Bandwidth enhancement is a key research area in design of microstrip patch antennas. Electromagnetic Band Gap (EBG) structures can assist in bandwidth enhancement by effectively reducing surface waves excitation in patch antennas. Unlike normal surface, EBG surface are selective in supporting surface waves. The same is affected in this paper to design patch antenna with its resonant frequency lying in the band gap of EBG substrate. The paper analyses the performance of single patch antenna and patch antenna array embedded with EBG substrate. It is observed that the performance of the realized antenna is found to be better as compared to microstrip patch antenna using conventional substrates. Simulation results show improvements in the return loss, gain, directivity, front to back ratio and the radiation efficiency. Further reduction in mutual coupling between different antenna elements is also realized.