## 2 Design of Ferrite-Loaded AMC
### Ferrite-Loaded AMC Unit Cell Design  
To design a compact unit cell for the target frequency of 6.78 MHz, the inductance, along with the lumped capacitance, must be increased. Hence, the ferrite layer can be loaded between the ground plane and the metal patch layers. However, practical issues must be considered before creating the design. First, the choices of commercially available ferrite cores for the MHz frequency range are limited. Second, ferrites with a hole are not  
Figure 2: Equivalent circuit of an LC resonator. (**a**) Conceptual description. (**b**) Equivalent circuit. commonly available, and punching a hole requires additional cost. Moreover, the use of a via pin is inevitable to increase the inductance for unit cell miniaturization. Thus, the right choice of ferrite tiles in terms of material properties and shape is important. In view of the manufacturing difficulties, the rounded square ferrite MP1040-200 from Laird was chosen. The permeability of the ferrite is approximately 310 at 7 MHz, and further details of the ferrite core can be found in [28]. Even though it is not strongly relevant to this work, it is worth noting that the biased ferrite is an anisotropic medium and its electromagnetic response will not be the same for the TE or TM incidences, and such characteristic could be encountered for more degrees of freedom in designing AMC structures [29]. The configuration of the proposed unit cell is shown in Figure 3. The unit cell is composed of four subunit cells at the top, the ground at the bottom, and the ferrite core stacked on it, as shown in Figure 3a,b. An air gap is present between the ferrite core and the patch layer and can be either a suspended microstrip line (SML) type (Figure 3c) or an IML type (Figure 3d) depending on the relative position of the dielectric substrate to the metal patches. In both types, a via pin is connected between the ground plane and the metal layer. The unit cell length and width \(p\) are fixed as 105.6 mm, considering the available ferrite size. A single rounded square ferrite has a size of 26.4 (\(l\prime\)) \(\times\) 26.4 (\(w\prime\)) mm\({}^{2}\) and a thickness \(l\prime\) of 1.91 mm. Using the curved edges of the ferrite tile marked by the dashed line in Figure 3b, the desired hole for the via pin on the ferrite layer can be achieved easily without any additional process. An SML is a type of microstrip line (MSL) consisting of a thin metal strip suspended above a ground plane by a dielectric layer or spacers (air gap) and is designed for performance comparison with the proposed IML type in this work. An IML is a type of SML in which the suspended thin metal strip faces toward the ground plane. These types of MSLs are popular for millimeter- and micro-wave applications owing to their minimum attenuation, small effective dielectric constant, and low propagation and insertion losses. In addition, they provide less stringent dimensional tolerances and dispersion compared with conventional MSLs [30; 31]. The lower losses in these types of MSLs are due to the air gap between the substrate and the ground plane, reducing the line dispersion. The IML design could be advantageous because it enables the utilization of the other side of the dielectric layer of the AMC, where the FSS patch is not printed. In other words, the metallic pattern of the Tx coil might be printed directly on top of the dielectric, which would minimize the overall weight and fabrication cost in a thinner profile. The infinite array of the unit cell simulation was performed using the high-frequency structure simulation (HFSS) tool from Ansys. The simulation setup and parameters can be found in Figure 3a,b. As seen in Figure 3a, the unit cell boundaries are set for the vertical sides, and the top side is excited with the Floquet port to replicate plane wave excitation. In Figure 3b,  
Figure 3: Unit cell simulation of the proposed design. (**a**) Simulation setup. (**b**) Top view. (**c**) Side view of the SML type. (**d**) Side view of the IML type.