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SUMMARYIn this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very e cient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning e ect on the resonant frequency and half-power bandwidth are also presented.

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SUMMARYIn this paper, a rigorous full-wave analysis of rectangular microstrip patches over ground planes with rectangular apertures in substrates containing isotropic and anisotropic materials is presented. The dyadic Green's functions of the problem are e ciently determined in the vector Fourier transform domain. The integral equations for the unknown patch current and aperture ÿeld are solved numerically by applying the Galerkin method of moments. The TM set of modes issued from the magnetic wall cavity model are used to expand the unknown current on the patch. Also, the same basis functions are used for approximating the aperture ÿeld in accordance with the concept of complementary electromagnetic structures. The validity of the solution is tested by comparison of the computed results with experimental data. Numerical results show that changes in aperture length can drastically shift the resonant frequency. The aperture width, on the other hand, can be used for a ÿne adjustment of the operating frequency. Other results also indicate that dielectric anisotropy e ect is especially signiÿcant when the size of the aperture is similar to that of the patch.

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A full-wave analysis for determining the resonant frequency and half-power bandwidth of a rectangular microstrip antenna with an air gap is presented. To make the study more general and valid for various antennas structures; during the theoretical formulation the metallic patch is assumed to be embedded in a multilayered media containing isotropic and/or uniaxial anisotropic dielectrics. The proposed method for determining the Green's function leads to a concise form of this, expressed in terms of a 4 Â 4 matrix multiplication, which is easily implemented. Using Galerkin's method in solving the integral equation numerically, the complex resonant frequency of the microstrip antenna with an air gap is studied with sinusoidal functions as basis functions, which show fast numerical convergence. The numerical results for Galerkin's method and experiments are in good agreement. The air gap tuning effect on the resonant frequency and half-power bandwidth is investigated. Finally, numerical results for the effects of uniaxial anisotropy in the substrate on the operating frequency of the rectangular microstrip antenna with an air gap are also presented.

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In this paper, the e!ects of both uniaxial anisotropy in the substrate and isotropic superstrate loading on the resonant frequency and bandwidth of a rectangular microstrip patch in a substrate}superstrate con"guration are investigated. The problem is rigorously formulated using an integral equation, the kernel of which is the full-wave spectral domain dyadic Green's function for multilayer dielectric substrates. The proposed method for determining the Green's function leads to a concise form of this, diagonalized in the (TM, TE) representation. Using Galerkin's moment method to solve the integral equation, the complex resonance frequencies for the TM mode are studied with sinusoidal basis functions. The improper double integrals of the moment method matrix are e$ciently calculated by means of a proper choice of the path of integration in the complex wavenumber plane, the upper bound of truncation, and the method of quadrature. For an isotropic substrate, it is demonstrated that the bandwidth decreases with increasing ratio of superstrate-tosubstrate thickness for high permittivity and low thickness of superstrate. Also, we show that the resonant frequency and bandwidth are highly dependent on the permittivity variations along the optical axis. Simple approximate formula for the resonant frequency is derived. Other theoretical results obtained show that the resonant frequency decreases monotonically with increasing superstrate thickness, the decrease being greater for high permittivity loading and negative uniaxial anisotropy of the substrate. Thin superstrate with high permittivity together with negative uniaxial anisotropy of the substrate are shown to be the favourable conditions for severe degradation of the half-power bandwidth of the antenna.