Research Articles (Electrical and Electronic Engineering)

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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.