# A Printed Wearable Dual-Band Antenna for Wireless Power Transfer
## 3 Experimental and Simulation Results  
The location of the receiving antenna while it was placed on a phantom body model is presented in Figure 3a-c. The experimental setup is depicted in Figure 3d. As it is shown in Figure 4a the reflection coefficient for the TX antenna (\(S_{11}\)) is \(-19.50\) dB at the first resonance frequency and \(-16.90\) dB at the second resonance frequency. The reflection coefficient for the RX antenna (\(S_{22}\)) is \(-15\) dB at the first resonance frequency and \(-21.90\) dB at the second resonance frequency and \(-21.90\) dB at the second resonance frequency. These values are taken from the measurement in free-space. Similarly, Figure 4b presents the reflection coefficient for the TX antenna (\(S_{11}\)) is \(-17\) dB at the first resonance frequency and \(-17.50\) dB at the second one. The reflection coefficient for the RX antenna (\(S_{22}\)) is \(-23.60\) dB at the first resonance frequency and \(-23.60\) dB at the second one, while it is placed on the muscle tissue. \(S_{21}\) in Figure 4a,b show the measured and simulated transmission coefficients for free-space and on body phantom cases, respectively. Figure 2: Transmitter (TX) and receiver (RX) antennas (a) antenna structure parameters, (b) TX and RX fabricated prototypes. Figure 4: Scattering parameters S\({}_{11}\), S\({}_{22}\), and S\({}_{21}\) with 5 mm gap between the RX and TX, the RX is placed on (**a**) in free space, (**b**) on phantom. Figure 3: Proposed antennas (**a**) wearable antenna on hand, (**b**) antenna structure, (**c**) flexible antenna on phantom body model, and (**d**) experimental setup. It is expected to see a slight difference in resonance frequencies of the TX and RX, due to the differences in the substrate's materials. A slight shift in the measured resonant frequencies compared to simulated ones were due to fabrication discrepancies. Scattering parameters of these antennas at different resonance frequencies are shown in Table 2. In this paper, \(S_{11}\) represents the reflection coefficient for the transmitting antenna (TX), \(S_{22}\) provides the reflection coefficient for the receiving antenna (RX), and \(S_{21}\) is the transmission coefficient. The simulated radiation patterns describe how the antenna radiates/receives energy into space. The antenna patterns are generally shown as plots in polar coordinates so the viewers have the ability to easily visualize how the antenna radiates in all directions. The ratio of the power gain in a given direction to the power gain of a reference antenna in the same direction defines the gain of the antenna [37]. The maximum gain of the TX at 2.5 GHz and 4.5 GHz is \(-5.34\) dBi and \(-4.49\) dBi, respectively, as shown in Figure 5. The radiation pattern was measured while the TX antenna is printed on an FR-4 substrate and was compared to simulation ones, as shown in Figure 6. The measured and simulated antenna specifications are listed in Table 3.  
Please note that in this case antennas are not necessarily in the far-field of each other. The antenna efficiency is not relevant in these applications. Instead, transmission efficiency is a good measure of the antenna's performance. We studied the effects of distance on the proposed dual-band antennas' transmission efficiency. To calculate transmission efficiency, we used (1). \[\eta=\left|S_{21}\right|^{2}\ \times 100\ \% \tag{1}\]  
where \(\eta\) is transmission efficiency and S\({}_{21}\) is the transmission coefficient. The distance was changed from 5 mm to 50 mm. The transmission efficiency variation was 3.94% for the first resonance frequency and 2.29% for the second one, as shown in Figure 7. It is concluded that the antenna performance is stable and does not change significantly due to this change of distance.