## 3 Parameter Characteristics of the Sensor
The low points in the S11 parameter curve correspond to the high peaks in the admittance curve, while the high points in the S11 parameter curve correspond to the low points in the admittance curve. These represent the resonant and anti-resonant frequencies of the MP-SAWS, respectively. The quality factor \(Q_{m}\) quantifies the energy efficiency during circuit resonance. The SAWS serves as a sensing detection device rather than an energy storage and utilization device. However, the SAWS needs to transmit sensing parameters from the sensor to the reader via wireless communication, which unavoidably leads to energy loss. In the SAWS, a high-quality factor indicates minimal energy loss during the transmission process. Excessive energy loss has adverse effects on signal quality and effective transmission distance in wireless communication. For a single-port resonator, the formula relating the dimension of the MP-SAWS to the quality factor is described as follows [62]:  
\[Q_{m}=\frac{\pi L_{c}}{\lambda_{0}\big{(}1-\tan\ h_{\text{LN}}\big{(}|r_{s}|N_ {g}\big{)}\big{)}} \tag{19}\]  
where \(L_{c}\) represents the effective length of the resonance cavity, \(r_{s}\) denotes the reflectivity of an individual electrode, and \(N_{g}\) refers to the number of electrodes within the reflective cavity. The parametric curve of the MP-SAWS mechanical quality factor \(Q_{m}\) is represented in Figure 4d. As depicted in the graph, the MP-SAWS exhibits a strong response near 1.8852 GHz, which is characterized by minimal noise, prominent peak values, and an achievable amplitude of 10\({}^{21}\). Evidently, the peak value of the mechanical quality factor also coincides with the resonant frequency. The sensor's sensing capability is influenced by noise present in the application environment. Since the working principle of the SAWS involves both positive and converse piezoelectric effects, the interference of external electric fields on the electric field of the SAWS cannot be ignored. To verify the effectiveness of the simulated devices, it is essential to validate the anti-interference ability of MP-SAWS through noise testing. In the anti-noise test, the electrodes are divided into odd and even groups, naturally staggered at intervals. Initially, the even-numbered electrodes are grounded, while the odd-numbered electrodes receive a 1V voltage input, and the resonant frequency is recorded. This is performed by increasing the voltage input to the odd-numbered electrodes and continuing to record the resonant frequency. Figure 5a represents the response result between the excitation terminal voltage and the characteristic frequency. Altering the electrode group voltage setting between electrode group 1 and electrode group 2, the odd-numbered electrodes are grounded, while the even-numbered electrodes receive a voltage input. Figure 5b represents another response result between the excitation terminal voltage and the characteristic frequency. Supplementary experiments can be conducted to eliminate the noise impact caused by the electrode position on external electric fields. In the same model, by outputting the wave velocity, the interference of the voltage on wave speed can be obtained. The results are shown in Figure 5c,d. Similarly, a set of magnetic field anti-interference tests was conducted under two grounding configurations. The magnetic field direction was set to the horizontal direction, and the excitation voltage was 1V for all cases, which is consistent with subsequent magnetic field tests. The interfering magnetic field was scanned from negative to positive. The results are shown in Figure 5e,f. From the anti-interference test, it is evident that the SAWS exhibits excellent resistance to external electric field noise and magnetic field noise. The sensing error caused by the electric field excited by different voltages can be ignored, as can the response of SAW  
Figure 5: The noise resistance test.