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The dynamic tunability of a terahertz(THz)passband filter was realized by changing the Fermi energy(EF)of graphene based on the sandwiched structure of metal-graphene-metal metamaterials(MGMs).By using plane wave sim-ulation,we demonstrated that the central frequency(f0)of the proposed filter can shift from 5.04 THz to 5.71 THz;this shift is accompanied by a 3 dB bandwidth(Δf)decrease from 1.82 THz to 0.01 THz as the EF increases from 0 to 0.75 eV.Additionally,in order to select a suitable control equation for the proposed filter,the curves of Δf and f0 under differ-ent graphene EF were fitted using five different mathematical models.The fitting results demonstrate that the DoseResp model offers accurate predictions of the change in the 3 dB bandwidth,and the Quartic model can successfully describe the variation in the center frequency of the proposed filter.Moreover,the electric field and current density analyses show that the dynamic tuning property of the proposed filter is mainly caused by the competition of two coupling effects at dif-ferent graphene EF,i.e.,graphene-polyimide coupling and graphene-metal coupling.This study shows that the proposed structures are promising for realizing dynamically tunable filters in innovative THz communication systems.