Improved gain and loss factor formulas for a conical horn

The gain and loss factor of the conical horn are revisited based on the spherical and quadratic aperture phase distributions. The gains are compared with the classical data by Gray and Schelkunoff which appeared in the paper by King, in an attempt to confirm their validity and accuracy and to determine whether they were derived based on spherical or quadratic phase distribution. In addition, more accurate loss factors, to account for amplitude and phase tapering over the conical horn aperture, are derived which improve the prediction of the conical horn gain. New formulas for the design of optimum gain conical horns, based on the more accurate spherical aperture phase distribution, are derived and reported, and guidelines are provided for their utility.