A graphical method for determining the magnitude and phase of the electric field in the neighbourhood of an antenna carrying a known distribution of current

Abstract

The development of the use of short waves and modern beam systems has given rise to a need for a knowledge of the electric field in the immediate neighbourhood of a transmitting aerial. The mathematical calculation of this field is somewhat laborious, and the following paper describes a graphical method of procedure by means of which calculations may be made for any desired arrangement of a transmitting aerial.A simplified form of Hertz's equations is used to give the field at a point on the ground due to a unit doublet at different heights in a vertical antenna two wavelengths long. A curve is drawn connecting the amplitude of the field at the point with the height of the doublet in the antenna. For convenience of integration of this field along the antenna, the amplitude is divided into two components—one in phase with the current in the doublet and the other in quadrature with it. Curves are given showing the variation of these two components of the electric field with height for distances of the point from the base of the aerial of 0.25, 0.5, 0.75 and 1.0 times the wavelength of the current in the doublet. The field at any intermediate distance can be found by interpolation. The unit doublet used in the calculation of these curves is supposed to carry a current of 1 ampere. The field due to any small element of the aerial with another current distribution is equal to that when it carries 1 ampere multiplied by the current in amperes now in the element. If the two components of the electric field at the point considered due to unit current are modified in this way for a few discrete points in the antenna, two new curves may be drawn connecting the two components of the electric field due to any element in the antenna and the height of that element. The areas which these two curves make with the axis denoting height give the total electric fields at the point due to the complete antenna, and in phase and in quadrature respectively with the current in it. The magnitude of the resultant field is equal to the square root of the sum of the squares of the two components, and its phase is given by the inverse tangent of their ratio. The phase is determined throughout with respect to the current at the base of the antenna. It is then shown that the method may be applied to find the field at points other than those on the radius vector through the base normal to the antenna. In this way the field may be determined at various points in another parallel antenna.The phase of the field is determined by the same method at various distances from different lengths of antenna, and a figure is given which shows that for distances greater than about 0.3λ there is a maximum difference of about 5° between the phase of the field of a half-wave antenna and that due to the doublet at its base. This small difference explains why certain calculations based on the assumption that an antenna is small compared with the wavelength are approximately true when applied to antennae in which this assumption no longer holds.The effect of the earth is next taken into account and it is shown how the same method may be used to find the field at any distance from an antenna when the dielectric constant and the cpnductivity of the earth are known.