## Materials and Methods
### Methods
#### 2.2.4 EMR Shielding, Reflection and Absorption  
Experimental investigations of reflection and transmission of electromagnetic waves normally incident on fabrics have been performed in the far-field area, using a semi anechoic chamber. The measurement setup is shown in Figure 2.  
It is seen that the measured sample of the fabric is surrounded with absorber sheets preventing for the diffracted wave directly get to the receiving antenna. We used tuneable microwave generator as a microwave source. Continuous wave signal was passed to the transmitting antenna. Transmitted and reflected power was measured using average power sensors from Rhode & Schwarz (Fleet, Hampshire, UK) NRP-Z24. The maximum absolute uncertainty for power measurements for such a sensor is 0.222 dB, which is equal to \(\pm\)5.24 %. The receiving antenna measuring reflection was positioned near the transmitting one. Direct coupling between them was less than \(-\)30 dB. The measured transmitted power \(P_{t}\) with an object under the test was normalized by the power \(P_{t0}\) measured in the absence of it. Therefore, the transmittance can be expressed in the following way:  
\[T=\frac{P_{t}}{P_{t0}} \tag{3}\]  
Results of transmittance are presented in a form of EMR shielding effectiveness SE expressed in decibels:  
\[SE=10\cdot\log_{10}\cdot T \tag{4}\]  
In order to calculate the microwave reflectance from the fabric under the test, the reflected microwave power from the fabric \(P_{r}\) is divided by the reflected power measured when the sample under the test is replaced with the same dimension metal plate \(P_{rm}\). Thus, the reflectance is calculated:  
\[\Gamma=\frac{P_{r}}{P_{rm}} \tag{5}\]  
Absorption in a tested sample has been determined as a difference between falling, transmitted and reflected waves:  
\[A=1-T-\Gamma \tag{6}\]  
Three sets of horn antennas for measurements in a frequency range 2.4-4.0 GHz (S-band WR284), 4-7.5 GHz (C band WR159) and 7.5-18.0 GHz (X-band WR90) were used in our experiments. Rohde & Schwarz average power sensor was connected to the receiving antennas using corresponding waveguide to coaxial line adaptor. Using our measurement setup EMR Shielding effectiveness of the order of 35 dB can be measured. Combined standard uncertainty for shielding effectiveness and reflection measurements is equal to \(\pm\)7.4 % for a single data point at a fixed frequency. Figure 2: Measurement setup of microwave transmission and reflection from the coated fabric. TA denotes transmitting and RA—receiving antennas. 2.2.5. Calculation of the Surface Conductivity according to the Measurements of Reflectance and Transmittance  
The fabrics covered with conductive paste can be considered as a thin layer with particular surface conductivity \(\sigma_{s}=1/R_{s}\), were \(R_{s}\) is surface resistance. Since the thickness of fabrics is much less than the wavelength of electromagnetic wave used in experiments, the dielectric properties of the fabric can be neglected. It also confirms our measurements of the substrate. We did not find any reflection or decrease of transmittance experimentally in the substrate fabric tests. We consider a plane electromagnetic wave incident normally on a surface of the conductive textile characterized by the only parameter--surface conductivity. A schematic view of the situation is shown in Figure 3.  
On the left side we have incident and reflected waves whereas on the right side we have transmitted wave only. The problem can be solved analytically applying boundary conditions at the interface \(z=0\). It is clear that the tangential component of electric field should be continuous in the interface of two regions, whereas the magnetic field component should have a step due to surface conductivity [41].