## 3 Analysis of the Electromagnetic Energy Harvester  
### Magnetic Flux Simulation Comparison  
Figure 3a-d present the magnetic flux density of the Halbach array at four different gaps. The maximum magnetic flux density decreases as the gap increases. The maximum magnetic flux density at a gap of 1 mm, 2 mm, 3 mm, and 4 mm is 0.48277 T, 0.36561 T, 0.27524 T, and 0.20551 T, respectively.  
Figure 3e-h demonstrate the magnetic flux density of the two-directional magnet array at four different gaps. The maximum magnetic flux density at a gap of 1 mm, 2 mm, 3 mm, and 4 mm is 0.40641 T, 0.27688 T, 0.18382 T, and 0.12046 T, respectively.  
A comparison of the magnetic flux density under different gaps between the Halbach array and the two-directional array is shown in Table 1. As the gap diameter increases, the magnetic flux density of the Halbach array decreases more slowly than that of the two-directional magnet array. The maximum magnetic flux density of the Halbach array is almost 2 times the maximum magnetic flux density of the two-directional array when the gap diameter is 5 mm. The difference in magnetic flux density at the magnetic poles of the two magnet arrays decreases as the gap diameter decreases. The maximum magnetic flux density of the two-directional array is close to the maximum magnetic flux density of the Halbach array when the gap diameter reaches 1 mm. Figure 4a,b show that the magnetic flux density at the poles of the two-directional array gradually approaches the magnetic flux density at the poles of the Halbach array when the gap diameter approaches 0. The magnetic flux density at the poles of the Halbach array is higher than that of the two-directional array at the same gap diameter. Figure 4c,d show the magnetic flux density versus the gap diameter at the poles of the two magnet arrays.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Gap Diameter** & **Bz (T)** & **1 mm** & **2 mm** & **3 mm** & **4 mm** & **5 mm** \\ \hline Halbach array & 0.48277 & 0.36561 & 0.27524 & 0.20551 & 0.15478 \\ Two-directional array & 0.40641 & 0.27688 & 0.18382 & 0.12046 & 0.07971 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of the peak magnetic flux density between the Halbach array and the two-directional array at different gap diameters.  
Figure 3: \(Cont.\)Figure 3: Comparisons of the magnetic flux density under different gaps between the two magnet arrangements: (**a–d**) magnetic flux density of the Halbach array; and (**e–h**) magnetic flux density of the two-directional magnet array.  
Figure 5 indicates the magnetic flux density of Halbach array versus the angle at different gaps when the radius is 21.5 mm. Figure 6 indicates the magnetic flux density of two directional magnet array versus the angle at different gaps when the radius is 21.5 mm.  
Figure 4: Sectional view of the magnetic flux density at the two magnet arrays’ poles: (**a**) two-directional magnet array; (**b**) Halbach array; (**c**) magnetic flux density at the poles of the two-directional magnet array; (**d**) magnetic flux density at the poles of the Halbach array.  
Figure 5: Magnetic flux density versus angle at four different gaps for the Halbach array.  
\(\Delta\)B, the difference in magnetic flux density, was calculated from the magnetic flux density at the junction of the coil and the selected arc, which had a radius of 21.5 mm. The calculated \(\Delta\)B also changed periodically with the rotation of the coil. As Figure 7 shows, the peak value of the calculated \(\Delta\)B by the two-directional array is larger than that of the Halbach array when the gap diameter is 1 mm. The peak value of the calculated \(\Delta\)B by the Halbach array is larger than that of the two-directional array when gap diameter is 3 mm. The magnetic flux difference \(\Delta\)B reflects the change in magnetic flux and also affects the induced voltage directly.