# Impact of Coil Misalignment in Data Transmission over the Inductive Link of an EV Wireless Charger
## 4 Analysis of the Results  
Due to the difficulties of obtaining a closed-expression for \(f_{B}^{comp}(M)\), a numerical-based approximation for this parameter was performed. Then, the previous equations were employed to study the capability of the compensation networks to offer a stable inductive channel, in terms of their capacity for different types of misalignments. To validate the previous model, a set of simulations in PSIM (11, Power Simulation Technology, Rockville, MD, USA) was conducted with the equivalent circuit of the ICPT system. In this simulation tool, the power delivered to the battery and the bandwidth can be derived. To obtain the bandwidth, the frequency of the source is changed so that it concludes when the voltage at a particular load is half of the voltage of this element at the resonant frequency. For the present study, an EV wireless charger was analysed, which has been designed with typical design procedures so that the conclusions derived in this work can be valid for other similar prototypes. The main features of the charger are listed in Table 2. The charger works at 85 kHz, as recommended by SAE TIR J2954. Regarding the communication system, the source provides a 1 V sinusoidal signal, which is modelled by \(V_{s}\) in the equivalent circuit represented in Figure 2.  
The mutual inductance depends on the relative distance between the two coils. It can be computed for any coil configuration by means of the equation expressed in [26]. Some specific values for \(M\) at specific relative positions are listed in Table 2 too. Figures 4-6 show the results for each misalignment separately. The lines correspond to the numerical solution of the theoretical model exposed in Section 3. This was solved in a MATLAB (R2017b, Mathworks, Natick, MA, USA) environment. In contrast, the points represent the results obtained by simulations in PSIM. In particular, this tool simulates the electrical features of the four circuits under analysis. For the central frequency, 85 kHz, the root-mean-square value of the voltage is computed. Then, the frequency of the signal is manually varied in order to obtain the cutoff frequency, that is, the frequency at which the voltage at the load decreases by \(\sqrt{2}\). It can be observed that both solutions show the same type of variation with misalignment. However, it can be noticed that there some differences between the theoretical model and the simulation results. This is due to the fact that the two methods (theoretical model and PSIM) lead to approximated solutions. Firstly, in MATLAB we have developed a code to obtain the bandwidth in the theoretical model. In particular, the proposed method computes the cutoff-frequency as the one in which the power load divided by the load delivered at the operational frequency is between 0.48 and 0.52 W. The exact cutoff-frequency should be the one in which this ratio is 0.50, but extensive computation resources may be required for this determination. On the other hand, PSIM results are based on the root-mean-square computation of the voltage at the load. This parameter is affected by the transient period, so no exact solutions are derived from this tool either.