## 3 Magnetic Field Intensity Measurement
### The Geometrical Correction
To investigate how important the geometric correction was, the field generated by a WPT emitting coil was scanned at 106,641 points, and the induced EMVs in the sensor coils were acquired and stored. After the linearity and axis deviation corrections (with the measured deviation values described in Section 3.1), the differences in the \(H\) vector's magnitude obtained by applying the correction algorithm were calculated for each scanned point. The statistical findings are presented in Figure 19.  
Figure 19: Error diagram of vector \(H\)’s magnitude, corrected by the described procedure. It was found that the maximum error of the EMF magnitude (modulus), introduced by the axis deviations of the sensor coil, ranged between \(-7\%\) and \(+7.7\%\), while around \(55\%\) of the measurements had a less than \(3.5\%\) error. The higher number of negative errors was due to the correlation between the deviations. The angular differences in the \(H\) vector direction obtained by applying the correction algorithm were also calculated for each scanned point. The statistical results are presented in Figure 20 and confirmed that the field direction errors were less than \(6^{\circ}\). Of course, the results shown in Figures 19 and 20 were valid for the set of 106,641 captured values in the case of a particular WPT emitter coil. For another coil (generating a different field, for which, from a statistical point of view, the ratios between the sizes of the field components in the three orthogonal directions are different) the statistical distribution of the errors to be corrected may be slightly different. However, the maximum error correction values did not exceed the values shown in Figures 19 and 20, because these maximum values were due to the deviations in the sensor coil axes (measured according to Section 3.1) and not to the field structure. The effectiveness of the geometric correction depended on the accuracy of the measurements regarding the deviation of the coil axes from the Cartesian coordinate system. Errors in the measurement process differed from point to point because the measured values for the three axes are closely correlated with their deviations. To statistically investigate the importance of deviation measuring, we simulated a geometric correction for a case in which the axis deviation was incorrectly measured by \(0.5^{\circ}\), i.e., for the following deviations:  
* \(\varepsilon_{xy}=-4.5^{\circ}\); \(\varepsilon_{xz}=-3.5^{\circ}\). * \(\varepsilon_{yx}=2.7^{\circ}\); \(\varepsilon_{yz}=1.3^{\circ}\). * \(\varepsilon_{xx}=-3.3^{\circ}\); \(\varepsilon_{xy}=2.8^{\circ}\). Here, \(\varepsilon_{xy}\) was smaller (the true value being \(\varepsilon_{xy}=3.3^{\circ}\)). The differences between the geometric corrected values, considering the correctly measured deviations, and the geometrically corrected values, taking into account the incorrect measured deviations, are shown in Figure 21.  
It was concluded that following an erroneous correction, due to an incorrect deviation measurement, errors in the measured EMF strength up to \(0.7\%\) and direction up to \(0.6\%\) were generated. In conclusion, the geometric correction method described above ensured a correct EMF measurement with more than \(0.5^{\circ}\) accuracy. Figure 20: Error diagram of vector \(H^{\prime}\)s direction, corrected by the described algorithm.