## 2 Design of High-Performance Flat Air-Coupled Ultrasonic Transducer  
Piezoelectric ultrasonic transducer is a kind of device which realizes the conversion of electrical energy and mechanical energy based on the piezoelectric effect and inverse piezoelectric effect of piezoelectric materials. The key problem in the design of high-performance air-coupled ultrasonic transducer is how to effectively solve the acoustic impedance mismatch between the piezoelectric material and the transmission medium air. In this paper, the 1-3 piezoelectric composite material and matching materials of low voice impedance are self-made, and the optimization design of matching layer thickness of air-coupled ultrasonic transducer with double matching layer structure is completed. In Figure 1, the 1-3 piezoelectric composite vibrator selected in this paper has a radius of 6.5 mm, a thickness of 3.2 mm, and a piezoelectric ceramic column size of 1.6 * 1.6 * 3.2 mm\({}^{3}\). The Matching Layer 1 material is a polymer of hollow glass beads and epoxy resin, which is self-developed by mixing epoxy resin and hollow glass beads in a certain proportion. This polymer has low acoustic attenuation coefficient and low acoustic impedance, and its characteristics (such as density, acoustic velocity, etc.) parameters can be adjusted (by adjusting the proportion and diameter of hollow glass beads, etc. ), so it is an ideal matching material for piezoelectric air-coupled ultrasonic transducer. The material of Matching Layer 2 is a low density porous material purchased. The specific parameters of matched materials are shown in Table 1.  
Compared with the acoustic impedance characteristics of the matching material, the thickness of the matching layer has a more significant impact on the matching effect [36]. In practical application, the thickness of the quarter wavelength matching layer is not the best matching layer thickness, which needs to be obtained through experiments on the basis of theoretical calculation. The optimal matching layer thicknesses of Matching Layer 1 and Matching Layer 2 obtained by this method are 1.24 mm and 0.50 mm respectively, and a 400 kHz air-coupled ultrasonic transducer with a diameter of 13 mm is designed. The performance of the transducer is evaluated by using the one-shot, one-take mode. Specifically, a Tek TDS3012C oscilloscope is used to test the reflected or transmitted signals without the use of a power amplifier by stimulating a single square wave signal at the same operating frequency as the air-coupled ultrasonic transducer from the signal source RIGOL DG1022Z. During the test, the transmitting voltage is 10 Vpp and the length of the air column between the transmitting/receiving ultrasonic transducers is 50 mm. The schematic diagram of the test equipment and its results are shown in Figures 2 and 3 respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Types** & **Density** & **Acoustic Velocity** & **Acoustic Impedance** \\  & **(kg/m3)** & **(m/s)** & **(MRxyl)** \\ \hline Matching Layer 1 & 550 & 2700 & 1.404 \\ Matching Layer 2 & 30 & 900 & 0.027 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of the matched material. Figure 1: Schematic diagram (**a**) and physical diagram (**b**) of air-coupled ultrasonic transducer. Figure 2: Schematic diagram of one-shot, one-take mode test. In addition, Equations (1) and (2) are used to calculate the insertion loss and 6 dB bandwidth. \[IL=20\text{lg}(V_{rx}/V_{tx}) \tag{1}\]  
\[BW_{-6 dB}=\frac{(f_{H}-f_{L})}{f_{\text{C}}} \tag{2}\]  
Among them, \(V_{rx}\) is the peak-to-peak value of the pulse-echo signal received by the ultrasonic transducer, and \(V_{tx}\) is the peak-to-peak value of the excitation voltage applied to the ultrasonic transducer. \(f_{H}\) and \(f_{L}\) are the high frequency point and low frequency point corresponding to the maximum peak drop of 6 dB in the frequency domain respectively, and \(f_{\text{C}}\) is the working frequency of the ultrasonic transducer.