# Revisiting the Analysis of Radiative Mid-Range Wireless Link for Pacemakers
## 3 Results
### Wireless Link Analysis Based on Related Formulas
#### 3.2.1 On-Axis Scenarios  
The integral coupling formula has been used to successfully evaluate the biomedical wireless link presented in [10]. The use of the diverse techniques is desirable to meet the requirement of establishing the biomedical wireless link where an efficient and accurate estimation is preferred. Other techniques used in this paper, compared to the previous work [10], are the asymptotic Friis formula and the Chu formula. The power transmission between two antennas is evaluated for the on-axis scenario where the implanted antenna is fixed while the reader antenna moves along the \(z\)-axis. The far-field gains and directivities applied to the formulas are provided in Table 2. The far-field gains are used to estimate the coupling level, including losses due to the implantation inside the human body, while directivities are used to calculate the gain reduction factors. The modified gain based on the switching function is used to determine both the gain reduction factors included in the asymptotic Friis formula and the Chu formula. Figure 5 shows a comparison for the related formulas and full-wave simulation FEKO. It is observed that the related formulas provide an excellent agreement with the results of full-wave simulation FEKO, except for the Friis formula. The Friis formulas provide maximum deviations (enhancements) of 1.7-2.5 dB from other methods. The case of the free-space power transmission provides more deviation (enhancement) compared to the case of the implanted antennas, since a relatively high gain of the antenna outside the human body produces more gain reduction in the near-field region. It is observed that the level for the case with 4 mm thickness is roughly 1.3-1.7 dB higher than the level of the case with 8 mm thickness. It is observed that the deviation from the Friis formula agrees well with the reduction in the antenna gain  
Figure 3: (**a**) Description of the evaluated cases, (**b**) simulated radiation patterns for the reader patch antenna outside the human body, (**c**) simulated radiation patterns for the implanted patch antenna immersed with 4 mm thickness of the human skin, and (**d**) simulated radiation patterns for the implanted patch antenna immersed with 8 mm thickness of the human skin.  
presented in Section 2. It is worth noting that the asymptotic Friis formula tend to diverge from a group of curves at 0.8\(\lambda\), since the gain reduction factor is starting to decrease rapidly, as discussed in Section 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Patch Antenna in** & **Implanted Patch** & **Implanted Patch** \\  & **the Air** & **Antenna (4 mm)** & **Antenna (8 mm)** \\ \hline Far-field gains & 6.8 dBi & \(-\)7.7 dBi & \(-\)9.1 dBi \\ Directivities & 6.6 dBi & 5.5 dBi & 5.2 dBi \\ \hline \hline \end{tabular}
\end{table}
Table 2: Far-field gains of the patch antennas at 400 MHz.  
Figure 4: A comparison of calculated and simulated gain reduction factors for: (**a**) the reader patch antenna outside the human body, (**b**) the implanted patch antenna immersed with 4 mm thickness of the human skin, and (**c**) the implanted patch antenna immersed with 8 mm thickness of the human skin.