# Monopole above Real Ground

Monopole antennas have been extensively investigated in the literature, especially in the first half of the 20^{th} century due to the advent of radio communications in LF and MF bands. For broadcasting applications it is important to take into account the effect of power losses in the earth soil since they affect both, antenna input impedance and radiation pattern.

Regarding the input impedance, it is directly affected by the soil parameters near the antenna, so it is customary to add buried wires just below the soil surface in order to increase the soil conductivity artificially. These buried wires take the form of **radial screens** that usually extended up to a distance of quarter-wave or half a wavelength from the monopole base.

Since monopoles are linear antennas, the methods to approach the solution of a monopole above a real ground plane and with a radial wire ground screen are based in the results obtained for cylindrical antennas in free space. Unfortunately, measured data are scarce due to experimental difficulties in obtaining high precision values in a real installation. Monopole antennas in LF and MF bands can be from tens to hundreds of meters high. Nevertheless, we can compare numerical results with well-known analytical approaches, as follows.

Prof. James R. Wait found analytical expressions to calculate the input impedance of a monopole above a radial wire ground screen, however these expressions are in the form of reaction integrals that must be solved numerically. Refer to “Impedance of a Top-Loaded Antenna of Arbitrary Length over a Circular Grounded Screen” by James R. Wait and Walter J. Surtees, Journal of Applied Physics 25, 553 (1954). On the other hand, **L. A. Dorado >** was the first to develop simple analytical equations to calculate the input resistance based on Poynting’s theorem and the calculation of the power lost in the soil below de antenna. Both approaches calculate the increment in the input impedance with respect to the impedance that the monopole would have if it were above a perfectly conducting ground plane.

Fig. 1 shows the increment in the input resistance of a monopole antenna above a radial wire ground screen with N = 20 and N = 100 radials and over an average soil, and as a function of the screen radius.

This figure shows a comparison between the Wait’s, Dorado’s and AN-SOF’s results. The curves are similar to each other, but a shift along the vertical axis is observed. In fact, this shift can be expected because Wait’s and Dorado’s results do not take into account accurately the effect of the monopole radius. **It is well known that the finite radius of a cylindrical antenna drastically affects the input impedance.** Prof. Wait used a perfect sine function to approximate the monopole current distribution, which corresponds to an infinitely thin vertical wire. Prof. Dorado pointed out this issue an tried to fix the results by applying a correction factor, which is a function of the antenna height-to-radius ratio. **In the case of AN-SOF, Poynting’s theorem is also used to compute the power lost in the soil and the effect of the finite radius of the antenna is calculated accurately because it uses the Exact Kernel >**. So we can say that AN-SOF constitutes an improvement to the Dorado’s method.

Another advantage of AN-SOF is that the imaginary part of the input impedance (the reactance) can also be obtained, unlike Dorado’s method that only allows us to compute the resistance. Since the input reactance is also available in Wait’s approach, Fig. 2 shows a comparison between AN-SOF’s and Wait’s results for the input impedance as a function of the screen radius. As we can see, the results are quite satisfactory, especially taking into account the effort it took in the days of Prof. Wait to carry out this type of complex calculations.