A combined complex image-induced EMF solution of vertical antennas above a dielectric half-space

A simple closed-form expression for the input impedance of a vertical antenna above a dielectric half-space is derived. The expression is obtained from the induced EMF (electromotive force) method using a complex-image spatial Green's function for the vector potential. The input impedance of the vertical antenna is found as the superposition of the antenna's self-impedance in free-space and the mutual impedances due to the quasi-dynamic and complex image antennas. Numerical results verify the accuracy of the derived impedance expression for vertical antennas above a dielectric half-space with or without loss.<>