Design of line-source antennas for narrow beamwidth and low side lobes

TLDR

Radiation from line‑source antennas behaves like diffraction from narrow apertures, yet antenna design permits non‑uniform field distributions across the aperture, enabling synthesis of patterns with a narrow main‑lobe width and low side lobes. The study investigates the mathematical relationships governing line‑source radiation to design a source that balances beamwidth and side‑lobe level, analogous to the Dolph‑Tchebycheff problem. The authors derive the radiation equations using function theory and provide a detailed procedure for synthesizing the line source to approximate the ideal pattern. They conclude that the ideal pattern is cos(π√(u²−A²)), which cannot be physically realized but can be approached arbitrarily closely, and they outline the key synthesis techniques.

Abstract

It is well known that the phenomenon of radiation from line-source antennas is very similar to that of the diffraction of light from narrow apertures. Unlike the optical situation, however, antenna design technique permits the use of other-than-uniform distributions of field across the antenna aperture. Line source synthesis is the science of choosing this distribution function to give a radiation pattern with prescribed properties such as, for example, narrow angular width of the main lobe and low side lobes. In the present article the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory. Some conclusions are drawn which outline the major aspects of synthesis technique very clearly. In particular, the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level (analogous to the Dolph - Tchebycheff problem in linear array theory) is considered. The ideal pattern is cos π √ {u /sup 2/ - A/sup 2/} , where u = (2a/λ) cos θ, a is the half-length of the source, and cosh π A is the side-lobe ratio. Because of theoretical limitations, this pattern cannot be obtained from a physically realizable antenna; nevertheless its ideal characteristics can be approached arbitrarily closely. The procedure for doing this is given in detail.