# Trade-Off Analysis for Array Configurations of Chipless RFID Sensor Tag Designs
## 4 Chipless RFID Array Design
### Unit Cell Tag  
A novel chipless RFID tag design features a resonator shaped like the mathematical symbol \(\Pi\), as illustrated in Figure 5a, with all dimensions provided in Figure 5b. The reason for choosing an open resonator with a ground plane is that it exhibits a higher Q-factor than a closed-shaped resonator as summarised in Table 1. In Table 1, we compare the Q-factors of the most common chipless RFID resonators in the literature by simulating them on the same Taconic TLX-8 substrate with dimensions of 20 \(\times\) 20 mm\({}^{2}\) and under the same simulation environment. The Q-factor is calculated using the following equation [25]:  
\[\text{Q Factor}=\frac{f_{0}}{BW_{\text{-3 dB}}} \tag{6}\]  
where \(f_{0}\) is the frequency at which the spectral dip occurs (i.e., resonance frequency), and \(BW_{\text{-3 dB}}\) is the \(-3\) dB impedance bandwidth at \(f_{0}\). Figure 4: Link budget of a chipless RFID array system. This definition is commonly used for transmittance measurements, where the resonance dip indicates energy absorption; however, in the case of backscattering (RCS) responses, multiple reflections and anti-phase interactions significantly affect the bandwidth. Reflected signal components can interfere destructively, leading to deep spectral nulls where the RCS nearly drops to zero, resulting in highly narrow bandwidths and causing the Q-factor to tend toward infinity. The interactions among metal structures, resonators, and array configurations influence the spectral variations. Measuring the bandwidth from the RCS response rather than from transmittance is crucial to accurately defining the Q-factor for backscattering scenarios. Therefore, we use the backscattering Q-factor for this study. The design of the Pi-shaped resonator is inspired by the U-shaped resonator, which exhibits a higher Q-factor, a smaller footprint, and the ability to resonate in a ground plane [25]. This tag is initially designed to operate at a frequency of 4.8 GHz, which belongs to the ultra-wideband (UWB) frequency range. However, it is further refined to achieve a better Q-factor, which results in adjusting the resonance frequency to 4.78 GHz. In our design, we modify the U-shaped resonator by inverting it to form a Pi-shaped one and stretching both the top and bottom resonator tips. This modification allows for better surface current distribution across the resonator surface as shown in Figure 6.  
Furthermore, the upper and lower tips in our Pi-shaped resonator design have different lengths, denoted by \(b\) and \(d\), respectively (e.g., \(b\
eq d\)). This asymmetrical configuration enhances the spectral dip's amplitude, improving the detectability of the resonator in the frequency signature as shown in Figure 7. The level of the spectral dip's amplitude increases when the length of the arm \(d\) increases from 0.7 to 1.4 mm. When the resonator arm length \(d\) equals \(b\), the spectral dip's amplitude level decreases. Therefore, this asymmetrical configuration benefits resonator detectability using the frequency signature. Figure 5: A novel Pi-shaped unit cell chipless RFID tag (\(a\) = 3.6 mm, \(b\) = 1.4 mm, \(g\) = 0.5 mm, \(d\) = 1.2 mm, \(e\) = 12 mm, \(W\) = 20 mm and \(t\) = 0.5 mm). (**a**) Plan view. (**b**) Perspective view. Figure 6: Surface current distribution of Pi-shaped resonator at resonance frequency, 4.78 GHz. Similarly, the thickness of the Taconic TLX-8 substrate, with a dielectric constant of 2.55 and a loss tangent of 0.0019, is optimised to 0.50 mm to enhance the resonator Q-factor further. Moreover, increasing the Q-factor reduces the variation in resonance frequency over a significant distance, allowing for a more accurate analysis of the RCS variation in the array configurations [26]. A higher Q-factor also improves the overall performance of the chipless RFID tag, as it minimises energy loss [25].