# High-Density 3D Printable Chipless RFID Tag with Structure of Passive Slot Rings
## 3 Design and Fabrication of 12-bit Chipless Tag Printed on F4 BM Substrate  
To fulfill a 12-bit-tag with the designed structure on F4 BM substrate, key geometry parameters are shown in Table 1.  
Figure 6 shows the simulation result of the designed 12-bit-tag with coding (111111111111) when thickness of printed conductor is 100 \(\upmu\)m and the thickness of substrate is 1 mm. The tag of ID (11111111111) is used as a reference tag in this paper. Other tags with different codes are formed based on the reference tag by adding and removing the corresponding bit slot rings. It can be seen in Figure 6 that the resonant frequencies of the reference tag are distinguished clearly, with frequency ranging from 2.12 GHz to 8.39 GHz, showing promising property as candidate of the chipless tag. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Side length of primary slot (\(a_{1}\)) & 8 mm \\ Width of slot (\(W_{slot}\)) & 0.5 mm \\ Distance of the adjacent slots (\(d\)) & 0.5 mm \\ The outmost side length of outmost slot (\(a_{12}\)) & 30 mm \\ Thickness of silver nanoparticle ink & 35 \(\upmu\)m \\ Area of tag & \(35\times 35\) mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key geometry parameters of 12-bit-tag printed on F4 BM substrate. Figure 5: RCS results of five Rectangular Slot Rings with different \(d\) while the slot width is fixed to be 0.5 mm. (**a**) d = 0.1 mm (**b**) d = 0.3 mm (**c**) d = 0.5 mm (**d**) d = 0.9 mm. Figure 6: Frequency spectra of the 12-bit-tag on F4 BM substrate. The thickness of substrate is 1 mm. Figure 7 shows the simulated resonant spectra of the reference tag, with the thickness of the silver nanoparticle conductive paste layer varied from 5 \(\upmu\)m to 35 \(\upmu\)m with the increment step 5 \(\upmu\)m. It can be seen that the resonant frequencies of every slots are almost fixed although the thickness of the conductivity nanoparticle silver paste is changed from 5 \(\upmu\)m to 35 \(\upmu\)m. This means the resonant frequency of the printed tag is robust to the printing thickness. The twelve notches of the spectrum signatures clearly demonstrate the correctness of the encoding state. However, the notch of spectra is turned to be shallower when the thickness of the silver nanoparticle conductive paste layer is decreased. When the thickness of conductive nanoparticle silver paste layer is 5 \(\upmu\)m, the notch is turned to be too shallow to be correctly decoded. The diagram in Figure 8 defines the angles of incident wave and reflection wave, in which \(\theta\) denotes the incident angle of the signal relative to the vertical orientation and \(\varphi\) is the angle of horizontal rotation. The spectra obtained by changing \(\theta\) and \(\varphi\) of incident wave are shown in Figures 9 and 10, separately. Figure 8: Schematic of incident angle of the signal \(\theta\) relative to the vertical orientation, angle of horizontal rotation \(\varphi\) defined on the tag. Figure 7: RCS results of Rectangular Slot Rings with different thicknesses of silver nanoparticle conductive ink layer. Figure 9 shows the RCS results while \(\theta\) changing from 0\({}^{\circ}\) to 30\({}^{\circ}\) and \(\varphi=0^{\circ}\). The transmitted code keeps correctly when \(\theta<30^{\circ}\). However, when \(\theta=30^{\circ}\), error data appears because of the occurrence of unusual offset. This reveals that the tag cannot rotate exceeding 30\({}^{\circ}\) on the vertical direction. Figure 10 shows the RCS curves on condition that \(\theta=20^{\circ}\) and \(\varphi\) changing from 0\({}^{\circ}\) to 60\({}^{\circ}\). The reader can receive data from tag correctly when the tag rotating on the horizontal direction from 0\({}^{\circ}\) to 360\({}^{\circ}\), demonstrating directly that the tag shows promising properties acting as RFID since the data in tag can be easily read in wide angle. The above analysis does not include the influence of the thickness of the substrate.