# Trade-Off Analysis for Array Configurations of Chipless RFID Sensor Tag Designs
## 5 Simulation Study of Array Configurations
### RCS Analysis
However, the mutual coupling between antenna elements in the planar array influences the overall RCS, leading to differences in scattering characteristics. In the \(2\times 2\) configuration, each element interacts more strongly with its three adjacent elements, which alters the overall response of the array. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Resonator Configuration** & **RCS Level (dBsm)** & \
\begin{tabular}{l} **Normalised RCS Level** \\ **(dBsm/Cells)** \\ \end{tabular} &
\begin{tabular}{l} **Resonance Frequency (GHz)** \\ \end{tabular} & **Simulated Q-Factor** \\ \hline Unit cell & \(-25\) & \(-25.00\) & \(4.78\) & \(4515\) \\ \(1\times 2\) Array & \(-20\) & \(-10.00\) & \(4.75\) & \(637\) \\ \(1\times 3\) Array & \(-17\) & \(-5.77\) & \(4.75\) & \(418\) \\ \(1\times 4\) Array & \(-15\) & \(-9.02\) & \(4.75\) & \(314\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of linear array configurations. Figure 11: Simulated RCS response of the different linear array configurations. (**a**) Frequency response. (**b**) Scattered RCS pattern when \(\phi=90^{\circ}\) at the resonance frequency. When the number of unit cells normalises the RCS, the efficiency of each configuration becomes clearer. The \(1\times 4\) array exhibits a normalised RCS of \(-9.02\) dBsm/cell, whereas the \(2\times 2\) planar array has a lower normalised RCS of \(-24.02\) dBsm/cell. This indicates that each unit cell in the linear array contributes more efficiently to backscattering than the planar array. The reduced efficiency in the planar array is attributed to stronger mutual coupling, where each element's interaction with multiple neighbours impacts its scattering behaviour more significantly than in the linear arrangement. Structural and Antenna Mode RCS of Array Configurations  
In the context of a chipless RFID system, the signal received by the reader from a chipless tag, denoted as \(y(t)\), is expressed as the sum of three components in the time domain:  
\[y(t)=y_{r}(t)+y_{s}(t)+y_{a}(t) \tag{9}\]  
where the transmitted pulse rejection \(y_{r}(t)\) is the highest and first signal to arrive at the reader. The second component is the structural mode RCS, \(y_{s}(t)\), related to the tag's reflective surface. The antenna mode RCS component, \(y_{a}(t)\), arrives last with lower strength and contains all data bit information about the chipless RFID tag [11]. Therefore, the structural and antenna mode RCS components are crucial in analysing the RCS of chipless tags, and the transmitted pulse rejection \(y_{r}(t)\) is removed from the time domain signal for further analysis by employing a raised cosine window as depicted in Figure 13.  
As the number of elements in an array configuration increases, the received signal strength of the structural mode RCS (\(y_{s}(t)\)) becomes more substantial due to the increased total reflective area. At the same time, the increased total reflective surface causes the tag structure to resonate itself, resulting in an additional spectral dip in the frequency signature. A time-domain analysis is conducted using a unit cell and a \(4\times 4\) array configuration to examine this phenomenon. Figure 12: Simulated RCS response of the different planar array configurations. (**a**) Frequency response. (**b**) Scattered RCS pattern when \(\phi=90^{\circ}\) at the resonance frequency. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Resonator Configuration** & **RCS Level (dBsm)** &
\begin{tabular}{l} **Normalised RCS Level** \\ **(dBsm/Cells)** \\ \end{tabular} & **Resonance Frequency (GHz)** & **Simulated Q-Factor** \\ \hline Unit cell & \(-25\) & \(-25.00\) & \(4.78\) & \(4515\) \\ \(2\times 2\) Array & \(-18\) & \(-24.02\) & \(4.78\) & \(1117\) \\ \(3\times 3\) Array & \(-12\) & \(-21.54\) & \(4.79\) & \(872\) \\ \(4\times 4\) Array & \(-7\) & \(-19.04\) & \(4.78\) & \(454\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of planar array configurations.