## 2 Materials and Methods
### Vector Network Analyzer  
A Vector Network Analyzer (VNA) is a precision electronic instrument used to measure the electrical properties of microwave devices, components, and systems. The primary  
\begin{table}
\begin{tabular}{c c c c} \hline
**Graphite** & **Carbon Black** & **Matrix** & **Fillet Ratio** \\
**Filled** & **Filled** & **in Weight \%** \\ \hline G1 & CB1 & & 1 \\ G3 & CB3 & Epoxy & 3 \\ G5 & CB5 & & 5 \\ G7 & CB7 & & 7 \\ \hline \end{tabular}
\end{table}
Table 1: Graphite and carbon black-filled sample compositions.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Graphite** & **Density** & **Carbon Black** & **Density** \\
**Filled** & **g/cm3** & **Filled** & **g/cm3** \\ \hline G1 & 1.310 & CB1 & 1.306 \\ G3 & 1.341 & CB3 & 1.318 \\ G5 & 1.348 & CB5 & 1.330 \\ G7 & 1.373 & CB7 & 1.342 \\ \hline \end{tabular}
\end{table}
Table 2: Sample densities.  
function of a VNA is to analyze the transmission and reflection characteristics of electrical networks. It measures and displays the complex-valued scattering parameters.  
The coaxial method was used to determine the shielding efficiency. One significant benefit of this technique is its comparability across different laboratories, as the results obtained can be easily compared. Moreover, using a coaxial transmission line allows for the resolution of the data into its reflected, absorbed, and transmitted components. The measurements can be performed at specific frequencies by utilizing a modulated signal generator, crystal detector, and tuned amplifier.  
The measurements are carried out by measuring the scattering parameters S11, S12, S21, and S22 (Figure 2) between 1-14 GHz according to the coaxial method, then dielectric parameters, including both real (\(\varepsilon^{\prime}\)) and imaginary parts (\(\varepsilon^{\prime\prime}\)) were derived using the Keysight N1500 software. Measurements were taken every 65 MHz at room temperature.  
Nicolson-Ross-Weir method, which is widely used in the derivation of dielectric parameters, the polynomial model in the software is carried out since it produces suitable results for materials without magnetic components, which eliminates discontinuity points that occur due to sample thickness [33]. Its algorithm is a computer-based technique that is utilized to indirectly obtain the dielectric properties of a material [34]. It achieves this by analyzing the scattering parameters of the material.  
Scattering parameters, also known as S-parameters, are a set of complex numbers that describe the behavior of a linear electrical network or device in terms of signal transmission and reflection. They quantify how an electrical signal is transmitted or reflected at various ports of a device. In a two-port network, the S-parameters are typically represented as S11, S12, S21, and S22. S11 represents the reflection coefficient at Port 1, S22 represents the reflection coefficient at Port 2, S12 represents the forward transmission coefficient from Port 1 to Port 2, and S21 represents the reverse transmission coefficient from Port 2 to Port 1.  
Before the measurement process, the device is calibrated, and then the measurement quality of the device is tested with air and Teflon. After the permittivity (real part) value of \(\sim\)1 for air and \(\sim\)2.1 for Teflon was observed, the measurements of the samples were carried out.  
Figure 1: Specim dimensions for co-axial method.  
Figure 2: Scattering parameters.