## 2 Structural Design and Analysis
As shown in Figure 2a, with the increase of the length of the meandering gaps, the resonance frequency shifts from 1.02 GHz to 0.81 GHz due to the increment of the equivalent inductance of the resonator. As the width of the meandering gaps increases from \(a=0.8\) mm to \(a=1.2\) mm, the resonance frequency rises by 0.04 GHz (Figure 2b), because the equivalent capacitance of the resonator reduces slightly. Correspondingly, with the growth of the meandering strips' width, the resonance frequency declines a little owing to the additive equivalent capacitance (Figure 2c). When the number of corners changes from \(N=4\) to \(N=8\), the resonance frequency of  
Figure 1: (**a**) Structural diagram of the miniaturized cross-meandering resonator. (**b**) Top view and geometric parameters of the resonator. The length and width of meandering gaps, the width of the meandering strips, and the number of corners and the size of the resonant element are denoted by \(l\), \(a\), \(b\), \(N\) and \(w\), respectively. Here, the number of corners, which refers to the number of bends in the resonator branches (green line marks), is \(N=6\). (**c**) Field distributions (\(\left|E\right|\)) of the resonator at the frequency of 900 MHz and 1000 MHz. (**d**) Power ratios of the cross-meandering resonator based on a full-wave simulation. the structure decreases dramatically because of the incremental equivalent inductance, as depicted in Figure 2d. In comparison, the length of the meandering gaps and the number of corners have more influence on the resonance frequency of the cross-meandering resonator. Overall, the resonance frequency of the structure can be flexibly adjusted by varying the geometry parameters, so that the designed resonator can be readily adapted to different frequency ranges to meet diverse application demands. In order to verify the power frequency electromagnetic field shielding effect of the cross-meandering resonator, the power frequency electric and magnetic field changes after passing through the resonator are simulated. Herein, five sides of a permalloy layer and one side of a copper layer form a hollow cube box (160 mm \(\times\) 160 mm \(\times\) 160 mm). The thicknesses of permalloy layer and copper layer are both 1 mm. The conductivity and relative permeability of the permalloy material are \(\sigma\) = 8.475 \(\times\) 10\({}^{5}\) S/m and \(\mu_{\mathrm{r}}\) = 10\({}^{5}\), respectively. The center of the copper layer is the cross-meandering resonator, and the parameters are \(w\) = 29 mm, \(l\) = 15 mm, \(a\) = 1 mm, \(b\) = 1 mm. A wire with a diameter of 30 mm is placed 50 mm from the resonator. The voltage applied on the wire is 110 kV. At \(f\) = 50 Hz, because the element size (29 mm) is much smaller than the corresponding wavelength (6 \(\times\) 10\({}^{6}\) m), the cross-meandering resonator is in a non-resonant state. By utilizing the high conductivity and relative permeability of the material, the structure can realize the power frequency electromagnetic field shielding. The simulated electric field and magnetic field distributions are displayed in Figure 3a,b. It is observed that the electric field intensity inside the cubic box decreases sharply, while the magnetic field intensity is relatively gradually decreased. Taking the distributions of electric field and magnetic field without the cubic box as a reference, the calculated ratios of \(|E|^{2}\) and \(|H|^{2}\) are as shown in Figure 3c. The shielding effect of the resonator composed of copper material on the electric field (black line) is better than that on the magnetic field (red line). At \(z<-5\) mm, the shielding's effectiveness on the electric field is greater than 60 dB. To improve the's effect on the magnetic field, the material of the resonator layer can be changed to permalloy. The simulated results are displayed in Figure 3d-f. It can be seen that the shielding effect of the resonator on the power frequency magnetic field has been significantly improved.