## 3 Results and Discussion
The penetration of the EM wave into the absorbing material depends on the degree of the impedance matching between the surface of the CNT-based material modified with substituted ferrites and the free space. The use of polymer matrices transmitting EM waves allows to reduce the effect of reflection of microwaves from the surface of the absorbing material. In our case, epoxy resin is a material that transmits EM waves and performs the impedance matching between (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT nanocomposite and the free space. Figure 6 shows the calculated absorption and reflection loss curves of polymer systems based on an epoxy matrix and carbon nanotubes modified with substituted ferrites. For comparative analysis of the absorption and reflection processes polymer systems depending  
Figure 5: Frequency dependencies of EM wave absorption coefficients (left column) and reflection losses (right column) of (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) substituted ferrites (**a**) and (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT nanocomposites (**b**): x = 0 (\(I\)), x = 0.5 (\(Z\)) and x = 1 (\(S\)). The thickness of the samples was 4 mm. on the filler content, a fixed thickness was chosen. Since the interference minima will shift in frequency as the sample thickness changes [42; 43], while the absorption at the corresponding sample thickness will not change significantly. As the filler volume content increases in the epoxy matrix for (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT-ER systems with a doping amount of manganese ions (x = 0, 0.5, and 1), there is an observed increase in the maximum peak values of the absorption coefficient, accompanied by a shift of these maxima to a lower frequency region. In particular, the (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT-ER system is characterized by shifts in the maximum peak value of the absorption coefficient as the filler content increases. For x = 0, there is a shift from 35.2 GHz to 30.4 GHz; for x = 0.5, a shift from 33.8 GHz to 19.7 GHz; and for x = 1, a shift from 34.2 GHz to 23.3 GHz. Additionally, for these polymer systems (x = 0, 0.5, and 1), the minimum reflection loss peaks and their shift to the low-frequency region are also observed. Specifically, the samples based on (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT  
Figure 6: Frequency dependencies of EM wave absorption coefficients (left column) and reflection losses (right column) in polymer-based systems (NiZn)\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT–ER: x = 0 (**a**), x = 0.5 (**b**), and x = 1 (**c**). Volume fractions of CNT: \(I\)—0.0025; \(I\)—0.005; \(I\)—0.0075; \(I\)—0.01; \(I\)—0.015; \(I\)—0.005 (pure ER). The thickness of the samples was 2.5 mm. (x = 1) with 0.0025 vol. % demonstrated electromagnetic absorption performance at frequencies around 30 GHz with \(RL<-18.7\) dB. It is noteworthy that, for all polymer composites with a filler content of 0.0025 volumetric fraction, the highest bandwidth (\(RL<-10\) dB) was determined. The polymer system based on (NiZn)\({}_{1-\mathrm{x}}\)Mn\({}_{\mathrm{x}}\)Fe\({}_{2}\)O\({}_{4}\)/0.07 CNT at x = 0.5 exhibited the highest value of the bandwidth (\(RL<-10\) dB) at 10.8 GHz. With the increase in the concentration of carbon nanotubes in polymer systems, a narrowing of the bandwidth and a decrease in the reflection loss were observed. It is known that dielectric losses, magnetic losses, and impedance matching characteristics affect the absorption properties of materials. The increasing content of carbon nanotubes in polymer-based systems, characterized by a high aspect ratio, results in the formation of a conductive network and leads to an increase in dielectric losses. However, the increase in the complex dielectric permittivity of polymer systems (Figure 4) affects impedance matching and results in more significant reflection.