**2.1 Capacitive power transfer**

The first methods of electromagnetic coupling were discovered by Tesla in the 1900s [7], by capacitive coupling, which is possible to use the electric field for power transfer in the near-field. However, there was a high voltage present between the transmitter and receiver, which could result in electric shock. The main reason is that the experiment was based on the electric arc. The two electrodes on the capacitor are the transmitter and the receiver of the power transfer system with the air being the dielectric. During each voltage pulse, the output voltage rises to the point where the air around the high voltage terminal ionises, causing corona, brush discharges, and streamer arcs to emerge from the terminal, as shown in the **Figure 3**. This event occurs only when the electric field strength surpasses the air's dielectric strength, which is around 30*kV* per centimetre. Because the electric field is strongest at sharp points and edges on the high voltage terminal, the air discharges begin there [8]. An electric arc discharges by visible light emission, high current density, and high temperature. The voltage on the high voltage terminal cannot rise above the air breakdown voltage because extra electric charge injected into the terminal from the secondary winding simply escapes into the air. Air breakdown limits the output voltage of open-air Tesla coils to a few million volts, but coils immersed in pressurised tanks of insulating oil can attain greater voltages [9, 10].

The CPT is based on this functionality, where two parallel plates (a capacitor) are on a very small distance apart because of safety issues of the above mentioned electric arc. The transmitter is attached to the first plate on each capacitor, and the

#### **Figure 3.**

*Recent demonstration of the Tesla experiment in Ref. [8].*

#### **Figure 4.**

*Principle of the capacitive power transfer (CPT).*

receiver is connected to the second plates, as shown in **Figure 4**. Air is the dielectric forming a capacitor of:

$$\mathbf{C}\_{T} = \varepsilon\_{\mathrm{R}} \cdot \varepsilon\_{0} \frac{d}{A} \tag{1}$$

where *d* is the distance and *A* is the area of the capacitive plate in the transmitter and in the receiver. This value depends on the dielectric material between the plates, distance, and plate area. Therefore, this value is limited because the permittivity constant *<sup>ε</sup>*<sup>0</sup> of air is as small as 8*:*<sup>85</sup> � <sup>10</sup>�<sup>12</sup>*F=m*.

This design can be expanded by adding two connected capacitor plates in both sides (transmitter and receiver) with an electric field between them, as shown in **Figure 4**. The created electric field causes an alternating current to pass in the receiver plates. Thus, power is being sent through the secondary plates of the receiver. The capacitive area is designed after the application, where plates can take on multiple shapes, for example, rectangular, disc, or cone, or specific architecture such as a matrix [10].

The amount of power transmitted (power loss on the components is neglected) through the capacitor electric field is thus approximately calculated:

$$P\_R \propto \frac{1}{2} \cdot f \cdot \mathbf{C}\_T \cdot \mathbf{V}\_T^2 \tag{2}$$

where *VT* is the magnitude of AC voltage in the transmitting capacitor *CT* and *f* is its frequency. It is important to notice that *VT*, *f* and *CT* shall be as large as possible in order to deliver more power to the receiver. However, the larger the *VT* and *f* are made, the more switching losses will occur in the electronics circuit. One

of the biggest disadvantages of the CPT has is a poor coupling capacitance *CT* and the safety concerns regarding the *VT* where in nearly all the applications has a huge value.
