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Investigation of Capacitively Coupled Ultrasonic Transducer System for Nondestructive Evaluation Cheng Huan Zhong, Paul D. Wilcox, and Anthony J. Croxford Abstract—Capacitive coupling offers a simple solution to wirelessly probe ultrasonic transducers. This paper investigates the theory, feasibility, and optimization of such a capacitively coupled transducer system (CCTS) in the context of nondestructive evaluation (NDE) applications. The noncontact interface relies on an electric field formed between four metal plates—two plates are physically connected to the electrodes of a transducer, the other two are in a separate probing unit connected to the transmit/receive channel of the instrumentation. The complete system is modeled as an electric network with the measured impedance of a bonded piezoelectric ceramic disc representing a transducer attached to an arbitrary solid substrate. A transmission line model is developed which is a function of the physical parameters of the capacitively coupled system, such as the permittivity of the material between the plates, the size of the metal plates, and their relative positions. This model provides immediate prediction of electric input impedance, pulse–echo response, and the effect of plate misalignment. The model has been validated experimentally and has enabled optimization of the various parameters. It is shown that placing a tuning inductor and series resistor on the transmitting side of the circuit can significantly improve the system performance in terms of the signal-to-crosstalk ratio. Practically, bulk-wave CCTSs have been built and demonstrated for underwater and through-composite testing. It has been found that electrical conduction in the media between the plates limits their applications.
I. Introduction
U
ltrasonic waves are widely used for nondestructive evaluation [1], [2] and structural health monitoring (SHM) [3]–[5]. Permanently attached sensors offer the possibility for online monitoring of a structure, but achieving robust connectivity to sensors is a major challenge. One possibility is to use direct electrical connections via wires to each sensor. A widely-researched alternative is to use wireless RF protocols (e.g., Wi-Fi or ZigBee) for communication [6], but these require sensors to have power storage and processing capability. Both of these approaches result in extra weight and complexity. An inductively coupled transducer system (ICTS) was first introduced by Greve and colleagues [7], [8], and further investigated by Zhong et al. [9]. The advantage of such a passive wireless transducer system over conventional wireless SHM sensor networks [10], [11] is the ability to transmit power Manuscript received June 4, 2013; accepted September 10, 2013. The authors are with the Department of Mechanical Engineering, University of Bristol, Bristol, UK (e-mail: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2013.2857
0885–3010/$25.00
and data through electromagnetic induction without the need for any power source or storage at the sensor. However, because of the formation of eddy currents on a metal surface near the transmitting coil, the ICTS works inefficiently if the coil is placed directly on the surface of a metallic structure. Similarly to other inductively coupled systems, the received signal from the ICTS is susceptible to electromagnetic interference (EMI) from other circuits, particularly when the source is close to the ICTS [12]. A capacitively coupled transducer system (CCTS), on the other hand, offers an alternative, employing the electric field rather than magnetic field to achieve wireless coupling to ultrasonic transducers. This means that metal components become less of a concern [13]. Because the electric field is constrained between metal plates, CCTSs also have the ability to reduce EMI [14]. A typical CCTS is shown in Fig. 1, consisting of four parallel conductive plates, two of which (denoted transducer plates) are physically connected to the electrodes of the transducer, whereas the other two (denoted probe plates) are in a separate probing unit, where they are connected to the output/input channel of the measuring instrumentation. Consequently, two capacitors (C1 and C2) are formed, one between each pair of plates. Both the theory and application of a capacitively coupled piezoelectric transducer are investigated in this paper. The development of the CCTS model and calculation of electrical elements within the model are stated in a theoretical outline (Section II). The experimental set-up and model validation are presented in Section III. Section IV investigates the optimization of CCTSs in terms of signal-to-crosstalk ratio. Finally, the application and limitations of CCTSs are discussed in Section V, followed by a short conclusion. II. Theoretical Outline Capacitive technology has been successfully developed for wireless power transfer [15], where the system is optimized to maximize the power transferred. This is in contrast to the work presented here, which is to design a CCTS that has the same performance as a directly connected (i.e., wired) transducer, which must itself have adequate performance for a given inspection. This condition does not necessary result in the absolute peak amplitude. Therefore, it is necessary to have a robust model that
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ary element method (BEM) developed by Brevia [18] and Nishiyama and Nakamura [19] is used to calculate the capacitance between plates. B. Equivalent Electrical Network
Fig. 1. Schematic presentation of capacitively coupled transducer system (CCTS).
can predict how the CCTS behaves with different system parameters and at different frequencies. The development of a transmission line model parameterized by the physical properties of the metal plates and the measured impedance of a bonded piezoelectric transducer is described. The measured transducer impedance is used in the model to separate the capacitive coupling optimization from the transducer and ultrasonic inspection optimization. The latter can be achieved with a physically wired transducer. The developed model can be used for predicting the effect of changing mechanical parameters such as the geometry and relative position of plates, as well as electrical parameters such as inductance and resistance on both the timeand frequency-domain performance of a CCTS operating in pulse–echo mode.
Ideally, the probe plates are perfectly aligned with the transducer plates, and two capacitors are formed between the plates as shown in Fig. 2(a). However, plate misalignment is inevitable for the capacitively coupled system, and can cause a significant drop in signal. Thus, it is necessary to understand the effect of the plate misalignment on the system performance. A typical misalignment in which the transducer plates stay within the area of the probe plates is shown in Fig. 2(b), where α and β represent the percentage of coupling between positive probe plate, Ptr, and positive transducer plate, Ppz, and negative probe plate, Ntr, and negative transducer plate, Npz, respectively [20]. For the CCTS application, the gap distance between the two probe plates is considerably smaller than the plate size. Therefore, in this paper, it is assumed that the actual coupled area (to both probe plates) is equal to the total area of each transducer plate. It is worth noting that C1 and C2, as shown in Fig. 2, are calculated by using the aforementioned BEM with coupling area corresponding to the size of the transducer plates. In this paper, the diamond circuit shown in Fig. 3 is employed to model the capacitive coupling interface and account for misalignment between plates as shown in Fig. 2(b). This can be mathematically described by the 3 × 3 impedance matrix given by
A. Capacitance Calculations Because the wireless interface of CCTSs is totally reliant on capacitive coupling, it is important to precisely calculate the capacitance between the plates. For the case in which the electric charge density on the plates is uniform and the fringing fields at the edges can be neglected, the capacitance C0 between two parallel plates can be approximated as [16]
C0 =
where the capacitive impedances Zci and Z c′i are defined as ′ = Z αc1 + αR s1, Z c1 = Z c1 + R s1, Z c1
Z c′′1 = Z (1−α)c1 + (1 − α)R s1
(3) ′ = Z βc2 + βR s2, Z c2 = Z c2 + R s2, Z c2 Z c′′2 = Z (1−β)c2 + (1 − β)R s2.
εS , (1) d
where ε is the dielectric constant, S is the coupling area, and d is the separation of the two plates. Eq. (1) is valid when the plate separation is much smaller than the plate width. As the separation becomes bigger, edge effects become significant, and the equation does not provide accurate results [17]. In practical CCTS applications, the plate separation can be large, particularly when used in a high permittivity environment such as water. Thus, more detailed quantitative analysis for the capacitance is required, and in this paper the bound-
Z ′ + Z ′′ ′ ′′ I c1 0 −Z c1 c1 c1 V c ′′ V = ′′ + Z c2 ′ ′ 0 Z c2 Z c2 I c2 , (2) c 0 ′ ′′ Z c1 −Z c2 Z pz + Z L pz I pz
Rs1 and Rs2 are the equivalent series resistances resulting from the loss tangent of the dielectric material between the probe and transducer plates, which can be calculated by
R si =
tan δ , (4) ωC i
where tanδ and Ci are the loss tangent of the dielectric materials and the capacitance between the plates, and ω is operating angular frequency of the system. It is worth noting that when Rsi is small, Vpz can be approximated as
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Fig. 2. (a) Perfect alignment between plates. (b) Typical misalignment between plates. (c) Misalignment between plates when α and β are equal to 0.5. The gap between the two probe plates is assumed negligible.
V pz ≈
Z c1
V c(α + β − 1) (Z + Z L pz ). (5) + Z c2 + Z pz + Z L pz pz
By including the resistance of the input channel, Rin, the impedance of output channel, Zout, of the measuring instrument, and the measured impedance of the piezoelectric transducer into the diamond circuit, the complete equivalent circuit of the capacitively coupled transducer system is developed, as shown in Fig. 3. Additional electrical elements can be added to the circuit to tailor the
system response to that required for ultrasonic measurements. For example, additional series tuning inductors, Lin, Ltr, and Lpz, can be fitted to the probe and transducer sides to compensate for the equivalent coupling capacitance and produce good performance at the desired ultrasonic frequency. A series resistor, Rs, can be integrated into the transmitting side as an electrical damper, as shown in Fig. 3. The objective of this work is to design a CCTS that has the same performance as a directly connected (i.e., wired) transducer, which must itself have adequate performance
Fig. 3. The equivalent electrical network of the complete capacitively coupled transducer system.
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for a given inspection. Because this is a linear system, the transducer and capacitive coupling interface can be optimized individually. This is also the reason why the measured impedance, Zpz, of a bonded transducer which has already been optimized for wired systems is used in the model. This, in turn, allows a conventional well-understood linear approach to be adopted for the system analysis. By using standard linear circuit analysis, the ratio between Vout and Vin, the pulse–echo response of the capacitively coupled transducer system, is calculated from
V out Z Z2 Z out Z 2 = out = , (6) V in Z IN Z sys + Z out Z 2
where ZIN = Vin/Iin is the input impedance of the system, and Zsys = Rin + Rs + Z L in, the impedance directly across the capacitively coupled transducer, Z2, is equal to Z L tr + ′ + I c2 ′′ )), where I c1 ′ and I c2 ′′ are calculated from (2). (V c/(I c1
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The capacitive impedance, ZC = ( jωC)−1, is inversely proportional to the operating frequency. Because the working frequency of guided waves is typically lower than that of bulk waves, to get similar signal strengths for both systems, bigger electrode plates were built for the guided-wave system. Here, two 100 × 123 × 2 mm and two 100 × 300 × 2 mm aluminum plates were used for the transducer and probe plates for the bulk-wave system and four 300 × 300 × 2 mm aluminum plates were used for the capacitive elements in the guided-wave system. For all verification tests, a 1-mm-thick polypropylene insulation layer with relative permittivity, εr = 1.5, is placed between the probe and transducer plates. Various plate misalignment arrangements, as shown in Fig. 2(b), were tested to validate the misalignment model developed in Section II-B. This was done exclusively with the guided-wave system, because the testing of bulk-wave system is sufficient to validate the misalignment model. B. System Response Verification
III. Experimental Verification of the Model A. Samples and Setup In parallel with the development of the system model, various experiments were performed to provide measurements for validation. Various arrangements were tested for both input impedance and pulse–echo response, as shown in Fig. 4, using an impedance analyzer (Cypher C60, Cypher Instrumentations Ltd., London, UK) and a computer-controlled measuring instrument (Handyscope HS3, TiePie Engineering, Sneek, The Netherlands) with output resistance Rin = 50 Ω and an input impedance, Zout, which consists of an input resistance Rout = 1 MΩ in parallel with a parasitic capacitance of Cout = 30 pF. Cyanoacrylate adhesive was used to attach piezoelectric discs (16 mm diameter, 2 mm thickness, 20 mm diameter, 1 mm thickness; Nolic Group, Kvistgaard, Denmark) to a 25-mm-thick aluminum block and a 1500 × 1000 × 3 mm aluminum plate for bulk wave and guided wave testing, respectively.
Fig. 4. Input impedance measurement (dashed lines) and pulse–echo response measurement (solid lines) setup.
Fig. 5 shows the measured system impedances, ZIN, and system outputs of the capacitively coupled transducers described in Section III-A with the theoretical predictions for both bulk wave and guided wave applications in the perfectly coupled and aligned case. Figs. 5(a) and 5(b) show that the system input impedance, ZIN, as shown in (6), fits the measured results well, with less than 3% variation between simulation and measurement of input impedances found for both systems. The reflected impedance of the coupled ultrasonic transducer at its resonant frequency is manifested as ripples in the impedance at approximately 1 MHz and 160 kHz (circled). They are correctly predicted by the model for the bulk wave and guided-wave systems. The measurement and simulation of bulk-wave system response with a 6-cycle, 1.1-MHz Gaussian windowed tone burst input, and guided-wave system response with a 5-cycle, 165-kHz Gaussian windowed tone burst input are illustrated in Figs. 5(c) and 5(d) and Figs. 5(e) and 5(f), respectively. It can be seen that the prediction obtained by using (6) and measurements are in good agreement, with approximately 5% difference in amplitude between analytical simulation and measurement on the first echo of both systems. This suggests that the model is accurate enough to be employed to optimize the capacitively coupled transducer system response. The simulated and measured bulk-wave system responses with different degrees of plate misalignment (α = 0.9, β = 0.9; α = 0.7, β = 0.7; α = 0.5, β = 0.5) are shown in Fig. 6. Fig. 6 shows that the system response with different degrees of plate lateral misalignment simulated by using (6) and (2) and their corresponding measurements are in good agreement. The amplitude of the back wall echo in the bulk-wave system decreases as the coupling ratio goes from 1 to 0.5. i.e., from perfectly aligned (α = 1, β = 1) to the situation in which both transducer plates are evenly
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Fig. 5. Measured and simulated system impedances of (a) bulk-wave and (b) guided-wave systems. Measured and simulated outputs of (c and d) bulk-wave and (e and f) guided-wave systems.
Fig. 6. Measured and predicted bulk-wave system response with (a and b) α = 0.9, β = 0.9, (c and d) α = 0.7, β = 0.7, and (e and f) α = 0.5, β = 0.5 plate misalignment, respectively.
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coupled with positive and negative electrodes of the probe plates (α = 0.5, β = 0.5), as shown in Fig. 2(c). Fig. 7 shows simulated and measured bulk-wave system responses with Lpz, Ltr, and Lout set individually to 0.1 mH in turn. It can be seen from Fig. 7 that the simulated and measured system responses with an inductor at different positions in the circuit are in excellent agreement. By comparing Fig. 7(a) to Fig. 5(c), it can be seen that by adding an inductor to the circuit, the first echo signal amplitude is increased from 5.139 × 10−4 to 13.22 × 10−4 (normalized to maximum value of crosstalk), nearly a factor of 3 increase. However, Figs. 7(e) and 7(f) show that serious signal ring down is induced by including a badly chosen inductor in the circuit. This is due to the resonant response of the system. Again, it is worth noting that the work presented here is to design a CCTS which has the same performance as a directly connected (i.e., wired) transducer to ensure good temporal resolution of signal, which is not necessarily the same as the resonant response most conventional capacitive power transfer systems are designed for. IV. System Optimization Having verified its performance experimentally, the model is used to investigate the effect on the system response of varying values of the tuning inductors, Lin, Ltr, and Lpz, as shown in Fig. 3 [21]. The same approach can be employed to optimize both guided and bulk systems, although only the latter system optimization process is demonstrated here. From Fig. 7, it can been seen that crosstalk exists in the received signal; for a wired pulse–
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echo system, the crosstalk only happens at times between −0.5δ to 0.5δ, where δ is the duration of the input signal and can be calculated from
δ=
N , (7) fc
where N and fc are the number of cycles and center frequency of the tone burst input signal, respectively. However, if the system resonates, a significant signal ring down is induced after 0.5δ, as shown in Figs. 7(e) and 7(f). This limits the closest defect that can be detected by a single transducer. In addition, the amplitude of the back wall echo indicates the performance of the capacitive coupling interface. Therefore, the signal-to-crosstalk ratio (SXR), defined as
H (V (t 1)) SXR = 20 log 10 , (8) δ 1 0.5δ ∫0.5δ H (V (t)) dt
is used to indicate the performance of the CCTS. In this experiment, H and t1 are, respectively, the Hilbert transform and the arrival time of a back wall echo in the bulk wave test. From Fig. 3, it can be shown that in the perfect alignment case (i.e., α = 1, β = 1, Z c′′2 = Z c′′1 = ∞ or α = 0, β = 0, Z c′2 = Z c′1 = ∞), Z2 = Z C 1 + Z C 2 + Zpz + Z L pz + Z L tr. Therefore, Lpz and Ltr have the same effect on the system performance when the coupling plates are perfectly aligned. Using the bulk-wave system described and validated in Section III, the effects of changes to the inductance Lin, Ltr, and Lpz on SXR are shown in Fig. 8.
Fig. 7. Measured and simulated system response with (a and b) Lpz = 0.1 mH , (c and d) Ltr = 0.1 mH , (e and f) Lout = 0.1 mH.
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Fig. 8. Magnitude of signal-to-crosstalk ratio (SXR) with respect to (a) Ltr plus Lpz and (b) Lin and Ltr. Black dashed line in (a) and green plane in (b) refer to the SXR of a capacitively coupled transducer system (CCTS) without inductors; the black dash-dotted line in (a) and yellow plane in (b) refer to the SXR of a wired system.
The overall effects of Lpz and Ltr on the system performance in terms of SXR are plotted in Fig. 8(a), which shows SXR is increased by 9.4 dB compared with the inductor-free CCTS, when the total inductance of Lpz and Ltr is equal to 0.115 mH. Although Lpz and Ltr have the same effect on the system performance, changes to Ltr are preferred because it is on the user side, which can be easily accessed. Because Lin is on the transmitting side, as shown in Fig. 3, the capacitive impedances of the complete circuit made up of contributions from both the coupling interface and Cout of output impedance Zout can be compensated. Thus, as shown in Fig. 8(b), further SXR improvement of as much as 17.6 dB compared with the SXR of the inductor-free CCTS can be achieved by integrating a 0.06-mH tuning inductor Lin on the transmitting side. Experimentally, the bulk-wave system responses of a directly wired transducer and CCTS with a 0.054-mH tuning inductor, Lin, are both measured, with the results shown in Fig. 9. The SXR of the wired system and CCTS with a 0.054-mH tuning inductor, Lin, calculated by (8) are 20.4 dB and 17.8 dB, respectively, which shows that the performance of tuned CCTS very close to a directly connected (i.e., wired) transducer, particularly in terms of SXR. Note that according to Fig. 8(b), a slight further SXR increase can be achieved if the inductance of Lin is increased to 0.06 mH, but the SXR of this optimized system is still 1.5 dB lower than a directly wired system. The plate misalignment tolerance test was performed for both an inductor-free system and a system with Lin = 0.06 mH. The experimental results are presented in Fig. 10, from which it can be seen that the overall system SXR is increased by 17.6 dB by setting Lin = 0.06 mH. In other words, for a given SXR, the lateral misalignment tolerance is greatly improved. Note that when Zin, Ltr, Lpz, and Zpz
are small, the crosstalk is independent of the values of α and β, and the amplitude of back wall is a function of α + β. Consequently, in that situation, the SXR is a function of α + β. Although SXR and misalignment tolerance can be improved by placing inductors in the circuit, it can be seen from Fig. 8 that there is only a small region above the green plane (SXR of CCTS without inductors), which means the design range is quite limited and if incorrect values are chosen, significant reductions in performance can result. Also, because most inductors are of fixed value, achieving the optimization point (peak) is a challenge. Thus, to expand the design range, the effect of including a series electrical damper, Rs, (shown in Fig. 3) on the SXR was also investigated, and the results are shown in Fig. 11. From Fig. 11(a), it can be seen that a sufficiently high Rs can be chosen such that the SXR is independent of the value of inductance, Lin. This is referred to a stable design range. However, Fig. 11(b) shows that as the resistance of Rs is increased, the magnitude of the back wall signal decreases. To maximize the SXR, but not at the expense of absolute signal amplitude, an inductor, Lin, close to the optimized value should be selected first, then the series resistor, Rs, adjusted to achieve the system response with satisfactory SXR and absolute signal amplitude.
V. System Performance Analysis Because the strength of the electric field between the coupling plates is highly dependent on the coupling media, the performance of a CCTS varies in different working environments. The bulk-wave CCTS specified in Section
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Fig. 9. Bulk-wave system responses of wired transducer and capacitively coupled transducer system (CCTS) with 0.054 mH Lin: (a) normalized to maximum amplitude of back wall echo and (b) normalized to maximum amplitude of crosstalk.
III-A is used here to investigate the feasibility of CCTS for different applications. It is worth noting that narrowband chirp excitation [22] was used to improve the signal–to– random-noise level in all cases. The narrowband chirp is created as the product in the frequency domain of the desired tone burst spectrum magnitude with the discrete Fourier transform of a broadband chirp, given by [22]
πBt 2 , (9) S c(t) = w(t) sin 2π f ot + T
where fo is the starting frequency, T is the duration of the chirp, and B is the chirp bandwidth. The function w(t) is a unit amplitude rectangular window starting at t = 0 and having duration of T. Consequently, the narrowband chirp signal effectively distributes the bandwidth of the tone burst over a longer time window. Suppose the length of the narrowband chirp is W times longer than the length of the desired tone burst, then the SNR is increased by a factor of W , which is the same degree of improvement expected if W signals are averaged.
Fig. 10. Magnitude of signal-to-crosstalk ratio (SXR) of (a) inductor-free capacitively coupled transducer system (CCTS) and (b) the system with 0.06-mH inductor Lin in the transmitting side with respect to α and β. The green plane refers to the SXR of perfectly-coupled, perfectly-aligned, inductor-free CCTS.
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Fig. 11. (a) Magnitude of signal-to-crosstalk ratio (SXR) with respect to Lin and Rs. (b) Magnitude of Vout/Vin with respect to Lin and Rs.
Because magnetic fields are heavily attenuated by conductive material such as carbon fiber, inductively coupled transducer systems work inefficiently through carbon-fiber composite structures. The feasibility of using the CCTS on a carbon-fiber composite was tested. Fig. 12 shows the CCTS performance when different orientations of singleply uni-direction carbon-fiber composite are inserted between the probe and transducer plates. From Fig. 12, it can be seen that the system performance is highly sensitive to fiber orientation. In the case in which the fibers span the plates, the system fails. This is due to the carbon fiber creating a conductive bridge within the medium between the two capacitors, effectively short-circuiting the transducer port, which can be treat-
ed as a low-value resistor directly across the transducer port. Consequently, no signal is transmitted to or from the transducer. The same test has been performed with glass fiber and, as expected, the signal is independent of the fiber orientation, because the glass fibers are nonconductive. Eq. (1) shows that the capacitance is proportional to the dielectric constant, ε, which means a wider plate separation can be achieved when the CCTS operates in an environment with high dielectric constant. Fig. 13 shows the comparison between CCTS performance when 70 mm of pure water and 1 mm of polypropylene insulation layer are used as the media between the plates, with other variables staying the same.
Fig. 12. (a) Carbon fibers spanning the plates, (b) carbon fibers not spanning the plates, and (c) capacitively coupled transducer system (CCTS) performance in cases (a) and (b).
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Fig. 13. Capacitively coupled transducer system (CCTS) performance in cases with (a) 1 mm polypropylene separation and (b) 70 mm pure water separation.
It can be seen from Fig. 13 that even though the separation of the coupling plates under water is 70 times the thickness of the polypropylene, a similar signal strength is maintained. This is because the permittivity of water is approximately 55 times that of polypropylene. The same test was also performed in salt water with salinity comparable to that of sea water. Because of the high conductivity of sea water and an electrical conduction between the positive and negative electrodes of plates, the system was found to be unsatisfactory in this scenario. VI. Conclusion This paper has investigated both the theory and feasibility of capacitively coupled piezoelectric sensors for nondestructive evaluation applications. A model based on linear circuit theory using the measured impedance of a bonded transducer has been presented. This model allows the simulation of various physical parameters such as geometry and relative position of plates, electrical elements such as inductors and resistors in the system, and optimization of the associated capacitive coupling. Although specifically developed for modeling ultrasonic inspection, the method is general and could be applied to any capacitively coupled system. The simulated results have been validated against experimental data and excellent agreement has been obtained. Using the model, a capacitively coupled transducer system can be designed for any piezoelectric transducer with known impedance and optimized in terms of the signal to crosstalk level. It has been found that placing a tuning inductor at the transmitting side of the capacitive coupled transducer system is a better option than at the transducer side, because this not only improves the signal-to-
crosstalk ratio but also increases the system misalignment tolerance. Additionally, a series resistor can be integrated into the transmitting side to increase design robustness, but a compromise between the signal strength and signalto-crosstalk ratio must be made. Practically, the study shows the robust performance of the developed capacitively coupled transducer, particularly when it is used in a high permittivity environment such as fresh water. Some limitations have also been found; for example, the current guide caused by placing conductive material across the positive and negative electrodes of coupling plates. Further developments will attempt to mitigate the effect of the current guide between plates and include direct modeling of the piezoelectric transducer to allow optimization of the complete system.
References [1] C. Holmes, B. W. Drinkwater, and P. D. Wilcox, “Post-processing of the full matrix of ultrasonic transmit-receive array data for nondestructive evaluation,” NDT Int., vol. 38, no. 8, pp. 701–711, 2005. [2] B. W. Drinkwater and P. D. Wilcox, “Ultrasonic arrays for nondestructive evaluation: A review,” NDT Int., vol. 39, no. 7, pp. 525– 541, 2006. [3] A. J. Croxford, P. D. Wilcox, B. W. Drinkwater, and G. Konstantinidis, “Strategies for guided-wave structural health monitoring,” Proc. R. Soc. A, vol. 463, no. 2087, pp. 2961–2981, 2007. [4] M. J. S. Lowe, D. N. Alleyne, and P. Cawley, “Defect detection in pipes using guided waves,” Ultrasonics, vol. 36, no. 1–5, pp. 147–154, 1998. [5] P. D. Wilcox, M. Evans, B. Pavlakovic, D. Alleyne, K. Vine, P. Cawley, and M. J. S. Lowe, “Guided wave testing of rail,” Insight– NDT Cond. Monit., vol. 45, no. 6, pp. 413–420, 2003. [6] S. Jang, H. Jo, S. Cho, K. Mechitov, J. A. Rice, S. H. Sim, H. J. Jung, C. B. Yun, J. Spencer, F. Billie, and G. Agha, “Structural health monitoring of a cable-stayed bridge using smart sensor technology: Deployment and evaluation,” Smart Struct. Syst., vol. 6, no. 5, pp. 439–459, 2010.
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[7] D. W. Greve, H. Sohn, C. P. Yue, and I. J. Oppenheim, “An inductively coupled Lamb wave transducer,” IEEE Sensors J., vol. 7, no. 1–2, pp. 295–301, 2007. [8] P. Zheng, D. W. Greve, and I. J. Oppenheim, “Crack detection with wireless inductively-coupled transducers,” in Proc. SPIE, 2008, vol. 6932, art. no. 69321H. [9] C. H. Zhong, P. D. Wilcox, and A. J. Croxford, “Investigation of inductively coupled ultrasonic transducer system for NDE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 60, no. 6, pp. 1115– 1125, Jun. 2013. [10] J. P. Lynch, “An overview of wireless structural health monitoring for civil structures,” Philos. Trans. R. Soc. A, vol. 365, no. 1851, pp. 345–372, 2007. [11] J. P. Lynch and K. J. Loh, “A summary review of wireless sensors and sensor networks for structure health monitoring,” Shock Vib. Dig., vol. 38, no. 2, pp. 91–128, 2006. [12] C. H. Zhong, P. D. Wilcox, and A. J. Croxford, “Inductively coupled transducer system for damage detection in composites,” in Proc. SPIE, 2012, vol. 8348, art. no. 83480H. [13] R. C. Jeff and L. J. Tao, “A capacitively coupled battery charging system,” Master’s thesis, Dept. of Electrical and Computer Engineering, the Univ. of Auckland, Auckland, New Zealand., 2006. [14] E. Culurciello and A. G. Andreou, “Capacitive inter-chip data and power transfer for 3-D VLSI,” IEEE Trans. Circuits Syst., II Exp. Briefs, vol. 53, no. 12, pp. 1348–1352, 2006. [15] M. Kline, I. Izyumin, B. Boser, and S. Sanders, “Capacitive power transfer for contactless charging,” in 26th Annu. IEEE Applied Power Electronics Conf. Expo., 2011, pp. 1398–1404. [16] W. H. Hayt and J. A. Buck, Engineering Electromagnetics. New York, NY: McGraw-Hill, 2011. [17] H. Nishiyama and M. Nakamura, “Capacitance of a strip capacitor,” IEEE Trans. Compon. Hybrids, Manuf. Technol., vol. 13, no. 2, pp. 417–423, 1990. [18] C. A. Brevia, The Boundary Element for Engineers. London, UK: Pentech, 1978. [19] H. Nishiyama and M. Nakamura, “Form and capacitance of parallelplate capacitors,” IEEE Trans. Compon. Packag. Manuf. Tech., vol. 17, no. 3, pp. 477–484, 1994. [20] C. Liu, A. P. Hu, N.-K. C. Nair, and G. A. Covic, “2-D alignment analysis of capacitively coupled contactless power transfer system,” in IEEE Energy Conversion Congress Expo., 2010, pp. 652–657. [21] C. Liu, A. P. Hu, and M. Budhia, “A generalized coupling model for capacitive power transfer systems,” in 36th Annu. Conf. IEEE Industrial Electronics Society, 2010, pp. 274–279. [22] J. E. Michaels, S. J Lee, A. J Croxford, and P. D Wilcox, “Chirp excitation of ultrasonic guided waves,” Ultrasonics, vol. 53, no. 1, pp. 265–270, Jan. 2013.
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Cheng Huan Zhong was born in WenZhou, China, in 1987. He received a B.Eng. degree in mechanical engineering from the University of Bristol, Bristol, England, in 2010. Since 2011, he has been a Ph.D. student in the Ultrasonic and NDT group at the University of Bristol, where he has worked on the development of passive wireless transducers for structural health monitoring. His current research interests include structural health monitoring, passive wireless transducers, and smart composites with embedded transducers.
Paul D. Wilcox was born in Nottingham, England, in 1971. He received an M.Eng. degree in engineering science from the University of Oxford, Oxford, England, in 1994 and a Ph.D. degree from Imperial College, London, England, in 1998. From 1998 to 2002, he was a Research Associate in the nondestructive testing (NDT) research group at Imperial College, where he worked on the development of guided-wave array transducers for large area inspection. From 2000 to 2002, he also acted as a Consultant to Guided Ultrasonics Ltd., Nottingham, England, a manufacturer of guided wave test equipment. Since 2002, Prof. Wilcox has been at the University of Bristol, Bristol, England, where he is a Professor in Dynamics. His current research interests include array transducers, ultrasonic particle manipulation, long-range guided wave inspection, structural health monitoring, elastodynamic scattering, and signal processing.
Anthony J. Croxford was born in Hatfield, England, in 1979. He received an M.Eng. degree in mechanical engineering and a Ph.D. degree from the University of Bristol, Bristol, England, in 2005. From 2005 to 2007, he was a Research Associate in the nondestructive testing research group at the University of Bristol, where he worked on the development of guided-wave structural health monitoring for permanently attached sensing systems. Since 2007, Dr. Croxford has been a Lecturer in the Department of Mechanical Engineering at the University of Bristol. His current research interests include structural health monitoring, nonlinear ultrasonic techniques, and fluidized bed dynamics.
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Investigation of Capacitively Coupled Ultrasonic Transducer System for Nondestructive Evaluation Cheng Huan Zhong, Paul D. Wilcox, and Anthony J. Croxford Abstract—Capacitive coupling offers a simple solution to wirelessly probe ultrasonic transducers. This paper investigates the theory, feasibility, and optimization of such a capacitively coupled transducer system (CCTS) in the context of nondestructive evaluation (NDE) applications. The noncontact interface relies on an electric field formed between four metal plates—two plates are physically connected to the electrodes of a transducer, the other two are in a separate probing unit connected to the transmit/receive channel of the instrumentation. The complete system is modeled as an electric network with the measured impedance of a bonded piezoelectric ceramic disc representing a transducer attached to an arbitrary solid substrate. A transmission line model is developed which is a function of the physical parameters of the capacitively coupled system, such as the permittivity of the material between the plates, the size of the metal plates, and their relative positions. This model provides immediate prediction of electric input impedance, pulse–echo response, and the effect of plate misalignment. The model has been validated experimentally and has enabled optimization of the various parameters. It is shown that placing a tuning inductor and series resistor on the transmitting side of the circuit can significantly improve the system performance in terms of the signal-to-crosstalk ratio. Practically, bulk-wave CCTSs have been built and demonstrated for underwater and through-composite testing. It has been found that electrical conduction in the media between the plates limits their applications.
I. Introduction
U
ltrasonic waves are widely used for nondestructive evaluation [1], [2] and structural health monitoring (SHM) [3]–[5]. Permanently attached sensors offer the possibility for online monitoring of a structure, but achieving robust connectivity to sensors is a major challenge. One possibility is to use direct electrical connections via wires to each sensor. A widely-researched alternative is to use wireless RF protocols (e.g., Wi-Fi or ZigBee) for communication [6], but these require sensors to have power storage and processing capability. Both of these approaches result in extra weight and complexity. An inductively coupled transducer system (ICTS) was first introduced by Greve and colleagues [7], [8], and further investigated by Zhong et al. [9]. The advantage of such a passive wireless transducer system over conventional wireless SHM sensor networks [10], [11] is the ability to transmit power Manuscript received June 4, 2013; accepted September 10, 2013. The authors are with the Department of Mechanical Engineering, University of Bristol, Bristol, UK (e-mail: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2013.2857
0885–3010/$25.00
and data through electromagnetic induction without the need for any power source or storage at the sensor. However, because of the formation of eddy currents on a metal surface near the transmitting coil, the ICTS works inefficiently if the coil is placed directly on the surface of a metallic structure. Similarly to other inductively coupled systems, the received signal from the ICTS is susceptible to electromagnetic interference (EMI) from other circuits, particularly when the source is close to the ICTS [12]. A capacitively coupled transducer system (CCTS), on the other hand, offers an alternative, employing the electric field rather than magnetic field to achieve wireless coupling to ultrasonic transducers. This means that metal components become less of a concern [13]. Because the electric field is constrained between metal plates, CCTSs also have the ability to reduce EMI [14]. A typical CCTS is shown in Fig. 1, consisting of four parallel conductive plates, two of which (denoted transducer plates) are physically connected to the electrodes of the transducer, whereas the other two (denoted probe plates) are in a separate probing unit, where they are connected to the output/input channel of the measuring instrumentation. Consequently, two capacitors (C1 and C2) are formed, one between each pair of plates. Both the theory and application of a capacitively coupled piezoelectric transducer are investigated in this paper. The development of the CCTS model and calculation of electrical elements within the model are stated in a theoretical outline (Section II). The experimental set-up and model validation are presented in Section III. Section IV investigates the optimization of CCTSs in terms of signal-to-crosstalk ratio. Finally, the application and limitations of CCTSs are discussed in Section V, followed by a short conclusion. II. Theoretical Outline Capacitive technology has been successfully developed for wireless power transfer [15], where the system is optimized to maximize the power transferred. This is in contrast to the work presented here, which is to design a CCTS that has the same performance as a directly connected (i.e., wired) transducer, which must itself have adequate performance for a given inspection. This condition does not necessary result in the absolute peak amplitude. Therefore, it is necessary to have a robust model that
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ary element method (BEM) developed by Brevia [18] and Nishiyama and Nakamura [19] is used to calculate the capacitance between plates. B. Equivalent Electrical Network
Fig. 1. Schematic presentation of capacitively coupled transducer system (CCTS).
can predict how the CCTS behaves with different system parameters and at different frequencies. The development of a transmission line model parameterized by the physical properties of the metal plates and the measured impedance of a bonded piezoelectric transducer is described. The measured transducer impedance is used in the model to separate the capacitive coupling optimization from the transducer and ultrasonic inspection optimization. The latter can be achieved with a physically wired transducer. The developed model can be used for predicting the effect of changing mechanical parameters such as the geometry and relative position of plates, as well as electrical parameters such as inductance and resistance on both the timeand frequency-domain performance of a CCTS operating in pulse–echo mode.
Ideally, the probe plates are perfectly aligned with the transducer plates, and two capacitors are formed between the plates as shown in Fig. 2(a). However, plate misalignment is inevitable for the capacitively coupled system, and can cause a significant drop in signal. Thus, it is necessary to understand the effect of the plate misalignment on the system performance. A typical misalignment in which the transducer plates stay within the area of the probe plates is shown in Fig. 2(b), where α and β represent the percentage of coupling between positive probe plate, Ptr, and positive transducer plate, Ppz, and negative probe plate, Ntr, and negative transducer plate, Npz, respectively [20]. For the CCTS application, the gap distance between the two probe plates is considerably smaller than the plate size. Therefore, in this paper, it is assumed that the actual coupled area (to both probe plates) is equal to the total area of each transducer plate. It is worth noting that C1 and C2, as shown in Fig. 2, are calculated by using the aforementioned BEM with coupling area corresponding to the size of the transducer plates. In this paper, the diamond circuit shown in Fig. 3 is employed to model the capacitive coupling interface and account for misalignment between plates as shown in Fig. 2(b). This can be mathematically described by the 3 × 3 impedance matrix given by
A. Capacitance Calculations Because the wireless interface of CCTSs is totally reliant on capacitive coupling, it is important to precisely calculate the capacitance between the plates. For the case in which the electric charge density on the plates is uniform and the fringing fields at the edges can be neglected, the capacitance C0 between two parallel plates can be approximated as [16]
C0 =
where the capacitive impedances Zci and Z c′i are defined as ′ = Z αc1 + αR s1, Z c1 = Z c1 + R s1, Z c1
Z c′′1 = Z (1−α)c1 + (1 − α)R s1
(3) ′ = Z βc2 + βR s2, Z c2 = Z c2 + R s2, Z c2 Z c′′2 = Z (1−β)c2 + (1 − β)R s2.
εS , (1) d
where ε is the dielectric constant, S is the coupling area, and d is the separation of the two plates. Eq. (1) is valid when the plate separation is much smaller than the plate width. As the separation becomes bigger, edge effects become significant, and the equation does not provide accurate results [17]. In practical CCTS applications, the plate separation can be large, particularly when used in a high permittivity environment such as water. Thus, more detailed quantitative analysis for the capacitance is required, and in this paper the bound-
Z ′ + Z ′′ ′ ′′ I c1 0 −Z c1 c1 c1 V c ′′ V = ′′ + Z c2 ′ ′ 0 Z c2 Z c2 I c2 , (2) c 0 ′ ′′ Z c1 −Z c2 Z pz + Z L pz I pz
Rs1 and Rs2 are the equivalent series resistances resulting from the loss tangent of the dielectric material between the probe and transducer plates, which can be calculated by
R si =
tan δ , (4) ωC i
where tanδ and Ci are the loss tangent of the dielectric materials and the capacitance between the plates, and ω is operating angular frequency of the system. It is worth noting that when Rsi is small, Vpz can be approximated as
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Fig. 2. (a) Perfect alignment between plates. (b) Typical misalignment between plates. (c) Misalignment between plates when α and β are equal to 0.5. The gap between the two probe plates is assumed negligible.
V pz ≈
Z c1
V c(α + β − 1) (Z + Z L pz ). (5) + Z c2 + Z pz + Z L pz pz
By including the resistance of the input channel, Rin, the impedance of output channel, Zout, of the measuring instrument, and the measured impedance of the piezoelectric transducer into the diamond circuit, the complete equivalent circuit of the capacitively coupled transducer system is developed, as shown in Fig. 3. Additional electrical elements can be added to the circuit to tailor the
system response to that required for ultrasonic measurements. For example, additional series tuning inductors, Lin, Ltr, and Lpz, can be fitted to the probe and transducer sides to compensate for the equivalent coupling capacitance and produce good performance at the desired ultrasonic frequency. A series resistor, Rs, can be integrated into the transmitting side as an electrical damper, as shown in Fig. 3. The objective of this work is to design a CCTS that has the same performance as a directly connected (i.e., wired) transducer, which must itself have adequate performance
Fig. 3. The equivalent electrical network of the complete capacitively coupled transducer system.
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for a given inspection. Because this is a linear system, the transducer and capacitive coupling interface can be optimized individually. This is also the reason why the measured impedance, Zpz, of a bonded transducer which has already been optimized for wired systems is used in the model. This, in turn, allows a conventional well-understood linear approach to be adopted for the system analysis. By using standard linear circuit analysis, the ratio between Vout and Vin, the pulse–echo response of the capacitively coupled transducer system, is calculated from
V out Z Z2 Z out Z 2 = out = , (6) V in Z IN Z sys + Z out Z 2
where ZIN = Vin/Iin is the input impedance of the system, and Zsys = Rin + Rs + Z L in, the impedance directly across the capacitively coupled transducer, Z2, is equal to Z L tr + ′ + I c2 ′′ )), where I c1 ′ and I c2 ′′ are calculated from (2). (V c/(I c1
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The capacitive impedance, ZC = ( jωC)−1, is inversely proportional to the operating frequency. Because the working frequency of guided waves is typically lower than that of bulk waves, to get similar signal strengths for both systems, bigger electrode plates were built for the guided-wave system. Here, two 100 × 123 × 2 mm and two 100 × 300 × 2 mm aluminum plates were used for the transducer and probe plates for the bulk-wave system and four 300 × 300 × 2 mm aluminum plates were used for the capacitive elements in the guided-wave system. For all verification tests, a 1-mm-thick polypropylene insulation layer with relative permittivity, εr = 1.5, is placed between the probe and transducer plates. Various plate misalignment arrangements, as shown in Fig. 2(b), were tested to validate the misalignment model developed in Section II-B. This was done exclusively with the guided-wave system, because the testing of bulk-wave system is sufficient to validate the misalignment model. B. System Response Verification
III. Experimental Verification of the Model A. Samples and Setup In parallel with the development of the system model, various experiments were performed to provide measurements for validation. Various arrangements were tested for both input impedance and pulse–echo response, as shown in Fig. 4, using an impedance analyzer (Cypher C60, Cypher Instrumentations Ltd., London, UK) and a computer-controlled measuring instrument (Handyscope HS3, TiePie Engineering, Sneek, The Netherlands) with output resistance Rin = 50 Ω and an input impedance, Zout, which consists of an input resistance Rout = 1 MΩ in parallel with a parasitic capacitance of Cout = 30 pF. Cyanoacrylate adhesive was used to attach piezoelectric discs (16 mm diameter, 2 mm thickness, 20 mm diameter, 1 mm thickness; Nolic Group, Kvistgaard, Denmark) to a 25-mm-thick aluminum block and a 1500 × 1000 × 3 mm aluminum plate for bulk wave and guided wave testing, respectively.
Fig. 4. Input impedance measurement (dashed lines) and pulse–echo response measurement (solid lines) setup.
Fig. 5 shows the measured system impedances, ZIN, and system outputs of the capacitively coupled transducers described in Section III-A with the theoretical predictions for both bulk wave and guided wave applications in the perfectly coupled and aligned case. Figs. 5(a) and 5(b) show that the system input impedance, ZIN, as shown in (6), fits the measured results well, with less than 3% variation between simulation and measurement of input impedances found for both systems. The reflected impedance of the coupled ultrasonic transducer at its resonant frequency is manifested as ripples in the impedance at approximately 1 MHz and 160 kHz (circled). They are correctly predicted by the model for the bulk wave and guided-wave systems. The measurement and simulation of bulk-wave system response with a 6-cycle, 1.1-MHz Gaussian windowed tone burst input, and guided-wave system response with a 5-cycle, 165-kHz Gaussian windowed tone burst input are illustrated in Figs. 5(c) and 5(d) and Figs. 5(e) and 5(f), respectively. It can be seen that the prediction obtained by using (6) and measurements are in good agreement, with approximately 5% difference in amplitude between analytical simulation and measurement on the first echo of both systems. This suggests that the model is accurate enough to be employed to optimize the capacitively coupled transducer system response. The simulated and measured bulk-wave system responses with different degrees of plate misalignment (α = 0.9, β = 0.9; α = 0.7, β = 0.7; α = 0.5, β = 0.5) are shown in Fig. 6. Fig. 6 shows that the system response with different degrees of plate lateral misalignment simulated by using (6) and (2) and their corresponding measurements are in good agreement. The amplitude of the back wall echo in the bulk-wave system decreases as the coupling ratio goes from 1 to 0.5. i.e., from perfectly aligned (α = 1, β = 1) to the situation in which both transducer plates are evenly
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Fig. 5. Measured and simulated system impedances of (a) bulk-wave and (b) guided-wave systems. Measured and simulated outputs of (c and d) bulk-wave and (e and f) guided-wave systems.
Fig. 6. Measured and predicted bulk-wave system response with (a and b) α = 0.9, β = 0.9, (c and d) α = 0.7, β = 0.7, and (e and f) α = 0.5, β = 0.5 plate misalignment, respectively.
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coupled with positive and negative electrodes of the probe plates (α = 0.5, β = 0.5), as shown in Fig. 2(c). Fig. 7 shows simulated and measured bulk-wave system responses with Lpz, Ltr, and Lout set individually to 0.1 mH in turn. It can be seen from Fig. 7 that the simulated and measured system responses with an inductor at different positions in the circuit are in excellent agreement. By comparing Fig. 7(a) to Fig. 5(c), it can be seen that by adding an inductor to the circuit, the first echo signal amplitude is increased from 5.139 × 10−4 to 13.22 × 10−4 (normalized to maximum value of crosstalk), nearly a factor of 3 increase. However, Figs. 7(e) and 7(f) show that serious signal ring down is induced by including a badly chosen inductor in the circuit. This is due to the resonant response of the system. Again, it is worth noting that the work presented here is to design a CCTS which has the same performance as a directly connected (i.e., wired) transducer to ensure good temporal resolution of signal, which is not necessarily the same as the resonant response most conventional capacitive power transfer systems are designed for. IV. System Optimization Having verified its performance experimentally, the model is used to investigate the effect on the system response of varying values of the tuning inductors, Lin, Ltr, and Lpz, as shown in Fig. 3 [21]. The same approach can be employed to optimize both guided and bulk systems, although only the latter system optimization process is demonstrated here. From Fig. 7, it can been seen that crosstalk exists in the received signal; for a wired pulse–
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echo system, the crosstalk only happens at times between −0.5δ to 0.5δ, where δ is the duration of the input signal and can be calculated from
δ=
N , (7) fc
where N and fc are the number of cycles and center frequency of the tone burst input signal, respectively. However, if the system resonates, a significant signal ring down is induced after 0.5δ, as shown in Figs. 7(e) and 7(f). This limits the closest defect that can be detected by a single transducer. In addition, the amplitude of the back wall echo indicates the performance of the capacitive coupling interface. Therefore, the signal-to-crosstalk ratio (SXR), defined as
H (V (t 1)) SXR = 20 log 10 , (8) δ 1 0.5δ ∫0.5δ H (V (t)) dt
is used to indicate the performance of the CCTS. In this experiment, H and t1 are, respectively, the Hilbert transform and the arrival time of a back wall echo in the bulk wave test. From Fig. 3, it can be shown that in the perfect alignment case (i.e., α = 1, β = 1, Z c′′2 = Z c′′1 = ∞ or α = 0, β = 0, Z c′2 = Z c′1 = ∞), Z2 = Z C 1 + Z C 2 + Zpz + Z L pz + Z L tr. Therefore, Lpz and Ltr have the same effect on the system performance when the coupling plates are perfectly aligned. Using the bulk-wave system described and validated in Section III, the effects of changes to the inductance Lin, Ltr, and Lpz on SXR are shown in Fig. 8.
Fig. 7. Measured and simulated system response with (a and b) Lpz = 0.1 mH , (c and d) Ltr = 0.1 mH , (e and f) Lout = 0.1 mH.
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Fig. 8. Magnitude of signal-to-crosstalk ratio (SXR) with respect to (a) Ltr plus Lpz and (b) Lin and Ltr. Black dashed line in (a) and green plane in (b) refer to the SXR of a capacitively coupled transducer system (CCTS) without inductors; the black dash-dotted line in (a) and yellow plane in (b) refer to the SXR of a wired system.
The overall effects of Lpz and Ltr on the system performance in terms of SXR are plotted in Fig. 8(a), which shows SXR is increased by 9.4 dB compared with the inductor-free CCTS, when the total inductance of Lpz and Ltr is equal to 0.115 mH. Although Lpz and Ltr have the same effect on the system performance, changes to Ltr are preferred because it is on the user side, which can be easily accessed. Because Lin is on the transmitting side, as shown in Fig. 3, the capacitive impedances of the complete circuit made up of contributions from both the coupling interface and Cout of output impedance Zout can be compensated. Thus, as shown in Fig. 8(b), further SXR improvement of as much as 17.6 dB compared with the SXR of the inductor-free CCTS can be achieved by integrating a 0.06-mH tuning inductor Lin on the transmitting side. Experimentally, the bulk-wave system responses of a directly wired transducer and CCTS with a 0.054-mH tuning inductor, Lin, are both measured, with the results shown in Fig. 9. The SXR of the wired system and CCTS with a 0.054-mH tuning inductor, Lin, calculated by (8) are 20.4 dB and 17.8 dB, respectively, which shows that the performance of tuned CCTS very close to a directly connected (i.e., wired) transducer, particularly in terms of SXR. Note that according to Fig. 8(b), a slight further SXR increase can be achieved if the inductance of Lin is increased to 0.06 mH, but the SXR of this optimized system is still 1.5 dB lower than a directly wired system. The plate misalignment tolerance test was performed for both an inductor-free system and a system with Lin = 0.06 mH. The experimental results are presented in Fig. 10, from which it can be seen that the overall system SXR is increased by 17.6 dB by setting Lin = 0.06 mH. In other words, for a given SXR, the lateral misalignment tolerance is greatly improved. Note that when Zin, Ltr, Lpz, and Zpz
are small, the crosstalk is independent of the values of α and β, and the amplitude of back wall is a function of α + β. Consequently, in that situation, the SXR is a function of α + β. Although SXR and misalignment tolerance can be improved by placing inductors in the circuit, it can be seen from Fig. 8 that there is only a small region above the green plane (SXR of CCTS without inductors), which means the design range is quite limited and if incorrect values are chosen, significant reductions in performance can result. Also, because most inductors are of fixed value, achieving the optimization point (peak) is a challenge. Thus, to expand the design range, the effect of including a series electrical damper, Rs, (shown in Fig. 3) on the SXR was also investigated, and the results are shown in Fig. 11. From Fig. 11(a), it can be seen that a sufficiently high Rs can be chosen such that the SXR is independent of the value of inductance, Lin. This is referred to a stable design range. However, Fig. 11(b) shows that as the resistance of Rs is increased, the magnitude of the back wall signal decreases. To maximize the SXR, but not at the expense of absolute signal amplitude, an inductor, Lin, close to the optimized value should be selected first, then the series resistor, Rs, adjusted to achieve the system response with satisfactory SXR and absolute signal amplitude.
V. System Performance Analysis Because the strength of the electric field between the coupling plates is highly dependent on the coupling media, the performance of a CCTS varies in different working environments. The bulk-wave CCTS specified in Section
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Fig. 9. Bulk-wave system responses of wired transducer and capacitively coupled transducer system (CCTS) with 0.054 mH Lin: (a) normalized to maximum amplitude of back wall echo and (b) normalized to maximum amplitude of crosstalk.
III-A is used here to investigate the feasibility of CCTS for different applications. It is worth noting that narrowband chirp excitation [22] was used to improve the signal–to– random-noise level in all cases. The narrowband chirp is created as the product in the frequency domain of the desired tone burst spectrum magnitude with the discrete Fourier transform of a broadband chirp, given by [22]
πBt 2 , (9) S c(t) = w(t) sin 2π f ot + T
where fo is the starting frequency, T is the duration of the chirp, and B is the chirp bandwidth. The function w(t) is a unit amplitude rectangular window starting at t = 0 and having duration of T. Consequently, the narrowband chirp signal effectively distributes the bandwidth of the tone burst over a longer time window. Suppose the length of the narrowband chirp is W times longer than the length of the desired tone burst, then the SNR is increased by a factor of W , which is the same degree of improvement expected if W signals are averaged.
Fig. 10. Magnitude of signal-to-crosstalk ratio (SXR) of (a) inductor-free capacitively coupled transducer system (CCTS) and (b) the system with 0.06-mH inductor Lin in the transmitting side with respect to α and β. The green plane refers to the SXR of perfectly-coupled, perfectly-aligned, inductor-free CCTS.
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Fig. 11. (a) Magnitude of signal-to-crosstalk ratio (SXR) with respect to Lin and Rs. (b) Magnitude of Vout/Vin with respect to Lin and Rs.
Because magnetic fields are heavily attenuated by conductive material such as carbon fiber, inductively coupled transducer systems work inefficiently through carbon-fiber composite structures. The feasibility of using the CCTS on a carbon-fiber composite was tested. Fig. 12 shows the CCTS performance when different orientations of singleply uni-direction carbon-fiber composite are inserted between the probe and transducer plates. From Fig. 12, it can be seen that the system performance is highly sensitive to fiber orientation. In the case in which the fibers span the plates, the system fails. This is due to the carbon fiber creating a conductive bridge within the medium between the two capacitors, effectively short-circuiting the transducer port, which can be treat-
ed as a low-value resistor directly across the transducer port. Consequently, no signal is transmitted to or from the transducer. The same test has been performed with glass fiber and, as expected, the signal is independent of the fiber orientation, because the glass fibers are nonconductive. Eq. (1) shows that the capacitance is proportional to the dielectric constant, ε, which means a wider plate separation can be achieved when the CCTS operates in an environment with high dielectric constant. Fig. 13 shows the comparison between CCTS performance when 70 mm of pure water and 1 mm of polypropylene insulation layer are used as the media between the plates, with other variables staying the same.
Fig. 12. (a) Carbon fibers spanning the plates, (b) carbon fibers not spanning the plates, and (c) capacitively coupled transducer system (CCTS) performance in cases (a) and (b).
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Fig. 13. Capacitively coupled transducer system (CCTS) performance in cases with (a) 1 mm polypropylene separation and (b) 70 mm pure water separation.
It can be seen from Fig. 13 that even though the separation of the coupling plates under water is 70 times the thickness of the polypropylene, a similar signal strength is maintained. This is because the permittivity of water is approximately 55 times that of polypropylene. The same test was also performed in salt water with salinity comparable to that of sea water. Because of the high conductivity of sea water and an electrical conduction between the positive and negative electrodes of plates, the system was found to be unsatisfactory in this scenario. VI. Conclusion This paper has investigated both the theory and feasibility of capacitively coupled piezoelectric sensors for nondestructive evaluation applications. A model based on linear circuit theory using the measured impedance of a bonded transducer has been presented. This model allows the simulation of various physical parameters such as geometry and relative position of plates, electrical elements such as inductors and resistors in the system, and optimization of the associated capacitive coupling. Although specifically developed for modeling ultrasonic inspection, the method is general and could be applied to any capacitively coupled system. The simulated results have been validated against experimental data and excellent agreement has been obtained. Using the model, a capacitively coupled transducer system can be designed for any piezoelectric transducer with known impedance and optimized in terms of the signal to crosstalk level. It has been found that placing a tuning inductor at the transmitting side of the capacitive coupled transducer system is a better option than at the transducer side, because this not only improves the signal-to-
crosstalk ratio but also increases the system misalignment tolerance. Additionally, a series resistor can be integrated into the transmitting side to increase design robustness, but a compromise between the signal strength and signalto-crosstalk ratio must be made. Practically, the study shows the robust performance of the developed capacitively coupled transducer, particularly when it is used in a high permittivity environment such as fresh water. Some limitations have also been found; for example, the current guide caused by placing conductive material across the positive and negative electrodes of coupling plates. Further developments will attempt to mitigate the effect of the current guide between plates and include direct modeling of the piezoelectric transducer to allow optimization of the complete system.
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Cheng Huan Zhong was born in WenZhou, China, in 1987. He received a B.Eng. degree in mechanical engineering from the University of Bristol, Bristol, England, in 2010. Since 2011, he has been a Ph.D. student in the Ultrasonic and NDT group at the University of Bristol, where he has worked on the development of passive wireless transducers for structural health monitoring. His current research interests include structural health monitoring, passive wireless transducers, and smart composites with embedded transducers.
Paul D. Wilcox was born in Nottingham, England, in 1971. He received an M.Eng. degree in engineering science from the University of Oxford, Oxford, England, in 1994 and a Ph.D. degree from Imperial College, London, England, in 1998. From 1998 to 2002, he was a Research Associate in the nondestructive testing (NDT) research group at Imperial College, where he worked on the development of guided-wave array transducers for large area inspection. From 2000 to 2002, he also acted as a Consultant to Guided Ultrasonics Ltd., Nottingham, England, a manufacturer of guided wave test equipment. Since 2002, Prof. Wilcox has been at the University of Bristol, Bristol, England, where he is a Professor in Dynamics. His current research interests include array transducers, ultrasonic particle manipulation, long-range guided wave inspection, structural health monitoring, elastodynamic scattering, and signal processing.
Anthony J. Croxford was born in Hatfield, England, in 1979. He received an M.Eng. degree in mechanical engineering and a Ph.D. degree from the University of Bristol, Bristol, England, in 2005. From 2005 to 2007, he was a Research Associate in the nondestructive testing research group at the University of Bristol, where he worked on the development of guided-wave structural health monitoring for permanently attached sensing systems. Since 2007, Dr. Croxford has been a Lecturer in the Department of Mechanical Engineering at the University of Bristol. His current research interests include structural health monitoring, nonlinear ultrasonic techniques, and fluidized bed dynamics.
