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.