# A High-Sensitivity Magnetic Field Sensor Based on PDMS Flexible Resonator
## 3 Results and Discussion
### PDMS with Different Mixing Ratios  
The Young's modulus of the PDMS cured with different mixing ratios is obtained by referring to the literature, as shown in Table 1.  
In Table 1, we can obtain the Young's modulus of the PDMS with different mixing ratios. As the ratio of the PDMS pre-polymer and curing agent gradually becomes smaller, it leads to the [PERSON]'s modulus of PDMS also gradually decreasing. The smaller the Young's modulus, the softer the PDMS flexible resonator, which makes the magnet sense the external magnetic field under the external magnetic field and thus translates into pressure on the PDMS, which directly affects the degree of the deformation of the PDMS flexible resonator and leads to the increased sensitivity of the sandwich structure. The [PERSON]'s modulus parameters in the table are brought into the COMSOL parameters to simulate and calculate the sensitivity. Based on the unchanged parameters of the PDMS flexible resonator with a radius of 1.5 mm and a coupling position at 0.3 h, the [PERSON]'s modulus of the PDMS flexible resonator is adjusted by changing the mixing ratio of PDMS pre-polymer and curing agent. By introducing the [PERSON]'s modulus of PDMS with different mixing ratios into the model, the magnetic field sensitivity of the sandwich structure under different magnetic fields is obtained, as shown in Figure 8a. The mixing ratio of the PDMS flexible resonator is 6:1, and its magnetic field sensitivity is almost doubled compared with the mixing ratio of the PDMS flexible resonator of 10:1, which shows the influence of [PERSON]'s modulus on the magnetic field sensor. \begin{table}
\begin{tabular}{c c} \hline \hline
**Mixing Ratio** & **[PERSON]’s Modulus** \\ \hline
10:1 & 1.47 MPa \\
8:1 & 1.34 MPa \\
7:1 & 1.2 MPa \\
6:1 & 0.93 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: [PERSON]’s modulus of PDMS with different mixing ratios [33]. Figure 8: (**a**) Magnetic field sensitivity for different mixing ratios. (**b**) Trend of magnetic field sensitivity with mixing ratio. From the results in Figure 8a, it is concluded that the decrease in [PERSON]'s modulus also affects the magnetic field sensitivity of the sandwich structure, which is 3.2 nm/mT, 3.63 nm/mT and 4.58 nm/mT for a PDMS polymer to curing agent ratio of 8:1, 7:1 and 6:1, respectively, while Figure 8b quantitatively depicts the difference in sensitivity between different mixing ratios of PDMS. As the PDMS prepolymer ratio decreases, the [PERSON]'s modulus gradually decreases, leading to an increase in the deformation of the PDMS flexible resonator, which leads to an increase in the magnetic field sensitivity of the sandwich structure. The simulation results lay the foundation for the subsequent structure optimization and illustrate the feasibility of this structure. From the above three results, it can be seen that in the PDMS-flexible-resonator-based sandwich structure, all three adjustments affect the sandwich sensor device to a greater extent: as the size of the PDMS flexible resonator decreases, the magnetic field sensitivity of the sandwich structure becomes larger, and when we design the radius adjustment to 0.65 mm, the magnetic field sensitivity reaches 5.14 nm/mT. When we change the coupling position of the PDMS flexible resonator, the magnetic field sensitivity increases as the coupling position approaches the top of the PDMS flexible resonator, and the magnetic field sensitivity is 5.51 nm/mT at the limit coupling position of 0.7 h which we can approach experimentally; the magnetic field sensitivity of the sandwich structure is affected by adjusting the Young's modulus using the PDMS proportional ratio, and the magnetic field sensitivity reaches 4.58 nm/mT at the Young's modulus of 0.93 MPa. Therefore, by changing the radius of the PDMS flexible resonator, adjusting the coupling position and the PDMS ratio can directly affect the sensitivity of the sandwich structure, which provides a theoretical basis for a magnetic field sensor with a PDMS flexible resonator.