Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Electrical Engineering


This paper treats, in an elementary way, the antenna array problems, the effect of varying antenna array spacing and the relative power intensity of antenna arrays. The radiation of a directive antenna might be projected from one to another with highest efficiency and a minimum of interference with adjacent stations. We have to improve the signal-to-noise ratio and discriminate against undesirable noise. The principles of radiation on the wave theory have been known for several centuries. The wave theory of light was first proposed by the English physicist Robert Hooke in 1665 and developed twenty years later by the Dutch scientist and mathematician Christian Huygens. When Gustav Hertz stated his celebrated experiments to verify Maxwell’s theory, he was in full knowledge of these phenomena and their explanation, and invoked their use in proving the existence of electric wave. Augstin Fresnel, a French scientist, offered the wave theory of light in the early part of the last century. Although this viewpoint was held for many years it was later abandoned in favor of a new wave theory of light. By adopting the wave hypothesis a complete and adequate account of reflection, refraction n, diffraction, interference, and polarization phenomena was finally understood. We consider each antenna as a spherical source of waves that radiates equal power in all directions. It is assumed that the current in each individual source is the same and is not materially affected in either magnitude or phase by its proximity to other sources. The interference patterns resulting from a number of individual sources of waves, such as antennas, are dependent on both their special arrangement and the magnitudes and relative phases of their currents. We first discuss a very simple case of wave interference in the following paragraph. We adopt the graphical method in a rough way to plot the interference patterns from two independent sources of spherical wave of the same amplitude. In figure 1a an array of two antennas are separated by half wave length and phase difference in phase. At points where either two crests or two toughs arrive other crests and toughs arrive also, thereby neutralizing each other’s effects. In the diagram we get a strong wave in northern and southern directions and two waves cancel out in eastern and western directions. In figure 2 is the second case that two antennas are separated by half wave length and phase difference in 1/8 wave length. In Figure 3 is the third case which is separated by one wave length and phase difference in half period. Accompanying each figure is a directive diagram (Figures 1b, 2b, and 3b) plotted in polar coordinates, which shows the effectiveness of the wave in each direction. The circle drawn outside each diagram indicates the effect. If the radiation had proceeded from a single non-directional source similar to each of the above antenna, a field of semicircles would have resulted. The ratio between the areas of the circle and the inscribed diagram gives roughly the power improvement of such a device as manifested in the intensity of the radiated wave. Most of the material of the field intensity pattern was given by Mr. R. M. Foster, who assembled it and published “Directive Diagrams of Antenna Arrays” in Bell Systems, Tech. Jour. 292, 1926.

Library of Congress Subject Headings

Shortwave radio -- Antennas


Includes bibliographical references



Number of Pages



South Dakota State University