# Ultrasonic Power and Data Transfer through Multiple Curved Layers Applied to Pipe Instrumentation
## 3 Acoustic Channel Analysis
### Power and Data Communication Analysis  
In order to evaluate the power and data communication of the experimental setup, a vector network analyzer (VNA) was used. The S21 scattering parameter was measured and used to evaluate the power transfer. With this equipment, it is also possible to measure the input impedance of the system. Therefore, from the curves of impedance for the two cases, open and shorted, the input voltage variation (\(VV\)) was calculated using Equation (1), through the difference of the input voltage when varying the input impedance  
\[VV=\frac{(|Z_{o}-Z_{c}|)}{(50+Z_{o}+Z_{c})+(Z_{o}\times Z_{c})/50}\times V, \tag{1}\]  
where \(Z_{o}\) is the input impedance when the transducer is open-circuited, \(Z_{c}\) is the input impedance when the transducer is short-circuited, and \(V\) is the voltage applied to the transducer. Equation (1) is obtained by considering that the input voltage in each case is provided by a voltage divider circuit between a 50 \(\Omega\) nominal impedance and the input impedance. One can notice that the amplitude of the input voltage variation is proportional to the applied voltage \(V\) and the impedance difference (\(|Z_{o}-Z_{c}|\)). A 50 \(\Omega\) resistor, the output impedance of the VNA, is used in the calculation.  
Figure 5a,b show the experimental and numerical results for the S21 scattering parameter and the input voltage variation, respectively. As it can be seen, there are several peaks in Figure 5a due to the wave reverberation within the channel caused by reflections in between the layers and at the ends of the channel, thus creating several resonance frequencies in the working bandwidth, as commonly occurs in this type of ultrasonic communication system [9; 21]. The simulated S21 curve of Figure 5a reasonably matches the more pronounced peaks of the experimental curves. Regarding the power transfer, the main maximums occur at (1.118 MHz; \(-\)9.28 dB) and (1.119 MHz; \(-\)10.79 dB) for the simulated and experimental curves, respectively, resulting in a difference of 1 kHz in the frequency and 1.51 dB of the insertion loss. This amplitude difference may be due to differences between the actual and the tabled material properties used in the numerical model. Additionally, it is also possible to observe that the experimental curve has additional peaks with lower amplitudes between the multiple resonances of the channel that might be caused by other ultrasonic modes of propagation created inside the channel. It is also worth noticing that the simulated model, however, does not include  
Figure 4: (a) Schematic diagram of the experiment: the outside transducer is bonded to the case, and the inside transducer is directly attached to the external pipe; (b) 3D isometric view of the experimental setup.  
the characteristics of a curved wall because it was developed to contemplate only one-dimension wave propagation [23; 24]. With respect to the input voltage variation shown in Figure 5b, the main maxima occur at (1.118 MHz; 0.43%) and (1.119 MHz; 0.40%) for the simulated and experimental curves, respectively. In this case the difference between the input voltage variations is 0.03%. It is straightforward to conclude that a good operating point is at 1.119 MHz as it represents an operating point where both power transfer and data communication are augmented. It is worth noticing that if the propagating distance were larger, lower S21 values would be expected due to the higher attenuation along the channel. Low S21 is, obviously, an issue for power transfer because lower power arrives at the inside block. However, it is also complicating for data transmission even though communication relies on the difference of input voltage. The latter holds due to noise; if the absolute level is too low, the voltage variation may be undetectable. Thus, the propagation distance may be a limiting factor of this method if very long.