## 3 Results and Discussion
### Evaluation of Button Sensor Antenna: Simulated Results
#### 3.1.3 Three-Layer and Single-Layer Body Phantom Models  
To deploy wearable designs for body monitoring applications, it is first necessary to study their performance while being placed on the body and the lossy tissues. Some of the models of interest are the chest and the arm. In this part, the BSA performance on the human chest and arm models will be discussed. A flat 3D-layered body model with skin, fat, and muscle layers was mostly used for the chest model as well thickness variation in biological tissues, as discussed in [54]. The overall volume of the three-layer phantom is \(200\times 200\times 50\) mm\({}^{3}\) and the thicknesses of the layers are as follows (in mm): skin: 4, fat: 8, muscle: 30, and air layer under the tissue layers: 8, for a total thickness of 50 mm. To consider the effect of bone, we also considered a four-layer phantom which has slightly different layers and thicknesses. After a layer of bone is added, the overall volume of the phantom is \(200\times 200\times 88\) mm\({}^{3}\). The layers thicknesses are as follows in (mm): skin: 2, fat: 8, muscle: 40, bone: 30, and air layer under the tissue layers: 8, for a total thickness of 88 mm. The skin has a dielectric constant (\(\varepsilon_{\mathrm{r}}\)) of 31.29 and conductivity (\(\sigma\)) of 5.0 S/m at 2.45 GHz, for the fat layer the values are 5.28 and 0.1 S/m; whereas at 5.8 GHz, the values for skin are 35 and 3.7 S/m and the values for are 5.0 and 0.3 S/m, respectively. The muscle layer has an \(\varepsilon_{\mathrm{r}}\) of 52.7 and 48.2 and a \(\sigma\) of 1.95 S/m and 6.0 S/m at the lower and upper-frequency bands, respectively. The bone layer has an \(\varepsilon_{\mathrm{r}}\) of and a \(\sigma\) 11.4 of 0.39 S/m, and of 9.674 and 1.1544 S/m at 2.45 and 5.8 GHz in the lower and upper frequencies, respectively [55; 56; 57; 58]. For modeling the arm, a simple layered cylindrical model was utilized. For the on-body arm communication, a phantom with a radius (r) of 50 mm and 100 mm and a length of 150 mm was chosen. Figure 10 shows these models and the results of the simulations. Generally, the analysis of the performance of a wearable antenna is difficult because the dielectric properties of the human tissues are dispersive and change with frequency. In addition, the tissue properties from one person to another may be different. To add to this difficulty, the body size is different for each person. In the three-layer model, we varied the layer thicknesses [59; 60]. Another important parameter to consider is the air gap between the skin surface and the bottom of the button antenna surface. The variation in the air gap may have a significant impact on wearable device functionality. We evaluated an air gap of 2 mm, 3 mm, and 5 mm. The resonant frequency and impedance bandwidth in both bands were affected by the air gap size. We present this effect through different simulations. Although we used an air gap with varying size, this may also mimic the combination of several textile layers and air, since textile and air have similar dielectric constants. Because of the significant loading effect of the body tissues on the BSA at the air gap of \(d=2\) mm, the impedance matching was affected. The impedance matching was unaffected by increasing the air gap to 5 mm, and the BSA was almost decoupled from the body at this distance. We recommended a 5 mm air gap and kept this value for the rest of the studies. S\({}_{11}\) at different air gaps is shown in Figure 11. A similar simulation was set up for a single-layer muscle phantom. Figure 12 depicts the single-layer model of a 50 mm and 88 mm single layer of muscle, and air layer under the tissue layers, with the total volume of \(200\times 200\times 50\) mm\({}^{3}\), and \(200\times 200\times 88\) mm\({}^{3}\). Similarly, for the arm model, a cylinder of homogenous muscle phantom with a radius of 50 m and 100 mm and a length of 150 mm was considered.