## 2 Theoretical Background of the Experiment  
Considering a shielding material \(S\) illuminated by an electromagnetic wave (Figure 1), shielding quality can be described using the shielding effectiveness (\(SE\)) parameter  
\[SE=-10\text{log}\left(\frac{P_{\text{T}}}{P_{\text{I}}}\right), \tag{1}\]  
where \(P_{\text{I}}\) is the incident power, \(P_{\text{T}}\) is the transmitted power, and \(P_{\text{R}}\) is the reflected electromagnetic power.  
According to the Schelkunoff theory [29], the \(SE\) can be expressed as  
\[SE=SE_{\text{R}}+SE_{\text{M}}+SE_{\text{A}}\approx SE_{\text{R}}+SE_{\text{A }}, \tag{2}\]  
where \(SE_{\text{R}}\) is the reflection loss, \(SE_{\text{M}}\) is the multiple reflection loss, and \(SE_{\text{A}}\) is the absorption loss inside the material. For very conductive materials for which \(SE_{\text{A}}\) is large, multiple reflection losses can be avoided. For the plane wave normal incident case, the \(SE_{\text{A}}\) and \(SE_{\text{R}}\) parameters can be calculated from the following expressions [29]:  
\[SE_{\text{A}}=8.69\ t\ \sqrt{\pi f\mu\sigma}, \tag{3}\]  
\[SE_{\text{R}}=20\text{log}\left|\frac{\left[\eta_{0}+\eta_{s}\right]^{2}}{4 \eta_{0}\eta_{s}}\right|, \tag{4}\]  
\[\eta_{s}=\sqrt{\frac{j2\pi f\mu}{\sigma+j2\pi f\epsilon}}, \tag{5}\]  
where material properties are characterized by the permeability \(\mu\), the permittivity \(\epsilon\), and the conductivity \(\sigma\). Hence, \(\eta_{S}\) is the intrinsic impedance of the material, \(\eta_{0}\) is the intrinsic impedance of free space, \(f\) is the operating frequency, and \(j=\sqrt{-1}\) is the imaginary part unit.  
Figure 1: Schematic diagram showing the incident, reflected, and transmitted electromagnetic radiations.  
Since direct measurements of electrical and magnetic parameters of textile materials are very difficult to perform at microwave frequencies, the shielding properties could be expressed in terms of the scattering parameters \(S_{ij}\)[2; 10; 30], where \(i\) represents the output and \(j\) represents the input in a two-port network. Therefore, \(S_{11}\) is the reflection coefficient at the first port, \(S_{12}\) is the reversed isolation, \(S_{21}\) is the insertion loss, and \(S_{22}\) is the reflection coefficient at the second port. The total shielding effectiveness \(SE^{\prime}\) can be calculated as follows:  
\[SE^{\prime}=SE^{\prime}_{\text{R}}+SE^{\prime}_{\text{A}}=-10\text{log}|S_{21} |^{2} \tag{6}\]  
\[SE_{\text{A}}{}^{\prime}=-10\text{log}\Bigg{(}\frac{|S_{21}|^{2}}{1-|S_{11}|^ {2}}\Bigg{)} \tag{7}\]  
\[SE_{\text{R}}{}^{\prime}=-10\text{log}\Big{(}1-|S_{11}|^{2}\Big{)} \tag{8}\]  
where \(SE_{\text{R}}{}^{\prime}\) is the reflection loss and \(SE_{\text{A}}{}^{\prime}\) is the absorption loss inside the material. Applying the properties of the scattering parameters [29]  
\[|S_{21}|^{2}=\frac{P_{\text{T}}}{P_{\text{I}}}, \tag{9}\]  
\[|S_{11}|^{2}=\frac{P_{\text{R}}}{P_{\text{I}}}, \tag{10}\]  
it can be easily shown that  
\[SE^{\prime}_{\text{R}}=-10\text{log}\bigg{(}\frac{P_{\text{R}}}{P_{\text{IN}}} \bigg{)}=-10\text{log}\bigg{(}\frac{P_{\text{R}}}{P_{\text{I}}-P_{\text{R}}} \bigg{)}, \tag{11}\]  
\[SE^{\prime}_{\text{A}}=-10\text{log}\left(\frac{P_{\text{T}}}{P_{\text{IN}}} \right)=-10\text{log}\bigg{(}\frac{P_{\text{T}}}{P_{\text{I}}-P_{\text{R}}} \bigg{)}, \tag{12}\]  
where \(P_{\text{IN}}\) is the power penetrating the shielding material. It should be noted that the total shielding effectiveness is defined identically in both theories but the quantities \(SE_{\text{A}}\) and \(SE_{\text{A}}{}^{\prime}\) have a slightly different physical meaning in each theory. The same remark applies to \(SE_{\text{R}}\) and \(SE_{\text{R}}{}^{\prime}\)[31].