## 3 Magnetic Field Intensity Measurement
### Linearity Correction  
Before making any corrections to the measured values, it was recommended to check that the measurement process did not transpose the ferromagnetic core of the emitting generator near to the saturation zone. If the high instantaneous values of the electric current intensity in the coil produced an intensity of the magnetic field \(H\) close to the intensity of the saturation field \(H_{\mathrm{S}}\), then the induction B in the core would no longer be proportional to H in these areas. This would mean a decrease in the inductance and, as a result, a decrease in the impedance of the coil connected to the sinusoidal voltage generator. One way to check this was to supply the coil with a sinusoidal voltage and measure the actual values of the impedance (indirectly through coil voltage and current measurement). The location of the core away from the saturation zone was indicated by the fact that the impedance did not change when the voltage changed in the emitting transmitter coil. To put this to the test, the WPT emitting coil was fed a 95 kHz sinusoidal signal (chosen according to the voltmeter accuracy), as shown in Figures 5 and 6. Figure 4: Block diagram for input signal processing, with adjustable amplification for each channel. Figure 5: Impedance measurement of WPT-EC. Figure 6: Impedance measurement setup. The current value was measured by the voltage drop in a 1 \(\Omega\) calibrated shunt, and the voltages V\({}_{1}\) and V\({}_{2}\) were measured with a precision multimeter. The multimeter input impedance in the measurement ranges applied (1 M\(\Omega\) and \(<\)100 pF) was much higher than the circuit impedances, so the systematic measurement error could be neglected. The multimeter provided (according to the data sheet) an accuracy of 0.15% of the measured value, resp. + 0.05% of the measuring range, for the measurement of alternating sinusoidal voltages up to 100 kHz. For the measured value ranges (2 to 3800 mV for V\({}_{1}\) and 0.1 to 350 mV for V\({}_{2}\)), the result accuracy was over 0.28% of the measured value. Thus, for the impedance of the WPT-EC (as a ratio between the voltage V\({}_{1}\) and the current V\({}_{2}\)/R\({}_{8}\)), we obtained an accuracy higher than 0.56% of the measured value. The impedance diagram of a current trip in the range considered (Figure 7) shows that the impedance of the WPT emitting coil ranged between 11.7 and 11.8 \(\Omega\) (the differences were within the measurement accuracy limits), while there were no significant changes under high current values that could denote proximity to the core saturation zone. In general cases, a measurement involves the existence of an injective function that ensures the proportionality between the measured quantity and the resulting numerical values over the whole measurement range. If this function does not provide linearity or at least proportionality between the actual field input and the numeric output, then there is the option of adjusting the numerical output values using a correction function. The linearity and, moreover, the proportionality of the original function could not be fulfilled with certainty, due to the general-purpose electronic components. Therefore, the viable solution consisted in identifying the correction function that was applicable after obtaining the numerical values and would finally ensure proportionality. According to the signal processing path presented in Figure 8, the measurement of EMF intensity required the linearity of tasks II, III and IV. Because there was linearity between the current in the WPT emitter coil and the induced EMV in the sensor coil (a fact verified by measuring the voltage drop in the 1 \(\Omega\) shunt), the procedure for identifying the correction function included the whole processing  
Figure 8: Signal processing path for global EMF measurement. Figure 7: Impedance values of the WPT-EC. path (tasks I-IV) by supplying the generator coil with an increasing current.