## 3 Results and Discussion  
In this experiment, toroidal bulk magnetic composites were first prepared to determine the optimum mixing ratio and electromagnetic properties between powders. Subsequently, the magnetic sheet was prepared at the optimum mixing ratio, to evaluate the volume fraction and physical properties of the sheet. The bulk magnetic material was manufactured in toroidal form, to confirm the optimum magnetic properties and volume fraction. The mixing ratio of Fe-6.5 wt.% Si powder (Figure 3a) and fine iron powder (Figure 3b) was adjusted from 10:0 to 7:3. Fe powder with a particle size of 10 nm (Figure 3c) was used for high volume fraction and improved permeability. At this time, the molding pressure was increased from 1.8 to 6.25 ton/cm\({}^{2}\), to test its effect on permeability and volume fraction. When only Fe-6.5 wt.% Si powder was used, many voids were created between the coarse powders, resulting in low volume fraction and permeability. When bulk magnetic composites were prepared with the addition of 20% by weight of fine iron powder, the permeability and volume fraction were greatly improved. This testing confirmed that the volume fraction and permeability increase with increasing molding pressure (Table 1). It was confirmed that the mixing ratio of Fe-6.5 wt.% Si powder and fine iron powder showed high permeability when at a ratio of 7:3. This ratio allowed the relatively small-sized fine powders to fill the voids more effectively between the coarse powders and improved the volume fraction, compared to the other ratios tested (Figure 4). Microstructure analysis of bulk composite by molding pressure and mixing ratio. Mixing ratio 10:0 (Figure 4a-d) with molding pressure 1.8 ton/cm\({}^{2}\) (Figure 4a,b) and 6.25 ton/cm\({}^{2}\) (Figure 4c,d). Mixing ratio 8:2 (Figure 4e-h) with molding pressure 1.8 ton/cm\({}^{2}\) (Figure 4e,f) and 6.25 ton/cm\({}^{2}\) (Figure 4g,h). Mixing ratio 7:3 (Figure 4i-l) with molding pressure 1.8 ton/cm\({}^{2}\) (Figure 4i,j) and 6.25 ton/cm\({}^{2}\) (Figure 4k,l)  
Figure 3: SEM image analysis of iron-based soft magnetic powders used in magnetic bulk composite and sheet fabrication: (**a**) Fe-6.5 wt.% Si, (**b**) fine iron powder, and (**c**) nano-sized Fe powder). Figure 2: Schematic diagram of magnetic-sheet casting process for a power inductor. In the case of bulk magnetic composites, the volume fraction and permeability are proportional to each other and can be explained by [PERSON]'s Equation [21]:  
\[\mu=\frac{\eta\mu_{0}(\mu_{m}-\mu_{0})}{N(1-\eta)(\mu_{m}-\mu_{0})+\mu_{0}} \tag{1}\]  
\(\mu\):relative permeability  
\(\mu\): volume packing fraction  
\(N\): coefficient of diamagnetic field (\(0\leq\mathrm{N}\leq 1\))  
\(\mu_{\mathrm{m}}\): Intrinsic permeability of material(bulk)  
\(\mu_{0}=4\pi\times 10^{-7}\) H/m. Using [PERSON]'s equation, we plotted the actual values (dotted lines) and the theoretical results (solid lines), taking into account the demagnetization fields (Figure 5) [21]. The experimental results and the results of [PERSON]'s equation are highly correlated. Therefore, to meet the demands of the IT device market requiring high performance/ultra-thin power inductors, an ultra-thin magnetic sheet with nano-sized soft magnetic powder should be developed (Figure 6). The previous experiment showed that the addition of nanopowder of 0.5 wt.% or less did not affect volume fraction or permeability. Based on this result, a mixing ratio of 7:2.5:0.5 of this nanopowder was selected for the experiment, to improve volume fraction. Sample preparation for the selection of the magnetic sheet conditions was SPL2 with nanopowders, SPL3 with nanopowder surface treatment only, and SPL4 with aging treatment at 3 \({}^{\circ}\)C for 24 h after surface treatment. The surface treatment of nanopowder with a 1 wt.% silane coupling agent showed a 3.5% increase in volume fraction and a slight improvement in permeability (SPL3).