# A Multi-Domain Model for Variable Gap Iron-Cored Wireless Power Transmission System
## 5 Experimental Validation and Results Comparisons
### Tests and Results  
The first experimental activity performed concerns the characterization of the self-inductance parameters of the coupled coils. In detail, the reported measurement campaign is performed identically for both the coils and for all the imposed air gap configurations. The terminals of one of the two coils are connected in parallel to a digital multimeter, which returns the measured value of auto-inductance for each measured gap configuration. To avoid influencing the obtained results, the terminals of the unconnected coil are left free. Figure 12 depicts the auto inductance of the coupled cores for the emitter and receiver side, respectively, consequent to a gap variation. The blue line identifies the measured trend with a discretization on the gap variation of 0.05 mm, due to the uncertainty on the measurement, and the possible errors introduced by the whole apparatus are considered a \(\pm\)10% deviation that is delimitated by the yellow area reported in the graph. The red line represents the numerical results estimated by the previously described 3D FVM model. As can be noticed, the numerical results are quite accurate for the entire considered gap window within the \(\pm\)10% error. This numerical-experimental comparison made it possible to validate the magnetostatic model and obtain, with a fair degree of reliability, the purely numerical estimation of the trends of mutual inductance and coupling factor consequent to a variation of the gap, as reported in Figure 5.  
The validation of the entire multi-domain co-simulation model took place through a comparison of the imposed end-resulting current and voltages for both the time domain and the frequency domain. The results of the time validation obtained over the three measurement channels are reported below. To keep the treatment as concise as possible but demonstrate the robustness of the co-simulation model, the experimental comparisons are reported for excitations equal to 1 MHz and 0.00 mm gap (see Figure 13), and excitations at 100 kHz with a 0.15 mm airgap (see Figure 14). Figure 11: (**a**) Side A of the controlled gap mover apparatus; (**b**) side B of the controlled gap mover apparatus. Figure 12: (a) \(L_{11}\) vs. air gap; (b) \(L_{22}\) vs. air gap. Figure 13: (a) CH1 signal comparison on a 7 \(\upmu\)s time window; (b) CH2 signal comparison on a 7 \(\upmu\)s time window; (c) CH3 signal comparison on a 7 \(\upmu\)s time window. The reported comparisons are obtained on the basis of the circuit depicted by Figure 10a, where CH1 represents the imposed voltage excitation, CH2 represents the current circulating on the primary side through the voltage drop across the shunt resistor and, finally, CH3 represents the voltage across the secondary side. Apart from the imposed signalde-picted by CH1, the resulting response of the model (CH2 and CH3) replicates with a good grade of approximation the real physical behavior for both the applied frequencies and the imposed gap. It is important to notice that for the probe named CH2, although the amplitude voltage of the estimated signal is practically identical to the real case, there is a slight phase shift between the numerical and experimental results. This is due to the quality of approximation of the intra-winding capacitance parameter of the coils, which obviously influences the natural frequencies of the coupled and non-coupled resonator. Finally, to complete the discussion about the experimental measurement activities, it is necessary to comment on and provide the resulting comparisons in the frequency domain (circuit shown in Figure 10b). The integration of a 1 nF capacitor allows the overall natural frequency to shift, therefore, enabling the resonance phenomenon for the coupled R-L-C circuit to be appreciated. Figure 15 depicts the CH3 normalized response for both the model and for the real device, consequent to a gap variation in the interval [0.00; 0.40] mm with a discretization step of 0.05 mm. The frequency range in which the sweep is calculated is [0.2; 1.1] MHz.