## 5 Results and Discussion  
Based on the simulation results, the resonant frequency of the three patch antennas is approximately 2.4 GHz, with a bandwidth range of 31 to 48 MHz. The highest simulated gain also occurs near 2.4 GHz, as shown in Figure 4. Figure 5 illustrates the simulated electric field distribution for the three sensor antennas, confirming their operation in the fundamental mode, which is transverse magnetic mode (TM mode), as supported by  
Figure 3: Experimental setup for evaluating the performance of the three sensor antennas: (**a**) communication distance measurement setup; (**b**) sensitivity measurement setup; (**c**) thermal evaluation on the thermal insulator surface. previous studies [21; 22; 23]. Additionally, the maximum electric field intensity is concentrated along the edges of the equilateral triangular patch, as depicted in Figure 5c. An investigation was conducted to examine the effect of placing an alumina foam thermal insulator cover between the sensor antenna and the interrogator antenna, with a fixed distance of 5 cm. Figure 6 illustrates the difference in S\({}_{11}\) magnitude with and without the thermal cover. The results show that the S\({}_{11}\) magnitude is higher without the thermal cover compared to when the cover is present. This reduction in magnitude is attributed to the re-radiated wave from the patch antenna experiencing reflections as it passes through the thermal insulator cover. These reflections introduce additional losses, leading to a decrease in the observed S\({}_{11}\) magnitude [7]. One approach to mitigate these additional losses is to utilize a low-loss dielectric material for the thermal cover, which would enhance electromagnetic wave transmission while minimizing reflection and absorption for future research directions. To evaluate the feasibility and reliability of this temperature monitoring system in various practical applications, the S\({}_{11}\) magnitude was investigated under different positioning angles of the interrogator antenna, as shown in Figure 7a. The distance between the interrogator and sensor antennas was fixed at 5 cm, while the incident angle of the interrogator antenna varied from 0\({}^{\circ}\) to 30\({}^{\circ}\) in 10\({}^{\circ}\) increments. Figure 4: The simulated S\({}_{11}\) and gain results: (**a**) S\({}_{11}\) reflection coefficients of the three sensor antennas; (**b**) Gain of the three sensor antennas. Figure 5: Simulated electric field distribution of the three sensor antennas: (**a**) rectangular patch antenna with \(TM_{10}\) mode; (**b**) circular patch antenna with \(TM_{11}\) mode; (**c**) equilateral triangular patch antenna with \(TM_{10}\) mode. As illustrated in Figure 7b-d, the maximum S\({}_{11}\) magnitude was observed at the 0\({}^{\circ}\) incident angle, where the interrogator antenna is directly facing the sensor antenna, achieving optimal polarization matching. At 10\({}^{\circ}\) and 20\({}^{\circ}\) incident angles, the S\({}_{11}\) peak was still detectable, indicating acceptable power transfer. However, at 30\({}^{\circ}\), a significant degradation in S\({}_{11}\) magnitude was observed across all three patch shapes, indicating  
Figure 6: The observed S\({}_{11}\) of backscattering signals with and without thermal cover. Figure 7: The observed S\({}_{11}\) of backscattering signal under various incident angles: (**a**) measurement setup; (**b**) rectangular; (**c**) circular; (**d**) equilateral triangular. reduced power transfer efficiency and insufficient coupling energy between the interrogator and sensor antennas. Figure 8 illustrates the maximum communication distance measurements for each sensor antenna. As the distance between the interrogator and sensor antennas increased, the S\({}_{11}\) peak magnitude decreased significantly until it became completely damped, indicating the limit of detectable communication.