## 6 Conclusions  
This study focused on the design and analysis of three patch antenna shapes for wireless passive temperature sensor applications. The process involved theoretical calculations, simulations using HFSS in Ansys Electromagnetic Suite(r) 2023 R1(Ansys Inc., Canonsburg, PA, USA), and fabrication with an alumina substrate and silver conductive paste. Each sensor dimension was 50 \(\times\) 50 \(\times\) 2.45 mm, making it practical for real-world implementation in applications such as industrial furnaces, bearing housings in engines, and nuclear reactors for early safety detection and hardware degradation prevention. Performance was evaluated through communication distance and sensitivity measurements over a temperature range of 25 to 500 \({}^{\circ}\)C, with increments of 50 \({}^{\circ}\)C at a fixed distance of 5 cm, which satisfies the far-field condition for both antennas. The equilateral triangular patch antenna demonstrated superior performance, achieving the maximum communication distance of 16.5 cm and a sensitivity of 0.129 MHz/\({}^{\circ}\)C. Its sharp edges concentrated the electric field, enabling efficient power transfer from the interrogator antenna, resulting in better stability of the backscattering signal. Additionally, the equilateral triangular antenna achieved the highest simulated gain of 5.84 dBi at 2.4 GHz. In contrast, the circular patch antenna exhibited the weakest performance due to its uniform electric field distribution, leading to reduced backscattering signal strength, particularly in high-temperature environments. The design of the sensor antenna is critical as it functions as both a sensing and communication component. For sensing, it requires substrate and conductor materials capable of withstanding harsh environments. For communication, the sensor antenna's frequency must align with the interrogator's resonant frequency and operate within a narrow bandwidth to lower the uncertainty of measurement, which in turn allows for a wider \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Rectangular** & **Circular** & **Equilateral Triangular** \\ \hline Maximum Distance & 15.0 cm & 14.5 cm & 16.5 cm \\ \hline Sensitivity & 0.120 MHz/\({}^{\circ}\)C & 0.116 MHz/\({}^{\circ}\)C & 0.129 MHz/\({}^{\circ}\)C \\ \hline Simulated Gain & 5.76 dBi & 5.75 dBi & 5.84 dBi \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The comparison of sensor antenna key performances. measurable temperature and maximize gain to ensure reliable wireless communication. A poorly designed antenna can weaken backscattered signals and compromise the sensor's functionality. Beyond the sensor antenna design, another crucial factor is the selection of the thermal cover material. It is recommended to use a low-loss material to maintain communication efficiency while ensuring low thermal conductivity to provide effective heat isolation. This combination is essential for establishing a safe and reliable temperature monitoring system in harsh environments. These findings underscore the vital role of antenna design in optimizing wireless passive temperature sensor systems. With its compact size, reliable performance without the need for local power, and simple design and installation, the equilateral triangular sensor antenna is a promising candidate for harsh environment applications. Future improvements could involve manufacturing the interrogator antenna using high-temperature-resistant materials to ensure its reliability in harsh environments, along with a broader bandwidth design to enhance temperature monitoring by capturing a wider range of frequency shifts. Conceptualization, T.A. and Y.-T.L. ; methodology, T.A. ; software, T.A. and Y.-T.L. ; validation, Y.-C.C. and C.-C.K. ; formal analysis, Y.-C.C. and T.A. ; investigation, T.A. ; data curation, T.A. and Y.-T.L. ; writing--original draft preparation, T.A. ; writing--review and editing, T.A., Y.-T.L., Y.-C.C. and C.-C.K. ; visualization, T.A. ; supervision Y.-C.C. and C.-C.K.