Field pattern of a long antenna with multiple excitations

The field pattern of an asymmetrically driven long antenna is obtained by the Wiener-Hopf procedure which was used by Wu [1] to calculate the field pattern of a center-fed dipole. The present analysis gives a formula which is algebraic in form and involves no numerical integration. The field pattern of a long antenna with multiple excitations or loadings can be obtained by superposition. The theory is compared with Altshuler´s experiment [2] on resistor-loaded traveling-wave antennas and agreement between theory and measurement is found to be good. Application of the present result to field pattern synthesis is possible. For instance, it is known that a traveling wave of current may be produced on a center-driven dipole antenna of finite length when two suitable loads are placed symmetrically at about quarter-wavelength from its ends [2], [3]. A traveling-wave antenna tends to radiate power in an end-fire direction. On the other hand, the field pattern can be made broadside, as is shown in this paper, when the generators and the loads are re-arranged. These facts seems to suggest that a long antenna may be controlled to radiate power in any desired direction by adjusting the values and the positions of its loadings. Due to the simplicity of the formula involved, field patterns can be calculated and plotted or displayed by a computer in a short time as a function of the position of the generator. By inspection and by trial and error, desired field pattern can be obtained when appropriate individual field patterns are superimposed. It may be worthwhile to note that in this procedure the driving voltages and the locations of the generators are found so as to give certain desired pattern, the current distribution on the antenna does not have to be found first. However, the current may be found by using a simple formula derived by Shen, Wu and King [4] after the voltages and locations of the generators have been determined. The proposed method of field pattern synthesis is an alternative to the usual approach in which collinear arrays are used. One of the advantages of the present long antenna theory is that the complicated problem of mutual coupling effects between elements of an array is automatically taken into account. Furthermore, a simple and accurate fo- rmula of field pattern of a long antenna is readily available. Besides, a long antenna is a continuous structure and does not have gaps which exist between elements of a collinear array. The absence of such gaps permits coaxial feed lines to run out inside the antenna and thus simplifies the external structure of feeding networks. Two examples are shown in this paper to demonstrate the fact that long antenna can be made to radiate power in broadside direction if appropriate driving voltages are chosen. The result is compared with ideal field patterns of collinear arrays.