# Model-Guided Manufacturing of Transducer Arrays Based on Single-Fibre Piezocomposites
## 4 Discussion  
The proposed assembly process allows reliable and time efficient manufacturing of our new TAS generation. The resulting transducers show a series resonance frequency \(f_{\mathrm{s}}\) at 1.94 \(\pm\) 0.05 MHz. The low standard deviation suggests also low deviations in acoustic performance, which is important for our imaging approach.  
After the assembly, the transducer capacitance \(C_{\mathrm{p}}\) more than doubled. This is mainly caused by an additional supply line capacitance coming from the PCB. However, the increase in \(C_{\mathrm{p}}\) from the matching layer to the final state cannot directly be explained by an additional electrical capacitance, as no conductor is added. Due to the electromechanical coupling of the PZT fibre, this can be caused by electrical or mechanical effects. In the electrical domain, a change in permittivity caused by the tungsten powder may be an explanation. In the mechanical domain, a change in stiffness also affects the capacitance, but mostly for frequencies close to \(f_{\mathrm{s}}\).  
With the extended KLM model, the change in EMI caused by attaching the PCB can be predicted. In addition, the effect of the backing on the transducer damping is covered accurately. Simulated effects induced by the matching layers do not match the measured responses. Especially the predicted additional resonance caused by the thickness of the single TMM4 matching layer is not present in the measured data. More dimensional modelling approaches seem necessary to investigate this difference. However, due to the low complexity of the proposed model, parameter evaluation can be done very quickly and easily. The obtained results can then be used as a starting point for more computational expensive modelling approaches such as finite element methods.  
The transducer condition during production can be monitored most effectively by measuring the phase angle \(\varphi_{\mathrm{t}}\) at thickness resonance. Ninety-four per cent of all backing defects should be detectable by setting the pass/fail classification criteria to \(-62.6^{\circ}\). For detecting defects in attaching the matching layer, a sensitivity of less than 50% can be achieved. To improve this, more EMI properties must be taken into account. Using K-means or hierarchical clustering methods [29], higher specificity should be achievable. Future work will therefore focus on finding the most sensitive property combination for ensuring a reliable quality control procedure.  
Conceptualization, M.A., M.Z. and N.V.R.; methodology, M.A. and M.Z.; validation, M.A.; resources, B.L.; writing--original draft, M.A.; and writing--review and editing, M.Z. and N.V.R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors thank [PERSON] from Fraunhofer IKTS for his valuable support in evaluating the PZT fibre disc performance. We acknowledge support by the KIT-Publication Fund of the Karlsruhe Institute of Technology.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} EMI & Electro-mechanical impedance \\ KLM & Transducer network model developed by [PERSON], [PERSON] and [PERSON] \\ PZT fibre disc & Single-fibre piezocomposite disc array \\ PCB & Printed circuit board \\ PZT & Lead zirconium titanate \\ ROC & Receiver operating characteristic curve \\ TAS & Transducer array system \\ TMM4 & Thermoset microwave material, Rogers Corp. \\ USCT & Ultrasound computer tomography \\ \end{tabular}