## 2 The Measuring Procedure  
In a WPT system with inductive power transfer, the distribution and intensity of the electromagnetic field in the space between the transmitter (emitting coil) and the receiver coil and in the space adjacent to it directly depends on the current intensity in the coils. To establish the appropriate investigation methods, in the first stage it was sufficient to study a situation wherein only the WPT-EC and its functional circuits were in operation. Of course, this did not exclude the need to check if the identified methods were valid for real situations, because the whole system influences the field configuration. In this simplified, perhaps idealized situation, the EMF characteristics (such as the modulus, direction, and orientation of the EMF strength vector at each point) generated by the emitting coil depend on the current value in the coil. However, if this current is high enough that the intensity of the generated magnetic field reaches the magnetic saturation zone of the ferrite structure (a basic component of the WPT-EC), then the field lines may change due to the non-uniformity in the ferrite material. Avoiding the proximity of the saturation zone to the WPT operation is, moreover, an important requirement of WPT system design. Non-compliance with this constraint causes increased power losses and decreased efficiency. Measuring an EMF to accurately determine its spatial distribution requires the accepted measuring device to have a sufficiently large dynamic range. Correlated with limiting the EMF to avoid ferrite saturation is the need to perform sufficiently accurate measurements in the low-field-strength area. This task should be executed very carefully. It is known that the intensity \(H\) and, implicitly, the density B (induction) of the magnetic field at a certain point in the WPT space depend linearly on the feed current in the emitting coil. This physical phenomenon makes it possible to determine the EMF configuration by exciting the emitting coil with an alternating sinusoidal current, regardless of the current waveform in normal operation (in the SOA--safe operating area) of the WPT system. However, the signal frequency applied should be close to the WPT operating frequency; otherwise, the field may be distorted due to the frequency behavior of the ferrite material. A measurable electromagnetic voltage (EMV) is induced in a wire, limiting a surface located in the non-constant WPT fields. If this surface delimits a small enough area compared to the transmitter dimensions (small enough that the field is approximately constant at every point on this surface), then the value of the induced EMV can be used as an indicator for the field strength at the center point of the surface, as will be seen below. The EMV \(e\), induced in a single turn located in the WPT field, can be calculated with:  
\[e=-\frac{d\Phi}{dt} \tag{1}\]\(\Phi\) is the magnetic flux passing through the turn surface:  
\[\Phi=\iint_{S}\mu\overrightarrow{h}\overrightarrow{a}\overrightarrow{s} \tag{2}\]  
where the vector \(h\) is the instantaneous magnetic field intensity; \(\mu\) is the magnetic permeability in the environment where the WPT system operates (the air)--very close to the magnetic permeability of the vacuum \(\mu_{0}\); and \(s\) is the normal vector at the surface. Assuming that the field intensity vector \(h\) is constant on the turn surface, \(\Phi\) becomes:  
\[\Phi=\mu hscos\varphi \tag{3}\]  
where \(h\) is the instantaneous modulus value of the magnetic field vector in the coil center point, and \(\varphi\) is the angle between the vector \(h\) and the normal direction at the coil surface \(S\). At the virtual point in the turns center, the vector \(h\) is proportional to the instantaneous intensity of the supply current in the emitting coil, which is sinusoidal in time, and so:  
\[h=Hsin(\omega t) \tag{4}\]  
where \(H\) is the peak value of the EMF strength vector modulus, and \(\omega\) is the current pulsation of the emitting coil.