# Characterization of a Mechanical Antenna Based on Rotating Permanent Magnets
## 4 Results
### Experimental Results up to 100 mm
#### 4.2.2 Mechanical Antenna with CABM  
The measurement results obtained in static and dynamic regimes (70 Hz) for the CABM are presented in Figure 14. In addition, because, for this case, there is an analytical equation that can be easily calculated, namely Equation (2), the calculated curve for the magnetic field emitted by the CABM was drawn (the black curve in Figure 14). In this case, the maximum percentage differences are as follows: static-calculated 30.3%, dynamic-calculated 14.8%, and measured dynamic-static 19.2%. \({}^{3}\) Dependence and the Maximum Receiving Distance of Magnetic Field in a Suburban Environment  
The magnetic field measurements in a suburban environment at a frequency of 70 Hz were made only with the CRRM using the house-made magnetic sensor coil with the Rohde&Schwarz UPGS microvoltmeter and Narda field sensor with the characteristics mentioned in Table 3. Table 4 below shows the magnitude of the received signal in mV and \(\upmu\)T, the ratio of these quantities, and \(1/r^{3}\) curves for the two types of measurements. Because of its lower sensitivity, the Narda sensor was only used for measurements up to 10 m. The noise level in the suburban area was around 10 \(\upmu\)V. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Distance** & **Voltmeter** & **Narda Sensor** & **Ratio** & **1/r\({}^{3}\)** & **1/r\({}^{3}\)** \\
**[m]** & **[mV]** & **[\(\upmu\)T]** & **mV/uT** & **[mV]** & **[\(\upmu\)T]** \\ \hline
1 & 320 & 1.2385 & 258.38 & 320 & 1.2385 \\
2 & 40 & 0.1478 & 270.64 & 40 & 0.154813 \\
3 & 12 & 0.0449 & 267.26 & 11.85 & 0.04587 \\
4 & 5.2 & 0.0203 & 256.16 & 5 & 0.019352 \\
5 & 2.4 & 0.0089 & 269.66 & 2.56 & 0.009908 \\
10 & 0.32 & 0.0012 & 266.67 & 0.32 & 0.001239 \\
15 & 0.08 & & & 0.095 & 0.000367 \\
20 & 0.02 & & & 0.04 & 0.000155 \\
25 & 0.005 & & & 0.02 & \(7.93\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Magnetic field level measured in an environment with a low 50 Hz component. Figure 14: The magnetic field generated by the CABM, measured in static and dynamic (70 Hz) regimes between 2 and 100 mm; comparison with the values calculated using Equation (2). Except for the column containing the ratio between the values measured with the mentioned equipment, Table 4 give the four dependencies plotted in Figure 15.  
The last two values were obtained by subtracting the noise value from the measured value. This explains the relatively large errors at 20 and 25 m.  
The Equivalence Between the Magnetic Field Emitted by the Rotating Magnet Relative to the Field Produced by Coils/Solenoid  
First, the magnetic field generated by a solenoid with 50 turns carrying a current of 4 A at 70 Hz was measured. The solenoid has geometric dimensions similar to those of the CABM (\(L\) = 50 mm, \(R\) = 4 mm). The measurements were performed at three distances by using the Hall probe presented in Table 2. The obtained values (minimum and maximum values from a set of 10 measurements) are plotted in Figure 16 and compared with the theoretical values resulted from Equation (1) for the same characteristics of the solenoid. These values can be found in Table 5 along with the values measured in the case of the CABM (same values in Figure 14). Also, Table 5 contains the ratios of these quantities for two cases: magnet (measured)-solenoid (theoretical) and magnet (measured)-solenoid (measured). On the other hand, we sought to make an equivalence between the magnetic field emitted by a rotating CRRM and the field generated by a coil-type circuit element. In this case, the dynamic field value emitted by the magnet at 70 Hz was compared with the values obtained with a coil whose characteristic data were found through a recurrent calculus using Equation (5) until a \(B=F(r)\) curve similar to that of the magnet was obtained (Figure 17). The following values were obtained for this coil: \(N=5\) turns, \(I=1000\) A, \(a=22\) mm.