Figure 3 shows the simulated return loss plots for different dimensions of the annular ring with fixed parameters as R_bi = 5 mm, R_bo = 18.5 mm, r_P = 0.6 mm, x_p = –12 mm, x_R = R_ro – 0.5 mm, and R = 56 Ω. From the simulated results of Figure 3, it is found that the resonant frequency is very sensitive to the patch size. As the outer radius (R_ro) or inner radius (R_ri) increases, the resonant frequency is decreased. The antenna impedance is well matched at 2.4 GHz with the combination of R_ri = 5.5 mm and R_ro = 17 mm, and the impedance matching is degraded while the patch dimensions deviate from the optimum values. Compared with the conventional annular ring patch antenna above mentioned, Figure 3 shows that a greater bandwidth can be obtained. There is also a notable decrease in the bandwidth as the outer radius (R_ro) increases, while the inner radius (R_ri) causes negligible effects.

In the process of analysis, it is also found that in comparison with the patch size the substrate size has relatively less effects on the resonant frequency. The resonant frequency slightly decreases with increasing outer radius (R_bo). To meet the compact requirements of the antenna, the outer radius of the substrate (R_bo) was selected as 18.5 mm with consideration of the optimized performance. The inner radius of the substrate (R_bi) was fixed at 5 mm due to the installation requirement of the sensor (shown in Figure 1).

To minimize the dimensions of the proposed antenna and increase the operating bandwidth, a chip resistor was introduced into the design to adjust the input impedance characteristics. When modeling in HFSS, a thin two-dimensional surface (0.3 mm × 3 mm) was placed in parallel with the z-axis at the loading position between the patch and the ground, and a lumped RLC boundary was assigned in parallel on the surface. Figure 4 shows the return loss curves for different positions of the loading point with other parameters of R_ri = 5.5 mm, R_ro = 17 mm, r_P = 0.6 mm, x_p = –12 mm and R = 56 Ω. There is an upward shift for the resonant frequency as the loading point is moved away from the circular center with the bandwidth improved significantly, and a notable agreement between the loading points at same radius along the x-axis is also observed. It was shown in [14,21] that for minimum area the loading point should be located closest to one of the radiating edges of the patch. As seen from Figure 4, the case of loading at the inner edge of the patch can result in a further reduction in resonant frequency, which corresponds to an even larger size reduction at a given operating frequency. In this case, the resistor loading has maximum effects on the resonant-frequency lowering due to the surface current has a maximum value around the inner edge of the patch, however, the matching level is poor. With consideration of the symmetrical characteristics [23] and easy of fabrication, the loading point was placed at the outer edge of the patch with x_R = 16.5 mm.

Another important parameter is the resistance of the loading resistor. Efforts were made to optimize the value of R to obtain optimum impedance matching for the proposed antenna. Figure 5 shows the return loss curves for different values of R and fixing other parameters as: R_ri = 5.5 mm, R_ro = 17 mm, r_P = 0.6 mm, x_p = –12 mm and x_R = 16.5 mm. It is evident that the resonant frequency of the antenna is dependent on the resistance of the loading resistor. As the R value increases, the center frequency decreases with the matching level slightly affected. No significant change in bandwidth is observed with the changes of R. Hence, the value of R can be adjusted to provide better resonant mode and good matching.

In comparison with the previously reported designs [24–26], an important change of this design, which kept the antenna operating at required frequency while allowing dramatically reduced dimensions, was the large resistance of the loading resistor. Several resistors with small resistance less than 10 Ω were analyzed, and the resonant frequencies were higher than that one in Figure 5 with poor matching levels. For example, the center frequency is 2.65 GHz as the resistance of R = 1 Ω, and the return loss is as low as 4.7 dB. In this case, the matching conditions are destroyed, and the impedance is mismatched. However, it should be noted that to reduce antenna dimensions the introducing resistor of large resistance was at the expense of the radiation efficiency, similar to the observation in [25–27]. The radiation efficiency of the conventional annular ring antenna above mentioned is 24.9%, with the introducing resistor (R = 56 Ω), the radiation efficiency of the proposed antenna is reduced to 14.6% and the peak gain is –1.5 dBi.

Figure 9 displays the simulated return loss curves of the proposed antenna with the steel installation base, and other parameters were set as the same values in Figure 5. By comparing the simulated results in Figure 9 and Figure 5, it is observed that when the steel installation base was introduced, the resonant frequencies were obviously increased. Taking the case of R = 56 Ω as an example, the resonant frequency in Figure 5 is 2.40 GHz with a return loss of 30.8 dB, while in Figure 9 that is 2.50 GHz with a return loss of 29.6 dB. Consequently, the addition of the steel installation base further strengthens the inductive nature of the patch antenna and hence increases the operating frequency, which makes it more difficult to realize the required compactness. Another variation between the results of Figure 9 and Figure 5 is the reduced bandwidth. As above mentioned, the simulated bandwidth is 16.3% in the case of R = 56 Ω, while it is reduced to 13.6% from 2.34 to 2.68 GHz due to the influence of the steel installation base.

In order to obtain a good impedance matching for the 2.4 GHz, as can be seen in Figure 9, the resistance of the loading resistor can be improved. It is observed that for R = 120 Ω, the antenna with the steel installation base resonates at 2.4 GHz with a return loss of 22.1 dB, and the bandwidth is 10.4% from 2.28 to 2.53 GHz.

Figure 10 shows the measured and simulated return loss curves of the antenna with the steel installation base for comparison. It is found that the measured resonant frequency is 2.4 GHz with a return loss of 34.2 dB, and the measured bandwidth is 11.7% from 2.27 to 2.55 GHz. Good agreement is achieved between the measured and simulated results. The slight discrepancy in the measured and simulated curves can be attributed to the fabrication tolerances.

The far-field patterns in both the E- and H-plane were simulated and measured, and the results are shown in Figure 11. In comparison with the results shown in Figure 8, the symmetric characteristics in co-polarization patterns are maintained with the polarization levels slightly reduced. Simultaneously, the backward radiations are weakened in both the planes due to the backed steel installation base, which can be explained as the restraining effects of the metal material. It is also noted that the cross-polarization patterns are changed obviously between Figure 11 and Figure 8, while the polarization levels are remained well.

The measured peak gain of the antenna backed with the installation base is plotted in Figure 12 along with its radiation efficiency. The peak gain is between –2.8 and –2.2 dBi within the operating band (2.3–2.5 GHz) with the radiation efficiency is from 12.2% to 13.3%. For the center frequency of 2.4 GHz, with the influences of installation base and resistor loading, the radiation efficiency of the antenna reduces to 12.7% and the peak gain is –2.5 dBi.

For further study to improve the gain of the antenna a substrate with relatively low permittivity can be used and its thickness increased suitably, however, the gain improvement may be relatively limited. Another approach to obtain an enhanced antenna gain is by covering the FR4 substrate with a high permittivity superstrate layer, and its thickness needs to be optimized to gain of the required compactness of the antenna. Furthermore, it may be possible to increase the gain by incorporating suitably meandered geometries.