# A Direction-Sensitive Microwave Sensor for Metal Crack Detection
## 3 Simulation Study on Metal Crack Detection and Characterization  
Electromagnetic simulations are performed with full-wave simulation software Ansys HFSS to verify the ability of the designed sensor for metal crack detection. Firstly, the frequency response of the sensor is simulated when there is no crack on the metal ground plane. The simulated reflection coefficient of each feeding port is shown in Figure 7. It can be found that the resonant frequency of port 1 is 2.430 GHz, while the resonant frequency of port 2 is 1.950 GHz.  
Figure 6: Current distribution of two different feeding methods. (**a**) Coupled feeding. (**b**) Direct feeding.  
Figure 7: Simulated reflection coefficients of the sensor for the case without cracks.  
Followingly, the sensor with a crack on the metal ground plane is simulated. Additionally, the influences of crack parameters such as width, depth and direction on the frequency response are also studied in the simulation.  
The simulated reflection coefficients of each feeding port for vertical cracks with different widths are shown in Figure 8. It can be seen from the results that a vertical crack has little effect on the resonant frequency of port 1. Additionally, for port 2, its resonant frequency will decrease from 1.946 GHz to 1.890 GHz when the crack width increases from 0 mm to 1 mm with a step of 0.2 mm.  
For the simulation results of horizontal cracks detection as presented in Figure 9, the resonant frequency of port 1 shifts from 2.426 GHz to 2.324 GHz with the crack width varies from 0 mm to 1.0 mm with a step of 0.2 mm.  
The definition of crack dimension sensitivity is shown in Equation (10), \(\Delta f\) is the change in frequency when crack dimensions changing, and \(\Delta x\) is the change in crack dimensions.  
\[Sensitivity=\left|\frac{\Delta f}{\Delta x}\right| \tag{10}\]  
The calculated frequency sensitivity of port 1 and port 2 for crack width detection is 102 MHz/mm and 56 MHz/mm, respectively.  
Figure 8: Simulated reflection coefficients of designed sensor for vertical crack with different widths. (a) Port 1. (b) Port 2.  
Figure 9: Simulated reflection coefficients of designed sensor for horizontal crack with different widths. (a) Port 1. (b) Port 2.  
Then, in order to study the influence of crack depth on the resonant frequency, the depth parameter sweeps from 1.5 mm to 2.5 mm with a step of 0.5 mm and crack width is fixed at 0.4 mm. The obtained simulation results are shown in Figures 10 and 11.  
It can be seen from Figures 10a and 11b that the resonant frequency of each port almost keeps same while crack depth change. As can be seen from Figures 10 and 11, the resonant frequency shifts toward lower frequencies with the increase in the depths, and the sensitivity of port 1 and port 2 is 16 MHz/mm and 10 MHz/mm, respectively.  
Furthermore, the sensor for crack direction detection is simulated. The depth and width of the metal crack are fixed at 2 mm and 0.6 mm, respectively, and the crack is rotated in counterclockwise direction with a step of 15 degrees (set the oy direction as 0 degrees). The simulation results of the reflection coefficient with the varying direction angle are as Figure 12 shows.  
We can find that the resonant frequencies of both feeding ports vary with the crack direction. As the crack direction rotates from 0 degrees to 90 degrees, the resonant frequency of port 1 will decrease from 2.432 GHz to 2.364 GHz, while the resonant frequency of port 2 will increase from 1.896 GHz to 1.942 GHz.  
Figure 11: Simulated reflection coefficients of designed sensor for horizontal crack with different depths. (**a**) Port 1. (**b**) Port 2.  
Figure 10: Simulated reflection coefficients of designed sensor for vertical crack with different depths. (**a**) Port 1. (**b**) Port 2.