## 2 Measuring Systems, Materials and Methods
### Measuring System and Samples
#### 2.2.2 Comparison of Measuring Systems  
Figure 10 illustrates the block diagram of the eddy current (EC) system, while Figure 11 depicts the corresponding magnetic flux leakage (MFL) system. The eddy current (EC) system comprises an E-shaped transducer and four subsystems: an XYZ scanner, an excitation subsystem, a data acquisition subsystem, and a control computer. The control computer generates the excitation signal using LabVIEW and a data acquisition card (DAC), which converts a digital signal to an analog. This signal is sent to the acoustic amplifier and, from there, to the transducer's excitation coils. In the experiments, four transducers were used (Figure 11). When a reinforcing bar is near the transducer, the magnetic field generated by the excitation coils (as described by [PERSON]'s law) induces eddy currents within the rebar. According to [PERSON]'s law, these currents produce an additional magnetic field that opposes the primary field. The interaction of all these fields affects the pick-up coil, leading to the induced voltage (pick-up coil). Figure 8: Samples: (**a**) 3D schematic presentation, (**b**) cross-section and parameters, (**c**) parameters. Figure 9: Example rebars used during supplementary measurements. When the transducer is located considerably far from the reinforcement, the signal obtained from the receiving coil tends to be weak and noisy. However, since the signal's frequency is known (equal to the frequency of the excitation signal), it can be effectively separated from the noise using a lock-in amplifier. The filtered signal is then directed through the A/D converter to the computer for further analysis. Typically, additional filtering with a Butterworth filter is necessary. The measuring robot moves the transducer perpendicularly to the reinforcing bar, enabling the measurement waveform to be recorded from the receiving coil. Figure 11: EC transducers used in the experiments: (**a**) cross-section and description, (**b**) small T5 transducer, (**c**) medium T13 transducer, (**d**) large T20 transducer, (**e**) largest T25 transducer. Figure 10: Block diagram of eddy current system. The magnetic fields generated by the excitation coils can either overlap (absolute transducer) or cancel each other out (differential transducer). Examples of both absolute and differential signals are illustrated in Figure 12.  
A differential transducer is chosen for the investigations. While its signal-to-noise ratio (SNR) is comparable to that of an absolute transducer, it facilitates a much simpler identification of characteristic points (attributes such as \(X_{\text{max}}\), \(X_{\text{min}}\), \(d_{\text{x}}=X_{\text{max}}-X_{\text{o}}\), etc.). Furthermore, it is less affected by interference generated by the measuring coils (\(X_{\text{r}}\) and \(X_{\text{s}}\)). In designing an EC system, several key factors must be considered:  
* Transducer size: a larger transducer size results in lower spatial resolution and higher effective range. * Excitation frequency: a lower frequency results in lower spatial resolution and higher effective range. * Magnetic induction (\(B\)). The value of magnetic induction is influenced by the current flowing through the excitation coil (\(I\)), the number of turns (\(N\)), the magnetic permeability of the core (\(\alpha\)), and the length of the winding wire (\(l\)), as described by Formula (4):  
\[\overset{\rightarrow}{B}=\frac{I\cdot N}{l}\cdot\mu \tag{4}\]  
The magnitude of the current (following [PERSON]'s law (5)) is influenced by the voltage applied to the excitation coil (\(U\)), the reactance of the inductive impedance (\(X_{\text{L}}\)), and the resistance (\(R\)):  
\[|I|=\frac{|U|}{\sqrt{R^{2}+X_{L}^{2}}} \tag{5}\]  
Resistance depends on the resistivity (\(\rho\)), the length of the winding (\(l\)), and the cross-sectional area of the winding (\(5\)).