A closed-form solution of vertical dipole antennas above a dielectric half-space

This paper derives a convenient closed-form expression for the input impedance of a vertical antenna above a dielectric half-space. The expression is obtained from the induced electromotive force (EMF) method using a complex-image spatial Green´s function. It is found that the effect of the dielectric half-space can be modeled by a short image array of three to five complex image antennas. Numerical results verify the accuracy and convenience of the method for a vertical antenna at any height above a dielectric half-space with and without loss