# A Novel Chipless Hybrid RFID Sensor for Metal Crack Detection
## 2 Materials and Methods
A metallic steel plate with a thickness of 10 mm is placed at the back of the sensor, as shown in Figure 2a. The PML layer with free radiation boundary condition is used with 1000 elements for the simulations. The minimum radiating distance is set to 2 cm. With the plane wave excitation, the tag is activated, and the plane wave transmits a linearly polarized wave in the z-direction with an E-plane parallel to the Y-axis and H-plane parallel to the X-axis. A frequency sweep of 3-5 GHz is applied with a resolution of 501 points. Figure 2 shows the simulation setup, current distribution, and the corresponding radiation pattern of the circular patch and the  
Figure 1: RFID sensing architecture and tag design. (**a**) Architecture of the crack detection system using chipless RFID sensing; (**b**) Tag design and dimensions. proposed tag at 4.19 GHz. The radiation pattern for the circular patch shows a maximum radial component at 6.64 dB at \(\theta=0^{\circ}\), while that for the proposed tag is 11.6 dB at \(\theta=0^{\circ}\) Figure 2d,e. Figure 3 shows the tag's resonant frequency. Since the plane wave excites the tag, the RCS shows a notch at a particular frequency, indicating the conductive structure of the tag resonating at this frequency. A comparison between the RCS of a circular patch and the proposed tag antenna is also shown. It can be observed that there is a narrower frequency notch for the proposed antenna, suggesting a better RCS in response to the circular patch. Figure 4 shows that a crack is introduced on the metallic structure, and the RCS spectrum is simulated for different crack orientations and widths. The crack will be part of the ground plane for the tag. Two orientations of the crack, horizontal (\(0^{\circ}\) orientation) and vertical direction (\(90^{\circ}\) orientation), with different respective depths are investigated. Different crack widths and depths over a range of 1-5 mm are detailed. Figure 3: Simulated RCS showing the resonant frequency of the proposed tag with a circular patch. Figure 2: (**a**) Simulation set up. Current distribution at 4.19 GHz: (**b**) Circular patch; (**c**) Proposed tag. Radiation pattern at 4.19 GHz: (**d**) Circular patch; (**e**) Proposed tag. For metallic crack detection, only one parameter of the tag changes, i.e., the resonant frequency, depending on the orientation of the crack. Figure 5 shows the simulation results for the horizontal orientation of the crack. The width is in the range of 1 mm to 5 mm with a step of 1 mm. The choice of analyzing crack widths in the range of 1 to 5 mm was motivated by practical considerations tied to real-world applications and constraints. Cracks within this range are critical as they represent the early stages of damage in metallic structures. Cracks below 1 mm are often challenging to quantify due to limitations in resolution and environmental noise interference. Cracks exceeding 5 mm are typically detectable through visual inspection or other conventional non-destructive testing (NDT) methods, making the 1 to 5 mm range an optimal target for our investigation. The depth of the crack is kept constant at 1 mm. Figure 5 shows the shift in resonant frequencies as the crack width is increased. It is graphically indicated in Figure 5, which shows a linear correlation (\(R^{2}=0.9732\)) of the change in frequencies. As the horizontal crack width increases the resonant frequency is reduced. Figure 6,b show the shift in resonant frequencies when the depth of the horizontal crack is increased. Here, the width is kept constant at 2 mm for different depths. For a constant width, as the depth increases, the resonant frequency is reduced (\(R^{2}=0.9961\)). Figure 4: Tag is designed on FR4 substrate, and placed on a metallic surface where a crack is introduced. Figure 5: RCS and resonant frequencies for horizontal crack widths. A similar analysis is performed for the vertical orientation of the crack. Figure 7 shows the resonant frequency shift as the width of the vertical crack is increased (\(R^{2}=0.9928\)).