Flat Luneberg lens based on a printed circuit with curved conductors

The use of a printed Luneberg lens is promising for powering ultra-wideband phased array antennas with full-azimuth scanning. This article describes in detail the model for constructing a flat Luneberg lens based on a printed circuit with curved conductors. A certain pattern(pattern) with a relative permittivity er ≈ 1 was etched on the copper-coated substrate. This was done in order to realize the value of the refractive index. By printing a grid of intersecting conducting lines, a refractive index of was achieved in the center of the lens. The diameter of the Luneburg lens antenna was chosen to be 28.6 cm, which corresponds to 12,4l0 (l0 is the wavelength of free space) to achieve a half-power beam width of ≈ 5° at an estimated frequency of up to 20 GHz. Since the design of the Luneberg lens is based on geometric optics, the lens diameter must be a multiple of the wavelength to limit diffraction effects. Operating frequencies up to 20 GHz were selected. The lens was sampled into single cells. If the unit cell size is small enough, the lens can be described as a medium with a certain effective refractive index. As a result, this propagation theory can be used for lens design. The substrate used for the lens was 1 mm thick, the material used was Rohacell 31HF, which has a permittivity of 1,046 and a loss tangent of tg(d) = 0,002.