The tapered slot antenna,such as Vivaldi,has been widely used due to its ultra-wideband,high gain,simple feed structure,and easy fabrication.However,there is no rigorous analytical theory for this type of antenna.This paper analyzed the metal parts of a tapered slot antenna in a conical coordinate system with the medium analyzed in rectangular coordinates.This mixed mode gave an approximate analytical form for the tapered slot antenna with the field distribution and radiation characteristics.A planar tapered slot antenna was proposed according to the results of the analysis methods.Measured and simulated results demonstrate the antenna performance.The antenna shows good impedance matching over a wide bandwidth of 9 GHz,from 2 GHz to 11 GHz,and good radiation patterns.It is suitable for ultra-wideband applications.