# A Circularly Polarized Antenna Array with Gain Enhancement for Long-Range UHF RFID Systems
## 3 Measurement Results and Discussion  
A prototype of the 2 \(\times\) 2 antenna array, depicted in Figure 7, was manufactured for verification. In particular, S\({}_{11}\) was measured with a vector network analyzer (Agilent N5230A, Agilent Technologies, Santa Clara, CA, United States), while far-field behavior was verified in an anechoic chamber. Specifically, antenna gain was determined by comparing the antenna's gain with that of a standard horn antenna, while AR was calculated from right-handed CP (RHCP) and LHCP electric field components as in [26]. Comparisons of ANSYS HFSS results and measured S\({}_{11}\), AR, and LHCP gain, and the simulated (with HFSS) radiation efficiency are shown in Figure 8 (only the bandwidth from 780 to 1020 MHz is depicted for the sake of representation clarity). An \(\left|\text{S}_{11}\right|\leq-10\) dB bandwidth from 759 to 1026 MHz (29.9%) was observed. Furthermore, AR \(\leq\) 3 dB was obtained within the frequency band of 828-994 MHz (18.2%), which covers the target band of 840-960 MHz. Finally, a peak gain value of 12.5 dBic at the frequency 900 MHz, a 3 dB gain bandwidth broader than 26.3% (800-1030 MHz), and a simulated efficiency larger than 82.7% within the bandwidth 840-960 MHz were obtained. Few discrepancies between the measurement and simulation results were observed, probably due to manufacturing tolerances, dielectric material parameter variations, and simulation and test errors. Figure 8: Comparison of simulation and measurement results: (**a**) S\({}_{11}\), (**b**) AR, and (**c**) broadside LHCP gain and simulated radiation efficiency (AR and gain measurement results available from 800 MHz). Figure 7: Manufactured antenna prototype: (**a**) top view and (**b**) side view. Measured and simulated radiation patterns for the frequencies 870 and 930 MHz were plotted, in Figure 9, for both _xz_- and _yz_-planes (only two frequencies are shown for brevity), while AR \(\leq\) 3 dB beamwidths are listed in Table 1 for the frequencies 840, 900, and 960 MHz. The measured performance of the proposed antenna array was compared with that of other wideband high-gain CP 2 \(\times\) 2 antenna arrays, and the results are presented in Table 2 (\(\lambda\) calculated at \(f_{0}\)). The proposed antenna exhibits an excellent trade-off between gain and size, wide 3 dB gain bandwidth and, in general, good overlapped bandwidth. Although similar results can be found in [14] due to employment of a similar structure, the presented antenna exhibits reduced gain degradation within \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency (MHz)** & **840** & **900** & **960** \\ \hline _xz_-plane (deg) & 31 & 38 & 35 \\ _xz_-plane (deg) & 26 & 27 & 37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Antenna array AR \(\leq\) 3 dB beamwidths. Figure 9: Simulated (dashed), measured (continuous), and theoretical (dashed-dotted) radiation patterns: (**a**) 870 MHz, on the _xz_-plane; (**b**) 870 MHz, on the _yz_-plane; (**c**) 930 MHz, on the _xz_-plane; (**d**) 930 MHz, on the _yz_-plane. the working bandwidth, as proved by a wider 3 dB gain bandwidth. Furthermore, it should be noted that in the case of mere broadside gain optimization, an estimated gain enhancement of about 0.8 dB has to be added to the peak gain value in Table 2, according to the analysis proposed in Section 2.5 (\(h=15\) mm and \(d=0.7\lambda\), which also correspond to a reduced normalized thickness of 0.053\(\lambda\)). Measured results are also compared with the theoretical \(Q\)-factor limit [27], and in terms of aperture efficiency \(e_{A}\) (a theoretical aperture efficiency larger than 90% can be verified for the antenna array with \(h=15\) mm and \(d=0.7\lambda\) according to the optimization process proposed in Section 2.5). Finally, the maximum read range has been experimentally characterized using a commercial Impinj Indy R2000 UHF reader (Impinj Inc., Seattle, WA, USA) (\(P_{th,trader}\approx-60\) dBm) and a tag device with \(P_{th,tag}\approx-25\) dBm.