This paper presents a study on developing a dual-band antenna equivalent circuit model for X-Band and LTE applications. MIMO antennas play a crucial role in modern wireless communication systems, and understanding their impedance behavior is essential. This work proposes a dual-band lumped equivalent circuit model, utilizing gradient optimization based on antenna-simulated S-parameters in Advanced Design System (ADS). The four radiating elements of the MIMO antenna are accurately modeled, considering their geometry and the defected ground structure (DGS) effect, which enhances the antenna's isolation and low correlation coefficient (ECC). The calculated lumped equivalent circuit model is validated through rigorous simulation and measurement data, demonstrating consistency with the expected results. The experimental measurements show measured isolation exceeding 20 dB while achieving a maximum realized gain of 5.9 dBi and an efficiency of 87%. The developed model holds promise for improving the design and performance of MIMO antennas for various applications
