# Trade-Off Analysis for Array Configurations of Chipless RFID Sensor Tag Designs
## 5 Simulation Study of Array Configurations
### RCS Analysis  
Upon activation by the plane wave, the RCS showcases a distinct behaviour tied to frequency. This behaviour is characterised by a notable dip or notch at a particular frequency. The origin of this notch can be attributed to the resonance of the Pi-shaped resonant structure present within the tag. At the specific resonance frequency, the Pi-shaped structure interacts with the excitation signal, leading to substantial energy absorption at these frequencies before any reflection occurs. This resonance phenomenon generates the frequency-selective response observed in the RCS. When the designed unit cell tag is impinged by a plane-wave excitation signal, it shows a unique surface current distribution across the surface of the tag. The low current density is concentrated inside the Pi-shaped resonant structure, corresponding to the presence of capacitive properties. On the other hand, the highest distribution of surface current is shown between the two arms of the resonator structure, indicating the presence of inductive effects. The presence of inductive and capacitive characteristics distributed throughout a single resonant structure causes a significant resonance dip. It can be easily observed in the RCS frequency response of the unit cell tag as illustrated in Figure 10(a). The simulated RCS for various configurations of the linear array is presented in Figure 10(a). The RCS of the unit cell tag is approximately \(-25\) dBm, which improves by \(+10\) dBm when configured as a \(1\times 4\) array. This trend indicates that the RCS level tends to increase with the number of elements in the array. A similar enhancement in RCS can be observed in the scattered RCS patterns shown in Figure 10(b). Moreover, the resonance frequency demonstrates variations compared to the unit cell tag, with a noticeable shift towards lower frequencies (from 4.78 GHz to 4.75 GHz) as the number of array elements increases as detailed in Table 2.  
Figure 10: Planar array configurations of the Pi-shaped resonator. (**a**) Unit cell. (**b**) \(2\times 2\) array. (**c**) \(3\times 3\) array. (**d**) \(4\times 4\) array. The minor variations in resonance frequency between unit cell and array configurations arise from electromagnetic coupling among adjacent elements, which alters the effective inductance and capacitance. The expanded reflective surface area in arrays enhances the RCS and modifies resonance conditions, while structural mode reflections also contribute to frequency shifts. Additionally, variations in substrate properties, fabrication imperfections, and environmental factors, such as measurement alignment and external noise, can influence the frequency response. For larger arrays, increased radiation losses and a reduced Q-factor can affect the resonance stability, leading to slight frequency deviations compared to a single unit cell. Finally, it is important to recognise that linear array configurations are sensitive to the reader's location due to their lack of symmetry along the z-axis of the reader. Consequently, these linear array configurations may not be ideal for chipless RFID applications because of the resulting deviations in measurement parameters. A simulated RCS of the different configurations of planar arrays is shown in Figure 12a, and it is clear that the RCS increases as the number of cells in the array increases. Furthermore, planar arrays are symmetric in both the x and y directions; therefore, they are resilient to the reader's small movements and show a constant resonance frequency. Moreover, as shown in Figure 12b, the scattered RCS patterns also show an improvement in the RCS level. Additionally, as summarised in Table 3, the RCS value of the \(4\times 4\) array tag is almost 18 dBm higher than that of the unit cell tag, demonstrating a significant enhancement in backscattering strength. Since the \(1\times 4\) linear array and the \(2\times 2\) planar array have the same footprint area, their total RCS values might be expected to be similar.