The aim of this paper work to design and analyzed a compact size Microstrip patch antenna. The conducting patches like rectangular and circular configurations are most commonly used for configurations. Mostly microstrip patch antenna is performed with narrow bandwidth. Here, an analytical mathematical model is used to calculate the impedance bandwidth, which improves the bandwidth of an antenna. In this paper Impedance Bandwidth of an Aperture Coupled Microstrip Patch Antenna (AC-MPA) using an accurate analytical model. The proposed mathematical model is used to calculate the impedance bandwidth of the antenna with high accuracy. MSP is mainly focused on the design of the compact-sized wideband Microstrip antenna. The return loss is -36.8785dB from 2 GHz to 4 GHz frequency with a bandwidth of 0.28 GHz. A maximum gain of 20 dB is achieved at 3.45 GHz frequency.