# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 2 Materials and Methods  
### The Wall Materials  
The wall component without 5G antenna in this study has a typical sandwich structure, as shown in Figure 1 below:  
For simplicity, the wall component depicted in Figure 1 is referred to as the \"sandwich wall\" in this paper. The developed ultrawideband back-to-back spiral antenna system (Figure 2) was integrated into the sandwich wall (Figure 1) to create the \"signal-transmissive wall\" (Figure 3) [15].  
Figure 1: Sandwich wall: 70 mm concrete (outer layer), 220 mm rockwood (insulation layer), and 150 mm concrete (inner layer). The dimension is 150 mm \(\times\) 150 mm.  
Figure 4: (a) Spiral antenna; (b) semirigid dual coaxial cable (two coaxial cables are wrapped into a rubber tube); (c) dimensions of coaxial cable.  
Figure 3: Signal-transmissive wall.  
Figure 2: Ultrawideband back-to-back spiral antenna system developed by the authors. The antenna system contains two identical spiral antennas and a semi-rigid dual coaxial cable.  
A spiral antenna, shown in Figure 4, consists of a copper two-arm spiral (0.035 mm thick, outer radius 17.4 mm, and inner radius 1.08 mm), a Rogers RT/Duroid 5880 PCB (0.5 mm thick), and a Styrofoam board (10 mm thick). The semirigid dual coaxial cable is composed of a rubber block (6.5 mm\({}^{2}\)) and two coaxial cables. Each coaxial cable includes a stainless steel outer connector (0.2 mm thick and 2.159 mm diameter), a PTFE (Teflon) dielectric block (diameter 1.76 mm), and a stainless steel center connector (0.287 mm diameter). The two center connectors (440 mm long) are connected to the spiral arms, while the rest of the dual coaxial cable elements (439 mm long) touch the PCBs. The PCB is embedded in the Styrofoam board at the same level as the concrete (Figure 3). Table 1 lists the material properties of the sandwich and signal-transmissive walls.  
This study did not take into account PCB finishes because their thermal impact is negligible due to their extremely thin layers. The illustration in Figure 3 shows that a 5G antenna should be placed in every 150 mm \(\times\) 150 mm area within an external wall. However, the size can be increased to mitigate the thermal effects of the antennae on the wall, which is the subject of ongoing research.  
In the building industry, the U-value of a wall is used to describe how well or how badly the wall transmits heat from the inside to the outside. In general, we expect a lower U-value, meaning that for every degree (K) of the temperature difference between the inside and outside, the wall loses less heat per square meter. Often, the heat flow through a wall is approximately one-dimensional [32]. However, the installation of a 5G antenna system in the sandwich wall (Figure 3) may cause a thermal bridging effect, which is a 3D heat flow and results in a higher U-value. To evaluate the thermal impact of the 5G antenna system on the sandwich wall, this study applied numerical modeling to estimate U-values primarily for three wall models: the sandwich wall (Figure 1), the signal-transmissive wall with outer and center connectors composed of stainless steel (i.e., the current design) (Figures 3 and 4), and the signal-transmissive wall with outer and center connectors composed of copper (i.e., the previous design) (Figures 3 and 4). Additionally, the study used three analytical methods, the parallel path, the isothermal planes, and the ISO 6946 combined methods, to calculate U-values for the three wall models, and the results were compared with the numerical results to determine a more reliable and accurate method to be used as a tool for future research. Sections 2.2 and 2.3 describe the three analytical methods and 3D numerical modeling, while Section 3 presents their results.