High frequency propagation losses on an open wire transmission line above dissipative Earth

Both exact and simplified approximate equations for the current on a pair of conductors above a dissipative Earth are developed. Since, in many practical cases, each conductor consists of a pair of wires, a method for reducing four-wire lines to equivalent two-wire lines is presented. The assumptions used in the approximate expression are that the cross-sectional dimensions of the line (e.g. the distances between conductors but not the height of the conductors above earth) are small compared to the wavelength, that the propagation constant in the Earth is larger than the one in air, and that the conductors are thin compared to the wavelength and any cross-sectional dimension. The first assumption restricts the validity of the equations for the current to below 100 MHz (λ=3 m) for typical transmission lines and the second assumption can be met for most practical air-Earth problems. Numerical results for transmission line loss are computed using both the approximate method and the exact method. It is seen that the two results agree well for frequencies less that 100 MHz. The loss is divided into conductor loss and Earth loss and plotted, and physical interpretation of the frequency dependence of each component is given. The results of a parametric study of transmission-line loss are given along with an interpretation