**1. Introduction**

There are currently many methods, links and approaches for wireless power transmission. Each of the available solutions is characterized by its advantages and disadvantages, which result in their application [1–3].

Inductive coupling is currently the most widely used method of wireless energy transfer. This method works on the principle of an air transformer with a tight magnetic coupling of the primary and secondary windings. The energy exchange between two or more coils takes place by means of an inductive current *Φ*, i.e. by means of an induced voltage. The main disadvantage of inductive coupling is the transmission distance, which ranges from millimeters to several centimeters [4].

Resonance compensation is a specific case of inductive coupling. Resonant compensation is used in cases where it is necessary to achieve impedance dependence on frequency. Resonant compensation is provided by adding a capacitive member to the primary as well as the secondary coil. After applying a magnetic field with a suitably selected frequency, the phenomenon of mutual interference of the impedance of the coil and the capacitor occurs, which ideally ensures zero phase shift against the current flowing through the primary coil. For resonant compensation, there are four configurations of the primary and secondary side of the wireless charging system [5, 6].

The system using resonant coupling fully compensates for the scattering fields of the coupling coils, thus significantly extending the working distance while maintaining high energy transfer efficiency. Thanks to its advantages, resonant coupling is used mainly in the field of electromobility, where it allows charging with high power and in the case of a variable load, it can be easily frequency-adjusted for optimal efficiency [7, 8].

The analysis of individual configurations is further provided, while and examples of characteristics derivations are based on the circuit parameters listed in **Table 1**.

*Theoretical and Practical Design Approach of Wireless Power Systems*

Serial-series compensation uses two external capacitors *C1* and *C2* connected in series with the primary and secondary windings. The circuit model of the system is

The system is powered by an inverter with a rectangular voltage profile with

*di*<sup>1</sup> *dt* <sup>þ</sup> *<sup>M</sup> di*<sup>2</sup>

*i*2*dt* � *uC*2ð Þ <sup>0</sup> � *RZi*<sup>2</sup> ¼ 0

*dt* <sup>¼</sup> <sup>0</sup>

*<sup>π</sup> um*<sup>1</sup> (2)

*U*´ 1 0

" #

� � � � �

*ωC*<sup>2</sup>

� �

(1)

(3)

amplitude um1, and therefore the circuit must be described by a system of integrodifferential equations forming a full-fledged dynamic model.

*dt* � *<sup>R</sup>*2*i*<sup>2</sup> � <sup>1</sup>

*i*1*dt* þ *uC*1ð Þ <sup>0</sup> þ *R*1*i*<sup>1</sup> þ *L*<sup>1</sup>

*C*2 ð*t* 0

*<sup>U</sup>*´ <sup>1</sup> <sup>¼</sup> <sup>2</sup> ffiffi 2 p

All models will be derived for the fundamental harmonic and therefore we can use Eq. (1) to describe the model, while the inverter voltage can be considered in

The solution we get loop currents, from which it is possible to further determine

�*jωM R*<sup>2</sup> <sup>þ</sup> *RZ* <sup>þ</sup> *<sup>j</sup> <sup>ω</sup>L*<sup>2</sup> � <sup>1</sup>

For a better idea, we draw the efficiency and power on the load depending on the frequency and the coupling factor, respectively the load. This creates two pairs

*Simplified equivalent circuit for series–series compensation, left – Circuit with initial variables, right – Circuit*

�*jωM*

**2.1 Series-series compensation**

*DOI: http://dx.doi.org/10.5772/intechopen.95749*

�*u*<sup>1</sup> þ

all operating variables of the system (3).

*<sup>R</sup>*<sup>1</sup> <sup>þ</sup> *<sup>j</sup> <sup>ω</sup>L*<sup>1</sup> � <sup>1</sup>

*ωC*<sup>1</sup>

� �

of maps in which two functions are plotted separately:

�*L*<sup>2</sup> *di*<sup>2</sup> *dt* � *<sup>M</sup> di*<sup>1</sup>

1 *C*1 ð*t* 0

shown in **Figure 1**.

the form of (2).

´*IS*1 ´*IS*2 " #

**Figure 1.**

**45**

*suited for loop current analysis.*

¼

Energy transmission through capacitive coupling is currently used relatively little due to limitations on the transmission distance, which is limited by the level of tenths of a millimeter. This method is mainly used for charging consumer electronics such as tablets, laptops and more. They also have great potential in the field of medicine for charging various implants. Capacitive coupling is a phenomenon occurring between all conductive objects, i.e. between systems between which there is a mutual difference of potentials and between them there is an environment with a positive dielectric constant (permittivity) [9–11].

This work aims to point out the main design issues related to wireless power transmission and demonstrate their operational characteristics. An important aspect in this area is undoubtedly interaction of living organisms with a strong electromagnetic field, and therefore it is necessary to pay attention also legislation and hygiene standards [12–15]. Another goal is to provide a clear mathematical description of the system using intuitive methods for circuit analysis. Mathematical models must consider, in addition to the coupling itself, the inverters (inverter and rectifier) on the primary and secondary side of the system. An equally important goal of the work is experimental verification of all achieved theoretical conclusions. For this purpose, it was necessary to develop a prototype of a WPT charging system capable to supply sufficient power needed to charge conventional electric car. The text is supplemented by accompanying graphics that illustrates efficiency characteristics and also analysis of the spatial distribution of the electromagnetic field at different states of the system.
