The microstrip antenna is one of the most preferable for small equipment, especially when a built-in antenna is required. It has many advantages such as low profile and easy fabrication. However for low-frequency applications, the microstrip size becomes too large for practical implementation. The problems in microstrip antenna technology are the reduction of the antenna sizes and to obtain a larger bandwidth. The aim of this dissertation is to design and simulate compact microstrip patch antennas with good bandwidth.A semi-elliptical microstrip patch antenna with semi-elliptical parasitic patch is designed and investigated for Ku-band applications in Chapter 2. In this chapter stepwise simulation results have been presented while changing the various parameters of the patch and ground. Ultra-wideband (UWB) antennas have been a research and development topic of increased interest in the industry. The Federal Communication Commission (FCC) has recently allocated 7.5 GHz of bandwidth (3.1 to 10.6 GHz) for Ultra-wideband (UWB) applications.