Novel broadband designs of patch antennas with an air substrate have been proposed in this dissertation. In the dual-frequency design, the study of single-fed dual-frequency microstrip antenna with a V-shaped slot has been first presented. As for the broadband patch antenna design, antennas with a U-shaped slot or a pair of wide slits can have an operating bandwidth more than 2.0 times that of a conventional one at a given operating frequency. The antenna bandwidth of then can be enhanced about 25%. In the designs of reducing cross-polarization, by using dual capacitive feeds with equal input powers, but with a 180¢X-phase shift, The cross-polarization radiation can be reduce about 10 to 15dB in the H-plane. Finally, A broadband shorted patch antenna fed by an aperture-coupled feed with an H-shaped coupling slot is proposed. By using an air substrate of thickness about 0.07 free-space wavelength of the center operating frequency, the proposed antenna can have an impedance bandwidth of about 26.2%. And the antenna design reduced the antenna size to be 40%~50%of the simple case.