**Appendix A**

From Equation (15), the magnetic flux density applying the geometric dimensions of Figure 14 is given by:

$$\begin{aligned} \mathbf{B}\_{\text{WPTtot}} &= \frac{\mu\_0 \mu\_m}{4\pi r^3} \Big( 2\cos\theta^2 - \sin\theta^2 \Big) \mathbf{a}\_x \\ \theta &= \frac{\max\left(90 + a\_1 \, 90 - a\_2\right)}{\sum\left(1 - a\_1 \, 90 - a\_2\right)} \Big| \mathbf{a}\_r \\ a\_1 &= \cos^{-1} \frac{\sqrt{\left(0.3375 - \text{SD}\_{\text{Ap}}\right)^2 + D\_1^2}}{\sqrt{\left(0.3375 - \text{SD}\_{\text{Ap}}\right)^2 + \left(0.2675 - \text{SD}\_{\text{An}} + \sum\_{N=1}^{\text{O}} (1 - N)D\_1\right)^2 + D\_1^2}}, \\ a\_2 &= \cos^{-1} \frac{\sqrt{\left(0.3375 - \text{SD}\_{\text{Ap}}\right)^2 + D\_1^2}}{\sqrt{\left(0.3375 - \text{SD}\_{\text{Ap}}\right)^2 + \left(2.6675 - \text{SD}\_{\text{An}} + l\_c + \sum\_{N=1}^{\text{O}} (1 - N)D\_1\right)^2 + D\_1^2}}, \\ r &= \sqrt{\frac{\left(0.3375 - \text{SD}\_{\text{Ap}}\right)^2 + \\ (0.2675 - \text{SD}\_{\text{An}} + l\_c + \sum\_{N=1}^{\text{O}} (1 - N)D\_1 + \left(\frac{69 \min\left(90 + a\_1; 90 - a\_2\right) - 0}{a\_1 + a\_2}\right)D\_1\right)^2 + D\_1^2}}, \end{aligned} \tag{A1}$$

where **B***WPTtot* is the sum of the magnetic flux density transmitted by the 70-turn loop of the ferrite antenna transmitter mounted on the secondary device to the 70-turn loops of the ferrite antenna receiver mounted on the primary device, μ0 is the permeability of free space, μ*r* is the relative permeability of the ferrite antenna, *m* is the magnetic dipole moment, α1 is the angle between the Nth loop of the ferrite antenna transmitter in the <sup>±</sup>y-direction mounted on the secondary device and the 1st loop of the ferrite antenna receiver in the <sup>±</sup>y-direction mounted on the primary device, α2 is the angle between the Nth loop of the ferrite antenna transmitter in the <sup>±</sup>y-direction mounted on the secondary device and the 2nd to 70th loops of the ferrite antenna receiver in the <sup>±</sup>y-direction mounted on the primary device, *SD*Δ*x* is the distance the secondary device moves in the ±x-direction, *SD*Δ*y* is the distance the secondary device moves in the <sup>±</sup>y-direction and *r* is the distance between the ferrite antenna in the <sup>±</sup>y-direction mounted on the secondary device and ferrite antenna in the <sup>±</sup>y-direction mounted on the primary device.

The Equation (16) of the open-circuit voltage received by the receiver of the ferrite antenna mounted on the primary device of the EV WPT system is replaced by:

$$V\_{\alpha\text{-}WPTt\forall t} = j\omega\mu\_r A \mathbf{B}\_{WPTt\text{at}}\mathbf{a}\_{\mathbb{Z}} \tag{A2}$$

Substituting Equation (17) into (A2),

$$Power\_{\text{WPT}ferrite\,\text{antenna}} = 10 \log\_{10}(1000 \frac{V\_{\text{acWPT}\,\text{at}}^2}{R}) \tag{A3}$$
