# A Novel Chipless Hybrid RFID Sensor for Metal Crack Detection
## 2 Materials and Methods  
The working principle of the chipless RFID system is shown in Figure 1a. The transmitter and receiver antenna pair are connected to the VNA, which acts as a reader. The tag is placed on a metallic sample and a sweep of interrogation frequency is sent to the tag by the transmitter (Tx); the tag reads the signals and reflects them back. The reflection from the sensor tag and the metallic sample results in a backscattered signal and is received by the receiver (Rx). Initially, a simple circular patch was designed for 5 GHz resonant frequency. Then, for miniaturization, to place the antennas in small areas, the circular patch antenna is designed with a hexagonal slot and a small hexagonal patch. The equations to calculate the circular patch parameters and hexagonal sides are given in Equations (1)-(4) [55]. The geometric lengths are calculated and adjusted with a parametric sweep of the hexagonal sides to determine the resonant frequency between 4 and 5 GHz. Even though the current configuration of the hexagonal patch is similar to a circular patch, the hexagonal patch has more notches than the rectangular and circular patch, thus increasing the bandwidth due to the accumulation of charges at the corners and can provide a good RCS [56], as shown in Figure 2.  
\[a=\frac{F}{\sqrt{1+\frac{2h}{\pi a\epsilon_{r}}F[ln(\frac{\pi F}{2h}+1.7726)]}} \tag{1}\]  
\[F=\frac{8.791e^{9}}{f_{r}\sqrt{\epsilon_{r}}} \tag{2}\]  
\[a_{e}=a\times\sqrt{1+\frac{2h}{\pi a\epsilon_{r}}\Big{\{}\ln\Big{[}\frac{\pi a }{2h}\Big{]}+1.7726\Big{\}}} \tag{3}\]\[\pi{a_{e}}^{2}=\frac{3\sqrt{3}}{2}S^{2} \tag{4}\]  
where \(f_{r}\) = resonant frequency of circular patch antenna, \(e_{r}\) = substrate relative permittivity, \(h\) = substrate height, \(a\) = physical radius of the patch, \(a_{e}\) = effective radius and \(S\) = side of the hexagonal patch. The goal of this work is to detect cracks on metallic surfaces, so the tag design depends on the metallic surface in such a way that metal has to be an integral part of the design. The chipless tag design with no ground plane can operate on a metallic surface. Since the design has no ground plane, the metallic surface acts as a ground plane for the tag due to its electrical conductivity [53; 57; 58]. Following are some of the designs for chipless tag resonators investigated earlier: folded dipole [59], circular patch antenna [53], and rectangular patch [48]. [PERSON] et al. showed a clear difference for crack detection on metallic structures using a simple circular microstrip patch antenna (CMPA). Moreover, the study shows that the resolution and sensitivity of the chipless RFID sensor for crack detection can be further improved by innovative tag designs for continuous monitoring of the surface cracks. This evidence provides motivation to design a tag with further size reduction and gives good geometric uniformity for crack detection. The design and dimensions of the tag are shown in Figure 1b. The proposed tag is a circular patch with a hexagonal slot and a small hexagonal ring embedded inside the patch. Since the current distribution of the tag design is similar to that of a CMPA, it can be treated as a patch, with the ground plane and the material in between the ground and patch as a cavity [55; 60]. The ground plane is the metallic structure under test; therefore, any physical or electrical changes in the structure will result in changes in the electrical properties of the tag. Thus, the presence of a crack will change the effective antenna radius, taking the permittivity of the air gap in the crack into consideration, so the resonant frequency of the tag shifts in the presence of the tag. The sensor tag is designed on an FR4 substrate with a dielectric constant of \(e\) 4.4 and the thickness of the substrate is 1.4 mm. The overall size of the tag is 16 mm in diameter. The simulation setup is created in HFSS software Version 17.2. The bistatic RCS is calculated at a distance of 10 cm from the tag.