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The effect of the thickness and relative permittivily of a dielectric cover on a printed microstrip dipole has been analyzed. It is shown that the current distribution and the input impedance are, in general, very sensitive to variations of the cover parameters. For a dielectric plate with a constant thickness the dipole resonant length decreases substantially with an increase of the relative permittivity. Because of the limited bandwidth presented by single-element microstrip antennas the effects of the dielectric cover on the design of these antennas have to be carefully considered. For the calculation of the current distribution, the Hertz vector potential associated with the problem was determined for an element of current located in a stratified medium with four layers. Pocklington's integral equation was solved for the currents, using Galerkin's method with piecewise-sinusoidal expansion and weighting functions.