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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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