# Trade-Off Analysis for Array Configurations of Chipless RFID Sensor Tag Designs
## 5 Simulation Study of Array Configurations
### Q-Factor Analysis  
According to the simulated Q of the different configurations of the linear and planar array, as depicted in Figure 15, the level of RCS increases with an increase in the number of elements, but the Q-factor decreases. As the number of elements in the array increases, there is a greater possibility of electromagnetic coupling between adjacent elements despite the reduced coupling during the design phase. This coupling can result in a wider resonance and a lower Q-factor. In addition, radiation losses may become more significant. When the chipless RFID array is excited, arrays may have more radiation losses, which can contribute to a further decrease in the Q-factor.  
As aforementioned, the Q-factor is generally higher in planar array configurations than in linear arrays, primarily due to stronger mutual coupling and enhanced energy  
Figure 14: Normalised structural and antenna mode backscattered signal obtained using FFT algorithm. (**a**) Unit cell. (**b**) 4 \(\times\) 4 array.  
Figure 13: Backscattered structural, \(y_{s}(t)\), and antenna, \(y_{a}(t)\), mode signal of the chipless tag in the time domain.  
confinement. In a \(2\times 2\) planar array, each element interacts with three adjacent elements, leading to improved energy storage and reduced radiation losses. As a result, this configuration achieves sharper resonance and a narrower bandwidth, making the system more frequency selective. In contrast, a \(1\times 4\) linear array exhibits weaker coupling, with each element interacting with only two adjacent elements. This limited interaction results in faster energy dissipation and a lower Q-factor.  
Taking into account the same footprint area of the tag, the linear array \(1\times 4\) and the planar array \(2\times 2\), it is noticed that the linear array shows a higher RCS value of 2 dBm but a lower Q-factor as shown in Figure 15. Indeed, a higher Q-factor influences the detectability more than the 2 dBm RCS difference. Furthermore, according to Figures 11b and 12b, the RCS level of the planar array shows a significant improvement compared to the RCS plot of the linear array. Therefore, considering the above-simulated results, planar array configurations based on a Pi-shaped resonator have been identified as the most suitable configuration for various applications and are fabricated to validate the simulation results.  
Additionally, our findings strongly align with the Chu-Harrington theory [34]. It is noted that as the array size increases, a decrease in the Q-factor occurs due to the broadening of the bandwidth. This suggests that with an increase in the effective electrical size of the resonator, a shift in the distribution of stored energy takes place, leading to a reduction in resonance sharpness. The increase in bandwidth associated with a larger array is consistent with the fundamental trade-off described in antenna theory, where it is acknowledged that electrically larger structures tend to exhibit improved radiation or scattering efficiency, albeit at the cost of a lower Q-factor. This behaviour aligns with the classical bandwidth limitations observed in electrically small antennas and further supports the applicability of the Chu-Harrington limit in the context of chipless RFID arrays.