## 3 Results and Discussion  
### Radio Frequency Range  
Typical frequency dependencies of dielectric permittivity and electrical conductivity for ceramics loaded with MWCNTs and hybrid MWCNT + SiC whiskers inclusions are presented in Figure 2. The frequency dependence of these parameters is caused by low frequency dispersion [35; 36], which is typical for the disordered media. At low frequencies (below 129 Hz) the dielectric permittivity is high (higher than 100) for all the investigated samples. The SiC whiskers addition leads to a significant increase of the permittivity and conductivity of the composites (see Figure 3). The percolation threshold in both types of ceramic based samples is near 0.5 wt. %. Particularly above the percolation threshold, the DC conductivity of hybrid composites is five orders of magnitude higher than the conductivity of composites filled only with MWCNT inclusions. Moreover, the dielectric permittivity at 129 Hz is at least 1000 times higher for hybrid composites than that of composites filled only with MWCNT. Figure 3: Dielectric permittivity (**a**) and (**b**) conductivity of the hybrid samples and MWCNT-filled samples as a function of MWCNT concentration at the fixed frequency of 129 Hz. Figure 2: Comparison of (**a**) dielectric permittivity and (**b**) conductivity of the hybrid samples and MWCNT-filled samples as a function of frequency. It was previously demonstrated, that the SiC whiskers/ceramics composites have a percolation threshold at a concentration of 25 wt. %. That is the addition of 10 wt. % of SiC would not create a percolation network. To understand the underlying physics the following idea may be proposed. It has been proven, that the conductivity of the MWCNT/ceramic composites has the tunnelling mechanism [33]. The tunnelling resistivity between two equivalent nanotubes can be calculated using the equation [37]:  
\[r=\frac{h^{2}}{e^{2}\sqrt{2m\mathit{l}}}\exp\left(\frac{4 pd}{h}\sqrt{2m\mathit{ l}}\right), \tag{1}\]  
where \(l\) is the potential barrier, and \(d\) is the separation distance. Next, if we add the SiC whiskers in the system it should affect both \(l\) and \(d\). When these values decrease, the total conductivity of the sample should increase drastically. To prove this idea, the low temperature measurements of the conductivity of the ceramics loaded with 2 wt. % MWCNT + 10 wt. % SiC and 2 wt. % MWCNT was done. The temperature dependences of the conductivity for the hybrid and one-component composites are presented in Figure 4.  
The measured experimental data can be fitted with the tunnelling law for both cases as one-component and hybrid composites [38]:  
\[\textsc{S}_{\textsc{DC}} = \textsc{So}^{-\frac{T_{1}}{T+T_{0}}}. \tag{2}\]  
Here \(T_{1}\) is the energy required for an electron to cross the gap between two conductive particles, and \(T_{  
In order to check the shielding properties of the produced samples the following method was used. Let us consider a thin planar layer in the free space with the electromagnetic irradiation incident perpendicularly. The scattering parameters for such system are given by the equations [39]:  
\[ \begin{cases}S_{11}=\frac{-j[(k_{z}/k_{2z})^{2}-1]\sin(k_{2z}t)}{2j(k_{z}/k_{2z}) \cos(k_{2z}t)+[(k_{z}/k_{2z})^{2}+1]\sin(k_{2z}t)}\\ S_{21}=\frac{2(k_{2z}/k_{z})}{-2(k_{2z}/k_{z})\cos(k_{2z}t)+j[(k_{2z}/k_{z})^{2 }+1]\sin(k_{2z}t)}\end{cases} , \tag{3}\]  
where \(k_{z}=2\rho/\,/\,\) and \(k_{2z}=2\rho\sqrt{\,}/\,\) are wave numbers in the vacuum and the sample's media correspondingly, and \(t\) is the thickness of the layer. The absorption of the layer may be computed as \(A=1-(S_{11}^{T})^{2}-(S_{21}^{T})^{2}\). We obtain absorption of the planar layer as a function of the irradiation frequency, sample thickness and the complex dielectric permittivity of the sample, \(A=A(\eta,\,t,\,f^{*})\). To simplify the complex function we can take fixed frequency and sample thickness as \(\eta_{0}=30\) GHz, \(t_{0}=1\) mm.