Integral equations based upon appropriate Green's functions are employed to rigorously treat the mutual coupling of microstrip patches on (1) an infinite grounded dielectric slab, and (2) a dielectric coated circular cylinder. A moment method solution for the first problem using the dielectric slab Green's function is presented. Calculated values of the mutual impedance are found to be in good agreement with measurements. The second problem is restricted to the calculation of the elements of the impedance and voltage matrices which are needed to carry out the solution by the moment method. These elements are derived using the Green's dyadic for the coated cylinder. It is found that the self impedance of a dipole mode at the surface of a coated cylinder converges to that of the infinite slab case as the radius of the cylinder increases. Two examples of the mutual coupling between two dipole modes are considered and numerical results are presented for cylinders of different size. In addition, alternative representations suitable for asymptotic evaluation are derived from the eigenfunction solution obtained by the Green's dyadic. A two-dimensional example is presented to illustrate the usefulness of asymptotic solutions when the dielectric coated cylinder is large in terms of a wavelength.
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