Input impedance change of a half-wave vertical antenna over a dissipative earth

The problem investigated here is that of calculating the input impedance of a thin vertical center-fed half-wave dipole over a dissipative ground. A variational expression for the input impedance is found which is valid for heights above the ground as small as
d\lambda = 0.3
(in many cases the limit is smaller than this) and for refractive indices such that
|n|^{2} \geq 10
. Using a zeroth-order trial function, a closed-form expression which represents the change in the input impedance of the antenna between the case of a perfectly conducting ground and the case of a dissipative ground is found.