Browsing by Author "Theron, Isak Petrus"

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    The accuracy of electromagnetic equivalence theorem models of microstrip patch antennas
    (Stellenbosch : Stellenbosch University, 1991) Theron, Isak Petrus; Cloete, J. H.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: In this report the application of an equivalence theorem model to a patch in a microstrip medium is considered. The problem originated with the application of the Leontovich boundary condition to an equivalent surface current in a moment method technique used by Mosig and Gardiol [1, 2] for the analysis of microstrip antennas and circuits. Their formulation consists of an equivalent electric source Js which satisfies a boundary condition Et = Zs Js. They thus apply a physical boundary condition to an equivalent source, completely ignoring the magnetic sources in the equivalent model. This approximation is analyzed to assess its accuracy. The Leontovich boundary condition is examined and it is found to be applicable to the physical or true current on a patch. The full equivalence model is then developed and compared to the Leontovich model to find the relationship between the true current flowing on the conductor and the equivalent current. It is found that, although the equivalent electric current is equal to the true current on each of the two sides of the patch, an equivalent magnetic current also exists. The contribution of this current to the total field is then examined for a patch on a single dielectric layer above a ground plane. This also gives an idea of what to expect in the case of a multi layered medium. To do the comparison the fields (also called Green's functions) radiated by an electric and a magnetic dipole on the surface of the dielectric are determined from the boundary conditions. This is done in the spectral domain and the spatial fields are then found by an inverse Fourier transform. The spectral functions are too complicated to have closed form solutions in the near field region and thus the integrals are solved numerically using the Hankel transform. The dipoles are scaled according to a relation between the electric and magnetic currents resulting from the application of the equivalence theorem. It is found that, for frequencies up to 30 GHz, the contribution of the magnetic current can be ignored over the whole region p ≠ 0 with an error of less than 0.5%. (This is for a pure copper patch on a substrate with Er = 2.5 and thickness of 0.04 λ.) At the point p = 0 the magnetic current causes a discontinuity in the electric field normal to the dipole axis and tangential to the surface of the dielectric. In the last chapter of this report a theory is developed assuming that the tangential electric fields on top of the patch are negligible in comparison to those on the bottom. The magnetic current then causes a jump in the field to comply with the condition of zero fields in the conductor. This is also the value of the tangential fields directly above the conductor. The boundary condition is then applied on the dielectric side of the patch while ignoring the magnetic sources completely. The value of the error in ignoring the magnetic sources is thus quantified enabling the accuracy of the approximations to be analyzed for any particular application.
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    The circular birefringence of artificial chiral crystals at microwave frequencies
    (Stellenbosch : Stellenbosch University, 1995) Theron, Isak Petrus; Cloete, J. H.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: The current interest of the electromagnetic engineering community in chiral media was stimulated by Jaggard et al. [11] through the publication of their paper in 1979. They used approximate electric and magnetic dipole moments to analyse a material composed of single turn helices randomly distributed and oriented in vacuum. Recently there has been a growing interest in anisotropic media, for which the constitutive relations are generalised by using second rank tensors. For anisotropic media the electric and magnetic dipole moments are, however, not sufficient. Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are therefore used to predict the circular birefringence experienced by an electromagnetic wave propagating in an artificial uniaxial chiral crystal which is non-magnetic. The multipole theory is mostly used by physicists and chemists to study optical activity. Due to the complexity of the chiral molecules interacting with the incident light, it is very difficult to accurately find the charge distribution in the molecule. Thus it is not easy to compute the multipole moments of a single molecule and the multipole moment tensors are mostly found experimentally. However, at microwave frequencies it is possible to construct a physical structure that can also be analysed theoretically. The first part of this research concerns the choice of a chiral element and the most efficient way to analyse it. The polarizability tensors which determine circular birefringence are computed symbolically from the single element multipole moments which are computed numerically. This requires careful treatment of the relationship between the applied field and the local field in the crystal. A study of crystallography was done to determine the best crystal lattice for manufacturing such a uniaxial chiral crystal and careful attention was given to the calculation of the single element multipole moments. The formulation is independent of the origin chosen for the computation of the multipole moments. Numerical values are presented, in the long wavelength regime, for the rotatory dispersion as a result of circular birefringence. It is quantitatively demonstrated that neglect of the electric quadrupole contribution would lead to a serious error in the predicted value for the rotation angle of the polarization plane in the case of a uniaxial crystal geometry. In fact, the contribution of the electric quadrupole moments to optical activity is comparable to that of the magnetic dipole moments. The numerical predictions were verified by measurements on a 2 m long artificial crystal. The geometry, dimensions and spacing of the chiral elements were chosen for relative ease of fabrication of the crystal as well as allowing experimentation at frequencies where microwave instrumentation is readily available. An S-band (2 to 4 GHz) waveguide was constructed to measure the rotation of the E-field polarization of a wave propagating down the guide. The rotation was found to be less than expected, but within 13% of the predicted value using electric quadrupole moments. The error is more or less to be expected when considered in the light of uncertainties in the construction and calculations. If the quadrupole term is ignored in the modelling, the measured value is 70% greater than predicted. This proves beyond doubt that the electric quadrupole term must be included when modelling anisotropic chiral media. The time convention e+jwt is used throughout this dissertation.