Modeling of an Ultrasonic Transducer for Cardiac Imagingmate.tue.nl/mate/pdfs/12271.pdf · An integrated ultrasonic transducer sends the acoustic waves into the heart wall and receives

Modeling of an UltrasonicTransducer for Cardiac Imaging

S. Moten

D&C 2010.049

Traineeship report

Coach(es): dr.ir N. Mihajlovic (Philips Research)

Supervisor: prof.dr. H. Nijmeijer

Eindhoven University of TechnologyDepartment of Mechanical EngineeringDynamics & Control Group

Eindhoven, October, 2010

Abstract

Within Philips Research, ultrasonic transducers are integrated into the minimallyinvasive needles and catheters for cardiac imaging. The existing ultrasonic trans-ducers have a low signal to noise ratio (SNR) and a low bandwidth of the receivedecho and, therefore, the transducer does not perform well for the cardiac imagingapplication. A high SNR is needed to increase penetration depth into heart tissueand an increased bandwidth is required to improve resolution.

Therefore, there is a need for a model that can predict the behavior of the ultrasonictransducer. In this report, a model is developed and implemented for the completeultrasonic measurement system. This model is used for the improvement of thedesign of a transducer and can also be used for design of ultrasonic transducer forvarious applications. Various parameters needed for the simulation are estimatedexperimentally. The comparison between the response of an ultrasonic transducerand obtained model indicates the high accuracy of the model to predict the behav-ior of an ultrasonic transducer.

i

ii

Preface

This traineeship report is written as a part of the fulfillment of my Master’s ed-ucation in Dynamic and Control group at department of Mechanical Engineering,Eindhoven University of Technology (TU/e). It is pleasure for me to thank all thosewho made this possible.

First of all, I owe my deepest gratitude to Prof. Henk Nijmeijer (TU/e) who madehis support available in a number of ways and made it possible to start my trainee-ship in Philips Research (High Tech Campus).

I am heartily thankful to Dr. ir. Nenad Mihajlovic (Philips Research) whose encour-agement and guidance from the beginning to the end enabled me to develop an un-derstanding of the subject. Finally, I would like to thank the whole team workingon transducer in Minimally Invasive Health Care group (Philips Research), espe-cially Dr. ir. Szabolcs Deladi for making it possible for me to attend the weeklygroup meetings and gave me an opportunity to discuss and share ideas amongstthe team.

Last but not least, I want to pay regards and blessings to my parents who alwaysstood behind me for support.

Sikandar Moten, EindhovenSeptember, 2010

iii

iv

Executive Summary

In this report, the model of an ultrasonic measurement system is implemented topredict the response of an ultrasonic transducer. The complete system is comprisedof an ultrasonic transducer, cable, pulser, receiver, attenuator and acoustic medium.

The main goal of the model is to improve the signal to noise ratio (SNR) and band-width of a transducer. In order to accomplish this, an ultrasonic system is dividedinto three systems: the generation system, the propagation system and the recep-tion system. The frequency response function for each of these linear time invariantsystems is determined. Some parameters needed for the simulation, which are notavailable in material data sheet, are found experimentally. Then, model results arevalidated for the existing configuration of the transducer.

It is shown that the implemented model has a good agreement with the measure-ment results. Based on this, the effects of the mechanical construction on the trans-ducer performance are studied. Finally, some improvements in the mechanical con-struction are suggested and adopted. For the specified input conditions, the signalto noise ratio (SNR) is increased by 160%, whereas, the increase in bandwidth isrecorded as 79%. Finally, further improvements are suggested to improve an ultra-sonic diagnostic system.

v

vi

Contents

Abstract i

Preface iii

Executive summary v

Contents vii

1 Introduction 1

1.1 Cardiac Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Cardiac Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Ultrasonic Measurement System–System Description . . . . . . . . . 3

1.4 Modeling of the Ultrasonic System–An Overview . . . . . . . . . . . 4

1.5 Project Description and Organization . . . . . . . . . . . . . . . . . . 5

2 Modeling and Validation of the Ultrasonic System 7

2.1 Sound Generation System . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Pulser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1.1 Characterization of pulser . . . . . . . . . . . . . . . 8

2.1.1.2 Attenuator (optional) . . . . . . . . . . . . . . . . . . 8

2.1.1.3 Measurement of circuit parameters of pulser withattenuator . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 Transmitting transducer . . . . . . . . . . . . . . . . . . . . . 10

2.1.2.1 Basic configuration of the ultrasonic transducer . . 10

2.1.2.2 Modeling of an ultrasonic transducer . . . . . . . . 10

vii

2.1.3 Frequency response function of the sound generation system 15

2.2 Acoustic/Elastic Propagation System . . . . . . . . . . . . . . . . . . 16

2.2.1 Frequency response function of the propagation system . . . 17

2.2.2 Blocked force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Sound Reception System . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Receiving transducer . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.3 Frequency response function of the sound reception system 23

2.4 Complete Ultrasonic Measurement System . . . . . . . . . . . . . . . 24

2.4.1 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Transducer Improvement 27

3.1 Front Layer Improvement . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Selection of the front layer . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Effect of the thickness of the front layer . . . . . . . . . . . . . 28

3.2 Backing Layer Improvement . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Selection of backing layer . . . . . . . . . . . . . . . . . . . . 29

3.2.2 Effect of the thickness of backing layer . . . . . . . . . . . . . 30

3.3 Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Results and Experimental Validation . . . . . . . . . . . . . . . . . . . 32

4 Conclusion and Recommendations 35

4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

A Parameter Estimation 37

A.1 Speed of Sound in the Backing Plate . . . . . . . . . . . . . . . . . . . 37

A.1.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 37

A.1.2 Calculation for the speed of sound and attenuation constant . 39

A.2 Properties of the Piezo Crystal . . . . . . . . . . . . . . . . . . . . . . . 40

A.2.1 Estimation of the capacitance . . . . . . . . . . . . . . . . . . . 40

A.2.2 Estimation of the electromechanical coupling coefficient . . . 41

viii

B Hardware Description 43

B.1 Motion Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

B.2 Network Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B.3 Digital Oscilloscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B.4 Current Probe and Amplifier . . . . . . . . . . . . . . . . . . . . . . . 44

References 48

ix

x

Chapter 1

Introduction

1.1 Cardiac Ablation

The heart is a pump that functions by pumping the blood in a controlled sequencethrough its four chambers: left atrium, right atrium, left ventricle and right ventri-cle. Each heart beat originates as an electrical impulse from a small area of tissuein the right atrium of the heart called the sinus node. The impulse initially causesboth of the atria to contract, then activates the atrioventricular node which is nor-mally the only electrical connection between the atria and the ventricles. The im-pulse then spreads through both ventricles causing a synchronized contraction ofthe heart muscle.

So, for a healthy person, this regular flow of electricity through defined paths isthe basis of normal heart muscle contractions which results in normal heart beat.But, sometimes this flow of electricity becomes irregular due to a faulty electricalpathway and, consequently, the heart beats very erratically. Such heart diseasesare termed arrhythmia in medical science. In adults the normal resting heart rateranges from 60 to 80 beats per minute. The resting heart rate in children is muchfaster.

Medicine often helps in various cases for the treatment of arrhythmia. However,an effective treatment is to destroy a heart tissue in a controlled manner. Conse-quently, sources of unwanted pulses or electrical pathways are destroyed. Cardiacablation is a minimally invasive procedure in which a catheter– a thin flexible tubeas shown in figure 1.1– is inserted in the blood vessel and then moved into theheart by surgeons. Once the tip of the catheter has reached the targeted place intothe heart, Radio Frequency(RF) energy is used to destroy the tissue.

1

Introduction

Figure 1.1: A typical catheter used for ablation [Courtesy: Philips Research]

1.2 Cardiac Imaging

During cardiac ablation, there is a potential risk to destroy the complete heart walldue to extra energy. There is a need to monitor the wall thickness and to measurethickness of lesion– abnormal tissue– throughout the ablation process as shownin figure 1.2 . In Philips Research, the group of Minimally Invasive Health Careintegrates the ultrasonic transducer in needles and catheters so that imaging andablation can be done simultaneously.

Catheter

Heart Wall

Insertion of catheter through blood vessel

Defective Site

Figure 1.2: Cardiac ablation process [Courtesy: Philips Research]

An integrated ultrasonic transducer sends the acoustic waves into the heart walland receives the echo to characterize the heart tissue. The signal received backfrom the transducer is processed and the image is created.

2

Introduction

1.3 Ultrasonic Measurement System–System Description

An ultrasonic measurement process involves the generation of ultrasound by thetransducer, propagation of these ultrasonic waves into the propagating mediumand then reception of these waves through the transducer again. The completemeasurement system consists of a pulser, transducer and receiver. The pulser sendsthe electrical pulse via a cable to an ultrasonic transducer. The transducer convertsthe electrical pulse into an acoustical pulse in the generation system and an acous-tical into an electrical signal in the reception system. In addition, a 50 Ω attenuatorcan be used in between the transducer and the pulser/receiver in order to avoidthe electrical reflections.

Transmission and reception of acoustic waves can occur via the same or a separateultrasonic transducer. The method where the same transducer is used is calledpulse echo method as shown in figure 1.3, whereas, with a separate transducer themethod is called pitch catch method as shown in figure 1.4. The pulse echo methodis used for cardiac imaging through a catheter. However, it is shown in AppendixA that to find some crucial material properties for the simulation we need the pitch-catch setup as well.

Generation /

Reception System

Acoustic Propagation

System

Figure 1.3: Pulse echo method

Acoustic Propagation

System

Generation

System

Reception

System

Figure 1.4: Pitch catch method

A fundamental study of acoustics revolves around the generation, propagation andreception of the acoustic waves. Generation and reception of acoustical wavesis usually done by transduction i.e. a transducer converts one form of energyinto acoustical energy and vice versa, whereas, in the propagation system acous-tic waves are influenced by properties of the propagating medium. The ultrasonicmeasurement system also follows this basic hierarchy as shown in figure 1.5, andbased on this hierarchy we will model the system in three parts.

3

Introduction

Generation System

Propagation

System

Reception System

Figure 1.5: Acoustic systems in an ultrasonic measurement system

1.4 Modeling of the Ultrasonic System–An Overview

Modeling of an ultrasonic measurement system comprises the individual modelingof electrical components (pulser, receiver etc.), the electro-mechanical transducerand the acoustic propagation medium.

The model of electrical components involved in transmission and the transducerwill be combined in a single Linear Time Invariant (LTI) system that characterizesthe complete sound generation system by the frequency response function tG(ω).This frequency response function relates the pulser voltage Vs and the force Ft gen-erated at the face of the transducer. Then, the frequency response function for theacoustic wave propagation tA(ω) relates the transmitting force Ft and the forcereceived back at the face of the receiving transducer Fb. Similar to the sound gener-ation system, the frequency response function for the reception system tR(ω) com-prises the receiving transducer and the electrical components involved in the recep-tion. This frequency response function relates the force Fb and the electrical signalmeasured at the output port of the receiver VR. The complete ultrasonic system isshown in figure 1.6.

Figure 1.6: Ultrasonic system model as a series of LTI system

With the combination of the first two frequency response functions, a 1D pressurefield in the acoustic medium can be simulated, whereas, with the combination ofall these frequency response functions we can get the echo at the output port of thereceiver due to the excitation by the pulser. Furthermore, it is very convenient towork in the frequency domain during the complete modeling of components and

4

Introduction

combination of LTI systems rather than to work in the time domain. Therefore,Fourier analysis at different stages of the modeling will become an integral part ofthe modeling.

1.5 Project Description and Organization

The existing ultrasonic transducers have a low signal to noise ratio (SNR) and alow bandwidth of the received echo and the transducer does not perform well forthe cardiac imaging application. A high SNR is needed to increase the penetrationdepth into heart tissue and an increased bandwidth is required to improve resolu-tion.

The aim of this project is to gain a better understanding of how the mechanicalconstruction of an ultrasonic transducer influences the overall performance of thetransducer. The focus is on an ultrasonic transducer with resonant frequency of 20MHz and size less than 3 mm so that it can fit into the catheter. To accomplish thistask, the project can be stated into three parts.

• Make a model of ultrasound transducer and perform experimental validationof the model.

• Based on the obtained model, study the influence of mechanical constructionon the overall performance of the transducer.

• Suggest technical (mechanical) improvements for such transducers.

Chapter 2 is based on modeling of the ultrasonic system and validation of obtainedmodel with measurements. Various parameters needed to simulate the model,which are not available in a material data sheet, are estimated in Appendix A.Chapter 3 discusses about improvements that can be done to increase the SNRand bandwidth of the transducer. Furthermore, prediction of the response of animproved transducer is verified again with the experimental measurements. Chap-ter 4 concludes the overall assignment and gives recommendations for further im-provements in an ultrasonic diagnostic system.

5

6

Chapter 2

Modeling and Validation of theUltrasonic System

In the previous chapter, we showed that complete ultrasonic measurement systemcan be modeled as a series of three LTI systems. Now, we present the modeling ofeach of those systems individually.

2.1 Sound Generation System

In the sound generation system,the model of pulser, attenuator, cable and trans-ducer are included in a single Linear Time Invariant (LTI) system that characterizesthe complete system by the frequency response function tG. This frequency re-sponse function relates the input source voltage and the force generated at the faceof the transducer. Cables are used to transfer the electrical pulse from the pulserto the ultrasonic transducer and from the transducer to the receiver. For frequen-cies in the range of 1 to 20 MHz, there is very little discussion of cabling effectsin literature [1] because of negligible effects of cable in this range. We neglect thecabling effects as the resonant frequency of our transducer is 20 MHz. Thus, weonly model the pulser in combination with the attenuator and the transducer in thesound generation system.

2.1.1 Pulser

In an ultrasonic measurement system, the pulser is used to generate the pulsewhich drives the transmitting ultrasonic transducer. For the existing measurementsetup, we are using a custom made pulser. This pulser provides broadband nega-

7

Modeling and Validation of the Ultrasonic System

tive spike excitation for maximum broadband transducer performance. For mod-eling purpose, the internal characteristics of the electrical driving circuit of pulserare not relevant since we are only interested in output characteristics of the pulse:the waveform of the spike excitation and the internal impedance of the pulser.

2.1.1.1 Characterization of pulser

The output of the pulser depends on the settings (mainly energy and dampingsettings) selected by the user. We noticed that the pulser does not act linearly withrespect to these settings. The cause of this non-linearity is reported as the internalprotection circuit for a commercial pulser in [1]. C. Dang et al. in [2] assume thepulser as a linear device and expressed the pulser by an equivalent voltage sourceand impedance using Thevenin’s theorem. This assumption is valid because wecharacterize the pulser for specific energy or damping settings. Both voltage sourceand impedance of the pulser depend on the combination of these two settings.

2.1.1.2 Attenuator (optional)

To transmit the electrical signal between the pulser and ultrasonic transducer, acoaxial cable of 50 Ω impedance is usually used in ultrasonic measurement system.If the output impedance of pulser is not 50 Ω, then, this creates an impedancemismatch between the frequency dependent internal impedance of the pulser andthe impedance of the cable. Due to this mismatch, electrical reflections take placeboth during transmission and reception of the electrical signal which may causethe electrical interference of signals during measurement. One possible solution todecrease electrical reflections is to attach an attenuator between the cable and thepulser.

2.1.1.3 Measurement of circuit parameters of pulser with attenuator

Using Thevenin’s theorem we can replace the electrical network of the pulser byan equivalent voltage source Vs and impedance Zs as shown in figure 2.1. In orderto determine Vs and Zs, we use an open circuit (figure 2.1) and a circuit where weattach a known impedance to the pulser (figure 2.2). In the open circuit no currentis flowing through the circuit; consequently, an equivalent source voltage Vs canbe estimated by measuring the open circuit voltage Vopen across the pulser outputport:

Vs = Vopen (2.1)

Then, we attach the known impedance Zi of 50 Ω to this circuit as shown in figure2.2. Now, we measure the voltage across the known load Vi and using the voltage

8


divider formula as given in equation (2.2), we can find the impedance of the pulser.

Zs = Zi

[Vs(ω)

Vi(ω)− 1]

(2.2)

Figure 2.1: Thevenin’s equivalent cir-cuit for the pulser

Figure 2.2: 50 Ω resistor attached tothe pulser circuit

Therefore, we can characterize the pulser completely. Both measurements are madeby an Agilent Technologies Oscilloscope DSO 6034A (hereby referred to as oscillo-scope) and converted in to the frequency domain by Fourier transformation. Themeasured source voltage both in time and frequency domain are shown in figures2.3 and 2.4, whereas, the equivalent impedance is shown in figure 2.5.

Furthermore, the addition of an attenuator makes the impedance of the overall in-put system, pulser and attenuator, close to 50 Ω over a wide band of frequencyrange as shown in figure 2.5. This inclusion reduces the electrical reflections signif-icantly, but, at the expense of a decrease of the energy transfer (voltage signal) asshown in figure 2.3 and figure 2.4. Keeping in mind that the purpose of the presentassignment includes the validation of the model, to avoid electrical interferencesduring measurements, we add the attenuator in the ultrasonic system and use themodel of the equivalent source voltage and impedance with attenuator.

.15 .25 .35 .45 .55 .65−250

−200

−150

−100

−50

0

50Pulser/Source Voltage

Without 3dB attenuatorWith 3dB attenuator

Vol

tage

[V]

Time [µ sec]

Figure 2.3: Measured effect of attenua-tion on the source voltage in the timedomain

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100


Mag

nitu

de [V

/MH

z]

Frequency [MHz]

Figure 2.4: Measured effect of attenu-ation on the source voltage in the fre-quency domain

9


0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100Source Impedance


Mag

nitu

de [O

hm]

Frequency [MHz]

Figure 2.5: Measured effect of attenuation on the impedance in the frequency do-main

2.1.2 Transmitting transducer

Before we start with the modeling of the ultrasonic transducer, it is necessary tounderstand the basic configuration of the transducer.

2.1.2.1 Basic configuration of the ultrasonic transducer

The outer diameter of the catheter shown in figure 1.1 is 7F (3F = 1mm), and anultrasonic transducer should fit in such catheter. For the modeling of the trans-ducer, we are not interested in the shape of the catheter (housing) and we considerthe transducer as an independent component irrespective of its application. Anultrasonic transducer represents a layered structure as shown in figure 2.6. The ba-sic component of a transducer is piezo crystal which converts the electrical energyinto mechanical (acoustic) energy and vice versa. In order to support the piezocrystal, a backing plate is used at the back of the piezo crystal. A wear protectionplate is used at the front side. One or more front layers can be used to improvethe power transmission between the piezo crystal and the propagating fluid. Theeffect of these plates is discussed in detail in the following sections. The diameterof the piezo crystal is 1 mm. A simplified construction of an ultrasonic transduceris shown in figure 2.6.

2.1.2.2 Modeling of an ultrasonic transducer

In this section, we model the ultrasonic transducer as a transmitter. The transducerhas a backing layer at the back and a single layer at the front side. In order to modelthe complete transducer, we have to model the piezo-crystal, the backing layer andthe front layer separately. Two well known models used for modeling of an ultra-

10


Figure 2.6: Simplified construction of an ultrasonic transducer

sonic transducer are Mason’s and KLM models, see [1]. These models are equiva-lent circuit models and use different electrical configuration,see [3]. These modelsare 1-dimensional in nature and are very effective in predicting the response of anultrasonic transducer. In this report, we used Mason’s model.

Piezo crystal: The equivalent circuit of Mason’s model of a piezo crystal is shownin figure 2.7. The circuit has three ports, one electrical and two mechanical portsrepresenting the front and back face of the piezo crystal. The front matching layersand backing layer can be added to the mechanical ports at the front and the backside respectively, in order to model the entire transducer. Finally, a load can beadded to the front side and electrical connections are made at the electrical port tomodel the entire sound generation system.

Figure 2.7: Three port Mason’s modelfor the piezo crystal

Figure 2.8: Conversion of three port intotwo port by Sittig,[4]

11


Backing port: The three port Mason’s model can be reduced to a two port modelif the material of backing plate is defined as a given acoustic impedance. Sittig in[4] specifies the acoustic impedance of the backing material and converts the threeport Mason’s model into a two port system; one electrical and one front mechanicalport, as shown in figure 2.8. For this two port model, Sittig explicitly shows anexpression for the frequency response function matrix which relates the voltageand current, on the electrical port, to the force and velocity, at the front mechanicalport: [

VI

]=

[A0 B0C0 D0

] [F0v0

](2.3)

Here,[A0 B0C0 D0

]=

1ϕQ0

[1 i ϕ2/ωC0

i ωC0 0

].[

cos(γ0) + i Zb sin(γ0)/Z0) Zbcos (γ0) + i Z0sin(γ0)i sin(γ0)/Z0 2cos (γ0)− 1+ i Zbsin (γ0)/Z0

],

Q0 = cos (γ0)− 1 + i Zbsin (γ0)/Z0

Here, Z0 is the acoustic impedance of the piezo crystal, Zb is the acoustic impedanceof the backing material, γ0 is the normalize frequency constant and ϕ is an idealtransformer ratio for the transducer . The relation of these quantities with backingmaterial properties and piezo crystal properties and size are given as:

Z0 = ρ0c0S0Zb = ρbcbS0

ϕ =ω0C0Z0k2

Tπ

γ0 =π ff0

=ω

c0l

(2.4)

For any frequency ω, the frequency response matrix for the Sittig model can bedescribed by the parameters given in table 2.1

12


Table 2.1: Description of parameters for the Sittig ModelParameter Description Symbol Value used

Piezo crystal (Lead Zirconate Titanate PZT-5A)Density of piezo disc ρ0 7500 kg/m3

Speed of sound in piezo disc c0 4119 m/sFundamental frequency of disc ω0 1256× 105 rad/sThickness of disc l 102× 10−6 mRadius of disc a 0.5× 10−3 mCross-sectional area of piezo S0 7.85× 10−7 m2

Electromechanical coupling coefficient kT 0.2Clamped capacitance C0 0.77× 10−10 F

Backing material (Zeonex E48R)Density of backing layer ρb 2700 kg/m3

Speed of sound in backing layer cb 6226 m/s

Most of these values can be found in material data sheets except kT, C0 and cb,which are estimated experimentally. This is due to the fact that electromechani-cal coupling coefficient kT and clamped capacitance of piezo crystal C0 are highlyinfluenced by type of mechanical construction and by the transducer manufactur-ing process, whereas, the speed of sound in the backing layer is not available inthe manufacturer’s data sheet. A detailed description for finding these parametersexperimentally is given in Appendix A.

Intermediate or matching layers: Front layers are normally used as wear pro-tection plate and impedance matching plate to improve the power transmission.These layers can be represented by two port acoustic system and behave as a trans-mission line. The equivalent circuit for any layer can be modeled as shown in figure2.9. This model can be found in electrical engineering text books.

Figure 2.9: Representation of an intermediate layer

13


Such two port acoustic transmission line relates the force and velocity of one portto the second port. The frequency response function matrix of this two port modelis given by: [

Fn−1vn−1

]=

[An BnCn Dn

] [Fnvn

](2.5)

Here n represents the layer number, with

[An BnCn Dn

]=

[cos(γn) i Zn sin(γn)

i sin (γn)/Zn cos(γn)

]The frequency response function matrix can be describe for any frequency ω bythe acoustic impedance of the intermediate layer Zn and the normalize frequencyconstant γn. The relation of these quantities with the layer properties and size aregiven as:

Zn = ρncnS0

γn =ω

cnln

(2.6)

For any frequency ω, the frequency response function matrix for parylene-C as amatching layer can be described by the parameters given in table 2.2.

Table 2.2: Description of parameters for the intermediate/matching layerParameter Description Symbol Value used

Matching layer (Parylene-C)Density of layer ρn 1289 kg/m3

Speed of sound in layer cn 2142 m/sThickness of layer ln 3× 10−3 m

OthersCross-sectional area of Piezo S0 7.85× 10−7 m2

Sittig’s model is particularly useful to consider any piezo-electrically inactive layer.Such individual layers can concatenate at the front acoustic port as shown in figure2.10. Mathematically, we can join these layers to Sittig’s model by simply multi-plying the frequency response function matrix of the piezo crystal by frequencyresponse function matrix of the layers in the same order as it will joined in practice.Thus for the first layer, we can write:

[T] =[

A0 B0C0 D0

] [A1 B1C1 D1

](2.7)

More than one layer at the front can be handled exactly in the same way and the

14


resulting frequency response function matrix becomes:

[T] =[

AT BTCT DT

]=

[A0 B0C0 D0

] [A1 B1C1 D1

]. . . . . .

[An BnCn Dn

](2.8)

Thus, we get the relationship between voltage and current at the electrical port andthe acoustical force and velocity at the mechanical port of the final layer as:[

VI

]=

[AT BTCT DT

] [Fnvn

](2.9)

2.1.3 Frequency response function of the sound generation system

Here, we combine the model of the pulser as shown in figure 2.1 with the model ofthe transmitting transducer. We also add the acoustic impedance of load or fluidto the front side of the last layer. This is done because the transducer is immersedin fluid while generating a sound. The equivalent circuit diagram for the completesound generation system can be obtained by concatenation of the pulser modelto the electrical port of the transducer as shown in the figure 2.10. The model oftransmitting transducer in combination with the model of pulser and immersionin fluid is termed as the sound generation system. With equation (2.9) and figure2.10, C.Dang et al. in [1] explicitly mention the frequency response function, whichrelates source voltage Vs with the force generated at the face of the transducer Ft =Fn, as:

tG (ω) =Ft(ω)

Vs(ω)=

Zrad

(Zrad AT + BT) + (ZradCT + DT) Zs(2.10)

Here, Zrad = ρ1c1S0 is the radiation impedance of the medium and can be calcu-lated by the values given in table 2.3.

We have completed the sound generation system. However, before going to theacoustic propagation system it is convenient to consider the model limitations.

Mason’s model has the following limitations:

• The model is one dimensional, therefore only a one dimensional pressurefield can be investigated.

• In the model it is assumed that the thickness of the backing is semi-infinitewithout losses [5], which means that any acoustic wave transmitted to theback does not back reflect from other interfaces. Practically, these reflectionscan interfere with the received echo from the front. However, we can removethis interference by using a highly attenuating material as backing plate sothat the signal attenuates enough and does not reflect back.

15


nradnt vZFF

V

nF

I

nv

Figure 2.10: Model of the complete sound generation system

• The model is valid for thickness mode which means the lateral dimension ofthe crystal should be much larger than the thickness. In our case, crystal hasa diameter of 1 mm with a thickness of 0.102 mm and therefore it satisfies thecondition of thickness mode.

• The model is made for a thin, loss-less, disc shape piezo crystal. This is alsovalid for our case as we are using a circular disc shape ceramic based PZT-5A as piezo material. Most of the ceramic based piezo crystals are near toloss-less in contrast to polymer based piezo material.

• The model can simulate only the first echo from the reflective surface (tissueor metal block). Inner penetration of the waves into material is not possible.But this first echo is enough to improve the transducer and to validate theresponse.

2.2 Acoustic/Elastic Propagation System

In previous sections, we described the complete sound generation system by thesimple frequency response function which relates the source (pulser) voltage and

16


the force exerted by the transducer in the fluid or propagating medium. For thepulse echo setup shown in the figure 1.3, this generated force travels as acousticwave through a fluid medium, reflects back from the front reflecting surface andthen returns back to the receiving transducer. This process of traveling of acousticwaves in the propagating medium is called the acoustic/elastic propagation sys-tem.

2.2.1 Frequency response function of the propagation system

The relationship between the force exerted by the transducer during transmissionFt and the force acting on the face of the transducer during reception FB representfrequency response function:

tA (ω) =FB(ω)

Ft(ω)(2.11)

Sound propagation in any medium involves complex mechanisms such as the at-tenuation of waves in the fluid and three dimensional wave diffraction and scat-tering effects. Many authors assume this propagation as a loss free ideal transmis-sion and compare the response of the transducer with the model without includingthese effects,see [6]. However, Sanchez et al. in [7] explicitly gives the frequencyresponse function which includes the effects of all these phenomena as:

tA (ω) =FB(ω)

Ft(ω)= 2R12exp (−2αw (ω) D) . (2.12)

1− exp

(i kp1a2

2D

)[J0

(kp1a2

2D

)− i J1

(kp1a2

2D

)]

Here, J0 and J1 are Bessel function of order zero and one respectively. The wavenumber kp1 for the propagating fluid and reflection co-efficient R12 for the planewave at normal incidence for the interface between fluid and block are given by:

kp1 =ω

c1

R12 =ρ2c2 − ρ1c1

ρ2c2 + ρ1c1

(2.13)

A description of the parameters used in equation (2.12) and (2.13) and actual valuesof these parameters for water as the propagating fluid and aluminum alloy as thereflecting block is given in table 2.3.

The formula mentioned in table 2.3 for frequency dependent attenuation in wateris derived from [7]. This attenuation is measured in Nepers/m with frequency fgiven in Hz.

17


Table 2.3: Description of parameters for the frequency response function of thepropagation system

Parameter Description Symbol Value usedPropagating Medium (De-mineralized Water)

Density of medium ρ1 1000 kg/m3

Speed of sound in medium c1 1482 m/sAttenuation in the medium αw (ω) 25.3×10−15 f 2 Nepers/m

Reflecting block (Aluminum Alloy)Density of block ρ2 2700 kg/m3

Speed of sound in block c2 6226 m/sOthers

Transducer distance from block D 0.003 mRadius of disc a 0.5× 10−3 mCross-sectional area of piezo S0 7.85× 10−7 m2

2.2.2 Blocked force

The force FB in equation (2.12) is called the blocked force and it acts on the face ofthe transducer during reception. It is defined as the force that would be exerted onthe receiving transducer if its face is held rigidly fixed (motionless).

In order to model the pressure field, we need some more insight in the blockedforce. Consider an immersion setup in which the acoustic waves incident on thereceiving transducer, as shown in figure 2.11. If we neglect any wave diffractioneffects at the edges of the receiving transducer, then, these waves will reflect backand the total pressure pB at the transducer face is:

pB = pinc + pre f = 2pinc (2.14)

If S0 is the area of the face of the transducer, then the blocked force FB =∫∫

S pB dS0is twice the force Finc =

∫∫S pinc dS0 exerted by the wave incident on the same area:

FB = 2Finc (2.15)

Finc and pinc are the incident force and pressure respectively acting on the area S0as if no transducer is present. Equations (2.14) and (2.15) are very useful becauseonce the frequency response function of the propagation system is obtained, wecan model the one dimensional pressure field of the transmitting transducer.

18


Figure 2.11: Blocked force due to the incident and reflected wave

2.3 Sound Reception System

Now, after completion of the sound generation and propagation system, we modelthe reception system in which we define a relationship between the blocked forceFB and the voltage received VR from the receiver. In the reception system, we haveto incorporate all the basic elements of the reception system which includes thereceiving transducer and receiver.

2.3.1 Receiving transducer

The receiving transducer can be modeled as a two port system which converts theacoustic waves at the mechanical port to the electrical energy at the electrical port.When the transmitting transducer is used as the receiving transducer, its frequencyresponse function matrix becomes (also see equation (2.9)):[

Vr−Ir

]=

[AR BRCR DR

] [Fn−vn

](2.16)

Here, Vr and Ir are the voltage and current at the electrical port respectively, andFn and vn are the total force acting on the face of the transducer and the velocity ofthe transducer surface respectively. This change in signs as compared to equation(2.9) for the transmitting transducer is due to the fact that the direction of currentand velocity is opposite as compared to those in generation system. Rearrangingthe above equation, we will get:[

VrIr

]=

[AT −BT−CT DT

] [Fnvn

](2.17)

Furthermore, as the reception system is the reciprocal of the transmitting system[1], it is convenient to express the mechanical and electrical quantities in the form.[

Fnvn

]=

[DT BTCT AT

] [VrIr

](2.18)

19


Here,[

AT −BT−CT DT

]−1

=

[DT BTCT AT

]because of reciprocity.

Since, the elements of the receiving transducer in equation (2.9) are identical tothose of the receiving transducer, we do not have to model the receiving transduceragain. If we define AR = DT, BR = BT, CR = CT and DR = AT then:[

Fnvn

]=

[AR BRCR DR

] [VrIr

](2.19)

To find the force Fn acting on the transducer face, we can divide the scenario in twocases.

Case 1: For case one, the face of the transducer is kept rigidly fixed as shown infigure 2.12. The pressure from the incident waves, pinc , and pressure from thereflected wave, pre f , will combine to have the blocked pressure pB at the transducerface. The integral sum of this blocked pressure over the entire face is the force FB.

Case 2: For case two, incident waves are absent and the pressure at the transducerface is created by the motion of the transducer face as shown in figure 2.13. This issame as if the transducer is radiating force during transmission. If the transducerface is moving with velocity vn then the force due to this motion, Fs, will be:

Fs = −Zradvn (2.20)

Here, the force is negative because we used the convention that the velocity is flow-ing into the transducer and the transducer face is moving normal outwards.

Figure 2.12: Blocked force due tothe incident and reflected wave

Figure 2.13: Force due to the motion of trans-ducer surface

In the sound reception system, the acoustic waves incident on the transducer faceare reflect back. These incident and reflected waves create a force on the transducerface and excite the piezo crystal. Due to this excitation, the face of the transducer is

20


set into motion which creates a force in the propagating medium. So, the total forceacting on the face of the transducer is due to the combination of case one and two:

Fn = FB + Fs = FB − Zradvn (2.21)

2.3.2 Receiver

In an ultrasonic measurement system, the receiver is used to get the signal fromthe receiving ultrasonic transducer, amplifies or attenuates it depending on the re-quirement and applies filtering to the signal. A custom made system (transceiver)that is used as a pulser also includes the receiver in it. Similar to the pulser, we arenot interested in the internal characteristics of the complex electrical driving circuitof the receiver because it is not relevant for modeling purposes. As the receiverprovides an electrical termination at one end of the cable and amplifies the signal,we model the receiver as an equivalent receiving impedance Zr(ω) and then wemodel the amplifier as an amplification factor K(ω).

For characterization of the receiver, we used the same approach as used by Schmerret al. in [3]. As for the application of imaging of heart, we have to use the ultrasonictransducer in pulse echo mode; so we characterize the transducer for that mode. Wemeasure both the voltage Vr(t) and current Ir(t) at the receiver input and only thevoltage VR(t) at the receiver output. An oscilloscope is used to measure the voltagemeasurements, while a current probe in combination with an oscilloscope is used tomeasure the current. The sampled data Vr(t), Ir(t) and VR(t) is transformed to thefrequency domain by taking its Fourier Transformation to get the correspondingfrequency domain values Vr (ω), Ir(ω) and VR(ω) respectively. The amplificationfactor and receiver impedance are obtained by:

K (ω) =VR (ω)

Vr (ω)

Zr (ω) =Vr (ω)

Ir (ω)

(2.22)

Both the electrical impedance and the amplification factor of the receiver are de-pendent on the chosen settings by the user and both are frequency dependent. Thereceiver part of the transceiver has two main parameters i.e. gain and attenuation.Combination of these parameters can provide many possible combinations of theamplification factor K(ω) and the electrical impedance Zr(ω). In pulse echo ex-periments as shown in figure 1.3, the transceiver uses the same port for sending orreceiving the signal, so the output signal from the receiver is also influenced by thedamping setting of the pulser. This means that amplification factor K(ω) and theelectrical impedance Zr(ω) also affect by the damping setting. The dependency ofreceiver gain and impedance on the damping settings can be seen in figure 2.14.

21


15 20 25

0.5

1

1.5

Setting 2Setting 1

Setting 3

Mag

nitu

de [G

ain]

0

Frequency [MHz]

Receiver Gain

15 20 250

100

200

300

400

500

600

Setting 1Setting 2Setting 3

Mag

nitu

de [O

hm]

Receiver Impedance

Frequency [MHz]

Figure 2.14: Receiver gain and impedance for the pulse-echo mode

Although, the damping setting influence the K (ω) and Zr (ω) non-linearly but weuse the specific setting and we characterize for that single setting only. Further-more, addition of an attenuator (to decrease electrical reflections) affects the re-ceiver characteristics. Figure 2.15 shows the effect of the attenuator on gain andequivalent impedance. For the model, we found the values of receiver gain andequivalent impedance with attenuator at 20 MHz from the figure 2.15. These val-ues are given in table 2.4.

15 20 25

0.5

1

1.5


Mag

nitu

de [G

ain]

0

Receiver Gain

Frequency [MHz]15 20 25

0

100

200

300

400

500

600


Receiver Impedance

Mag

nitu

de [O

hm]

Frequency [MHz]

Figure 2.15: Receiver gain and impedance with and without attenuator

Table 2.4: Gain and impedance of the receiver with 3dB attenuator at 20 MHzParameter Symbol Value usedGain K (ω) 0.65Equivalent Impedance Zr (ω) 120 Ω

22


2.3.3 Frequency response function of the sound reception system

In this section, we combine the model of the receiver with the model of receivingtransducer which is the same as a transmitting transducer. If we compare figure2.10 with figure 2.16, it can be clearly seen that the front part of transmitting modelis replaced by the blocked force and the equivalent impedance. This configurationof the front part represents the total force acting on the transducer, as given by therelation shown in equation (2.21). Moreover, pulser is replaced by receiver withan impedance termination and gain. With equations (2.19), (2.21), (2.22) and figure2.16, C.Dang et al. in [2] explicitly mention the frequency response function, whichrelates voltage at the output port of the receiver VR and the blocked force acting onthe transducer FB, as:

tR (ω) =VR

FB=

ZrK(Zrad DR + BR) + (Zrad CR + AR) Zr

(2.23)

rV

nF

nv

rI

Figure 2.16: Model of the complete reception system

23


2.4 Complete Ultrasonic Measurement System

With all the three frequency response functions given in equations (2.10), (2.12) and(2.23), we can simulate the output response from the receiver VR of the ultrasonicmeasurement system for the input source voltage Vs by:

VR

Vs= tR.tA.tG =

VR

FB.FB

Ft.Ft

Vs

⇒ VR(ω) = (tR.tA.tG) Vs(ω) (2.24)

We can also simulate the 1-D pressure field at any distance from the transducer inthe propagating medium as shown:

FB

Vs= tA.tG =

FB

Ft.Ft

Vs

⇒ p (ω) =FB(ω)

S0= (tR.tA.tG)

Vs(ω)

S0(2.25)

Where, S0 is the cross-sectional area of the piezo crystal. Both equation (2.24) and(2.25) can be converted by inverse Fourier transformation to get the time domainresponse.

2.4.1 Model validation

After completion of the modeling, it is implemented in MATLAB. Using all thephysical variables that are described earlier, we can simulate the model. The modelis simulated for an existing design of the transducer with backing material asZeonex E48R and front layer of parylene-C with thickness of 3 µm. Furthermore, analuminum alloy block is used as the reflector(target) in the acoustic medium. Thefrequency dependent pulser voltage and impedance used in the model are shownin figure 2.4 and 2.5 (with 3dB attenuator case) respectively. The parameters for thereceiver used in the model are shown in table 2.4.

The echo response obtained by the actual measurement and model is shown infigures 2.17 and 2.18 for a target distance of 1.5 mm and 2.2 mm respectively. Itcan be clearly seen that the measured results are in good agreement with the modelresults.

The radiating pressure field of transducer is measured in a water bath at room tem-perature in front of the transducer as shown in figure 2.19. A detailed scheme ofthe experiment is shown in figure A.1 without specimen case. This is done witha needle hydrophone with a 0.2 mm diameter of sensor (Polyvinylidene fluoridefilm). The pressure field obtained experimentally is in terms of voltage which is

24


1.8 2 2.2 2.4 2.6 2.8 3.0 3.2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Measured Echo SignalModel Echo Signal

Time [µ sec]

Vol

tage

[V]

Model validation by Pulse−Echo at 1.5 mm

Figure 2.17: Echo response for the targetat a distance of 1.5 mm

2.8 3 3.2 3.4 3.6 3.8 4.0 4.2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2


Time [µ sec]

Vol

tage

[V]

Model validation by Pulse−Echo at 2.2 mm

Figure 2.18: Echo response for the targetat a distance of 2.2 mm

converted into pressure by division of frequency dependent sensitivity S( f ) of hy-drophone.

p (t) =voltage measured (t)

Sensitivity o f hydrophone at 20MHz(2.26)

Note that the sensitivity of the hydrophone is taken at 20 MHz i.e. S(20 MHz) =72.3 × 10−9V/Pa . This is done because the measured waveform of voltage signalis dominated by the resonant frequency (20 MHz) of the ultrasonic transducer. Al-though this will not give the exact conversion from voltage signal to pressure, thisis enough to measure the performance of transducer. The pressure field obtainedby the actual measurement and model is shown in figures 2.20 and 2.21 for the hy-drophone at a distance of 3 mm and 4.5 mm respectively. It can be clearly seen thatthe measured results are in good agreement with the model results.

Transducer Hydrophone

Figure 2.19: Experimental setup in water bath

25


1.8 2 2.2 2.4 2.6 2.8 3.0 3.2−4

−2

0

2

4Model validation by Hydrophone at 3mm

Measured Pressure SignalModel Pressure Signal

Time [µ sec]

Pre

ssur

e [M

Pa]

Figure 2.20: Pressure field at a distanceof 3 mm

2.8 3 3.2 3.4 3.6 3.8 4.0 4.2−4

−2

0

2

4Model validation by Hydrophone at 4.5mm

Measured Pressure SignalModel Pressure Signal

Time [µ sec]

Time [µ sec]

Pre

ssur

e [M

Pa]

Figure 2.21: Pressure field at a distanceof 4.5 mm

As the model predicts well for both the received echo and radiating pressure field,it is established that we can use this model to improve the transducer.

26

Chapter 3

Transducer Improvement

The design of a piezoelectric ultrasound transducer demands careful selection anddesign of front and backing layer for the required performance. So in order toimprove the transducer bandwidth and signal to noise ratio, we focus on front andbacking layers.

3.1 Front Layer Improvement

3.1.1 Selection of the front layer

The front layer is not only used to protect the piezo crystal from the environmentbut also used to improve the energy transmission. For designing the ultrasonictransducer for in-vivo (within the living) applications such as our heart imagingapplication, material of the front layer should be bio-compatible as well.

To improve the energy transfer, the simplest way is to select the front layer withacoustic impedance Z1 such that it provides matching between impedance of thepiezo-ceramic Z0 and load impedance Zrad. This can be done by taking the geomet-ric mean of two impedances as shown below [8].

Z1 =√

Z0Zrad (3.1)

But for wide-band transducer, the above matching formula is modified to the fol-lowing as mentioned in [9]:

Z1 = 3√

Z0Z2rad (3.2)

For our case, acoustic impedance of piezo crystal is Z0 ≈ 31 MRayls, whereas,acoustic impedance of fluid or load is Zrad ≈ 1.5 MRayls. So, material with theacoustic impedance of Z1 ≈ 4 MRayls is required.

27


In the existing transducer, parylene-C is used as the front layer which is bio-compatible material and has an acoustic impedance of Z1 ≈ 2.8 MRayls. This valueis very near to the required impedance for the wide band transducer. Therefore, theexisting selection of parylene-C is a good selection as the matching layer.

3.1.2 Effect of the thickness of the front layer

Theoretically, the maximum power transfer takes place when the thickness of thefront layer is set equal to quarter wavelength λ/4 of the acoustic plane waves init. This will increase the efficiency of the transducer which results not only in anincrease in amplitude of the acoustic wave transferred to the medium but due tothe lower loses over the wide bandwidth it also increases the bandwidth of thetransducer.

For the existing transducer the thickness of parylene-C is 3 µm. Since, the resonantfrequency of piezo crystal is f = 20 MHz, and the speed of sound in parylene-C isc1 = 1289 m/s. The wavelength of the acoustic wave in the front layer will be:

λ =cf= 107µm (3.3)

The maximum power transfer takes place at quarter wave length of 26.8 µm. Toimprove the power transmission we have to change the thickness to the quarterwave length.

In order to validate the effect of the thickness changes experimentally, a transduceris made with piezo crystal PZT-5A with 20 MHz resonating frequency. ExistingZeonex E48R is used as the backing material. Thickness of the front layer (Parylene-C) is deposited in steps to measure effect of thickness. This is performed by thevacuum deposition system PDS 2010 Labcoter 2.

Each time after deposition of a layer, the radiating pressure field of transducer ismeasured in a water bath at room temperature at a specified distance of 3 mm infront of the transducer as shown in figure 2.19. A detailed scheme of the experimentis shown in figure A.1 without specimen case. The transducer with a matchinglayer thickness of 3µm, 12µm, 17µm, 26µm and 35µm is developed and tested.Figure 3.1 shows the voltage signal measure from hydrophone for 26µm parylene-C. The maximum of that signal is taken and plotted in the figure 3.2 after convertinginto pressure (using the sensitivity of hydrophone S = 72.3× 10−9V/Pa) as shownby the blue line with an accuracy of ± 17% given by the manufacturer. The sametest is performed for all the transducers and then compared with the pressure fieldpredicted by the model. It can be clearly seen that the behavior for both the modeland experiment is identical. The result clearly shows that the maximum pressurewill be obtained if the thickness of the front layer is set equal to 26.8 µm.

28


2.0 2.2 2.4 2.6 2.8

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Voltage measured by Hydrophone

maximum amplitude = 0.1725 mV

Vol

tage

[V]

Time [µ s]

Figure 3.1: Pressure signal in terms ofvoltage for 26µm parylene-C

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6Model validation by Hydrophone

Model Pressure SignalMeasured Pressure Signal

Pre

ssur

e [M

Pa]

Thickness of Front layer (Parylene−C) [ µm]

Figure 3.2: Maximum amplitude in thepressure signal for all thicknesses

3.2 Backing Layer Improvement

3.2.1 Selection of backing layer

To select the appropriate backing layer, there are several design considerationswhich are necessary to take into account. Brown in [10] discussed in detail theseconsiderations. Based on that discussion, the following design considerations arenecessary to take into account.

1. The impedance of the backing material has to be according to the requiredbandwidth of the ultrasonic transducer. For the imaging of a heart tissue, weneed higher bandwidth transducers. This gives a fast ringing down of the sig-nal and, a higher resolution for imaging. However, increasing the bandwidthwith an increase of the backing impedance, also decreases the efficiency [11]and thus the SNR. This means there is a tradeoff between these parameters.

2. The attenuation coefficient of the backing material should be as high as possi-ble so that acoustic waves transmitted to the back cannot reflect back and wereceive an echo without interference.

There are other design considerations which do not influence the performance ofthe ultrasonic transducer but these considerations are necessary for manufacturingthe transducer.

1. The backing material should be easy to machine and should be shaped intodifferent thickness and size.

29


Table 3.1: Properties of the several candidate backing materials

Material

Density

ρ[kg/m3]

Speed ofSound

c[m/s]

Specific AcousticImpedance

z = ρc[MRayls]

AttenuationConstant

α[dB/mm]

Zeonex E48R 1010 2593 2.62 7.57Zeonor 1020R 1010 2390 2.41 7.07Zeonex 790R 1010 2489 2.51 6.42Zeonex 690R 1010 2438 2.46 7.09Zeonex RS420 950 2195 2.08 11.53Epotek 353ND 1240 2578 3.19 4.81TPX 822 2162 1.78 3.04Epotek 353ND withGlass bubbles

871 2402 2.10 23.50

2. The backing material should have good adhesion properties so that it canadhere with the piezo ceramic.

3. The backing material should have high surface quality to ease the transfer ofenergy to the back and reduce noise.

For improving the design, properties of several materials, other than the existingZeonex E48R, which are readily available, are investigated using the same experi-mental procedure as described for Zeonex E48R in Appendix A. The found prop-erties are given in the table 3.1. In order to increase the attenuation constant, a mix-ture of epoxy (Epotek353ND) and glass balls (3M Glass bubbles S22) is tested. Thisis made by mixing glass balls 9% by weight with epoxy (i.e. 9 gm glass balls with91 gm epoxy) and the mixture is cured afterwards. It is noticed that the attenuationincreased significantly due to the scattering of waves inside the backing materialbut the acoustic impedance of the mixture becomes less than the epoxy. However,the noise level of transducers also increases due to high scattering of such backingmaterials.

3.2.2 Effect of the thickness of backing layer

Mason’s model does not have any parameter for the thickness of the backing be-cause the backing port with known impedance is fixed. In fact, the model assumesthat the thickness of the backing is semi-infinite. This is a valid assumption becausethe model is not made to accommodate for the responses due to the reflections fromthe back surface. It predicts only the response due to the power transmission from

30


the piezo to the front side and reception of the echo from the front side. This pre-diction is enough to improve the transducer before experimental realization of theparticular design.

To validate the effect of backing thickness experimentally, three transducers aremade with PZT-5A of 20 MHz resonating frequency and with 26 µm parylene-C asthe front layer. The thickness of Zeonex E48R as the backing material was set to 0.5mm, 1 mm and 2 mm.

The radiating pressure field of the transducer is measured in a water bath at roomtemperature at the specified distance of 3 mm in front of the transducer. The exper-imental configuration is identical as used in figure 2.19. In figure 3.3, the voltagesignal is shown that is received from the three different transducers. These voltagesignals are converted into the pressure using the formula given in equation (2.26)with a sensitivity of hydrophone S = 72.3× 10−9V/Pa. The comparison of theseexperimental results for different backing plate thicknesses with model for semi in-finite thickness is shown in figure 3.4. The result clearly shows that thickness of thebacking has no influence on the pressure field which means that the amplitude andbandwidth of the transducer is independent of the backing plate thickness. Also, itcan be seen that there is a good match between the model and actual measurement.

1.9 2 2.1 2.2 2.3 2.4 2.5−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Pressure signal for 26µ m Parylene−C

Transducer 0.5 mm backingTransducer 1 mm backingTransducer 2 mm backing

Vol

tage

[V]

Time [µ sec]

Figure 3.3: Measured pressure signalin terms of voltage for different thick-nesses of the backing plate

1.9 2.0 2.1 2.2 2.3 2.4 2.5

−6

−4

−2

0

2

4

6

Pressure signal for 26µ m Parylene−C

Transducer 0.5 mm backingTransducer 1 mm backingTransducer 2 mm backingModel

Aco

ustic

Pre

ssur

e [M

Pa]

Time [µ sec]

Figure 3.4: Measured pressure signalfor different thicknesses of the back-ing plate and its comparison with themodel

3.3 Decision Making

To improve the SNR and bandwidth, it is decided to change the thickness of thefront layer from 3µm to 26.8µm without changing the material (parylene-C) be-cause its impedance is near to the optimal impedance for power transmission and

31


it is also bio-compatible. This increases both the SNR and bandwidth. A change ofbacking material is not adopted for current improvement. We investigated severalother materials available but their properties are close to the Zeonex E48R as shownin table 3.1. A mixture of epoxy and glass balls is also tested, which improved theattenuation constant but has less value of impedance which will decrease the band-width. Therefore, by changing the thickness of front layer we can get an increase inboth the SNR and bandwidth.

3.4 Results and Experimental Validation

An improved transducer is developed in the Philips Research Laboratories and istested for the pulse echo case, with the block of aluminum alloy with known prop-erties. The frequency dependent pulser voltage and impedance used in the modelare shown in figure 2.4 and 2.5 (with 3dB attenuator case) respectively. The param-eters for the receiver used in the model are shown in table 2.4. The echo responseobtained by the measurement and model for both the old and new transducer isshown in figure 3.5 and figure 3.6 respectively.

It is found that, for improved transducer, the percentage increase in maximum ofsignal magnitude is 160% which is improved from 250mV to 650mV. Where as, thepercentage increase for 3dB bandwidth is 79% which is improved from 2.4 MHz to4.3 MHz. The results for the actual echo signal bandwidth is shown in figure 3.7for old and new transducers.

1.8 2 2.2 2.4 2.6 2.8 3.0 3.2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2Model validation by Pulse−Echo


Vol

tage

[V]

Time [µ sec]

Figure 3.5: Echo signal for 3µmparylene-C

1.8 2 2.2 2.4 2.6 2.8 3.0 3.2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2Model validation by Pulse−Echo


Vol

tage

[V]

Time [µ sec]

Figure 3.6: Echo signal for 26µmparylene-C

32


0 10 20 30 400

0.02

0.04

0.06

0.08

0.1

0.12

Old transducerImproved transducer

New Transducer: 3 dB BW = 4.3 MHz

Old Transducer: 3 dB BW = 2.4 MHz

Mag

nitu

de [V

/MH

z]

Frequency [MHz]

Figure 3.7: Comparison of bandwidth for the old and new (improved) transducer

33

34

Chapter 4

Conclusion and Recommendations

The complete model of an ultrasonic measurement system includes a model oftransducer, a pulser, a receiver and a propagating medium that completely de-scribes the ultrasonic diagnostic setup.

4.1 Conclusion

The main objective of this project is to improve the SNR and bandwidth of an ul-trasonic transducer. To accomplish this task, there is a need of a model that canpredict the behavior of the ultrasonic transducer before realization.

In this report, an approach to make an equivalent circuit model for the transduceris adopted. The model of each individual component in an ultrasonic measure-ment system is implemented to predict the response of the ultrasonic transducer.Although, the focus is to improve the ultrasonic transducer, however, other com-ponents are also simulated and the model is validated both for the echo responseand radiating pressure field experimentally.

It is shown that the implemented model has a good agreement with measurementresults. Based on this, the effects of the mechanical construction of the transducerare studied. Finally, some improvements in the mechanical construction are sug-gested and adopted. For the specified input conditions, the signal magnitude isincreased by 160%, whereas, the increase in bandwidth is recorded as 79%. We metall the required goals of the project as defined in Chapter 1.

The modeling procedure described in this report provides a tool for analyzing thecomplete ultrasonic measurement system. The present modeling has dealt with animmersion system, however, this is also applicable to the contact ultrasonic systemsthat are widely used for different applications.

35

Conclusion and Recommendations

4.2 Recommendations

• The implemented model is one dimensional in nature and its purpose is topredict the response of transducer in order to improve SNR and Bandwidthof the transducer. However, there are other aspects which influence the per-formance of the transducer such as the three dimensional pressure field andbeam forming etc. These three dimensional effects cannot be studied by theone dimensional equivalent circuit models and, there is a need for Finite ele-ment analysis (FEA). Commercial software’s like ANSYS and COMSOL andPZFLEX can be very useful in this regard.

• Detailed material research is needed to find a suitable backing plate withthe required impedance and high attenuation constant. This material canbe made by combination of epoxies and fine metal or rubber or glass par-ticles. The change in mechanical properties can be studied with respect tothe change in concentration of these particles. Thus, optimum custom madematerial can be made to employ in the transducer as backing plate. By adopt-ing this, bandwidth can be set to the required value and adverse effects ofinterference through back reflections can be avoided.

• The transducer is improved using the aluminum block as the reflecting sur-face in the propagating medium. Real ex-vivo tissue experiments need to bedone with different types of tissues such as heart tissue, fat etc., before per-forming the clinical trials for in-vivo experiments.

• Furthermore, all of the above improvements suggested and adopted are en-tirely related to the mechanical improvements. During the modeling process,the effect of the transceiver(pulser/receiver) settings on impedance is shownand it is noticed that the impedances in the transmitting and receiving partare not matched to 50 Ω with the cable. This causes unwanted electrical re-flections within the cable. To avoid this, an improved transceiver for the ul-trasonic system is required.

The modeling process involved in this report is not only useful for the ultrasonictransducer used in cardiac imaging, but, it is applicable to any ultrasonic measure-ment system for inspection. Such a system can be a non-destructive evaluationsystem for an aerospace structure or underwater pipe line inspection or any medi-cal diagnostic system.

New horizons need to be found for the application of ultrasonic transducers eitherby using a single ultrasonic transducer or in array. In future, the need of ultrasonictransducers in medical diagnostics can be more demanding due to the reduction insize of ultrasonic transducers to micro scale level.

36

Appendix A

Parameter Estimation

In order to simulate the obtained model, we need to determine and estimate allthe parameters in the model. Most of these parameters are calculated based on thematerial properties. However, the speed of sound in the backing plate needs to beestimate as it is not available in the manufacturer’s material data sheet. Further-more, the electromechanical coupling coefficient and the clamped capacitance ofthe piezo crystal are highly influenced by the mechanical construction and trans-ducer manufacturing process. So, we estimate these two properties for the specificdesigns of transducer.

A.1 Speed of Sound in the Backing Plate

The measurements that we performed for finding the longitudinal speed of soundis also used to find the attenuation constant for the backing material. The attenu-ation constant is not needed for the simulation, however, in Chapter 3 we showedthat this parameter can be used to improve the other aspects of the transducer.

A.1.1 Experimental setup

The longitudinal speed of sound and attenuation constant are found experimen-tally in a pitch-catch setup. In this setup, the acoustic waves are generated in awater bath using an ultrasonic transducer. The acoustic pressure is measured bya Precision acoustic hydrophone needle at some specified distance. This commer-cial hydrophone is an ultrasonic transducer with a sensor diameter of 0.2 mm. De-mineralized water is used at the room temperature as the propagating medium. Wekeep the distance between the hydrophone and the ultrasonic transducer as smallas possible to avoid the scattering effects. A three axis motion controller is used to

37

place the hydrophone in front of the transducer. The received pressure waveformfrom the amplifier/coupler (attached to the hydrophone) is sampled by a digitaloscilloscope. At first, we measure the pressure without a specimen, and then weput a specimen between the hydrophone and the ultrasonic transducer as shownin the Figure A.1. This experimental setup is used by many authors; see [12], [13]and [14].

Figure A.1: Measurement of pressure through hydrophone with and withoutspecimen

When a specimen is placed between the transducer and hydrophone, the acousticwaves are attenuated due to the specimen and we received the waves earlier orlater depending on the speed of sound, as shown in figure A.2 for a specimen ofZeonex E48R (Cyclo Olefin Optical Grade Polymer).

19.5 20.0 20.5

−20

−10

0

10

20

Zeonex E48R

Without specimenWith specimen

Vol

tage

[mV

]

Time [µ sec]

← ∆ → t

Figure A.2: Pressure signals in terms of voltage from the hydrophone (with andwithout specimen

38

A.1.2 Calculation for the speed of sound and attenuation constant

In order to calculate the longitudinal speed of sound in the material and the at-tenuation constant, several authors discuss about the time domain techniques, see[12].

For the materials with high attenuation constant, the wave shape for the pressurewave changes dramatically as it transmitted through the material. In order to locatethe equivalent points for finding the amplitude ratio is detrimental [13]. Otherauthors use the frequency domain technique developed by Sachse and Pao (1978),see [14]. In this report, we adapt the frequency domain technique. Wang et al. in[14] explicitly mention the formulae to calculate the speed of sound and attenuationconstant as given below:

cs =cw

1 +(ϕs − ϕw + 2π f4t)cw

2π f d

(A.1)

αs = αw +1d

20log10

(TAw

As

)(A.2)

In equations (A.1) and (A.2),4t is the trigger delay of the signal as shown in figureA.2, cw is the speed of sound in water, f is the frequency, d is the thickness ofthe specimen, Aw, As, ϕw and ϕs are the amplitude and phase spectra, obtainedby taking the Fourier transformation of the pressure signal, without and with aspecimen respectively as shown in figure A.3. T is the product of the transmissioncoefficients for the interface of water to specimen and specimen to water:

T = Tw−→sTs−→w =4zwzs

(zw + zs)2 (A.3)

Here, zw = ρwcw and zs = ρscs are the specific acoustic impedance of the waterand specimen respectively. Figure 2.19 shows a picture of the transducer and hy-drophone in water bath during the measurement. The results are given in tableA.1.

Table A.1: Properties of Zeonex E48R (found experimentally)

Material

Density

ρ[kg/m3]

Speed ofSound

c[m/s]

Specific AcousticImpedance

z = ρc[MRayls]

AttenuationConstant

α[dB/mm]

Zeonex E48R 1010 2593 2.62 7.57

39

0 10 20 30 40 50 60 70 80 900

0.2

0.4

0.6

0.8

1.0

1.2 Zeonex E48R


Am

plitu

de [m

V/M

Hz]

Frequency [MHz]

← A w

← A s

0 10 20 30 40 50 60 70 80 90

−100

−80

−60

−40

−20

0

← φ w

Zeonex E48R

φ s →


Pha

se [r

ad]

Frequency [MHz]

Figure A.3: Magnitude and phase of the pressure signals (with and without speci-men)

A.2 Properties of the Piezo Crystal

Two of the main properties of the piezo crystal, i.e. capacitance and electromechan-ical coefficient, are highly influenced by the mechanical construction. There is aneed to estimate these values experimentally. We find these values by fitting themeasured input impedance of the transducer to the model input impedance.

A.2.1 Estimation of the capacitance

The purpose of a piezo crystal is to convert one form of energy into other. From themanufacturer, we get a piezo crystal sandwiched between two electrodes. So, it actsas a capacitor with some capacitance. The cross-sectional area of these electrodesis equal to that of a crystal i.e. S0 = π

(0.5 × 10−3)2

. However, we used addi-tional electrodes larger in size with these electrodes for the manufacturing ease.This changes the effective capacitance to some other value. This value of effectivecapacitance is also dependent on the insulation used between the additional elec-trodes.

To investigate the effect of mechanical construction experimentally, two transduc-ers with different type of construction are tested as shown in figure A.4 and fig-ure A.5. Type A construction is the replica of a transducer thats fits into catheter,whereas, Type B is developed for investigation purposes.

An Agilent HP 8753ES Network Analyzer is used to find the reflection co-efficientS11 of these transducers. Before measuring the reflection coefficient, it is necessaryto calibrate the network analyzer for the open, short and known load (50 Ω in ourcase) termination conditions. The measured reflection coefficient S11 is converted

40

Figure A.4: Type A construction Figure A.5: Type B construction

to the input impedance Zin of the transducer by the relation:

Zin,measured = 50(

1 + S11

1− S11

)(A.4)

The effective capacitance is estimated by fitting the frequency dependent modelimpedance, given in equation (A.5), with the measured impedance except near res-onances.

Zin,model =VI=

Zrad AT + BT

ZradCT + DT(A.5)

In equation (A.5), all the parameters are same as defined for the frequency re-sponse function of the sound generation system (see equation (2.10)). This inputimpedance of model can be derived easily by solving equation (2.9) and also men-tion in [3]. We found the values for the capacitance as 0.77× 10−10 F for the type Aand 1.23× 10−10 F for the type B construction respectively.

A.2.2 Estimation of the electromechanical coupling coefficient

The ability of a piezo crystal to convert one form of energy into another is mea-sured by its electromechanical coupling coefficient kT. This parameter is one of themeasures of the performance of a transducer. The electromechanical coupling coef-ficient of PZT-5A piezo ceramic with a resonant frequency of 20 MHz is not givenin the manufacturer’s data sheet. Tuning the capacitance fits the model impedancecurve with the measured impedance over the range of frequencies except near theresonant frequency. To fit the curve near the resonant frequency, kT is tuned manu-ally and its value is found equal to 0.2 for both type of the construction.

The magnitude and phase of the measured impedance and model impedance, aftertuning the capacitance and electromechanical coupling coefficient, can be seen infigure A.6 and figure A.7 for the type A and type B construction respectively. Thelower order harmonics that can be seen in measurement except at 20 MHz are theresonances of the modes other than the thickness mode and these are not includedin the Mason’s model.

41

0 5 10 15 20 25 300

200

400

600

800

1000

1200Input impedance of transducer

MeasurementModel

Mag

nitu

de [O

hm]

Frequency [MHz]0 5 10 15 20 25 30

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2


MeasurementModel

Pha

se [r

ad]

Frequency [MHz]

Figure A.6: Magnitude and phase of the input impedance of transducer forthe type A construction

0 5 10 15 20 25 300

200

400

600

800

1000


MeasurementModel

Mag

nitu

de [O

hm]

Frequency [MHz]0 5 10 15 20 25 30

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2


MeasurementModel

Pha

se [r

ad]

Frequency [MHz]

Figure A.7: Magnitude and phase of the input impedance of transducer forthe type B construction

42

Appendix B

Hardware Description

Following are the devices which are used apart from the ultrasonic measurementsetup during the experiments.

B.1 Motion Controller

Newport Universal motion controller (Driver ESP300) is a 3-axis motion controller(shown in figure B.1) and it is used to position the hydrophone in front of the trans-ducer to measure the radiating pressure. Manually, it is difficult to place the hy-drophone in front of the transducer. This motion controller has a resolution of0.005 mm in any direction of movement.

Figure B.1: Motion controller

43

B.2 Network Analyzer

An Agilent HP 8753ES Network Analyzer (as shown in figure B.2) is used to mea-sure the reflection coefficient of the transducer. This reflection coefficient is con-verted into input impedance of the transducer. Before doing the measurements onthis analyzer, it is necessary to calibrate for the open, short and known load termi-nation conditions.

Figure B.2: Network analyzer

B.3 Digital Oscilloscope

For measuring the voltage signals, an Agilent Technologies DSO 6034A digital os-cilloscope is used (as shown in the figure B.3). This oscilloscope has a capability tosample the data at the rate of 2Giga samples per second for four different channelssimultaneously .

B.4 Current Probe and Amplifier

For measuring the current during the characterization of the receiver, a TektronicsTM502A AM 503B current probe amplifier (as shown in figure B.4) is used. Thiscurrent probe has a capability to measure a very small current even in the order ofmagnitude of mA.

44

Figure B.3: Digital oscilloscope

Figure B.4: Current probe

45

46

References

[1] C. Dang, L.W. Schmerr Jr., and A. Sedov, “Modeling and measurement all theelements of an ultrasonic nondestructive evaluation system I: Modeling foun-dations,” Research in Nondestructive Evaluation, vol. 14(4), pp. 141–176, 2002.

[2] C. Dang, L.W. Schmerr Jr., and A. Sedov, “Modeling and measuring all the ele-ments of an ultrasonic nondestructive evaluation system II: Model based mea-surements,” Research in Nondestructive Evaluation, vol. 14, pp. 177–201, 2002.

[3] L.W. Schmerr and S.J. Song, Ultrasonic nondestructive evaluation system: Modeland Measurements. Springer, 2007.

[4] E.K. Sittig, “Effects of bonding and electrode layer on the transmission param-eters of piezoelectric transducers used in ultrasonic digital delay lines,” Sonicsand Ultrasonics, IEEE transactions, vol. 16(1), pp. 2–10, 1969.

[5] J.Assaad, M. Ravez, C. Bruneel, J.M. Rouvaen, and F. Haine, “Influence of thethickness and attenuation coeficeint of a backing on the response of transduc-ers,” Ultrasonics, vol. 34, pp. 103–106, 1996.

[6] H.W. Persson and C.H. Hertz, “Acoustic impedance matching of medical ul-trasound transducers,” Ultrasonics, vol. 23(2), pp. 83–89, 1985.

[7] A.L.L. Sanchez and L.W. Schmerr Jr., “Determination of an ultrasonic trans-ducers sensitivity and impedance in a pulse-echo setup,” Ultrasonics, Ferro-electrics and frequency Control, IEEE transactions, vol. 53(11), pp. 2101–2112,2006.

[8] T.L. Szabo, Diagnostic ultrasound imaging - Inside out. Elsevier, 2004.

[9] K.K. Shung, Diagnostic ultrasound - Imaging and blood flow measurements. Taylorand Francis Group, 2004.

[10] L.F. Brown, “The effects of material selection for backing and wearprotection/quarter-wave matching of piezoelectric polymer ultrasound trans-ducers,” IEEE Ultrasonic Symposium, vol. 2, pp. 1029–1032, 2000.

47

[11] S.J.H. van Kervel and J.M. Thijssen, “A calculation scheme for he optimumdesign of ultrasonic transducers,” Ultrasonics, vol. 21(3), pp. 134–140, 1983.

[12] N.T. Nguyen, M. Lethiecq, B. Karlsson, and F. Patat, “Highly attenuative rub-ber modified epoxy for ultrasonic transducer backing applications,” Ultrason-ics, vol. 34, pp. 669–675, 1996.

[13] J. Wu, “Determination of velocity and attenuation of shear waves using ul-trasonic spectroscopy,” Acoustical Society of America, vol. 99(5), pp. 2871–2875,1996.

[14] H. Wang, W. Cao, and K.K. Shung, “High frequency properties of passive ma-terials for ultrasonic transducers,” Ultrasonics, Ferroelectrics and frequency Con-trol, IEEE transactions, vol. 48(1), pp. 78–83, 2001.

48

Documents

Modeling of an Ultrasonic Transducer for Cardiac Imagingmate.tue.nl/mate/pdfs/12271.pdf · An integrated ultrasonic transducer sends the acoustic waves into the heart wall and receives