Power Distribution among the Half-wave Dipoles of an Array

Author: Edmund A. Laport

Certain unique currents must be established in the various dipoles of an array to obtain a specified radiation pattern. The mutual impedances of such a system cause the resistive components of impedance of the various radiators to differ. When fed to provide the specified currents in radiators of different resistances, the power inputs will not be equal. In many systems, this requires that the feeder system divide the power in the specified manner among the different radiators, using appropriate power-dividing circuits and impedance-matching networks, while maintaining control of phase differences within the feeders so as to come out with the correct phases as well as amplitudes of the various radiator currents. All the techniques of transmission-line transforming and coupling sections are employed in one way or another for this purpose. Chapter 4 outlines some of the common methods that have proved practical. The application of these techniques must be made without introducing couplings between feeders and radiators, and with a high degree of balance when balanced feeders are used.

High-frequency dipole arrays in use at the present time are almost universally of the elementary half-wave-dipole half-wave-spacing type that are intrinsically simple to feed by employing standing waves on the feeders for either current or voltage feed. It is possible that future engineering may tend to more complicated systems, the feeding of which may approach the complexity of the arrays used for directive medium-frequency broadcast transmission.

The simplest type of array of parallel half-wave dipoles is that using half-wavelength spacing and half-wavelength feeders that are unmatched. The currents in the several dipoles of the array are assumed to be equal since presumably they are all fed with equal driving potentials. This implies the further assumption that all the radiators have equal impedances. A simple computation of the driving-point impedance of each radiator in such an array, using mutual impedances between all radiators and their images, reveals that when the desired currents exist in the system the individual impedances are not equal, owing to the effects of radiation couplings with all the other radiators and images in the system. Those on the perimeter of the curtain have the greatest differences from anything that can be called a common value. Proximity to ground and to reflectors has a major influence on the operating impedance of each dipole.

When the radiators are spaced at arbitrary distances, and when specific current amplitudes are required in the various radiators to obtain a specified radiation pattern, the system has then to be fed so that each radiator is correctly excited. This requires a knowledge of the self-impedance and all the mutual impedances in order to determine the driving-point impedance of each radiator. The feeder system must then provide for the correct power, potential, and current phase at each radiator, which are determined by its impedance and its position in the array.

The computation of mutual impedances may be very laborious since the only available precomputed figures are for parallel half-wave dipoles, with their ends opposite each other, and for collinear dipoles (see Figs. 3.61 and 3.62). The echelon dispositions are too numerous to compute for all rases and only a small number of data are published. Therefore one must compute the impedances according to the circumstances of each problem. Unfortunately it is necessary to take into account the most remote dipoles of the system, so that the labor cannot be avoided.

In order to design properly a radiating system with a specified current distribution, the exact impedance of each radiator must be known and the feeder system designed to provide exactly the required excitation before the system is constructed.

FIG. 3.61. Mutual impedance between two parallel nonstaggered half-wave dipoles with spacing S. (After Carter.)

Unless the complete project is done in this manner, its objective may not be realizable because it is always impractical, and usually impossible, to cut and try here and there to correct for errors in the system design. There are too many interdependent variables involved to permit adjustment by manipulation, even if the critical locations were accessible after the array is in place.

The system must therefore be built precisely to the final dimensions, and it must work the first time. This requirement is the same as for the medium-frequency broadcast directive systems discussed in Sec. 2.7.3; but there the feed terminals of the various radiators were physically accessible, and it was therefore possible to trim the adjustments slightly to obtain the final degree of correct operation. This is usually impossible in high-frequency antennas.

FIG. 3.62. Mutual impedance between two collinear thin half-wave dipoles. (d is the distance between dipole centers.) (After Carter.)