Theory and performance of corner reflectors for aerials

The paper opens by arguing that the problem of constructing a highly directive aerial system is dominated by the difficulty of providing the necessary feeding cables. Continuous reflecting sheets are used as a device for reducing the number of such cables. A construction which readily suggests itself is a pair of sheets inclined to one another to form a V, with a single aerial on the bisector, more especially because the field would be known everywhere if the sheets extended to infinity. For the field of an aerial in a V can be calculated by image treatment, and an algebraic formula for the diffraction pattern can be found when the angle of the V is a proper fraction of 180?. It is shown that such algebraic expression can be expanded in a Fourier series which has the same form for all angles of the V and has coefficients which are the Bessel functions JN, J3N, J5N, etc. It follows at once from this expansion that the ideal pattern must be indistinguishable from a simple sine curve unless the circumferential width across the V at the aerial exceeds ??, and will not differ appreciably from a sine curve unless this width is verging on 3?/2. Recognition of this general condition is very valuable in practice and saves much wasted effort in laborious computation. A numerical example illustrates the convenience of the Fourier series for evaluating the pattern when the aerial is sufficiently distant from the apex to make the main beam much sharper than a sinusoid, and concurrently to produce side lobes. The second part of the paper describes an experimental investigation, at a wavelength of about 1.25 m, of the equatorial pattern produced by a half-wave aerial on the bisector of a V formed by two sheets, 3?/2 high and about 2? wide, inclined at 90?, 60? or 45?. The purpose of the experiments was to compare the observed pattern with the ?ideal pattern? appropriate to infinite sheets: they are restricted to the range in which the ideal pattern differs insensibly from a simple- sinusoid. Sheets 2? wide produce a beam narrower than the ideal when inclined at 90?, and wider than the ideal when inclined at 60?. If the sheets are 2? wide then the best angle between them is about 60?. Experiment shows the pattern is not modified appreciably if the apex of the V is amputated and the resulting hole closed by a flat sheet. Such an amputation affords a saving of space and also shows that the pattern is insensitive to the shape of the back of the reflector: therefore it is not necessary to construct V reflectors to close tolerances of manufacture. Moreover, the optical concept of the advantage of a concave mirror does not apply when the source is distant only some ?? from it. Experiment shows that the pattern is affected insensibly by replacing continuous sheets by wire netting whose mesh has a side of about ?/40. Experiment also shows that the continuous sheets can be replaced by a comb of open rods, about ?? long, without appreciable detriment to the pattern. A blunt resonance effect occurs when the frequency is such as to make the rods precisely ?? long, but such as it is this resonance is undesirable. The distribution of current in a flat reflecting sheet is solved analytically in Appendix 11.1.