## 3 Results
### Measurements and Model Validation
#### 3.2.2 Computer Model Validation  
A 355 mm \(\times\) 160 mm \(\times\) 255 mm polystyrene tank was filled with the corresponding tissue mimicking liquids of Table 4 as a reference design. At lower frequencies (402 MHz, 868 MHz), the chosen height y (160 mm) was below the minimum threshold defined by Table 1 for deep implants. Oscillations coming from reflections on the boundaries due to the electrical small phantom size should be expected. This phenomenon should be captured by the probe antennas inserted in the physical phantom. If the phantom is electrically large with dimensions mainly above the thresholds dictated by Table 1, as the present case for the upper frequencies 2.45 GHz and 5.8 GHz, the tendency should be decreasingly linear with minimum oscillations, regardless of the type of antenna. In Figure 8, the measured results for the characterization of plane wave attenuation for the proposed phantom size with the liquids corresponding to Table 4 and the setup described in Section 2.3 are shown for both antennas and both polarizations for each position. Matching of the antennas was corroborated in each situation (Figure 9), disregarding antenna 2 at 402 MHz in Figure 8a, as expected. The performances of the antennas at 2.45 GHz (Figure 8c) and 5.8 GHz (Figure 8d) followed the same trend in all cases. In each case, the difference between the antennas was due to the gain variety and polarization sensitivity. For distances larger than 60 mm at 2.45 GHz and 20 mm at 5.8 GHz, the measured \(\mathbb{S}_{21}\) parameter was below \(-110\) dB and became erratic in at least one polarization, so this region was neglected as noise. The four plots mainly overlapped for each frequency (2.4 GHz, 5.8 GHz) once the values were normalized by their respective maximum (Figure 10). This demonstrated that the antenna and its polarization did not have an impact on the normalized expected results for these high frequencies and that the phantom was representative of the whole body. Figure 7: (**a**) Measured real part of permittivity (black lines) and (**b**) conductivity (grey lines) for different sugar concentration liquids and muscle theoretical values [25; 26; 27]. Figure 8: S\({}_{21}\) dB vs. distance for the different antennas and polarizations: (**a**) f = 402 MHz, (**b**) f = 868 MHz, (**c**) f = 2.45 GHz and (**d**) f = 5.8 GHz. Figure 9: S\({}_{11}\) dB vs. distance for each antenna at different frequencies. A good agreement between the measurements and simulations can be observed when the properties that were used in the simulation were the ones of the fabricated phantom (Figure 10, markers and dashed lines, respectively). When real (theoretical) [25; 26; 27] properties were imported in the model, as in the previous section, a different slope with respect to the measured results was observed (Figure 10, solid lines), as expected. The difference between the real (theoretical) and the phantom's conductivities explains the variability of the plane wave attenuation. On the other hand, at 402 MHz and 868 MHz, the tendency was not consistent. The dips were a sign of internal reflections, which were not negligible for lower frequencies as the phantom exhibited a small electrical size. The internal reflection phenomena at the phantom boundaries made the radiation pattern variability between antenna 1 and 2 have an impact on the results. This is consistent with a phantom size smaller than the indicated by Table 1. Moreover, the anechoic chamber was prepared to work efficiently for frequencies above 1 GHz. According to Section 2, in the computational model, ideal probes were used inside the phantom to monitor the field. The equivalence \"antenna in the measurement-probe in the model\" was only fulfilled for the 2.45 GHz and 5.8 GHz frequencies where the phantom was above the dimensions stated by Table 1 for deep implants: convergence was achieved and reflections were kept at a low level.