Formula for Generating Gaussian Beams Using Smooth-Walled Conical Horn Antennas

By studying the design procedures of smooth-walled conical horn antennas and the gaussian beam they create, formulas were derived that relate the antenna's dimensions with the beam parameters. These are presented here, enabling the fast design of horns with specific quasioptical characteristics. Using these formulas, two different sets of horn antennas were designed for wireless power transfer applications which were later built by 3D printing or additively manufactured, at 5.8 GHz and 24 GHz, respectively. These antennas are discussed here, validating the formulas derived previously.