## 3 Results of Magnetic Measurements and Discussion
### AC Properties  
Further measurements at higher frequencies and field strengths confirmed the substantial increase of the material coercivity and core losses accompanied by the decrease in its maximum permeability. As the samples exhibit \(5\times 5\) mm bulk cross-sectional area, significant eddy currents are induced, which are responsible for the majority of hysteresis curve shearing and growth of its area. The shearing effect is visualized in Figure 7, presenting the measured hysteresis curves at 50 Hz in the magnetization range of 1-1.5 T, alongside the calculated total iron loss for each curve. The behavior of sample relative magnetic permeability and coercivity are shown in Figure 8 in the range of 1.1 to 1.5 T at 1, 10 and 50 Hz. The highest maximum relative AC permeability \(\mu_{\text{max}}\) in the study was measured at 10,850 (1.11 T, 1 Hz) post-annealing, which decreased to 2200 (1.5 T, 1 Hz) and was further reduced to 200 at higher excitation frequency (1.5 T, 50 Hz). Figure 7: Hysteresis curves measured at 50 Hz in the magnetization range of 1–1.5 T (annealed). The unannealed sample exhibited considerably lower \(\mu_{\max}\) of 2400 (1 T, 1 Hz), 1650 (1.5 T, 1 Hz) and 380 (1.5 T, 50 Hz). Coercivity of the samples ranged from 87 A/m (1.08 T, 1 Hz) post-annealing, which increased to 334 A/m (1.5 T, 1 Hz) and was further increased to 2400 A/m at higher excitation frequency (1.5 T, 50 Hz). Both the material coercivity and total iron losses increased roughly above the knee point of the material over all measured frequencies after the annealing process. Calculated iron losses in the magnetization range of 0.9-1.5 T at 1, 10 and 50 Hz are presented Figure 8. The summary of the iron losses is presented in Table 3 with the losses ranging from 83.7 W/kg (Annealed, 1.5 T, 50 Hz) to 0.022 W/kg (Annealed, 1 T, 1 Hz). The total iron losses decreased after the annealing at 1 T magnetization, however increased at 1.5 T over all the measured frequencies. Loss segregation was performed for clarification of the loss behavior through the subtraction of hysteresis (obtained through quasi-static measurements) and eddy current losses (obtained through simulation) from the total measured losses. Eddy currents were identified as the main component of the measured losses, generated due to the unlaminated, fully dense cross section of the sample toroid. FEM analysis of the toroid cross section correlated with the losses measured: comparison of the simulated hysteresis curve expressing only the FEM eddy current losses and the measured total losses at 1.5 T, 50 Hz is shown in Figure 9. The difference of the area between the hysteresis curves presented in Figure 10 represents the sum of hysteresis and excess eddy current losses. The area of the hysteresis curves was then used for the calculation of hysteresis losses. Excess eddy currents are not calculated and are obtained from the segregation. Table 4 presents the segregated losses of both the annealed and unannealed samples at 1 and 1.5 T.  
Figure 8: Measured (**a**) maximum relative permeability and (**b**) coercivity of the toroid before and after annealing at 1, 10 and 50 Hz, in the magnetization range of 1.1 to 1.5 T. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **1 Hz (W/kg)** & **10 Hz (W/kg)** & **50 Hz (W/kg)** \\ \hline Annealed, 1 T & 0.022 & 0.60 & 8.17 \\ Unannealed, 1 T & 0.077 & 1.37 & 14.17 \\ Annealed, 1.5 T & 0.23 & 7.1 & 83.7 \\ Unannealed, 1.5 T & 0.16 & 3.5 & 47.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Iron losses at 1, 10, and 50 Hz. Figure 10: Comparison of simulated eddy current losses and total iron losses at 1.5 T, 50 Hz before and after annealing.