In this paper a compact dual-band microstrip patch antenna operating in the X-band is proposed and analysed for radar and satellite communication applications. The antenna is designed on a low-loss Teflon substrate with a relative permittivity of 2, thickness of 1.58 mm, and loss tangent of 0.000194, and is simulated using the Advanced Design System (ADS) Momentum solver. This study investigates the effect of introducing a dielectric superstrate layer on antenna performance by systematically varying its dielectric constant and thickness. The results show that the superstrate significantly influences key parameters such as resonant frequency, bandwidth, gain, directivity, and efficiency. Increasing the dielectric constant enhances directivity but causes a descending frequency shift and reduced efficiency, whereas a low dielectric constant (εr ≈ 1.3) with increased thickness improves impedance bandwidth and maintains stable radiation characteristics................. Keywords:................ X band, Superstrate, dual band, dielectric constant, height of superstrate.