Long Wires with Standing Waves

Author: Edmund A. Laport

If it were possible to excite a long, straight wire so as to have several successive nodes and antinodes of current along its length in the form of a pure standing wave, such a wire, in free space, would have a radiation pattern of the form shown in Fig. 3.65. Such patterns, in general, have the following properties:

Each lobe is actually a cone of radiation, the largest being that between the axis of the wire and the first node in the pattern. The pattern is symmetrical about the normal plane passing through the middle of the wire. Each side of this plane there is a lobe, or cone of radiation, for each full wavelength of wire.

If the amplitude of current at each antinode is identical throughout the wire, and if the wire is an integral number of half wavelengths, then the envelope for the field-strength pattern for the system is a line (or cylinder) parallel to the wire itself and tangent to the main lobe. This is illustrated by the right-hand pattern of Fig. 3.66, which represents the pattern of an eight-wavelength wire with sinusoidal standing-wave current distribution.

If the wire is of arbitrary length, then the various minor lobes are irregular and do not extend as far as the tangent to the main lobe. The left-hand portion of Fig. 3.66 shows the radiation pattern for a 7 3/4-wave-length antenna to illustrate this effect.

When the wire is end-fed, as is often the case in practice, the radiation losses for a long wire cause a substantial traveling wave to exist, which causes the amplitude of successive current maximums to taper off toward the free end. This causes the pattern for a system to become intermediate between that of a pure standing-wave system and a pure traveling-wave system. This effect is shown in Fig. 3.23.

Fig. 3.65. Idealized polar patterns for straight wires with an integral number of half waves of pure standing-wave current distribution.

The shape of the field-strength pattern for a pure standing-wave system an integral number of half wavelengths long is specified by the relation:

in which m is the number of half wavelengths in the length of the straight wire bearing a pure standing wave. When m is an even number, the sine is used; the cosine is used when m is odd.

FIG. 3.66. Comparison of pure standing-wave radiation patterns for current distributions of 7% wavelengths and 8 wavelengths. (After Carter.)