The discone antenna is a vertically polarized antenna, and consists of a flat disc of about 0.17 wavelength diameter at the lowest desired frequency, with the disc plane horizontal, mounted atop but insulated from a cone that has a length of 0.25 wavelength on the side. It has been used in modified form for HF communications in the 2 to 30 MHz range where a wide range of frequencies must be covered. It is popular for scanner use in order to receive the entire VHF and UHF spectrum with one antenna. The discone antenna is fed with a 50 ohm cable, the outer conductor connected to the cone, the center to the disc. Actual impedance varies from 50 ohms depending on the cone angle, frequency, and disc to cone spacing.
Nothing is critical.
A 30 degree angle is generally used, so the diameter of the base of the cone is equal to the length of the side in this case, although not critical. This would typically be 24 to 30 inches for the reception of all bands 108 MHz and up to about 1000 MHz. The disc and cone in this size would be a little impractical mechanically and also would have considerable wind resistance, if constructed of solid sheet metal, It is possible to simulate the disc and cone with metal rods called radials, in order to realize a practical structure. 16 rods or more is desirable in both disc and cone, but 8 can be used with a slight loss in performance, this being 1 to 2 DB or so. Fewer than 8 as some cheaper antennas have is not very efficient.