Conventionally, in order to acoustically match thickness mode piezoelectric transducers to a low acoustic impedance load medium, multiple quarter wavelength (QW) matching layers are employed at the front face of the device. Typically a number of layers, 2-4 in number, are employed resulting in discrete impedance steps within the acoustic matching scheme. This can result in impedance matching with limited bandwidth characteristics. This paper investigates the application of tapered transmission line filter theory to implement a graded impedance profile, through the thickness of the matching layer scheme, to solve the impedance mismatch problem whilst accounting for enhanced transducer sensitivity and bandwidth

Hayward, Gordon

Mackintosh, Allan

Mulholland, Anthony

O'Leary, Richard

Pethrick, Richard

Ramadas, Sivaram Nishal

Troge, Alexandre

English

Name not available

Tapered transmission line technique based graded matching layers for thickness mode piezoelectric transducers

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryRamadas, Sivaram Nishal and O’Leary, Richard and Mulholland, Anthony and Hayward, Gordonand Mackintosh, Allan and Troge, Alexandre and Pethrick, Richard (2009) Tapered transmissionline technique based graded matching layers for thickness mode piezoelectric transducers. In:2009 IEEE International Ultrasonics Symposium. IEEE, Piscataway, pp. 1695-1698. ISBN9781424443895Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/ 1  Abstract — Conventionally, in order to acoustically match thickness mode piezoelectric transducers to a low acoustic impedance load medium, multiple quarter wavelength (QW) matching layers are employed at the front face of the device. Typically a number of layers, 2-4 in number, are employed resulting in discrete impedance steps within the acoustic matching scheme. This can result in impedance matching with limited bandwidth characteristics. This paper investigates the application of tapered transmission line filter theory to implement a graded impedance profile, through the thickness of the matching layer scheme, to solve the impedance mismatch problem whilst accounting for enhanced transducer sensitivity and bandwidth.    Keywords— Acoustic transducers, graded matching layer, impedance matching, photopolymerisation, transmission line I. INTRODUCTION IEZOELECTRIC devices convert mechanical stress to electrical charge or voltage (direct effect), and vice versa (indirect effect). The piezoelectric property can be found in many materials (such as quartz, Lead Zirconate Titanate, and Polyvinylidene Fluoride) and finds a wide range of application in many fields including SONAR, bio-medicine, non destructive evaluation and industrial process control. Typically, piezoceramics (with high acoustic impedance around 30 MRayl) are often used as a active material in such transducers, and using such devices in low impedance loads such as water or human tissue (approximately 1.5 MRayl) will make the device usable only in a very narrow band of frequencies due to the mechanical mismatch. Consequently, matching layers whose acoustic impedance is intermediate between the ceramic and the load medium are used to improve device sensitivity, while operating into such low acoustic impedance loads. Designing matching layers will greatly increase the operational bandwidth and efficiency of a transducer and has to be considered carefully at any design stage. This paper investigates an analogue filter technique based approach to design and optimise graded matching layers   for conventional thickness mode piezoelectric transducers.   Firstly, the theory to calculate the reflection/transmission coefficients of a tapered impedance profile is presented. Examples include, but are not limited to, exponential, and triangular taper profiles. Secondly, matching layers with a broad range of acoustic properties for application in piezoelectric probe assemblies are manufactured using a methodology based on photopolymerisation of epoxy resins. The photopolymerisation allows for the rapid fabrication of polymer materials by successive photocuring of thin layers of polymer. The method is elegant in implementation, since the layers can be readily deposited directly onto the front face of the transducer element, eliminating additional bond lines. Indeed, by employing different monomers and dispersing particles into the monomers prior to polymerization, a stratified structure can be produced with the desired acoustic impedance profile.  Finally, experimental results are presented in order to demonstrate the effectiveness of this approach – device fractional bandwidths around 80% are demonstrated, for a nominal 1MHz thickness mode transducer design.  II. TAPERED TRANSMISSION LINE THEORY Several authors have proposed different methods for calculating optimum values for intermediate acoustic matching layers and hence overcome the impedance mismatch problem. Notably, Lewis [1] and Desilets [2] used multiple matching layers, with each layer impedance being a fixed percentage lower (or higher) than the preceding one. Also, multiple QW transformers using analog filter techniques such as Chebyshev (type I and II) and Binomial transforms, have been studied in depth for many years for electrical impedance matching problems [3]. The suitability of applying similar filter design methods to the problem of acoustic matching has been reported by the authors [4-6].  Unlike multi-section matching with discrete QW sections, the impedance can be continuously tapered to achieve broadband matching. Figure 1 illustrates schematically a tapered transmission line used to match an input impedance (i.e. composite transducer, ZC) to a low impedance water load (ZL).  Tapered transmission line technique based graded matching layers for thickness mode piezoelectric transducers S. N. Ramadas1, R. L. O'Leary1, A. J. Mulholland2, G. Hayward1,  A. R. MacKintosh3 A. Troge3 and R. A. Pethrick3 1Centre for Ultrasonic Engineering, University of Strathclyde, 204 George Street, Glasgow, UK 2 Department of Mathematics, University of Strathclyde, Glasgow, UK 3 Department of Chemistry, University of Strathclyde, Glasgow, UK P 2 1(a)  1(b) Figure 1.  Tapered transmission line matching section (a) ideal and  (b) an approximation to the continuous taper used in modelling.  Theory for the tapered transmission line is readily available [3]. Relation between the characteristic impedance and the reflection coefficient (г) is given by:                                (1)           Where L = total taper length and β = 2π/λ   By changing the type of taper profile one can obtain different passband characteristics. Two most commonly used and practical taper design line will be considered in this paper. A. Exponential Taper If the impedance profile varies exponentially when a function of the form ln Z is substituted in Equation 1 (i.e. Z(z) = ZC eaz, where a = ln(ZL/ZC)/L), the reflection coefficient (Г) can be derived [3] as shown below:                                             (2)                           B. Triangular Taper A matching section with a more desirable property could be achieved if a triangular function of the form shown below in Equation 3 is chosen. The impedance profile for this triangular taper and the overall reflection coefficient can be obtained from straightforward substitution of Equation 3 in Equation 1 and integrating it, and the result is shown below in Equations 4 and 5, respectively.                  (3)                                (4)                                                            (5)                             A comparison of the synthesized impedance profile as a function of taper length and reflection coefficient as a function of  for both the taper designs, is shown in Figure 2. For both the designs, the reflection coefficient is quiet small, approximately 22% for exponential taper and 5% for the triangular taper. However, the length of the triangular taper is almost twice that of an exponential taper.  (a)  (b) Figure 2. Comparison of an exponential & triangular taper profile (a) synthesised impedance profile to match a composite transducer (16 MRayl) to a water load, and (b) the modelled normalised input reflection coefficients.  π 2π 4π 3π 5π 6π 7πβL = 2πL/λ  3III. MANUFACTURE AND ASSEMBLY OF PASSIVE LAYERS A. Manufacture of graded matching structure using photopolymerisation method  A range of photopolymerisable polymers have been investigated in order experimentally assess the tapered matching layer designs. Such an approach allows for a rapid realization of the tapers and eliminates additional bond-lines between the layers. Eliminating bond lines has been shown theoretically to improve device behavior in devices comprising multiple acoustic matching layer [4], it will also facilitate manufacture. A range of polymers, produced using a photocuring methodology have been investigated [7], the materials based on the glycidyl ether of bisphenol A (BisA) and 1,4-cyclohexanedimethanol diglycidyl ether (CHDG). The polymerization is initiated by the action of ultraviolet light on photoacid generator (PAG) that comprises triarylsulfonium hexafluorophosphate salt in 50% solution in propylene carbonate. When cured, Bis A produces a rigid material with a high glass transition temperature (Tg) whereas CHDG cures to a more flexible lower Tg material, by blending the two monomers a range of materials can be manufactured. Furthermore, the addition of particles to the uncured resin allows the acoustic impedance of the resultant polymer to be varied across a wider range. Therefore methodology facilitates the successive photocuring of thin layers of polymer, blends of polymer or particle loaded polymers in order to create the tapered profile required for the matching layer.  In order to manufacture the graded layers for the desired transducer design the following methodology was employed – 20g of monomer were mixed with 0.4g of PAG, using a Thinky planetary mixer (Intertronics, Oxon, UK). In order to reduce the viscosity during mixing and deposition, samples containing between 50 to 100% w/w BisA were heated to 60°C. In addition to blends of polymers, a range of materials based on the BisA resin and incorporating barium sulphate (BaSO4) particles were also prepared. Incorporation of BaSO4 inot the polymer will result in increase acoustic impedance. Specimens were produced containing 12, 18, 26, 35 and 51g of BaSO4 with 20g of BisA with 0.4 g of PAG to obtain 13, 19, 25, 31 and 40% volume fractions of BaSO4, respectively.  The range of specific acoustic impedances that can be achieved using the blends of BisA and CHDG is illustrated in Figure 3. These data were determined by through transmission time-of-flight measurements at 500kHz and an Anton Paar Digital DMA601 density-measuring cell and a DMA60 density meter (Stanton Redcroft, London). The CHDG material is more flexible at room temperature and this in reflected in the lower value of specific acoustic impedance for this material. Increasing the amount of BisA in the formulation, results in an increase in the specific acoustic impedance of the resultant polymer. The density variation is minimal across the range of materials and the increase in the acoustic impedance reflects the increased acoustic velocity, and concomitant increase in moduli of the material as the percentage of BisA in increased. Figure 4 details the variation of the specific acoustic impedance, determined at as before, for the range of samples containing BaSO4, an almost linear variation with respect to volume fraction is observed.   Figure 3. Variation in specific acoustic impedance of the matching layer, as the percentage of BisA is varied  Figure 4. Variation in specific acoustic impedance as the volume fraction of BaSO4 in BisA is varied  In order to manufacture the films in thin film format to manufacture the graded matching layer structure a K-Bar deposition system (RK Print and Coat, Herts, UK) was used. The general procedure was as follows, a 1ml aliquot of the monomer was deposited onto a Teflon plate, and the K-Bar system was used to produce a wet film thickness of 100μm, the wet film was exposed to UV light using an IUV 250 flood lamp (Intertronics, Oxon, UK) for 3 minutes, giving a dose of 5000mJ/cm2. This resulted in a ~90μm cured film. The monomer to form the next layer of the matching layer gradient was then deposited on top of the cured layer and the process repeated till all of the layers had been deposited and cured. An overall taper length of 0.76mm thick (approx. λ/2 in water), with an exponential gradient profile is considered for the initial investigation. The salient properties of a graded matching profile manufactured using the photopolymerisation technique is presented in Table 1. B. Transducer fabrication  The fabricated graded matching layer is bonded onto a conventional thickness mode composite device, made of 50% volume fraction (PZT-5A) and hard-set polymer (CY1300/1301), with a nominal operating frequency of 1MHz. A 6MRayl non-conducting backing based on tungsten loaded epoxy was attached to the active layer prior to marinising the device.  4 Layer #  1 2 3 4 5 6 7 8Modelled Z (MRayl)  6.26 5.44 4.73 4.12 3.57 3.1 2.7 2.34 Measured Z  (MRayl) 6.26 5.47 4.69 4.13 3.57 3.02 2.7 2.32 Material  39% 31% 25% 19% 5% 0% 45% 80% Volume fraction BaSO4 % BisA Velocity Long (m/s)  2519 2473 2417 2257 2369 2568 2297 2003Velocity Shear (m/s)  1281 1208 1169 1156 1152 1093 932.5 799.5Ρ (kg/m3)  2487 2214 1991 1829 1324 1178 1175 1159Table 1. Manufactured matching layer materials properties  for an exponential taper design  IV. EXPERIMENTAL RESULTS  Device operational impedance characteristic of the prototype device was measured coupled to a water load using a HP impedance/gain-phase analyser (Agilent, South Queensferry, UK), the result is shown in Figure 5. It is clear that the device operates around a centre frequency around 1MHz. Also the electrical impedance change within the operational bandwidth is reasonably smooth. Consequently the device ring-down time will be shorter - resulting in a wider bandwidth. Attaching such graded matching layers at the front face of the transducer also enhances the sensitivity of the device, as it efficiently propagates energy into the load medium. Pulse-echo measurement was performed in water with a planar Crown glass block used as the reflector. The device was connected via BNC cable to a JSR PR35 Pulser/Receiver (JSR Ultrasonics, Pitttsford, NY) and the signal recorded using an Infiniium 54832D digitizing oscilloscope (Agilent, South Queensferry, UK.). The time, and Fourier transformed frequency domain, impulse response of the device is shown in Figure 6. The device exhibits approximately 80% fractional bandwidth.  Figure 5. Active layer operational impedance profile measured using an impedance analyser    Figure 6. Time and frequency domain pulse echo impulse response result of the 1 MHz thickness mode transducer with graded matching layers radiating into a water load, and 6MRayl backing   V. CONCLUDING REMARKS A preliminary investigation into the use of tapered transmission line filter techniques to design matching layers for piezoelectric transducers.  In order to achieved the desired layer structure a photopolymerisation polymer has been employed. The experimental and simulation results that have been presented demonstrate the feasibility of the technique in. In the current context an exponential equal taper, with consistent layer thickness and acoustic impedance taper is considered. However, it is expected that difference taper profile and optimized the layer parameters will results in improved behavior of this type of device. This will be the subject of future work. ACKNOWLEDGMENT The author’s acknowledge Grant Smillie and Thomas McCunnie of Centre for Ultrasonic Engineering for their diligence in preparing the prototype devices. REFERENCES [1] G. K. Lewis, "A matrix technique for analyzing the performance of multi-layered front matched and backed piezoelectric ceramic transducers'', J. Acoust. Soc. Am, pp. 395-416, 1980. [2] C. S. Desilets, J. D. Fraser and G. S. Kino, "The deisgn of effecient broadband piezoelectric transducers'', IEEE Transactions on sonics and ultrasonics, vol SU-25, no. 3, May 1978. [3] R. E. Collins, "Foundations of Microwave Engineering'', McGraw-Hill, 1966. [4] A. J. Mulholland, S. N. Ramadas, R. L. O'Leary, A. Parr, A. Troge, R. A. Pethrick and G. Hayward, “Enhancing the performance of piezoelectric ultrasound transducers by the use of multiple matching layers.” IMA Journal of Applied Mathematics, 73, 936 - 949, 2008. [5] G.~Hayward and M.~N.~Jackson, “A Lattice Model of the Thickness - Mode Piezoelectric Transducer”, IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control, vol. 33, no. 1, pp. 41-50, 1986. [6] S. N. Ramadas, “A knowledge based approach to design ultrasonic transducers and arrays”, Ph.D. Thesis, University of Strathclyde, Glasgow, UK, 2009.  [7] A. R. Mackintosh, A.J.C. Kuehne et al,’Novel polymer systems for deep UV microlens arrays’ Journal of Physics D: Applied Physics, Vol 41, 094007, 2008 

A knowledge based approach to design ultrasonic transducers and arrays”,

A matrix technique for analyzing the performance of multi-layered front matched and backed piezoelectric ceramic transducers'',

Enhancing the performance of piezoelectric ultrasound transducers by the use of multiple matching layers.”

Foundations of Microwave Engineering'',

Kuehne et al,’Novel polymer systems for deep UV microlens arrays’

Lattice Model of the Thickness -Mode Piezoelectric Transducer”,

The deisgn of effecient broadband piezoelectric transducers'',

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http://dx.doi.org/10.1109/ULTSYM.2009.5441463

Tapered transmission line technique based graded matching layers for thickness mode piezoelectric transducers

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