# Research on Penetration Loss of D-Band Millimeter Wave for Typical Materials
## 2 Materials and Methods
The schematic diagram of signal transmission [21] is shown in Figure 3.  
In Figure 3, \(P_{in}\) is the incident signal power, \(P_{out}\) is the transmitted signal power, \(P_{inf}\) is the reflected signal power, and D is the thickness of the barrier. The fading coefficient can be obtained from the transmission attenuation caused by material penetration [21], as follows:  
\[\zeta=\left|\frac{\sqrt{\epsilon_{r}}-1}{\sqrt{\epsilon_{r}}+1}\right| \tag{2}\]  
Figure 3: Schematic diagram of D-band millimeter-wave signal transmission. Figure 2: Transmission attenuation model diagrams of D-band millimeter-wave signal passing through obstacles. where  
* \(\varepsilon_{r}\) is the relative permittivity of the barrier materials. The relationship between \(P_{in}\) and \(P_{out}\) (that is, the transmittivity of penetration selected below) can be expressed as follows:  
\[\frac{P_{out}}{P_{in}}=\frac{\xi}{e^{200D-1}}\Big{(}1-\zeta^{2}\Big{)}^{2}e^{-2D\chi} \tag{3}\]  
\[\chi\approx\frac{\pi tg\delta}{\lambda\sqrt{\varepsilon_{r}}} \tag{4}\]  
where  
* \(D\) is the thickness of the obstacles, and its measurement unit is meters;
* \(\lambda\) is the operating wavelength;
* \(tg\delta\) is the tangential loss angle;
* \(\varepsilon_{r}\) is the relative permittivity of the blocking material. For almost impenetrable barriers, such as slates, the relationship between \(P_{in}\) and \(P_{out}\) can be expressed as follows:  
\[\frac{P_{out}}{P_{in}}=\Big{(}1-\xi^{2}\Big{)}^{2}e^{-2D\chi} \tag{5}\]  
Then, the penetration loss can be expressed as follows:  
Figure 1:0  
Conversely, the relationship between \(P_{in}\) and \(P_{out}\) can also be calculated from the penetration loss measured in the experiment. For a more intuitive comparison, we select the transmittance index for comparison. It should be emphasized that the parameters of relative permittivity and tangent loss angle have been given in Refs [20; 22; 23; 24; 25; 26; 27; 28], and we use these parameters directly in the measured D-band mmWave system. The real part of wood permittivity was measured by a quasi-optical Mach-Zahnder interferometer with a backward-wave oscillator and the result was 1.60-1.89 in the D-band [25]. However, some of the parameters were not measured in the case of the D-band, so there is a certain error. The parameters are shown in Figure 1:1  
The experimental setup of the D-band millimeter-wave transmission system is shown in Figure 1:2 The signal generator (Agilent 83711B, 1-20 GHz) generates an IF signal from 11.4 GHz to 13.5 GHz, which is extended to the D-band (138 GHz to 163.2 GHz) after passing through a six-multiplier and a two-multiplier. D-band signals are transmitted to free space via a standard horn antenna (LB-6-25-A). After passing through the artificially placed shelter, the receiving end is received by the same type of standard horn antenna at the transmitting end. The received signal is first amplified by an electric amplifier with a gain of 30 dB (the specific parameters of LNA are shown in Table 2), and then down-converted to the intermediate frequency (1.2 GHz) in the mixer. At this point, the frequency range of the signal is already within the effective bandwidth of the digital oscilloscope. After that, the IF signal is amplified by an electric amplifier with a gain of 26 dB, and finally captured by a digital oscilloscope (E4407B ESA-E, 9 kHz-26.5 GHz). Therefore, the center \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Frequency** & \(\varepsilon_{r}\) & \(tg\delta\) \\ \hline \multirow{2}{*}{Wood} & \(<\)100 GHz & 1.99 [24] & 0.0040 \\  & 110–170 GHz & 1.6–1.89 [25] & 0.0040 \\ \hline \multirow{2}{*}{Plexiglass} & 143 GHz & 2.60 [26] & 0.0050 \\  & 60–300 GHz & 2.581–2.602 [27] & 0.0050 \\ \hline \multirow{2}{*}{Concrete board} & 1–95.9 GHz & 6.2–7 [28] & 0.0491 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of relative permittivity and tangent loss angle of different materials. frequency and received power of the IF signal are observed.