## 2 Topology of Inductive Power Transfer System  
The IPT module is conducted in harmony to \"SAE J2954\" standard [16], and its draft is shown in Figure 2. Several parameters potentially impact the IPT module efficiency and EM field strength.  
Figure 1: A schematic overview of inductive power transfer (IPT) charging station architecture.  
They can be conditionally separated into electricals and mechanicals, and some of their calculation is discussed in References [1; 6; 12; 17].  
First and foremost are the ratio of magnetic coupling \(k\) and mutual inductance \(M_{TX\text{-}RX}\) between transmitting and receiving coils. The physical essence is related with the distribution of the magnetic flux between the coils and could be calculated by  
\[M_{TX\text{-}RX}=\oint_{S_{RX}}\frac{\Phi_{TX\text{-}RX}(I_{TX})}{I_{TX}}dS_{ RX}=k\sqrt{I_{TX}L_{RX}} \tag{1}\]  
where \(\Phi_{TX\text{-}RX}\) is the magnetic flux linkage, \(S_{RX}\) is the area of the receiving side, \(L_{TX}\) and \(L_{RX}\) are the inductance of the transmitting and receiving coils, and \(I_{TX}\) is the current through the transmitting coil.  
From Equation (1), it can be seen that some of the important factors for \(k\) and \(M\) are the area \(S_{RX}\) and inductances \(L_{TX}\) and \(L_{RX}\). The developed IPT module suggests several extreme restrictions. While the inductances can acquire values over a wide range by using a different number of turns or supplementary ferrite cores, the coupling coefficient depends mainly on the dimensions of the two coils. The magnetic coupling with rectangular coils (Figure 1) is equal to  
\[k(z)\approx\left(2n/\left(4n^{2}+12z^{2}\right)\right)^{3/2},\ n=(x+y)/2, \tag{2}\]  
Equations (1) and (2) in Figure 3 present the dependence of \(k\) as a function of geometrical dimensions and the distance between the transmitting and receiving coils. The main conclusion that can be drawn is that an increase in the active width of the windings leads to an increase of \(k\). There is also a strong correlation between the distance between the coils and \(k\). At a distance over 200 mm, the coefficient \(k\) becomes smaller than 0.2, which corresponds to an ineffective energy transfer. This confirms one of the basic IPT design rules [1]--for efficient energy transfer, the distance between the coils should not exceed coil diameter divided by 4.  
Figure 3: The effect of distance and IPT dimensions upon coupling coefficient (k).  
Figure 2: A 3D model of IPT coils.  
Another key point, directly related to the efficiency of the IPT module, is coil loses--\(P_{LOSS}\). The ratio of \(P_{LOSS}\) toward the output power \(P_{OUT}\) is equal to  
\[\lambda=P_{LOSS}\ /P_{OUT}=2\bigg{(}1+\sqrt{1+(kQ)^{2}}\bigg{)}/(kQ)^{2} \tag{3}\]  
where \(Q\) is equivalent IPT quality factor.  
Based on Equation (3), an analysis was made, the results of which are presented in Figure 4. It can be concluded that in order to achieve better efficiency, it is necessary that \(\lambda<<1\). The value of losses increases dramatically at \(k<0.1\) and \(Q<10\). The implemented analysis proves that, for the reliable operation of an IPT module, it is necessary that \(k>0.2\) and \(Q>20\); in other words, \(kQ=4\div 10\). Hence, it follows that Equation (3) could be simplified using the above values,  
\[\lambda=P_{LOSS}\ /P_{OUT}\approx 2\bigg{(}1+\sqrt{\beta_{IPT}^{2}}\bigg{)}/ \beta_{IPT}^{2}\approx 2/\beta_{IPT} \tag{4}\]  
where \(kQ=\beta_{IPT}\), \(\beta_{IPT}\gg 2\).  
If the coupling coefficient \(k\) has low value (\(k<0.2\)), it is possible by optimizing \(Q\) (increasing the inductance) to keep the ratio \(kQ\gg 4\). Otherwise, the IPT module will have bad economic indicators. This condition strongly depends on the dimensions of the IPT coils (x\({}_{0}\) and y\({}_{0}\)) and the distance between them \(z\). If the air gap is \(z<(x_{0}+y_{0})/4\)), the transmission efficiency will become greater than 80%, if \(z/[(x_{0}+y_{0})/2]<0.2\), the transmission efficiency could be close to 90-95%.