refletores axialmente simétricos (parabolóides e hiperbolóides) com diâmetro entre 10 e 20 (lambda) empregando-se as três classes. É feita uma comparação entre os resultados variando-se o número de funções base por comprimento de onda para cada classe e os resultados obtidos ao empregar-se a Ótica Física (PO). / [en] The problem of electromagnetic scattering from perfectly conducting circularly symmetric bodies is considered. The mathematical formulation herein employed uses the Electrical Field Integral Equation (EFIE), which is applicable to either open or closed surfaces. The solution is effected by the Method of Moments. Test functions are chosen to be equal to basis functions (Galerkin´s alternative). Three different classes of basis functions are studied: local (pulses and triagles), global (sines and cossines) and band-limited ones (sampling-like functions). Results from the analysis (i. E., determination of induced electric currents)of different Kinds of cononical scatters (spheres, discs and cone-spheres) illuminated by an axially incident plane wave, using local and global functions, are compared with results found in the literature. In addition, circularly symmetric reflector antennas (paraboloids and hyperboloids with diameters between 10-20 lambda) are analyzed using the three different classes. The analysis involves the determination of induced currents, scattered and radiated fielsd. A comparision is made among the results obtained when employing different numbers of basis funcions and with the ones derived from Physical Optics (PO) approxomation.

Estimation of the Radar Cross Section of large inhomogeneous scattering objects such as composite aircrafts, ships and biological bodies at high frequencies has posed large computational challenge. The detection of scattering from wake vortex leading to detection and possible identification of low observable aircrafts also demand the development of computationally efficient and rigorous numerical techniques. Amongst the various methods deployed in Computational Electromagnetics, the Method of Moments predicts the electromagnetic characteristics accurately. Method of Moments is a rigorous method, combined with an array of modeling techniques such as triangular patch, cubical cell and tetrahedral modeling. Method of Moments has become an accurate technique for solving electromagnetic problems from complex shaped homogeneous and inhomogeneous objects. One of the drawbacks of Method of Moments is the fact that it results into a dense matrix, the inversion of which is a computationally complex both in terms of physical memory and compute power. This has been the prime reason for the Method of Moments hitherto remaining as a low frequency method. With recent advances in supercomputing, it is possible to extend the range of Method of Moments for Radar Cross Section computation of aircraft like structures and radiation characteristic of antennas mounted on complex shaped bodies at realistic frequencies of practical interest. This thesis is a contribution in this direction. The main focus of this thesis is development of parallel Method of Moments solvers, applied to solve real world electromagnetic wave scattering and radiation problems from inhomogeneous objects. While the methods developed in this thesis are applicable to a variety of problems in Computational Electromagnetics as shown by illustrative examples, in specific, it has been applied to compute the Radar Cross Section enhancement due to acoustic disturbances and flow inhomogeneities from the wake vortex of an aircraft, thus exploring the possibility of detecting stealth aircraft. Illustrative examples also include the analysis of antenna mounted on an aircraft. In this thesis, first the RWG basis functions have been used in Method of Moments procedure, for solving scattering problems from complex conducting structures such as aircraft and antenna(s) mounted on airborne vehicles, of electrically large size of about 45 and 0.76 million unknowns. Next, the solver using SWG basis functions with tetrahedral and pulse basis functions with cubical modeling have been developed to solve scattering from 3D inhomogeneous bodies. The developed codes are validated by computing the Radar Cross Section of spherical homogeneous and inhomogeneous layered scatterers, lossy dielectric cylinder with region wise inhomogeneity and high contrast dielectric objects. Aerodynamic flow solver ANSYS FLUENT, based on Finite Volume Method is used to solve inviscid compressible flow problem around the aircraft. The gradients of pressure/density are converted to dielectric constant variation in the wake region by using empirical relation and interpolation techniques. Then the Radar Cross Section is computed from the flow inhomogeneities in the vicinity of a model aircraft and beyond (wake zone) using the developed parallel Volume Surface Integral Equation using Method of Moments and investigated more rigorously. Radar Cross Section enhancement is demonstrated in the presence of the flow inhomogeneities and detectability is discussed. The Bragg scattering that occurs when electromagnetic and acoustic waves interact is also discussed and the results are interpreted in this light. The possibility of using the scattering from wake vortex to detect low visible aircraft is discussed. This thesis also explores the possibility of observing the Bragg scattering phenomenon from the acoustic disturbances, caused by the wake vortex. The latter sets the direction for use of radars for target identification and beyond target detection. The codes are parallelized using the ScaLAPACK and BiCG iterative method on shared and distributed memory machines, and tested on variety of High Performance Computing platforms such as Blue Gene/L (22.4TF), Tyrone cluster, CSIR-4PI HP Proliant 3000 BL460c (360TF) and CRAY XC40 machines. The parallelization speedup and efficiency of all the codes has also been shown.