“…While, the parallel components L 3 and C 3 represent the selfinductance and capacitance of metallic viaâ Ȃ Źs, as seen in the equivalent circuit model, and are serially coupled to the inductance L 1 and L 2 of the dual split ring and square bracket structure. There is a coupling gap C m that exists between the top of the substrate and the dual split ring, which is physically evaluated and expressed as C m = ε r d h , where ε r is the permittivity of 3D-MTM substrate, d is the crosssectional area of the coupling gap, h is the height of the coupling gap between dual the top of the dielectric substrate and the dual split ring [30]. Hence, L 3 , C 3 , and C m do not affect the obtained desired frequency and these elements are not explicitly considered and their impact on calculating the resonant frequency was considered minimal.…”