## 3 Magnetic Field Intensity Measurement
### Linearity Correction
This approach had the advantages that the voltage values were in a more easily measurable range, and there was an adaptation between the sensor coil and the amplifier. The operation area outside the saturation area led to the conclusion that the induced EMV in the sensor coil was proportional to the current in the emitting coil (as an r.m.s. value, measured by the voltage drop in the 1 \(\Omega\) shunt). This fact was verified by measuring the induced EMV in the sensor coil--located very close to the center of the WPT-EC. The validation of the linearity function was carried out based on the investigations summarized in Figure 9.  
The current variation required in the emitting coil (I\({}_{\text{WPT}}\)), according to the 15-bit digital range and with the EMV amplifier set to a median position, was 50 uA-1 A. Because the multimeter ensured sufficient accuracy only for an AC voltage greater than 1 mV (corresponding to an I\({}_{\text{WPT}}\) = 9.4 mA), the signal linearity of the current in the EC with the induced voltage in the sensor coil was checked only for a current higher than 10 mA. Assuming that the relationship between the WPT-EC current and the induced voltage in the sensor coil (I\({}_{\text{WPT}}\)\(\rightarrow\) U\({}_{\text{EMV}}\)) corresponded to a linear function with a proportionality constant, the relative differences in the measured values of the EMV related to this function (variable deviations due to multimeter accuracy) were as depicted in Figure 10. The differences identified (\(\Delta\)U\({}_{\text{EM}}\) = \(-\)0.16%... + 0.59%) ranged within the measurement errors, which confirmed the assumed linearity. Taking this into account, the solution could be to place the sensor coil in the EMF in a fixed position, excite the WPT-EC using an adjustable sinusoidal voltage source, and measure the current intensities. Because the numerical findings obtained from the  
Figure 10: Experimental linearity validation: WPT-EC current [mA] \(\rightarrow\) relative deviation [%]. Figure 9: Experimental linearity validation: WPT-EC current [mA] \(\rightarrow\) induced EMV [mV]. measurements were within a wide range (due to the big number of ADC bits), the solution of using currents in a geometric progression may be appropriate. As the linearity correction function had to be applied to the numerical values resulting from the measurement process, a suitable solution was to correlate it based on a table. This table contained numerical values that expressed the correlation:  
\[n\to kI \tag{7}\]  
where \(n\) is the measured value; \(I\) is the current in the emitting coil that led to the \(n\) value; and \(k\) is a constant, valid for all ranges of the current values. The choice of the k constant was arbitrary, but the \(kI\) numbers had to be in approximately the same range as the \(n\) numbers (represented by the same bit number). In the process of effective EMF measurement, the algorithm of linearity correction was implemented by linear interpolation, based on the abovementioned table. For this reason, two more converters were inserted into the signal processing path, namely rms-to-dc and AD converters. According to the data sheet for the rms-dc small signal converter [18] (Figure 11), it was observed that for an input signal dynamic range of only 1:1000 (between 3 mV and 3 V) at 150 kHz, the accuracy was lower than \(+/-3\) dB. The subsequent AD converter [19] provided at 15 bits a range of 1:32,678 with nonlinearity, as displayed in Figure 5:0 The measurement error for the AD converter was therefore much smaller than that introduced by the rms-dc converter \(10^{-3}\). Figure 5:1 Freq. response of rms–dc converter [18]. Figure 5:2 Output voltage nonlinearity of the ADC depending on voltage and temperature [19]. In conclusion, the main nonlinearity source was introduced by the rms-dc analog converter, and the globally applied linearization procedure provided good enough data for the purpose of this study, namely, to determine the spatial EMF distribution (magnitude, direction, orientation).