Unbalanced Feeder of the Corner Type

Author: Edmund A. Laport

Type XIII (Fig. 4.17), using a 90-degree corner, forms, with its images, one quadrant of the field of a feeder of the cross-connected four-wire balanced type XVIII. When the metallic corner is of sufficiently large width to collect a very high percentage of the electric flux from the high-potential conductor located inside it and on its bisector line, it approaches very closely a sector of the analogous balanced prototype line, but with two adjacent zero-potential surfaces replaced by metallic sheets. There results from this principle the possibility of a line with very high power capacity that may be a good substitute for large concentric feeders.

Fig. 4.17

The metallic corner may be a continuous sheet forming a weather-protective hood for the high-potential conductor, or it may be a multiplicity of parallel wires of small radius. Lines of low characteristic impedance and very low attenuation can be realized with this configuration. The characteristic impedance can be altered further by setting the high-potential conductor off of the bisector line, in which case the corner becomes a sector of an analogous balanced line that is a quasi-regular polygon. The equations for this latter form can be easily developed as required.

One method of constructing a corner-type line is that shown in Fig. 4.18, where economy is achieved by a simple but substantial structure. Post insulators for the high-potential conductor may not be required at as frequent spacings as for the sheet-metal corner. Longitudinal angle members between support poles, in addition to the one at the ridge, make a solid framework for the entire length of the line and maintain a neat and uniform appearance. When h > > > s and w >> s,

When h is small,

where h₀ = h in the figure, h₁ = h + s, and h₂ = h + 2s. Some electrical characteristics for lines of this type are as follows:

There arises the question of the minimum permissible width w of the corner sheets in order to conform to the principle that the image charges on the sheets be essentially those of infinite sheets. The greatest charge concentration will be on the surfaces nearest the high-potential conductor and will taper off to zero at infinity. In fact, the rate of decrease of the

charge (or the current density) as the distance from this nearest point on the sheet is increased is very rapid in many practical cases. The larger the radius p of the high-potential conductor and the smaller the value of s, the greater is the charge concentration on the sheets near the conductor and the more rapid the decay in value with distance.

FIG. 4.18. Construction of type XIII feeder.

The following equation¹ provides the solution of the current density J in the sheet as a function of the distance y from the projection of the axis of the high-potential conductor on the sheet:

in which I is the current in amperes in the high-potential conductor and p and s are the same values used in the equation for the characteristic impedance. A plot of J as a function of y will yield the information that will permit the designer to judge an acceptable minimum current density and thus choose the minimum sheet width w. All the geometrical dimensions are of course in the same units.

1)	G. H. Brown, C. N. Hoyler, and R. A. Bierwirth, "Radio-frequency Heating," p. 76, Eq. 8.14, D. Van Nostrand Company, Inc., New York, 1947.