### Use of a Resonant Circuit to Increase the Range of Reading Data from the Identifier  
One of the simplest solutions to increase the level of the measured signal is to use a resonance system tuned to the frequency of the carrier wave used in the HF-band RFID system, i.e., 13.56 MHz. Due to the high frequencies used in the system, the additional capacitance in the system must take into account the impedances of the spectrum analyzer and oscilloscope used in the research. The actual circuit for determining the frequency response of the resonant circuit consisted of a spectrum analyzer with a high-impedance input and its tracking generator, an oscilloscope, a transmitting coil with an inductance of approx. 10 \(\mu\)H (12 coils, 6.5 \(\times\) 3.5 cm), and a receiving coil with an inductance of 5 \(\mu\)H with a 22 pF capacitor [17; 18; 19; 20]. The diagram of this circuit is shown in Figure 13 and the circuit for simulation in the LTspice program is shown in Figure 14. During the simulations carried out using the LTspice program, the parasitic parameters of individual elements were not  
Figure 12: Recorded signal waveforms corresponding to distance measurements: (**a**) 1.5 cm (\(m=38\%\)), (**b**)10 cm ( \(m=14\%\)). Elements with determined capacitance and inductance values during the measurements and simulations were used in the next stage of measurements, the purpose of which was to determine whether the applied solution would allow to increase the range of emission from the NFC system identification card (MIFARE). For this purpose, the measurement system shown in Figure 16 was implemented. Instead of a regular magnetic coil, it was necessary to use a computer NFC reader. This was due to the need to send appropriate queries to force the transmission of the identifier. The continuous carrier wave, which could be used in the LF-band RFID system, in the case of HF-band RFID systems, did not force the start of transmission between the badge and the reader. The measuring equipment listed in Table 4 was used to carry out the measurements. During the tests, the ID card was placed at a distance of 3 cm from the reader. The coil and capacitor were placed at different distances from the identifier and on the basis of the obtained oscillograms the modulation depth factor and the signal level were determined as a function of the distance of the coil from the identifier. The values of \(U_{max}\) and \(U_{min}\) read using the oscilloscope and the calculated values of the modulation depth factor m are shown in Table 5, while examples of images recorded by the oscilloscope are shown in Figure 17. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Device** & **Type** & **Producer** \\ \hline Oscilloscope & DSOX1102A & Keysight \\  & & Colorado Springs, CO, USA \\ Spectrum analyzer & 3588A & Hewlett Packard \\  & & Everett, WA, USA \\ Reader LF-band RFID & & YiToo \\ and HF-band RFID & NS106 RFID Reader Writer & Guangzhou, China \\ ID card & NTAG213 & \\ Receiving coil (65 \(\times\) 35 mm, & & \\
6 coils) with 22 pF capacitor & MCI-NRI 1  \\ \hline \hline \end{tabular}
\end{table} 
Table 4: List of apparatus used to carry out the measurements. Figure 16: Measuring system for determining the modulation depth factor using a resonant system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Distance d** & \multicolumn{4}{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
3.0 & 12.4 & 7.10 & 27.0 \\
5.0 & 4.75 & 2.80 & 26.0 \\
10.0 & 1.39 & 1.00 & 16.0 \\
15.0 & 0.75 & 0.75 & 14.0 \\
20.0 & 0.43 & 0.35 & 10.0 \\
25.0 & 0.29 & 0.25 & 7.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Recorded signal parameters and calculated value of modulation depth factor for selected receiver coil distances from the identifier for the resonant circuit use case.