Ultra-wideband (UWB) antennas are widely used in many fields, such as television, FM radio, telemetry technology, aerospace, satellite communications, and so on. Because of the rise of ultra-wideband wireless communications technology in recent years, these antennas have become the focus of research in this field.Analysis method and design theory of ultra-wideband are researched in this paper. The work is divided into two parts in this thesis. An ultra–wideband microstrip wide-slot antenna at 2.7~18GHz is studied in the first part. A kind of conical log-spiral antenna at 2.0~8.0GHz is designed in the second part.Firstly, based on the UWB theories, several kinds of wide-slot antenna with ultra–wideband performances are designed and simulated. By comparing the graphs of return loss, a novel ultra-wideband with inverted arch slot antenna fed by microstrip is designed. The radiation patch is circular. The relationship of the impedance bandwidth and feed gap is studied. When the coupling gap between the feed and the slot is optimized, a better impedance bandwidth will be obtained. The antenna can be used in ultra-wideband wireless communication systems.Secondly, in order to realize the circularly polarized characteristics of wide-band and single directional radiation, the conical log-spiral antenna at 2.0~8.0GHz is simulated and designed based on the theory of frequency independent antenna. The performance of the wide-band circularly-polarized radiation is well at the working band. Compared with the classical antenna, the geometry size of the proposed antenna is smaller. Also, the experimental sample antenna is fabricated. Meanwhile, the antenna is measured. The results indicate that the electric characteristics of the antenna meet the application requirements in working band.