# Numerical Modeling, Analysis, and Optimization of RFID Tags Functioning at Low Frequencies
## 6 Conclusions  
This study was conducted in order to improve RFID tags functioning at 13.56 MHz due to their versatility and wide range of applications in which they are used. Our main goal was to create an easily integrated structure with small dimensions and high gain, while also considering the decrease in manufacturing costs. To achieve this, we first developed and implemented software designed to identify possible structures that meet specific conditions, such as the external diameter, an inductance greater than 1 \(\mu\)H, and an internal diameter large enough to accommodate circuit elements for operation at the target frequency of 13.56 MHz. The software enables users to quickly view all potential dimensions and make an informed selection. The accuracy of the results was validated through numerical modeling using Ansys Q3D Extractor and Ansys HFSS. After evaluating four different shapes of planar inductors--square, circular, hexagonal, and octagonal--it was found that the algorithm used to create and implement the designs allows for additional possible structures under the given constraints. Furthermore, when comparing structures with the same number of turns and identical spacing (s) and width (w), square planar inductors were found to be superior due to their higher gain values. Analysis of the dielectric material revealed that the type of dielectric did not affect the structures' output parameters, but changes in the dielectric thickness did influence the peak gain and resonance frequency. From a thermal perspective, temperature did not have a significant short-term thermal or mechanical impact on the tags studied. As a general conclusion, the tags can be improved by decreasing their dimensions and using a cheap dielectric, although a larger exterior diameter is better, and a smaller number of turns provides better gain. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Shape of** \\ **Spiral Indicator** \\ \end{tabular} & \begin{tabular}{c} **I. Calculated** \\ **(uH)** \\ \end{tabular} & \begin{tabular}{c} **C Calculated** \\ **(pF)** \\ \end{tabular} & \begin{tabular}{c} **L Numerical** \\ **Modeling (uH)** \\ \end{tabular} & \begin{tabular}{c} **C Numerical** \\ **Modeling (pF)** \\ \end{tabular} & \begin{tabular}{c} **L Measured** \\ **(uH)** \\ \end{tabular} & \
\begin{tabular}{c} **C Included in Circuit** \\ **(pF)** \\ \end{tabular} &
\begin{tabular}{c} **Circuit Elements** \\ **Inserted** \\ \end{tabular} \\ \hline \hline \multirow{2}{*}{Square} & 1.92 & 71.58 & 1.85 & 84 & 2.051 & 78 & \\  & & & & & & & \\ Circular & 1.66 & 82.97 & 1.59 & 95 & 1.71 & 88 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values obtained for the circular and rectangular planar spiral inductors. **Author Contributions:** Conceptualization, C.C., C.P., A.G. and C.M. ; methodology, C.C., A.G. and C.P. ; validation, C.C., A.G., C.P., M.G. and S.A.; formal analysis, C.C. ; investigation, C.C., C.P., A.G. and C.M. ; resources, S.A., R.L. and M.G. ; data curation, C.C., C.P., A.G. and C.M. ; writing--original draft preparation, C.C. ; writing--review and editing, C.C., A.G. and C.P. ; visualization, R.L., S.A. and M.G. ; supervision, C.M. ; project administration, C.C. ; funding acquisition, C.C. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Academy of Romanian Scientists, grant number 31/08.04.2024, \"Digitalizarea procesului de proiectare al antenelor multifrecventa RFID si evaluarea expunerii umane la radiatiille emise de acestea\". **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data are contained within the article. **Acknowledgments:** This work was supported by a grant from the Academy of Romanian Scientists, project title: Digitalization of the Design Process for Multifrequency RFID Antennas and Evaluation of Human Exposure to the Radiation Emitted by Them.