The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere

Completely general formulas are given for computing at any point above a plane earth of finite conductivity the vector electric field for a source which may be a combination of vertical and horizontal electric dipoles or a loop antenna with its axis parallel or perpendicular to the earth. As illustrations of the above general methods, formulas are derived for the ground-wave radiation from (1) a grounded vertical antenna carrying a sinusoidal current distribution and (2) elevated vertical and horizontal half-wave antennas. The "effective height" of the grounded vertical antenna is determined as a function of the ground constants, and this formula is then used to determine the effect of the ground constants on the groundwave field intensity in the neighborhood of a quarter-wave antenna. The formulas are also used to show the influence of antenna height on the attenuation of high and ultra-high frequencies. The forward tilt, i.e., Er/Ez, which occurs for the electric vector lying in the vertical plane passing through the antenna, is also easily computed from the formulas given and is shown graphically. An expression for the Poynting vector is derived, and it is shown that a part of the energy in the wave near the ground flows downward into the ground.