**2.2 Inductive power transfer**

The use of a magnetic field for power transfer has the safety benefit of not using high voltages and not interacting with most biological material. As a result, the magnetic field is used in the majority of modern near-field WPT studies and has a vast range of applications. A non-radiative magnetic field is produced by passing an alternating current (AC) through a coil known as the transmitter, as shown in **Figure 5**. When a load circuit is in vicinity to the reactive area, an electromotive force (EMF) is produced in a second coil, known as receiver. In this way, the electrical power is passed from the transmitter's coil to the receiver's coil. There is a mutual inductance between between the transmitting and receiving coils. This inductance is one of the most significant parameters that affects the power transmitted in inductively coupled wireless power transfer systems.

The mutual inductance M between two coils, Tx and Rx, is shown in **Figure 5**, where alternating current is guided inside coil, Tx, and induced current appears in the coupled coil, Rx. The current flowing in *LT* or the transmitter coil sets up a magnetic field, which passes through the receiver coil *LR* giving us mutual inductance. When the inductances of the two coils are the same and equal, *LT* is equal to *LR*, the mutual inductance that exists between the two coils will equal the value of one single coil (as the square root of two equal values is the same as one single value) as shown:

$$M = k\sqrt{L\_T L\_R} = kL \tag{3}$$

where *k* is the coupling coefficient expressed as a fractional number between 0 and 1, where 0 indicates zero or no inductive coupling, and 1 indicating full or maximum inductive coupling. One coil induces a voltage in an adjacent coil; therefore, the transmitter *LT* induces a voltage *vin <sup>R</sup>* in the receiver, and viceversa.

$$\begin{cases} \boldsymbol{\upsilon}\_{R}^{in} = \boldsymbol{L}\_{R} \frac{d\boldsymbol{I}\_{R}}{dt} + \boldsymbol{M} \frac{d\boldsymbol{I}\_{T}}{dt} \\ \boldsymbol{\upsilon}\_{T}^{in} = \boldsymbol{L}\_{T} \frac{d\boldsymbol{I}\_{T}}{dt} + \boldsymbol{M} \frac{d\boldsymbol{I}\_{R}}{dt} \end{cases} \tag{4}$$

The amount of power transmitted (power loss on the components has been neglected) through the magnetic field is thus approximately calculated:

$$P\_R \propto \frac{1}{2} \cdot f \cdot \mathbf{M} \cdot I\_T^2 \tag{5}$$

**Figure 5.** *Principle of the inductive power transfer (IPT).*

where *IT* is the magnitude of AC current in the transmitting coil *LT* and *f* is its frequency. It could be noticed from this equation that *IT*, *f* and *M* shall be as large as possible in order to deliver more power to the receiver. However, the larger the *IT* and *f* are, the more switching losses will occur in a power electronics circuit. The current *IT* alone will increase the conducting loss on the transmitting coils. Optimising the mutual inductance *M* is the most efficient option.

Research studies into the inductive power transfer in IPT has been focused on increasing the yield. Performance and reliability are sure to be improved as new designs, components, such as core, coil shapes and configurations, and ways of handling conductivity, are further researched [11–13]. Finite element analysis (FEA) is a computerised method to predicting how the magnetic field is distributed in the air and how coils react to real-world forces, heat and other physical effects. In **Figure 6** it is shown the simulation of WPT system by using ANSYS Electronic v14, where it can be seen the diffusion (**Figure 6a**) and the flux lines (**Figure 6b**) of the magnetic field.

## *2.2.1 Resonance technique*

A largely adopted technique in the near-field magnetic coupling is the resonance which has largely extended the potential of the near-field WPT. A capacitor is connected to the coils to form the LC resonant tank. Therefore, an impedance transformation network is made by the resonant tank at the oscillation frequency *f* <sup>0</sup>, such that the source VA is minimised and the power transferred to the load is

maximised. The transmitter and receiver circuitry are made to resonate at the same frequency as shown in the equation below.

$$f\_0 = \frac{1}{2\pi\sqrt{L\_T C\_T}} = \frac{1}{2\pi\sqrt{L\_R C\_R}}\tag{6}$$

where *LT*, *LR* are the coils and *CT*, *CR* are the capacitors of the transmitter and receiver, respectively. It is possible to achieve a high device efficiency by developing high-detailed transmitter and receiver coils, even if the system becomes less efficient the further the transmitter coil is away from the receiver.

As a whole, WPT (both IPT and CPT) throughput power decreases in a linear trend (for a log scale) with increasing frequency. It is likely that this limitation is primarily determined by power electronics limitations, rather than coupling characteristics, since it affects IPT and CPT equally. As the frequency increases, the output power is limited by losses. This limitation appears in both IPT and CPT applications. The average power is increased by 10-fold in the last 10 years, with the frequency also increased by 10-fold. In part, this is attributed to the development of wide bandgap devices and the refinement of coupling structures to minimise losses. It is expected that the power-frequency empirical limitation will continue to increase with time, essentially like a "Moore's Law" trend or variant for WPT. In **Table 1**, there is a further summary between typical differences in the development between CPT and IPT.
