### Modulation Depth Factor as a Function of Distance of Receiving Coil from ID Card  
The modulation depth factor (Figure 9) is one of the most important parameters of a signal that determines its readability. It is defined by two signal parameters--\(U_{max}\) and \(U_{min}\) and its value is calculated according to the relationship (1). The modulation depth factor is often expressed as a percentage (2).  
\[m=\frac{U_{max}-U_{min}}{U_{max}+U_{min}} \tag{1}\]  
\[m_{\%}=100.\frac{U_{max}-U_{min}}{U_{max}+U_{min}} \tag{2}\]  
Figure 8: Universal LF-band RFID and HF-band RFID ID reader–programmer and frequency characteristics of its radiation.  
Figure 9: Parameters defining the modulation depth factor.  
Signals with a modulation depth factor of less than 2% are usually difficult to identify on the one hand and susceptible to electromagnetic disturbances occurring in the environment on the other. Examples of NFC signal waveforms corresponding to modulation depth for \(m=27\%\) and \(m=7\%\) were presented in Figure 10.  
Figure 10: Examples of NFC signal waveforms corresponding to modulation depth: (**a**) \(m=27\%\), (**b**) \(m=7\%\).  
Measurements of the modulation depth factor as a function of the distance of the receiving coil from the identifier card were carried out in the measurement system shown in Figure 11. The ID card was placed at a distance of 3 cm from the reader. The reader was characterized by a constant level of emitted electromagnetic field with a frequency of 13.56 MHz. The receiving coil was set at distances of 1.5, 3, 5, 10 and 15 cm from the ID card and the parameters of the signal received by the coil were read. The measuring equipment listed in Table 2 was used to carry out the measurements.  
The obtained values of \(U_{max}\) and \(U_{min}\) and the values of the modulation depth factor determined on their basis are presented in Table 3, while exemplary images recorded by the oscilloscope are shown in Figure 12.  
Measurements carried out at distances greater than 15 cm were characterized by low signal levels and were practically unreadable due to the almost zero modulation depth factor \(m\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Device** & **Type** & **Producer** \\ \hline Oscilloscope & DSOX1102A & Keysight \\ Reader LF-band RFID & & Colorado Springs, CO, USA \\ and HF-band RFID & NS106 RFID Reader Writer & YiToo \\ ID card & NTAG213 & Guangzhou, China \\ Receiving coil & & \\ (65 \(\times\) 35 mm, 6 coils) & & MCI-NRI 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of apparatus used to carry out the measurements.  
Figure 11: Measuring system for determining the modulation depth factor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Distance d** & \multicolumn{3}{c}{**Signal Parameters**} \\ \cline{2-4}
**[cm]** & \(\mathbf{U}_{max}[\mathbf{V}]\) & \(\mathbf{U}_{min}[\mathbf{V}]\) &
\begin{tabular}{c} **Modulation** \\ **Depth Factor m [\%]** \\ \end{tabular} \\ \hline
1.5 & 4.75 & 2.15 & 38 \\
3.0 & 2.48 & 1.36 & 29 \\
5.0 & 1.50 & 0.93 & 23 \\
10.0 & 1.37 & 0.28 & 14 \\
15.0 & 0.14 & 0.10 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Recorded signal parameters and calculated value of modulation depth factor for selected receiver coil distances from the identifier.