# Characterization of a Mechanical Antenna Based on Rotating Permanent Magnets
## 5 Discussion and Conclusions  
This article is based on a consistent bibliographic study in order to establish the current performances of mechanical antennas with rotating permanent magnets and to relate these \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Magnet Type**} & \multirow{2}{*}{**Units**} & \multirow{2}{*}{**Fundamental**} & \multicolumn{2}{c}{**2 nd**} & \multicolumn{2}{c}{**3 rd**} & \multicolumn{2}{c}{**4 th**} \\  & & & **Harmonic** & **Harmonic** & **Harmonic** \\ \hline \multirow{2}{*}{CRRM} & Hz & 70.9 & 141.8 & 212.8 & 283.5 \\  & dBm & 38.8 & \(-\)10.2 & \(-\)18.6 & \(-\)29.9 \\ \hline \multirow{2}{*}{CABM} & Hz & 71.5 & 142.9 & 214.4 & 285.9 \\  & dBm & 25.6 & \(-\)26 & \(-\)6.25 & \(-\)44.7 \\ \hline \multicolumn{5}{c}{Harmonics weight relative to fundamental frequency} \\ \hline \multirow{2}{*}{CRRM} & & 49 dBm & 57.4 dBm & 68.7 dBm \\  & & **1/282** & 1/741 & 1/2690 \\ \hline \multirow{2}{*}{CABM} & & 51.6 dBm & 31.85 dBm & 70.3 dBm \\  & & 1/380 & **1/39** & 1/3162 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values obtained in the harmonic analysis for the two types of rotating magnets. Figure 19: The spectrograms obtained with the two devices (Narda sensor and magnetic sensor coil) for the CABM. performances to the experiments performed by the authors. The two mentioned configurations (CABM and CRRM) are employed, the latter proving to have better performance in all aspects. Regarding the material, at this time, NdFeB permanent magnets are the most efficient. One of the competitors is the SmCo permanent magnet which has higher temperature stability and corrosion resistance but is economically uncompetitive at the moment. The numerical results prove a good agreement between the numerical analysis and measurements: 5% error for the CRRM over the range 0-80 mm considering a remanent induction \(B_{\mathrm{r}}=1.17\) T and 5% for the CABM over the range 5-60 mm considering a remanent induction \(B_{\mathrm{r}}=1.21\) T.  
In the next stage, we sought to establish to what extent the intensity of the emitted magnetic field presents differences between the static and the dynamic (harmonic) regimes. Through these measurements, it was proven that the configuration with CRRM is superior from this point of view, with the maximum difference between the two regimes being of 3.16% while for the CABM, the differences are much bigger. For this last configuration, there is a simple analytical relationship--Equation (2)--used to calculate the magnetic field; therefore, in Figure 14, the theoretical curve was also drawn. For a CRRM, there is no simple analytical relationship to calculate the magnetic field; the algorithm presented in [28; 29] requires numerical calculation. Thus, in the case of the CRRM, it can be concluded that the static regime and the harmonic regime at a frequency of 70 Hz are quasi-identical in terms of the emitted field. The analytical calculations and experimental results presented in the article highlight some aspects of novelty/originality relative to the research in the field so far:  
* The equivalence between relations (1) and (2) is a matter that has not been specified so far. Moreover, it is analytically demonstrated that the distance dependence of the magnetic field of these configurations scales as \(1/r^{3}\). A similar approach, but without theoretical explanations, is attempted in [30]. * Demonstrating the \(1/r^{3}\) dependence up to a distance of 15-20 m; in the studied bibliography, these distances are much smaller. * Harmonic analysis via competing test methods (replicate testing), which was not found in the bibliography. This is of great importance in the analysis of the efficiency of these types of antennas. * Experimental demonstration of the quasi-identity for the magnetic fields emitted as a function of distance in the static and harmonic regimes at the used frequencies.