Research and validation of design principles for PVDF wideband ultrasonic transducers based on an equivalent circuit model

Measurement 141 (2019) 324–331

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Research and validation of design principles for PVDF wideband ultrasonic transducers based on an equivalent circuit model Dan-Dan Zheng ⇑, Yang Mao, Sheng-Hong Lv Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin, China

a r t i c l e

i n f o

Article history: Received 21 September 2018 Received in revised form 11 April 2019 Accepted 15 April 2019 Available online 25 April 2019 Keywords: Piezoelectric films Piezoelectric transducer Equivalent circuits Wideband ultrasonic transducer

a b s t r a c t With the increasing use of ultrasonic measurement technology in many fields, the demand for the wideband ultrasonic transducers is also growing. In order to design a wideband piezoelectric ultrasonic transducer, the design principles of wideband PVDF piezoelectric ultrasonic transducers are studied in this paper. A new equivalent circuit model of piezoelectric ultrasonic transducer is used here to simulate the piezoelectric ultrasonic transducer, which combines with the controlled source model and the lossy transmission line model. Based on this model, the relationships between physical structures and properties of PVDF transducers are studied both in simulation and experiment. It shows that the center frequency and many other property parameters of PVDF ultrasonic transducers are strongly related to the physical structures of it. Finally, a wideband PVDF piezoelectric ultrasonic transducer is produced with the center frequency of about 5.3 MHz ± 0.1 MHz and the bandwidth of more than 90%. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction As a universal measuring device, the sandwich piezoelectric ultrasonic transducers are widely used in many measurement systems, such as the medical imaging systems and the nondestructive testing systems. There is a fundamental relationship between the properties of ultrasonic transducers and the accuracy of ultrasonic measurement systems. Generally, higher center frequency means a better lateral resolution and wider bandwidth provides a better axial resolution [1]. Because of the large electromechanical coupling factors and stable material characteristics of PZT ceramics, the PZT ultrasonic transducers became a widely used electro-acoustic conversion device in many ultrasonic measurement systems [2]. However, the high mechanical quality factor Q and inherently high acoustic impedance of PZT ceramics greatly limit the bandwidth of PZT transducers, which consequently reduced the accuracy of the measurement systems [3]. Since the discovery of the large piezoelectric effect in organic polymer polyvinylidene fluoride, PVDF, this material has also been used for the fabrication of ultrasonic transducers [4]. The relatively low mechanical quality factor Q makes PVDF very suitable for making the wideband piezoelectric ultrasonic transducers. Besides, the low acoustic impedance and flexibility of the PVDF film greatly widening the application of piezoelectric ultrasonic transducers ⇑ Corresponding author. E-mail address: [email protected] (D.-D. Zheng). https://doi.org/10.1016/j.measurement.2019.04.050 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

[5]. It is a very ideal substitute for PZT ceramics when the bandwidth of PZT transducers can’t meet the requirements of measurement systems. So, it is important to do some researches on the design and fabrication of wideband ultrasonic transducers based on PVDF films. In this paper, the sandwich PVDF piezoelectric ultrasonic transducers are our main research objects. Fig. 1 shows the simplified diagram of the typical sandwich piezoelectric ultrasonic transducers. There are silver electrode layers tiling on both sides of the piezoelectric material (the PVDF piezoelectric film in this paper). As an adhesive agent, the epoxy bonds the backing and the PVDF piezoelectric film together. The shell is used to protect the transducer from physical damage and the electrode leads are used to conduct the electrical signals. Many researches have been conducted to study the relationships between the physical structure shown in Fig. 1 and the properties of PVDF transducers. In general, the center frequency and bandwidth of piezoelectric ultrasonic transducer as well as the amplitude of received signals are the parameters that we are most concerned. Theoretically, the center frequency of piezoelectric ultrasonic transducer is mainly related to the thickness of the piezoelectric material [3]. The thicker the piezoelectric material, the lower the center frequency of the transducer. At the same time, the center frequency of piezoelectric ultrasonic transducer is also affected by the backing [6]. When a high acoustic impedance backing is used, the center frequency of transducer is reduced by half as compared to using a low acoustic impedance backing. Meanwhile,

D.-D. Zheng et al. / Measurement 141 (2019) 324–331

Fig. 1. Simplified diagram of PVDF ultrasonic transducer.

the backing will affect the transducer’s bandwidth too. As an adhesive layer between the backing and silver electrode layer, the epoxy resin will slightly shift the center frequency of transducers. As the thickness of epoxy resin increases, the effect of this shift will become more pronounced [7]. When the PVDF is used to fabricate piezoelectric ultrasonic transducers with center frequency higher than a few megahertz, the PVDF film will become very thin, reaching hundreds of microns or even tens of microns. In this case, the electrode layers (typically 3–10 lm thick), tiling on both sides of the PVDF film, will have a large damping effect on the vibration of PVDF film. So, the thickness of the electrode layers must be carefully selected to provide adequate electrical performance without acoustical loading on the PVDF film. Generally, the thickness of electrode layers must be negligible compared with the thickness of piezoelectric material [6]. In the studies mentioned above, most researchers usually only studied the influences of a certain part in the transducer without comprehensive consideration. Besides, the influences of some parameters, such as the area of the transducer’s backing, have not been investigated. In this paper, a detailed study about the design and fabrication of wideband PVDF ultrasonic transducers based on simulation and experiment is given. The design considerations of physical structures for PVDF ultrasonic transducer are summarized from the simulation. On this basis, some simple PVDF piezoelectric ultrasonic transducers are fabricated to verify the conclusions obtained in simulation. The experimental results and simulation results are in good agreement, which gives some guidance for the complete process of wideband PVDF piezoelectric ultrasonic transducer’s design and fabrication.

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els have been proposed to explain the electrical and mechanical characteristics of piezoelectric ultrasonic transducers, such as the Mason model [9], the KLM model [10], the Rhyne’s model [11], the Redwood’s model [12] and so on. In this paper, in order to simulate the various physical structures of PVDF piezoelectric ultrasonic transducers, an equivalent circuit model of piezoelectric ultrasonic transducers based on the controlled-source model and the lossy transmission line model is used to conduct this research [13]. The controlled-source model is used to simulate the piezoelectric effect of piezoelectric material and the lossy transmission line model is used to simulate the propagation of sound waves in transducers. Fig. 2 shows the equivalent circuit model which is established using the OrCAD Capture software [13]. The equivalent circuit model consists of three main parts: the piezoelectric material part (the red part), the silver electrode part (the blue part) and the backing part (the green part). The piezoelectric material part is consisting of the lossless transmission line model (T4) and the controlled source model (E1, F1, F2), they jointly complete the simulation of the piezoelectric effect of piezoelectric material. The silver electrode part and the backing part are respectively simulated by the lossy transmission line model T9, T11 and T13. Usually, the adhesive layer in Fig. 1 is so thin that it has little effect on the properties of piezoelectric ultrasonic transducer. In addition, due to the limitation of experimental conditions, the thickness of adhesive layer in experiment is very difficult to be measured and controlled, therefore, the adhesive layer is ignored in this model. However, in the design and fabrication of piezoelectric ultrasonic transducers, it must be ensured that the thickness of the adhesive layer is sufficiently thin. Since this model is only a tool for us to study the piezoelectric ultrasonic transducers in this paper, rather than the main research contents, the specific information about this model and the validation of its validity can be found in reference [13]. All the parameters needed in this model are shown in Eqs. (1) and (2) [14]:

8 Z 0 ¼ qAz up > > > > > TD ¼ udp > > > qffiffiffi > > > c > > < up ¼ q 33

h ¼ ee > > > > > > C 0 ¼ eAdz > > > > > R1 ¼ 1kX > > : C 1 ¼ 1F

ð1Þ

Eq. (1) lists the modeling formulas of the piezoelectric material part, where q is the density of piezoelectric material. Az represents the cross-sectional area of the piezoelectric material along the acoustic wave propagation direction. d is the thickness of piezoelectric material. c is the relative elastic constant. C 0 is the capacitance between electrodes. e is the permittivity.

2. The equivalent circuit model for transducers In order to study the piezoelectric ultrasonic transducers, many methods have been proposed. There are two main methods now for studying piezoelectric ultrasonic transducers: the finite element model and the equivalent circuit model. The finite element model considers the transducer as a composite of many small cells which are called finite elements and computes each element by mathematical approximation separately to obtain an approximate solution [8]. The finite element model has high precision, but requires a lot of calculating time, and the requirements for computing equipment are also relatively high. In contrast, the equivalent circuit model has a very fast calculating speed and a high calculation accuracy. There are numerous equivalent circuit mod-

Fig. 2. The equivalent circuit model of piezoelectric ultrasonic transducer [13].

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8 > > > > > > > <

D.-D. Zheng et al. / Measurement 141 (2019) 324–331

R ¼ 2quAa L ¼ Aq

C ¼ Aq1u2 > > > G ¼ q2uA atc > > > > : aðT Þ ¼ 2w2 gðTÞ

ð2Þ

3qðT Þu3 ðT Þ

The parameters needed in the lossy transmission line model are shown in Eq. (2), where q is the density of medium. u is the velocity of sound in medium. A is the cross-sectional area of medium in the direction of acoustic propagation. ais the coefficient of attenuation due to viscous losses and atc is the coefficient of attenuation due to thermal conduction. gðTÞ is the viscosity. w is the angular frequency. Because the material used in this paper have a low heat conductance, the loss due to thermal conduction is negligible, therefore, the conductance G can be taken as 0. Therefore, to model a lossy acoustic layer as an electrical transmission line, the following material data are needed: the acoustic beam’s cross-sectional area A(m2), the density q(kg/m), the speed of sound u (m/s), and the attenuation constant a(Np/m) at the chosen frequency and temperature. Parameters that are temperature sensitive, like viscosity, need to be obtained at the desired temperature for single temperature simulation or as a function of temperature for parametric simulation over a temperature range [14]. In this model, some parameters such as the area and thickness of the PVDF film, the thickness of the silver electrode, etc. can be selected according to actual needs. Other parameters such as the relative dielectric constant of the PVDF film, the density of the PVDF film, and the sound speed in the silver electrode are constant and can be obtained from literatures. Table 1 summarizes some of the parameters that are useful for building models given in reference [13]. 3. The relationships between physical structures and properties of PVDF transducer Based on the equivalent circuit model of PVDF ultrasonic transducers introduced above, the relationships between the physical structures and properties of PVDF transducers are studied in this section to obtain some guidelines for the design and fabrication of wideband PVDF ultrasonic transducers. In general, the properties of piezoelectric ultrasonic transducer such as center frequency, bandwidth, etc. mainly depend on its physical structures. As can be seen from Fig. 1, these structures mainly include PVDF films, backings, electrode layers and so on. In order to design a transducer with the target properties, the parameters of these physical structures must be determined one by one. Therefore, the research is carried out in the following four aspects. 3.1. The selection of PVDF thickness

transmitting and receiving of ultrasound are all dependent on the piezoelectric effect and the inverse piezoelectric effect of PVDF film. Theoretically, the relationship between the center frequency of a piezoelectric film and its thickness follows:

f ¼

u kb d

ð3Þ

where f represents the center frequency of piezoelectric film.u represents the sound speed. d represents the thickness of piezoelectric film and kb is a constant coefficient. However, as the PVDF transducer contains the electrode layer, adhesive layer and other structures in addition to the PVDF film, the relationship between the center frequency of PVDF transducers and the thickness of PVDF film does not exactly agrees with Eq. (3). In simulation, the air is used as backing and the thickness of electrode is set as 6 lm. At the same time, the area of PVDF film is set as 20 mm * 15 mm and the thickness of PVDF films are set as 28 lm, 110 lm and 200 lm respectively. Fig. 3 shows the spectrogram of received signals with different PVDF film thickness in simulation. As it shown in Fig. 3, the center frequency of the PVDF transducer is inversely proportional to the thickness of the PVDF film. The thinner the PVDF film, the higher the center frequency of PVDF transducer. The change trend is the same as the theoretical formula shown in Eq. (3). Table 2 shows the center frequency of these PVDF films in theory and simulation. In Table 2, all the center frequencies in simulation are smaller than that in theory, the error between the theoretical value and simulation value are 20.7 MHz ± 0.05 MHz, 0.8 MHz ± 0.05 MHz, and 0.9 MHz ± 0.05 MHz respectively. These errors are caused by the existence of the electrode layers which are tiled on both sides of the PVDF film. The thickness of the electrode layer is 6 lm that can’t be ignored compared with the thickness of the PVDF film. The damping effect of the electrode layer on the vibration of PVDF film will slow the vibrating frequency of PVDF film, and then lower the center frequency of PVDF transducers. Furthermore, in the case where the thickness of the silver electrode keeps a constant, the thinner the PVDF film, the stronger the damping effect, and the larger the error between the theoretical value and the simulation value. Here, the 6-lm-thick electrode layer is too thick compared to the 28-lm-thick PVDF film, it will have a tremendous impact on the vibration of the PVDF film and make the center frequency in simulation much smaller than that in theory. When the thickness of the PVDF film is 110 lm and 200 lm, much larger than 6 lm, the error between theory and simulation becomes relatively small but still exists. Therefore, careful considerations must be paid to the thickness of electrode layers when the desired center frequency is high and the PVDF film is very thin.

As a core part of the PVDF ultrasonic transducers, PVDF film has a very important effect on the properties of PVDF transducers. The

Table 1 Some useful parameters for building models given in Ref. [13]. Parameters Piezoelectric stress constant of PVDF Relative permittivity of PVDF Sound speed in PVDF Density of PVDF Elastic stiffness factor of PVDF Sound speed of silver electrode Density of silver electrode Sound speed in air backing Density of air backing

Symbol e

33

e

u Ρ c u1

q2

u2

q3

Value

Unit

0.06 5 2000 1800 1.77 * 1010 3607 10,490 343 1.2

C/m2 F/m m/s kg/m3 N/m2 m/s kg/m3 m/s kg/m3

Fig. 3. The spectrogram of received signal with different PVDF film thickness in simulation.

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D.-D. Zheng et al. / Measurement 141 (2019) 324–331 Table 2 The center frequency of PVDF films with different thickness. The thickness of PVDF film

28 lm

110 lm

200 lm

The center frequency in theory The center frequency in simulation Error between simulation and theory

35.7 MHz 15 MHz ± 0.05 MHz 20.7 MHz ± 0.05 MHz

9 MHz 8.2 MHz ± 0.05 MHz 0.8 MHz ± 0.05 MHz

5 MHz 4.1 MHz ± 0.05 MHz 0.9 MHz ± 0.05 MHz

At the same time, as it shown in Fig. 3, the amplitude of the received signal also varies regularly with the thickness of PVDF films. The thicker the PVDF film is, the stronger the received signal is. 3.2. Backing material selection Selection of proper backing material for a PVDF ultrasonic transducer demands careful considerations [6]. The backing will greatly influence the center frequency and bandwidth of PVDF transducers. Generally, the backing can be divided into two categories based on their acoustic impedance: the heavy backing with a relatively high acoustic impedance and the light backing with a relatively low acoustic impedance. The relationship between the backing and the center frequency of PVDF transducer can also be expressed by Eq. (3). When the acoustic impedance of backing is much larger than that of PVDF film (the heavy backing), kb equals to 4, and when the acoustic impedance of backing is much smaller than that of PVDF film (the light backing), kb equals to 2. In order to verify the theory mentioned above, a PVDF film with the thickness of 110 lm was chosen in the simulation. As the acoustic impedance of PVDF film is about 3.6 MRayl, the air (0.0004 MRayl) is used as the light backing and the aluminum cube (17.01 MRayl) is used as the heavy backing here. The area of the backing is the same as that of the PVDF film. Fig. 4 shows the spectrogram of the received signal when using light backing and heavy backing in simulation. Usually, the 6dB bandwidth of a piezoelectric ultrasonic transducer can be defined as follows [15]:

Table 3 The center frequency and bandwidth with light backing and heavy backing. Parameters

Light backing

Heavy backing

Center frequency Bandwidth

8.3 MHz ± 0.1 MHz 36%

4.5 MHz ± 0.1 MHz 85%

quency of PVDF transducers and increase the bandwidth of it. Meanwhile, as it can be seen from Fig. 4, a heavy backing will also reduce the amplitude of received signals. Therefore, a careful selection between the bandwidth and the amplitude of received signal is necessary in the design of a wideband PVDF ultrasonic transducer. 3.3. Consideration for backing size In addition to the backing materials that can significantly affect the properties of the PVDF transducers, the size of the backing also has a large impact on the properties of the PVDF transducers. Therefore, when designing the PVDF ultrasonic transducers, the size of backing also needs a careful consideration.

where f is the center frequency of the PVDF ultrasonic transducer, f1 and f2 are the 6dB spectral frequencies of the received signal respectively. According to the simulation results shown in Fig. 4, the center frequency and the bandwidth of the PVDF ultrasonic transducers changed with the backing materials are summarized in Table 3. It is clearly that different backing materials have a significant impact on the transducer’s center frequency and bandwidth. When a heavy backing is used instead of a light backing, the center frequency of PVDF transducer is reduced from 8.3 MHz ± 0.1 MHz to 4.5 MHz ± 0.1 MHz. At the same time, the bandwidth of the PVDF transducer is increased from 36% to 85%, a significantly exaltation. This indicates that a heavy backing will reduce the center fre-

3.3.1. The area of backing In order to study the influence of different backing area on the properties of PVDF ultrasonic transducers, a PVDF film with the thickness of 110 lm is used in the simulation. The area of PVDF film is set as 20 mm * 15 mm, at the same time, the aluminum blocks with the thickness of 15 mm are chosen as the backing and the area of backings are set as 10 mm * 10 mm, 20 mm * 10 mm, 20 mm * 15 mm, 20 mm * 20 mm respectively. All other parameters of them are the same. Fig. 5 shows the spectrogram of received signals under different backing area. As it can be seen from Fig. 5, when the area of PVDF film remains unchanged, the center frequency of PVDF transducer will decrease as the backing area increasing, and when the backing area increases to the same area of the PVDF film, the center frequency reaches the minimum value. When the area of backing continues to increase, the center frequency of PVDF transducer no longer changes. At the same time, the bandwidth of received signal varies between 80% and 90%, which changes very slightly and it is very difficult to find out the law of changes. Besides, it is obvious that the amplitude of received signal changes regularly with the changes of backing area, the smaller the backing area, the smaller the amplitude of received signal.

Fig. 4. Spectrogram of received signal in simulation.

Fig. 5. The spectrogram of received signal under different backing area in simulation.

BW ¼

f1  f2  100% f

ð4Þ

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3.3.2. The thickness of backing Except for the area of backing, the thickness of backing is also a very important parameter that must be concerned when considering the backing size. In simulation, the thickness of PVDF film is set as 110 lm and the area of it is set as 20 mm * 15 mm. Two aluminum blocks with the area of 20 mm * 15 mm are selected as backing, and the thickness of them are set as 20 mm and 25 mm respectively. Except for the thickness, all other parameters of these two backings are the exactly same. Fig. 6 shows the spectrogram of received signal with different backing thickness in simulation. In Fig. 6, the spectrogram of received signal with the 20 mmthick backing are completely coincide with the spectrogram of received signal with the 25 mm-thick backing. It means that changing the thickness of backing won’t affect the properties of PVDF ultrasonic transducers. 3.4. The influence of electrode layer As a basic part of the PVDF transducer, the electrode layer is mainly used to ensure the stable transmission of electrical signals, so the influence of electrode layer on the PVDF transducer is also well worth studying. Currently the most commonly used electrode material on PVDF film is aluminum or silver. Since the electrodes are usually laid on both sides of PVDF film in the form of electrode layers, and the elastic properties of the metal electrode are greatly different from the elastic properties of the PVDF films, the electrode layer will have a damping effect on the vibration of PVDF film. Therefore, the electrode layer with different thickness will have a non-negligible influence on the properties of PVDF transducers and must be considered in the design of PVDF ultrasonic transducers. In order to study the influence of different electrode thickness on the properties of PVDF transducers, a PVDF film with the thickness of 110 lm and the area of 20 mm * 15 mm is selected in the simulation, an aluminum block with the size of 20 mm * 15 mm * 20 mm is selected as backing, and the silver is selected as the electrode material. As comparisons, the thickness of the electrode layer (typically 3–10 lm) are set as 3 lm, 6 lm and 9 lm respectively. The spectrogram of received signals with different electrode thickness are shown in Fig. 7. As it can be seen from Fig. 7, in the case where the other parameters are identical, the thicker the electrode layer, the lower the center frequency of the PVDF transducer. This is consistent with the theory that a thicker electrode layer will have a stronger damping effect on the vibration of PVDF film. At the same time, the bandwidth of the transducer varies between 80% and 90%, the thinner the electrode layer, the wider the bandwidth of received signal, but this change is very slightly. Similarly, when the thickness of electrode changes, the amplitude of received signal also changes very little.

Fig. 7. The spectrogram of received signal with different electrode thickness.

4. The experimental study of PVDF ultrasonic transducer In order to realize the design of wideband ultrasonic transducers and verify the conclusions obtained in section III, some PVDF ultrasonic transducers were made in this section. Since the center frequency of the desired PVDF transducer is about 5 MHz, the thickness of PVDF film is selected as 110 lm and the area of PVDF film is set as 15 mm * 20 mm here. In order to compare the influence of different structural parameters on the properties of PVDF transducer, there are five PVDF ultrasonic transducers have been made for comparison. The detailed parameters of them are listed in the Table 4. In addition to the parameters in Table 4, the other parameters of the PVDF transducers are basically the same. The electrical excitation signal of these five transducers are set as 4 cycles of 5 MHz pulse signal to match the resonant frequency of the target transducer for stronger transmitting ultrasound. The received signals of different transducers under the same pulse-echo experiment conditions are collected for comparison. Because the PVDF films used in the experiment are all purchased from the manufacturer, the thickness of silver electrode layer is fixed as 6 lm and can’t be changed. Therefore, the experimental study of different silver electrode layer thickness is not conducted in this section. Fig. 8 shows the spectrogram of received signals of transducer A and transducer C. The only difference between transducer A and transducer C is the backing material, the backing of transducer A is a light backing and the backing of transducer C is a heavy backing, all other parameters are the same. As it can be seen from Fig. 8, a heavy backing (the red line) will greatly reduce the center frequency of PVDF ultrasonic transducers and the amplitude of received signal compared to the light backing (the blue line). Simultaneously, the using of heavy backing makes the bandwidth of received signal increased from 59% to 100% compared with using the light backing, a substantial increase. The change trends of the center frequency, bandwidth and signal amplitude in the experiment is consistent with that in simulation. Therefore, we can draw a conclusion that using a heavy backing will reduce the center frequency of the transducer and the amplitude of received signal compared to using a light backing, but it can significantly increase the bandwidth of transducer. Considering that the design goal of this paper is a 5 MHz wideband ultrasonic transducer, the aluminum is finally selected as the backing material.

Table 4 The detail parameters of the PVDF transducers made in the experiment.

Fig. 6. The spectrogram of received signal with different backing thickness in simulation.

Transducer Transducer Transducer Transducer Transducer

A B C D E

Backing material

Backing area

Backing thickness

air aluminum aluminum aluminum aluminum

15 mm * 20 mm 10 mm * 10 mm 15 mm * 20 mm 20 mm * 20 mm 15 mm * 20 mm

none 20 mm 20 mm 20 mm 25 mm

D.-D. Zheng et al. / Measurement 141 (2019) 324–331

Fig. 8. The spectrogram of received signal with different backing material in experiment.

Fig. 9 shows the spectrogram of received signals of transducer B, transducer C and transducer D. The only difference between these three transducers is the backing area of them. In these three transducers, the area of PVDF film is 15 mm * 20 mm, however, the backing area of them are set as 10 mm * 10 mm, 15 mm * 20 mm and 20 mm * 20 mm respectively. The experimental results in Fig. 9 shows that keeping the area of PVDF film a constant, a smaller backing area means a higher center frequency and smaller amplitudes, but the bandwidth is almost unchanged. When the area of backing gradually increases beyond the area of PVDF film, the center frequency of the transducer does not change, at the same time, the amplitude and bandwidth of the received signal also changes very slightly. The change trends of the experimental results agree with that of the simulation result shown in Fig. 5 very well. The spectrogram of received signals with different backing thickness are shown in Fig. 10, As it can be seen from the experimental results shown in Fig. 10, keeping the other parameters unchanged, increasing the thickness of backing has almost no effect on the center frequency and bandwidth of the transducers. However, the amplitude of the received signal decreases a little as the thickness of backing increases, this is different from the conclusion obtained in the simulation shown in Fig. 6. The change in the amplitude of received signal is due to the sound absorption ability of backing. As a sound-absorbing component in the transducer, the backing will absorb some of the sound waves and attenuates the vibration of PVDF film. When the thickness of backing increases, more acoustic energy will be absorbed by the backing. Therefore, a thinner backing usually provides a stronger receive signal theoretically. In fact, the thickness of backing can’t be designed too thin. After being energized by electrical signal, the PVDF emits ultrasonic waves simultaneously to the backing in the back and the measured medium in the front. The ultrasonic waves entering the backing are useless and need to be absorbed by the backing. Therefore, the backing must have good enough sound-absorbing properties, which is usually related to the thickness of it. When the thickness of backing is too thin, the sound absorption ability of backing may not be sufficiently to absorb all

Fig. 9. The spectrogram of received signal with different backing area in experiment.

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Fig. 10. The spectrogram of received signal with different backing thickness in experiment.

the useless sound. As it shown in Fig. 11, when the thickness of backing is set as 20 mm, there will be two peaks in the received signal, the first peak is the measurement signal we need, the second peak is the unwanted signal which has not been absorbed by the backing and reflected from the interface of backing and air. When the backing is too thin, the useless secondary echo will overlap with the first peak, thus affecting the measurement accuracy. Thence, the thickness of backing should be thick enough to ensure that the backing can have good enough ability to absorb useless ultrasonic waves. At the same time, other methods to improve the sound-absorbing ability of backing should also be considered.

5. The fabrication of target PVDF ultrasonic transducer Under the guidance of simulation and experimental conclusions obtained above, a wideband PVDF ultrasonic transducer with the center frequency of about 5 MHz has been made. A PVDF film with the thickness of 110 lm is selected as the piezoelectric material and the aluminum is selected as the backing material. The detailed parameters of the transducer are summarized in Table 5. Figs. 12 and 13 show the received signal of the fabricated PVDF ultrasonic transducer and the spectrogram of received signal for this transducer. The center frequency of this fabricated PVDF ultrasonic transducer is about 5.3 MHz ± 0.1 MHz, the error is about 6% compared to the expected 5 MHz. The amplitude of the received signal is about 1.5 V ± 0.05 V, high enough for most signal processing systems. At the same time, the 6dB bandwidth of this PVDF ultrasonic transducer is about 104%, which is far higher than the traditional piezoelectric transducers, and 14% larger than the expected 90%. An ultrasonic transducer with such a wide bandwidth is of great interest in the field of industrial measurement. For example, when measuring the thickness of thin liquid film in a pipe under the twophase flow condition, especially the annular flow condition, the film-resonance method is usually an ideal measurement method [16]. Fig. 14 shows the fabricated PVDF ultrasonic transducer and a thickness measurement system for the static liquid film based on the film-resonance method. When energized by the excitation

Fig. 11. The received signal with different backing thickness in experiment.

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Table 5 The detailed parameters of the wideband PVDF ultrasonic transducer. Parameters

Value

The The The The The

15 mm * 20 mm 110 lm 6 lm 15 mm * 20 mm 25 mm

area of PVDF film thickness of PVDF film thickness of silver electrode layer area of aluminum backing thickness of aluminum backing

Fig. 12. The received signal of the PVDF ultrasonic transducer.

Fig. 13. Spectrogram of received signal for the wideband ultrasonic transducer.

Fig. 14. A thickness measurement system for the static liquid film.

circuit, the transducer will emit ultrasound into the plexiglass plate and the ultrasound will be reflected at the plexiglass-liquid interface and at the liquid-air interface. The reflected ultrasound will be received by the transducer and the receiving circuit. By analyzing the change of the reflection coefficient obtained by these two reflected signals, the thickness of the liquid film can be obtained. The increase in the bandwidth of ultrasonic transducer will greatly improve the accuracy and reliability of the result.

has been studied in this paper. An equivalent circuit model of PVDF piezoelectric ultrasonic transducer is used in the simulation, which combines with the controlled-source model and the lossy transmission line model. On this basis, the design considerations of the physical structures for wideband PVDF ultrasonic transducer are studied in detail by the simulation and experiment. The relationships between physical structures of PVDF transducer and its main property parameters such as the center frequency and bandwidth are our primary concerns. The simulation and experimental results show that there is a qualitative relationship between the physical structures of PVDF transducer and its properties. The specific relationships are as follows: a. The thickness of PVDF film largely determines the center frequency of PVDF transducers. In general, the thinner the film, the higher the center frequency. However, when the film is too thin, usually up to several tens of micrometers, the electrode layer will dampen the vibration of the PVDF film and affect its center frequency. Therefore, the influence of electrode layer must also be considered when choosing the PVDF film thickness according to the desired center frequency. b. When other parameters are the same, the center frequency of PVDF ultrasonic transducers with heavy backing is reduced by about half compared to the center frequency when light backing is used and the 6dB bandwidth is significantly increased. At the same time, the amplitude of received signal also decreases when the light backing is changed to heavy backing. c. When the backing material had been selected, changing the thickness of backing within a certain range does not affect the property parameters of PVDF transducers. However, the backing should not be too thin, as this may cause noise in the received signal. At the same time, the area of backing affects the transducer’s center frequency. When the area of backing is smaller than the area of PVDF film, reducing the area of backing will increase the center frequency of PVDF transducer and reduce the amplitude of received signal a little. When the backing area is greater than or equal to the PVDF film area, increasing the backing area does not affect transducer properties, the center frequency of the transducer and the amplitude of received signal are basically unchanged. Therefore, the properties of PVDF transducer can be fine-tuned by selecting a suitable backing area. However, the bandwidth of the transducer changes very slightly when the area of backing changes. d. The electrode layer reduces the center frequency of the PVDF piezoelectric ultrasonic transducer. The thicker the electrode layer relative to the PVDF film, the more the frequency of PVDF transducer decreases. Therefore, when designing the high-frequency PVDF transducer, careful consideration must be paid to the thickness of the electrode layer. In the case of good electrical conductivity, thinner electrode layers are usually a better choice. The simulation methods in this paper and the conclusions mentioned above may provide some design basis and references for other people who want to design and fabricate the wideband PVDF ultrasonic transducers.

Acknowledgments 6. Conclusion Based on the combination of simulation and experimentation, the design and research of wideband PVDF ultrasonic transducer

This work is supported by the National Natural Science Foundation of China (Grant No. 61671317, 61101227) and the Natural Science Foundation of Tianjin (Grant No. 13JCQNJC03300, 13JCQNJC00800).

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