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The influence of pulser parameters on the transmission response of piezoelectric transducers
The influence of pulser parameters on the transmission response of piezoelectric transducers G. HAYWARD A model is presented for the analysis of thickness-mode piezoelectric transmitters under practical operating conditions. The systems feedback approach is employed to clearly isolate the individual quantities relating to electromechanical interaction within the system. As a result, important parameters are highlighted and their influence on transducer response is demonstrated using a number of simulation diagrams. Wherever possible, performance is related to practical excitation devices and a summary of their relevant properties is included. KEYWORDS:
ultrasonics,
transducers,
excitation
systems
List of symbols h
Piezoelectric charge constant thickness direction
k
Electromechanical clamped)
CCI
Transducer
T
Transit time for mechanical the transducer thickness
ZC
coupling
factor (laterally
static capacitance
Mechanical
impedance
waves to cross
of transducer
author
Glasgow
IS I” the
Department
of Strathclyde. Gl
1 XW,
of Electronic
Royal
Scotland.
College
UK.
Paper
MAY 1985
Electrical
Building.
204
recewed
16
0041-624X/85/0301 ULTRASONICS.
and
impedance
of front face
Z,
Mechanical
impedance
of rear face medium
RF
Front
Rt3
Rear face reflection
s
The Laplace
w
Angular
George October
03-l
complex
coefficient coefficient
(force) (force)
variable
frequency
Frequency
Although techniques for assessing the relative merits of individual transducer probe assemblies are well developed. such methods tend to utilize cw or gated cw excitation from a standard pulse generator of known electrical characteristics’. The influence of the generator is largely ignored and hence the extrapolation of calibration results to non-standard generators cannot readily be performed. Practical excitation circuits invariably involve some form of switching network whereby the transducer is stimulated by the rapid deposition of a quantity of charge. The electrical characteristics of such pulser systems are often considerably more complex than those of the standard pulse generator and as a result. strong electrical interaction with the transducer element may occur. This can have a marked influence on the transmitted acoustic wave profile.
Engineermg, Street, 1984.
O/$03.00
face reflection
efficient piezoelectric transducers normally employed can be difficult to assess and calibrate under practical, transient operating conditions. Moreover, the influence of the driving circuit and the subsequent electromechanical interaction is often neglected.
Accurate characterization of the transducer system is a necessary feature for almost all applications of ultrasound. The ability to predict and define transducer performance is of particular importance in sonar. nondestructive testing and diagnostic ultrasound where the acoustic pulse parameters are used extensively for imaging defect sizing. materials analysis and tissue characterization. Since the transmission (and reception) response characteristics of thickness-mode transducer assemblies are functions of the electrical. mechanical and piezoelectric properties of the system. it is required to include all three parameters for an accurate assessment of probe behaviour. For example. transducer performance in both time and spatial domains may be influenced by the electrical load conditions. The extent of this influence depends on transducer efficiency, external mechanical loading and the particular operating frequency range. However, the University
Mechanical medium
f
Introduction
The
2, in the
0
1985
Butterworth
8 Co (Publishers)
Ltd
103
It has been suggested* that a standard pulser bc configured to provide a more realistic performance test. Before this can be carried out. a comprehensive investigation of transducer electromechanical interaction is required. Moreover, the characteristics of the switching device and associated circuitry must be clearly defined. To achieve this, it is necessary to construct a model which accurately predicts the behaviour of the transducer system over a wide range of practical operating conditions. In subsequent sections, the transducer feedback model3’4 is used to explain and simulate the performance of a variety of different excitation systems over a range of mechanical load conditions. By reducing the complete system into a number of relatively straightforward functional blocks. the complex electromechanical processes are readily explained and the factors which influence device behaviour arc clearly isolated.
Modelling
the transmission
system
Consider the transmitting configuration outlined in Fig. 1, in which r represents the excitation voltage source and FF corresponds to the force generated at the transducer front face. Two lumped impedances, Z, and ZE, are included to represent the impedance of the generator and any coupling or matching networks. The systems feedback concept is used to model transducer behaviour. A block diagram feedback model is outlined in Fig. 2. in which the transducer is subject to the physical constraints of linear, planar. lossless and unidirectional wave motion in the thickness direction. It is also assumed to radiate directly into semiinfinite, real media which are situated at each face. For this configuration. a Laplace transfer function relating output force to excitation voltage is given by -
--
FF _ -;-e
- hC, YIKFAF/2
1 - i5&TF/2
104
Transmitter
1
Transducer
conflguratlon
for the transmlttlng
mode
Equations (2) and (3) are dimensionless transfer functions which describe the influence of external electrical load conditions on primary and secondary piezoelectric action respectively. Mechanical wave propagation within the device is described by the reverberation factors KF and Ka and the transmission coefficients A tJ2. TF/2 and Ta,12. That is. -
KF
= (1 -eeST)(l
-RB
e-“*)/(I
-RFR,
KB
= (1 -e-“‘)(l
-RF
e -“T)/(l
- RFRB e-2sT)
TF
=
2zc/(z,
+ZI)
TB
=
~&J/(&J
+z,)
AF
=
=-I@,
+Z,)
emzsT)
RF
=
PC
(4) (5)
(1) -Z,MZc
R, = (z, -z,)/(zc
where.
Fig 2
+KBTB/2)k2/sT
1 Fig.
+Z,>
tz2>
model
ULTRASONICS.
MAY 1985
In this notation. the bar symbol denotes Laplace transformation. A study of Fig. 2 reveals that the output wave of force is strongly dependent on both electrical and mechanical loading factors in addition to the piezoelectric properties of the transducer. For example. the electrical load directly influences the output force via the forward loop parameter Yt. The extent of this influence depends on the exact form of ZE and Z,. In general. the magnitude of the output wave of force decreases for low values of ZE and for high values of Z,. It should be noted that conditions which correspond to zero force (Z, zero or Z, infinite). are unlikely to be encountered in a practical excitation system. In a similar manner, both feedback loops contain the parameter Yr and hence secondary piezoelectric action is expected to increase for low values of ZE or Z,. It may be observed that for Z, equal to zero. the system transfer function is independent of ZE, with Yt and Yr both equal to unity. Mechanical load conditions at each face of the transducer also exert a significant influence on the device response. For example. both reverberation factors exhibit minima and maxima at even and odd multiples of the mechanical resonant frequency respectively3,4. Maximum response occurs under narrowband conditions, when the transducer is lightly damped. Maximum secondary action is also expected to occur under similar conditions. The amount of feedback is also directly proportional to the square of the coupling coefficient and inversely proportional to frequency. In general. secondary piezoelectric effects give rise to a reduction in transducer centre frequency to a value below mechanical resonance. This may be accompanied by a small increase in overall signal bandwidth and distortion of the output waveform3. Under conditions of zero feedback the transducer behaves electrically as a pure capacitance of value C,. Consider now the basic pulser conliguration outlined in Fig. 3. in which a blocking capacitor, Ca, is charged to the HT potential via a current limiting resistor, R. Depending upon the particular application, the HT voltage may vary from +5 V to +2.5 kV, while the system pulse repetition frequency is generally limited by the R-Ca time constant. The switch S,, is invariably a fast electronic device which, when activated, results in a transference of charge from the blocking capacitor to the transducer and its associated electrical load. The load may comprise a matching resistor, the parallel
combination of a resistor and tuning inductor or additional R-C differentiating networks for optimizing the pulse shape. For those applications where significant lengths of lossy interconnecting cable are involved. a lumped transmission line equivalent circuit may be employed to simulate cable effects. However. for most applications a simple L-C network is sufficient. Suitable types of switches include valves. thyristors, switching MOSFET transistors and avalanche transistors. The electronic switch may in turn be approximately characterized by turn-on time (t,). peak current capability (lp), ‘on’ resistance when in the conducting state (R,) and maximum blocking voltage when in the non-conducting state. These characteristics vary widely from device to device and care must be taken when specifying a suitable switch for a particular application. For example, turn-on time may vary from a few nanoseconds for an avalanche transistor to several hundred microseconds for some of the slower thyristors and valves. Similarly, ‘on’ resistance may vary from 100 n in some thyristors to less than 1 a in some MOSFET devices. The relevant characteristics and main application areas for a selection of pulser devices are discussed in the appendix. The mode of operation described by Fig. 3 is equivalent to that outlined in Fig. 4. where a non-linear ramp function is applied to the blocking capacitor via a resistance R,. (In general. R B R, and RE.) The ramp function descends from HT to zero volts in a time equal to r, and may be assumed to remain at zero volts for the remainder of the excitation period. Two points should be noted concerning the model. Firstly. the electrical turn-on characteristics of the switching device are assumed uniform over the turn-on period and are represented solely by a resistive element. This is not strictly correct, as a time-varying impedance is generally involved. However, the approximation has been experimentally verified3T5,6 and is considered valid for the majority of excitation systems. Secondly. the turn-on characteristics of the pulser are often functions of the driving circuitry and the electrical load conditions. Consequently, the input waveshape may be approximated by a step function (that is, zero turn-on time). a smooth ramp function or a nonlinear ramp function. depending on the particular operating conditions. Analysis
and simulation
The nominal transducer parameters outlined in Table 1 (corresponding to PZT-SA) were used for the simulation results presented in this section. The timedomain simulations were performed using the discretetime approach described in Ref. 6. By expressing the transducer transfer functions in mixed differential-
+HT
r-.>-4; R~::
-’
+ HT
LE i
L-______-!
Fig. 3
results
Pulser
configuration
ULTRASONICS.
MAY 1985
RE::
Fig. 4
Pulser
equivalent
circuit
105
Table
1.
Nominal
Mechanical resonant frequency
transducer
k
In general. source resistance may be assumed to exert negligible influence on the transmission response it oCbRs < 1.This condition is satisfied for PZT-SA ceramic transducers subject to arbitrary mechanical damping if.
parameters
Z, -2 kg m
s-1]
33.712
x IO6
CdW
[MHz1
WC, Rs < 0.05
1
0.486
1
delay format_ the system may be modelled in the form of a recursive digital filter. This technique is particularly useful for the modelling of non-linear input waveforms and is also amenable to computer implementation. The influence
of generator
Consider firstly a transducer voltage generator possessing For this condition, ZO = Ignoring
Next, consider a switching dcvicc possessing an ‘on‘ resistance R,.which is used to stimulate the transducer via a blocking capacitor CB from a voltage supply, HT. For convenience, the switch is assumed to turn on in zero time. No additional matching elements are connected across the transducer and any interconnecting cable is negligibly short. Consequently, Z, is infinite and.
impedance
excited via a standard an output resistance Rs.
z,
= R, + l/sCu
rr
= YF
cabling
where C = COCu/(C,
effects.
In addition.
?t = YF = (1 +sCoRcJ1
(8)
+sCR,)
= C/C,(l
Rs and ZE = *
(7)
+ Cu)
since
(6)
As expected a finite value of source resistance serves to reduce both input and feedback currents. The output force magnitude will thus be reduced as source resistance increases. and a corresponding reduction in secondary piezoelectric action shifts the centre frequency upwards, towards mechanical resonance4. This may readily be observed from Fig. 5, which describes the output force spectral magnitude for three different values of source resistance. The transducer is assumed to be lightly damped (RF= RB = 0.9). a condition which tends to maximize secondary action. However, under conditions of heavy damping secondary action is reduced and the influence of source resistance on the output centre frequency has the opposite effect. In Lhis case, the frequency-dependent decay inherent in Yt serves to reduce the centre frequency with increasing source resistance. This may be observed from the three simulation results presented in Fig. 6, where reflection coefficients of RH = 0. RF = 0.5are assumed.
e = -HT/s The input current 7 = -
to the transducer
is thus given by
HTC/(I+sCR,)
(9)
The magnitude of the input current is thus reduced for increasing values of ‘on’ resistance and/or decreasing values of blocking capacitance. The magnitude of the output wave of force will also be reduced. with a corresponding reduction in the amount of secondary action, Efficient pulser systems thus require low values of ‘on’ resistance (
0 Frequency Fig. 5 damped resistance
106
Output
force
transducer
spectral under
magnitude
different
characterlstlcs
condttions
05
IO
15
20
25
Frequency
[MHZ] for a lightly
of electrical
source
Fig. 6 damped
Output
force
transducer
spectral under
magmtude
different
3.0
35
40
45
[ MHz 1
characterlstlcs
condmons
=o
for a heavily
of electrvzal
source
resistance
ULTRASONICS.
MAY 1985
50
The influence of the blocking capacitor may readily be observed by considering the transducer response over a truncated time period corresponding to a single transit interval. For an ideal step input and assuming zero ‘on’ resistance. the output wave of force over this interval is given by3 F&)
=
(co
CB + c,)
~CO 64F12)
The influence of pulser turn on time
Consider the transmitter configuration outlined in Fig. 4. in which the pulser has a uniform turn-on characteristic of duration t,,. For this case, the input voltage may be expressed by the following transform equation.
(11)
F = - HT( 1 - emfio )/s2 to
k2 (TF/~ + TB/2)t/T
(10) I
for
In this analysis, it is assumed that pulser ‘on’ resistance may be ignored and that an inductive matching section with resistive damping is connected across the transducer. The voltage applied to the device is thus given by
O
(12)
Under conditions of no secondary action (for example, k = 0), the output force over this time interval is a step function of amplitude P
where fI
= s2 RELECB/
(s2 RELE(Co
•t C,) + SLE + RE ) (13)
The exponential term in (10) describes secondary piezoelectric action and is a function of the piezoelectric. electrical and mechanical properties of the system. As expected both primary and secondary action are maximized under the condition Ca > C,,.
Equation I_ nY
+ Cr.,) = 0.9,
R.
= 5 f&R0
C,/(C,
+ C,)
Ro = 5 !A
V*(t) = -+
given
( sin j?t - eearo sin/3 (t - to) )
(14)
where
= 100 52
Q =
The transducer is subject to conditions damping and step voltage excitation.
transform
0
(2 = (CO +
= 0.1,
inverse
-cut
To illustrate the effects of pulser impedance, consider Fig. 7. which depicts the output force profiles in the time domain for the following three conditions: C,/(C,
(12) has a standard
cB)/c,
( 2RE(COtc,))-’
(15)
of light P = (l/L&CO
The influence of secondary piezoelectric action is readily apparent for the higher value of blocking capacitance. as indicated by the strong positive exponentials. A reduction in secondary action and output force magnitude with increasing ‘on’ resistance may also be observed. For the smaller value of blocking capacitance, little secondary action is evident and there is a considerable reduction in response magnitude.
+Cg)-
l/4R&(Co
+C&’
Equation (14) represents the actual voltage developed across the transducer static capacitance, in the absence, of secondary piezoelectric action. At t = t,,, this voltage is given by
V*(t) =
- HT ema* CB (CO +c,)
(16)
For to equal to zero. the switch is ideal and
020
0.15
vt(t)
= -HTCB/(Co
t=ro -0
0.10
+ c,) (17)
$ g
This is the maximum value of voltage which may be applied to the transducer, for fixed values of C,, and Cu. A comparison between (16) and (17) indicates that increasing t,, serves to reduce the efficiency of the transmitting configuration.
005
$ 0
g S
z -0.05 ‘Z _o d -0.10 -015 -Ox,
0
I
I
I
I
I
I
I
I
I
05
IO
I5
2.0
25
30
3.5
4.0
4.5
Time [ps] Fig. 7 Output force temporal characteristics for a lightly damped transducer subject to variations in pulser impedance
ULTRASONICS.
MAY 1985
5.0
Turn-on time can also have a marked influence on the output wave characteristics. This may readily be observed from Fig 8, which depicts the output force spectra for two different values of turn-on time (to = T/10 and to = 27). In the figure, a lightly damped transducer is assumed, in conjunction with a pulser ‘on’ resistance of 1 s1 and a blocking capacitor of 1 nF. The corresponding time domain waveforms are shown in Fig. 9. Differences in the magnitude and form of the
107
018
However. care must be taken with some of the higher frequency ceramic and polymer film devices which possess transit times in the region of 10 ns - 50 ns. For such cases. the appropriate switching device should be carefully selected for the required system efficiency and pulse characteristics. Variations in pulser turn-on time also have a more marked influence on the output response than in the lower frequency devices. Avalanche transistors have potential switching times of under 5 ns’ and despite relatively low blocking voltages and shorter lifetimes, they are often the most suitable switches for driving polymer film and high frequency ceramic transducers.
016
The influence 0
Ftg. 8
05
Output
damped
IO
force
transducer
15
spectral subject
20
25
30
Frequency
[MHZ]
magnwde
35
characterlstlcs
to different
conditions
40
45
50
for a lightly
of pulser
turn-on
time
of the matching
network
A matching or pulse shaping network in the form of a resistor or the parallel combination of a resistor and an inductor is often connected across the transducer electrodes. The network is usually incorporated to maximize the system sensitivity and/or optimize the pulse width to meet resolution requirements. Although narrowband excitation systems. utilizing low efficiency transduction devices. have received much attention in the literature. (see for example Ref. 8) little data are available on practical pulser matching configurations. It is the purpose of the present section to examine the influence of the matching network on an efficient piezoelectric transducer system driven under the practical transient conditions commonly encountered in ndt and biomedical applications. Consider firstly a purely resistive element connected across the transducer which is driven via a blocking capacitor and an ideal pulser.
-0.08
I 0
I
I
1
I
I
I
I
I
I
05
IO
15
20
25
30
35
40
45
Time Fig. 9
Output
transducer
force
subject
temporal
to different
characteristics conditions
50
For the majority of piezoceramic devices. this condition is approximated very closely by the use of a switching MOSFET. For such a configuration.
[ps] for a lightly of pulser
turn-on
damped
Yr = SC&E/(1 r,
output wave profiles are clearly evident, with the higher value of to giving rise to a reduction in magnitude and increase in pulse rise-time. It should be noted that the extensive ringing normally associated with a lightly damped system has been substantially reduced by increasing the turn-on time. This serves to illustrate a simple method of electrically controlling transducer response and a variety of output spectra may be achieved by varying turn-on times in this fashion. Switching MOSFET devices lend themselves to such an application. as their switching characteristics may be varied by suitably adjusting the driving circuitry. In general, if r, < T/10. the driving waveshape may be considered ‘ideal’, and the input approximated very closely by a step function. This condition applies to most of the piezoceramic transducers used in nondestructive testing and biomedical applications. where transit times of 100 ns - 250 ns are commonly encountered. Avalanche transistors and switching MOSFET devices possess turn-on times well within this range and so do some thyristors and valves. Consequently, pulsers with turn-on times in the range IO ns - 20 ns would serve to maximize the system efficiency. if operated in the correct manner.
108
+ s (C, + Cu)R=)
(18)
time
= (1 + SC&E)/(
1 •t s (C, + CB)RE)
(19)
That is. as RE is reduced. the transmission efliciency lowered and the amount of secondary action is increased. Alternatively.
is
YF -+ 1 and Yr -+ 0
RE
+
0,
RE
+
O"> YF>YI
-+ cB/(cfl +cB)
The influence of RE on both primary and secondary piezoelectric action may be neglected if MC’,,+ CB)RE > I. For most piezoceramic devices operating under lightly damped conditions. this condition is satisfied if w (Co + CB)RE 2 20
(20)
This criterion may of course be relaxed with respect to secondary action under conditions of increased mechanical damping increased frequency of operation or when using reduced efficiency polymer-film devices. The time constant (Cb + CB)Rk is also mainly responsible for determining the width of the voltage pulse applied to the transducer and hence the bandwidth of the transmitted force waveform. From (18). the voltage developed across the transducer static capacitance under ideal pulsed conditions is given by.
ULTRASONICS.
MAY 1985
V,(t)
= -HT
CB (CO
+CBjRE)
exp(-r/(CO
(2l)
+cB)
Consequently. for wideband operation, a low value of R, (or Ca) is often required. reducing the overall transmission efficiency of the system. The addition of further R-C differentiating networks to approximate impulse excitation will also reduce overall system sensitivity. To illustrate some of these factors. consider Fig. 10. which depicts the normalized force magnitude frequency response for three different values of load resistor. Other parameters used in the simulation are to = 20 ns. R, = 1 s1. c‘a = 2.2 nF, under conditions of heavy damping. It,may be observed that a reduction in R, serves to reduceethe transmission efficiency and broaden the pulse bandwidth. Fig. 11 shows the corresponding spectra under conditions of light damping. It should be noted that for this case, the influence of RE is considerably reduced. The response is in fact dominated by the external mechanical load conditions. A tuning network invariably the parallel combination of a resistor and an inductor. is often employed to increase the efficiency of a pulser configuration, usually at the expense of the system bandwidth. For the ‘ideal’ pulser. three possible conditions arise. From (15)
In this case fi is imaginary, giving rise to an overdamped system. This results in a wide. smooth voltage waveform developed across the transducer static capacitance and is not normally encountered practice. (b)LE
= 4Rg(Co
In this case /3 is real. corresponding to an underdamped system. It gives rise to an oscillatory voltage waveform developed across the static capacitance, the frequency of which is determined by (15). This is a necessary condition for inductive tuning under pulsed conditions. In practice. L, is selected to tune with C,, at the transducer resonance and RE is chosen to produce the required degree of damping compatible with the system resolution requirements. However, because of the complex electromechanical interaction associated with high efficiency transducers, such a technique is really only applicable under certain rigid circumstances. To illustrate this, consider a feedback model of the tuned system driven under ideal pulsed conditions. That is
?I = s~LERECB/(S~LERE(CO +CB)
+sLE +REj
or
+ (oLE/RE)~
1%
(22)
and fF
= (s~LERECB +sLE +RE)/{
s~LERE(CO
+CB)
or 1YF 1 = [ ((1 - ‘d2LECB)’
+ (WLE/RE)2 )/
in
+Cu)
In this case /3 is zero, corresponding to a condition of critical damping. It is a condition difficult to achieve in practice. as some degree of overshoot or undershoot usually results.
)] ’
(( 1 - o~LE(CO + CB))~ + (wLE/RE)~
(23)
It is apparent from (22) and (23) that both primary and secondary piezoelectric actions are maximized at a tuned frequency given by f,,,
=
+cB)LE
1/277((c0
1"
(24)
“.L”
024
-
0.22 -
-
R,
= IO ka
0.20-
-.-
R,
= 220
-o-RE= 018 ’.z
n
500.
-
0.16 -
6 0.14 -
z gOl2,b 0.10-
0 Frequency Fig. 10 damped
Output
force
transducer
spectral
subject
magnnude
to different
resistance
ULTRASONICS.
[MHz
characteristics conditions
0.5
IO
1.5
2.0
2.5
Frequency
] for a heavily
of parallel
load
Fig. 1 1 damped
Output transducer
force
spectral
subject
magmtude
to different
30
35
40
45
50
[MHz] characterlstlcs
conditions
for a lightly
of parallel
load
resistance
MAY 1985
109
which is subject to light mechanical loading All other parameters arc as in the previous example. A distinct minimum may be observed in the vicinity of tuned resonance the extent of which varies inversely with the degree of electrical damping. Note that for R, = 50 CR. the response is dominated by the damping component and the inductor has little or no influence. The damping resistor has little or no influence on the system performance if the condition R, > wLFi is valid. This requirement is fulfilled for lightly damped, piezoceramic transducers if R, 2 20 wLk.
-
RE = IO k.Q -.RE = 220 a -o-RR,=50R $
07
1 C
6 0.6 z Ql 05 2 P 2 0.4 .B G 03
.~L__&
02 01
0
Fig.
12
force
transducer
parallel
tuned
1.5
IO
Output
damped
1.8
05
spectral
subject
20
25
30
Frequency
[MHz]
magmtude
to variations
35
charactertstics in the dampmg
40
45
50
for a lightly resistance
of a
network
,
I -RE=IOkLL
RE 220 J-l RE = 50 0.
-o-
q
-o-
0
05
15
IO
20
2.5
Frequency Fig. 13 damped parallel
Output transducer tuned
force
spectral
subject
magnitude
to variations
30
35
40
45
50
[MHz] characteristics
I” the damplng
for a medium resistance
of a
network
The influence of the damping resistor on primary and secondary action is also evident from (22) and (23). For example, in the absence of a damping component. both Yt and YF are in theory infinite at the tuned resonant frequency. In addition, it may also be observed that the amount of feedback is minimized at a frequency of I127r(L&‘t9”Z Hz. In the absence of RE, the amount of secondary is zero at this particular frequency.
The twin peaks on either side of tuned resonance arise directly from the strong secondary interaction within the system. As a result, they are reduced by: increasing the mechanical and/or the electrical damping: operation at higher frequencies, where secondary effects are reduced: or use of a transducer with a lower value of coupling coefficient. For example, Fig. 13 shows the same three responses under conditions of medium mechanical damping (RF = RB = 0.5). In this case, secondary action is sufficiently reduced to permit a degree of electrical tuning at the required frequency. Similar effects occur for other situations in which the total amount of secondary action is reduced. As an example. Fig. 14 shows the frequency response for the same transducer system tuned to the third harmonic of mechanical resonance. The transducer is subject to light mechanical loading and a damping component of 10 kR was selected to maximize the tuning effect. Although a distinct minimum may be observed, a comparison with Fig. 12 indicates a significant reduction in the intluence of secondary piezoelectric action. The time domain responses corresponding to light and medium damping are shown in Fig. 15. (All other parameters are as in the previous examples.) The enhanced response under conditions of reduced secondary action is readily apparent. Dual frequency components in the lightly damped output may also be observed. In fact, under conditions of heavy damping. the response may be shown to approximate closely to the open loop case, and a significant improvement in system efficiency may be obtained by an appropriate tuning network (at the expense of system bandwidth).
action
At the frequency of tuned resonance. primary and secondary action is maximized and it may be expected that maximum system efficiency occurs under such conditions. However, because of phase changes within the feedback loops, there is no guarantee that the input and feedback currents sum in a constructive marine?**** In fact_ the feedback is often negative at particular frequencies. resulting in a considerable reduction in the total input current. Furthermore, such effects are often compounded under complex electrical load conditions. This may be illustrated by considering Fig. 12, which depicts the frequency response of a parallel tuned system for three different values of damping resistance. The inductance was selected to resonate with (CO + C,) at the mechanical resonant frequency of the transducer.
110
0
05
IO
15
20
25
30
Frequency Fig.
14
damped
Output transducer
force
spectral
tuned
magnitude
to the third
35
characterwlcs
harmomc
40
45
[MHz] for a lightly
of mechanical
ULTRASONICS.
resonance
MAY 1985
50
they are still used in some high intensity applications where high voltages and fast turn-on times are required. For example, the Krytron KN-22” can switch in excess of 2.5 kV in under 50 ns and is comparable in size with most commercially available solid state devices. However, they are relatively expensive. require additional driving circuitry for optimum switching and possess relatively low lifetimes. Thyristors These devices are commonly used in ultrasonic pulser applications where energy and reliability are a primary requirement. However, as ultrasonic transmitters, they suffer from the following disadvantages. 0
05
IO
15
20
25 Time
Fig. 15
Output
subject
to different
force
temporal
condltlons
30
40
45
tuned
system
50
1~~1
characteristics of mechanlcal
35
for a pulsed
Commercially available thyristors are limited in speed and there is invariably a trade-off between HT voltage and turn-on time. Thyristors with turn-on times less than 100 ns tend to be relatively expensive.
damping
The ‘on’ resistance is relatively 20 Cl for many devices. In general, this form of electrical tuning under pulsed conditions is advantageous only if secondary piezoelectric effects are reduced. This is in agreement with the work performed by Legge’O. who used a narrowband model to illustrate some of the concepts. For the majority of piezoceramic devices, a reduction in the amount of feedback by a factor of 20 is generally sufficient to permit electrical tuning at a single frequency. However, for polymer film devices, which are not only less efficient in transmission but are relatively straightforward to damp mechanically, inductive tuning of this type may be performed without unexpected distortion of the output response.
Conclusion Some of the electrical variables associated with transient piezoelectric transmission have been investigated. Characteristics of practical switching devices have been included in the model and their influence on transducer response evaluated by means of the systems approach. The effect of pulser ‘on’ resistance, turn-on time and matching circuitry have been modelled for a variety of transducer and mechanical load conditions. It is anticipated that this work will eventually lead to more realistic transducer assessment under pulsed conditions. Similar studies have been made on the spatial field characteristics and also on the piezoelectric receiver. This will be reported at a later date.
Appendix Characteristics
of some common
pulser
devices
Practical excitation devices include valves. thyristors, avalanche transistors and switching MOSFETs. Their relevant characteristics are broadly outlined in this section. Note that no attempt is made to discuss the theoretical operation of the devices: such information may readily be obtained from an appropriate reference manual.
Although capable of handling large amounts of current and, in some instances, possessing fast switching times, valves have been largely superseded by solid state devices in pulsed ultrasonic applications. However,
ULTRASONICS.
MAY 1985
high, in the region of
Thyristors are difficult to switch off, limiting the maximum pulse repetition frequency. Although gatecontrolled devices are available. their switching times are still relatively slow when compared with avalanche transistors and switching MOSFETs. Avalanche transistors Bipolar transistors operating in the avalanche moder2 are characterized by fast switching times (0.1-100 ns) and low values on ‘on’ resistance (less than 10 Sz typically, although the value is a function of current). However, the maximum HT voltage on commercial devices is limited to approximately 300 V. Although higher voltages are possible by cascading devices, the associated driving circuitry becomes more complex in order that simultaneous conduction is ensured13. Switching M0SFET.s These devices possess high operating voltages (1 kV), very fast switching times (10 ns) and low ‘on’ resistances (0.3 a)“. Such characteristics render them ideal for ultrasonic transducer drive circuits and they are already superseding thyristors and avalanche transistors in the majority of cases. A typical example outlining the performance characteristics of the devices is the IRFS30i4, which is capable of handling peak currents of 7 A (3 A continuous) and operates up to 500 V with a rated switching time of 30 ns. The resistance in the conducting state is only 1.3 Sz and consequently. the switch approximates closely to the ideal situation. It should be noted however, that the driving circuitry must be carefully designed to produce optimum switching performance and avoid damage to the device.
Acknowledgements The author wishes to express gratitude to the UKSERC Marine Technology Directorate for funding the research programme from which the present work developed; also to Mr M. Jackson, for his assistance with the simulation diagrams.
References I
Erikson, E.K. Tone-Burst Testing of I!XE Tmn.\: Sonicr (ilrrasonics, W-26
Pulse Echo Transducers. (I) (1979) 7-14
111
7
3 4
S
6
7
112
Carson, D.L. What a Hospital Physicist Needs in a Transducer Characterisation Standard: Arc Tissue Equivalent Test Objects Necessary? IEb::‘ETTrtrt7.,. Sorlia U/rru.\onic.~, SU-26 ( I ) ( 1979) I-h Hayward, G., MacLeod, C.J., Durrani, T.S. A Systems Model of the Thickness - Mode Piezoelectric Transducer. JI /Icou.\r sot Am. (1984) Hayward, G. A Systems Feedback Representation ol Piezoelectric Transducer Operational Impedancs. Ulrvcwr~ict 22(4)(19X4) 1.53-162 Hayward, G., Jackson, M.N. The IJac of I’ - Transforms in Modelling Piezoelectric Transducers. IEEE Illtrasonics Symposium, Atlanta, (Nov. 19X3) Hayward, G., Jackson, M.N. Discrete-Time Modclling of the Thickness-Mode Piezoelectric Transducer. Il;b1b: Tram S0nic.r Ultrasonics SU-31 (3) (19X4) 137-120 Hansen, J.P., Schmidt, W.A. A I,ast Risctimc Awlanchc
X
9 IO
11 I? I3 14
Transistor Pulse Generator for Driving Injection Lasers. Proc. IEm: (Lett) 55 ( 1967) 2 lb-2 I7 Thurston, R.N. Effect of Electrical and Mechanical Terminating Resistancca on Los> and Bandwidth According to the Conventional Equivalent Circuit of a Pieroclcctric Transducer. IRE Trmu. L’/trrr.sor~ic:cEngg (1960) I h-25 Brown, A.F., Weight, J.P. Generation and Rcccption 01 Wideband Illtrasound. Cbwwnicv 12 (1974) 161-167 Legge, R.D. The Effect5 of Tuning Inductance on the Performance of Ultrasonic Probes Used for Non-Destructive Testing, CEGB Report No. NW/SSD/RRIj4/79, (Jan. 19x0) EG and G (ElectrtrOptics Division) Data Sheet K55OOB-2 Fcrranti Semiconductors Ltd: The USC of Transistors in the Avalanche Mode Prince, P.R. Paralleling Avalanche Transistors. pr/‘roc:fl_E:‘E (correspondence). 53 (March 1‘965) 303 Mospower Design Catalog. Siliconix Inc (Jan. ISXi)
ULTRASONICS.
MAY 1985
ultrasonics,
transducers,
excitation
systems
List of symbols h
Piezoelectric charge constant thickness direction
k
Electromechanical clamped)
CCI
Transducer
T
Transit time for mechanical the transducer thickness
ZC
coupling
factor (laterally
static capacitance
Mechanical
impedance
waves to cross
of transducer
author
Glasgow
IS I” the
Department
of Strathclyde. Gl
1 XW,
of Electronic
Royal
Scotland.
College
UK.
Paper
MAY 1985
Electrical
Building.
204
recewed
16
0041-624X/85/0301 ULTRASONICS.
and
impedance
of front face
Z,
Mechanical
impedance
of rear face medium
RF
Front
Rt3
Rear face reflection
s
The Laplace
w
Angular
George October
03-l
complex
coefficient coefficient
(force) (force)
variable
frequency
Frequency
Although techniques for assessing the relative merits of individual transducer probe assemblies are well developed. such methods tend to utilize cw or gated cw excitation from a standard pulse generator of known electrical characteristics’. The influence of the generator is largely ignored and hence the extrapolation of calibration results to non-standard generators cannot readily be performed. Practical excitation circuits invariably involve some form of switching network whereby the transducer is stimulated by the rapid deposition of a quantity of charge. The electrical characteristics of such pulser systems are often considerably more complex than those of the standard pulse generator and as a result. strong electrical interaction with the transducer element may occur. This can have a marked influence on the transmitted acoustic wave profile.
Engineermg, Street, 1984.
O/$03.00
face reflection
efficient piezoelectric transducers normally employed can be difficult to assess and calibrate under practical, transient operating conditions. Moreover, the influence of the driving circuit and the subsequent electromechanical interaction is often neglected.
Accurate characterization of the transducer system is a necessary feature for almost all applications of ultrasound. The ability to predict and define transducer performance is of particular importance in sonar. nondestructive testing and diagnostic ultrasound where the acoustic pulse parameters are used extensively for imaging defect sizing. materials analysis and tissue characterization. Since the transmission (and reception) response characteristics of thickness-mode transducer assemblies are functions of the electrical. mechanical and piezoelectric properties of the system. it is required to include all three parameters for an accurate assessment of probe behaviour. For example. transducer performance in both time and spatial domains may be influenced by the electrical load conditions. The extent of this influence depends on transducer efficiency, external mechanical loading and the particular operating frequency range. However, the University
Mechanical medium
f
Introduction
The
2, in the
0
1985
Butterworth
8 Co (Publishers)
Ltd
103
It has been suggested* that a standard pulser bc configured to provide a more realistic performance test. Before this can be carried out. a comprehensive investigation of transducer electromechanical interaction is required. Moreover, the characteristics of the switching device and associated circuitry must be clearly defined. To achieve this, it is necessary to construct a model which accurately predicts the behaviour of the transducer system over a wide range of practical operating conditions. In subsequent sections, the transducer feedback model3’4 is used to explain and simulate the performance of a variety of different excitation systems over a range of mechanical load conditions. By reducing the complete system into a number of relatively straightforward functional blocks. the complex electromechanical processes are readily explained and the factors which influence device behaviour arc clearly isolated.
Modelling
the transmission
system
Consider the transmitting configuration outlined in Fig. 1, in which r represents the excitation voltage source and FF corresponds to the force generated at the transducer front face. Two lumped impedances, Z, and ZE, are included to represent the impedance of the generator and any coupling or matching networks. The systems feedback concept is used to model transducer behaviour. A block diagram feedback model is outlined in Fig. 2. in which the transducer is subject to the physical constraints of linear, planar. lossless and unidirectional wave motion in the thickness direction. It is also assumed to radiate directly into semiinfinite, real media which are situated at each face. For this configuration. a Laplace transfer function relating output force to excitation voltage is given by -
--
FF _ -;-e
- hC, YIKFAF/2
1 - i5&TF/2
104
Transmitter
1
Transducer
conflguratlon
for the transmlttlng
mode
Equations (2) and (3) are dimensionless transfer functions which describe the influence of external electrical load conditions on primary and secondary piezoelectric action respectively. Mechanical wave propagation within the device is described by the reverberation factors KF and Ka and the transmission coefficients A tJ2. TF/2 and Ta,12. That is. -
KF
= (1 -eeST)(l
-RB
e-“*)/(I
-RFR,
KB
= (1 -e-“‘)(l
-RF
e -“T)/(l
- RFRB e-2sT)
TF
=
2zc/(z,
+ZI)
TB
=
~&J/(&J
+z,)
AF
=
=-I@,
+Z,)
emzsT)
RF
=
PC
(4) (5)
(1) -Z,MZc
R, = (z, -z,)/(zc
where.
Fig 2
+KBTB/2)k2/sT
1 Fig.
+Z,>
tz2>
model
ULTRASONICS.
MAY 1985
In this notation. the bar symbol denotes Laplace transformation. A study of Fig. 2 reveals that the output wave of force is strongly dependent on both electrical and mechanical loading factors in addition to the piezoelectric properties of the transducer. For example. the electrical load directly influences the output force via the forward loop parameter Yt. The extent of this influence depends on the exact form of ZE and Z,. In general. the magnitude of the output wave of force decreases for low values of ZE and for high values of Z,. It should be noted that conditions which correspond to zero force (Z, zero or Z, infinite). are unlikely to be encountered in a practical excitation system. In a similar manner, both feedback loops contain the parameter Yr and hence secondary piezoelectric action is expected to increase for low values of ZE or Z,. It may be observed that for Z, equal to zero. the system transfer function is independent of ZE, with Yt and Yr both equal to unity. Mechanical load conditions at each face of the transducer also exert a significant influence on the device response. For example. both reverberation factors exhibit minima and maxima at even and odd multiples of the mechanical resonant frequency respectively3,4. Maximum response occurs under narrowband conditions, when the transducer is lightly damped. Maximum secondary action is also expected to occur under similar conditions. The amount of feedback is also directly proportional to the square of the coupling coefficient and inversely proportional to frequency. In general. secondary piezoelectric effects give rise to a reduction in transducer centre frequency to a value below mechanical resonance. This may be accompanied by a small increase in overall signal bandwidth and distortion of the output waveform3. Under conditions of zero feedback the transducer behaves electrically as a pure capacitance of value C,. Consider now the basic pulser conliguration outlined in Fig. 3. in which a blocking capacitor, Ca, is charged to the HT potential via a current limiting resistor, R. Depending upon the particular application, the HT voltage may vary from +5 V to +2.5 kV, while the system pulse repetition frequency is generally limited by the R-Ca time constant. The switch S,, is invariably a fast electronic device which, when activated, results in a transference of charge from the blocking capacitor to the transducer and its associated electrical load. The load may comprise a matching resistor, the parallel
combination of a resistor and tuning inductor or additional R-C differentiating networks for optimizing the pulse shape. For those applications where significant lengths of lossy interconnecting cable are involved. a lumped transmission line equivalent circuit may be employed to simulate cable effects. However. for most applications a simple L-C network is sufficient. Suitable types of switches include valves. thyristors, switching MOSFET transistors and avalanche transistors. The electronic switch may in turn be approximately characterized by turn-on time (t,). peak current capability (lp), ‘on’ resistance when in the conducting state (R,) and maximum blocking voltage when in the non-conducting state. These characteristics vary widely from device to device and care must be taken when specifying a suitable switch for a particular application. For example, turn-on time may vary from a few nanoseconds for an avalanche transistor to several hundred microseconds for some of the slower thyristors and valves. Similarly, ‘on’ resistance may vary from 100 n in some thyristors to less than 1 a in some MOSFET devices. The relevant characteristics and main application areas for a selection of pulser devices are discussed in the appendix. The mode of operation described by Fig. 3 is equivalent to that outlined in Fig. 4. where a non-linear ramp function is applied to the blocking capacitor via a resistance R,. (In general. R B R, and RE.) The ramp function descends from HT to zero volts in a time equal to r, and may be assumed to remain at zero volts for the remainder of the excitation period. Two points should be noted concerning the model. Firstly. the electrical turn-on characteristics of the switching device are assumed uniform over the turn-on period and are represented solely by a resistive element. This is not strictly correct, as a time-varying impedance is generally involved. However, the approximation has been experimentally verified3T5,6 and is considered valid for the majority of excitation systems. Secondly. the turn-on characteristics of the pulser are often functions of the driving circuitry and the electrical load conditions. Consequently, the input waveshape may be approximated by a step function (that is, zero turn-on time). a smooth ramp function or a nonlinear ramp function. depending on the particular operating conditions. Analysis
and simulation
The nominal transducer parameters outlined in Table 1 (corresponding to PZT-SA) were used for the simulation results presented in this section. The timedomain simulations were performed using the discretetime approach described in Ref. 6. By expressing the transducer transfer functions in mixed differential-
+HT
r-.>-4; R~::
-’
+ HT
LE i
L-______-!
Fig. 3
results
Pulser
configuration
ULTRASONICS.
MAY 1985
RE::
Fig. 4
Pulser
equivalent
circuit
105
Table
1.
Nominal
Mechanical resonant frequency
transducer
k
In general. source resistance may be assumed to exert negligible influence on the transmission response it oCbRs < 1.This condition is satisfied for PZT-SA ceramic transducers subject to arbitrary mechanical damping if.
parameters
Z, -2 kg m
s-1]
33.712
x IO6
CdW
[MHz1
WC, Rs < 0.05
1
0.486
1
delay format_ the system may be modelled in the form of a recursive digital filter. This technique is particularly useful for the modelling of non-linear input waveforms and is also amenable to computer implementation. The influence
of generator
Consider firstly a transducer voltage generator possessing For this condition, ZO = Ignoring
Next, consider a switching dcvicc possessing an ‘on‘ resistance R,.which is used to stimulate the transducer via a blocking capacitor CB from a voltage supply, HT. For convenience, the switch is assumed to turn on in zero time. No additional matching elements are connected across the transducer and any interconnecting cable is negligibly short. Consequently, Z, is infinite and.
impedance
excited via a standard an output resistance Rs.
z,
= R, + l/sCu
rr
= YF
cabling
where C = COCu/(C,
effects.
In addition.
?t = YF = (1 +sCoRcJ1
(8)
+sCR,)
= C/C,(l
Rs and ZE = *
(7)
+ Cu)
since
(6)
As expected a finite value of source resistance serves to reduce both input and feedback currents. The output force magnitude will thus be reduced as source resistance increases. and a corresponding reduction in secondary piezoelectric action shifts the centre frequency upwards, towards mechanical resonance4. This may readily be observed from Fig. 5, which describes the output force spectral magnitude for three different values of source resistance. The transducer is assumed to be lightly damped (RF= RB = 0.9). a condition which tends to maximize secondary action. However, under conditions of heavy damping secondary action is reduced and the influence of source resistance on the output centre frequency has the opposite effect. In Lhis case, the frequency-dependent decay inherent in Yt serves to reduce the centre frequency with increasing source resistance. This may be observed from the three simulation results presented in Fig. 6, where reflection coefficients of RH = 0. RF = 0.5are assumed.
e = -HT/s The input current 7 = -
to the transducer
is thus given by
HTC/(I+sCR,)
(9)
The magnitude of the input current is thus reduced for increasing values of ‘on’ resistance and/or decreasing values of blocking capacitance. The magnitude of the output wave of force will also be reduced. with a corresponding reduction in the amount of secondary action, Efficient pulser systems thus require low values of ‘on’ resistance (
0 Frequency Fig. 5 damped resistance
106
Output
force
transducer
spectral under
magnitude
different
characterlstlcs
condttions
05
IO
15
20
25
Frequency
[MHZ] for a lightly
of electrical
source
Fig. 6 damped
Output
force
transducer
spectral under
magmtude
different
3.0
35
40
45
[ MHz 1
characterlstlcs
condmons
=o
for a heavily
of electrvzal
source
resistance
ULTRASONICS.
MAY 1985
50
The influence of the blocking capacitor may readily be observed by considering the transducer response over a truncated time period corresponding to a single transit interval. For an ideal step input and assuming zero ‘on’ resistance. the output wave of force over this interval is given by3 F&)
=
(co
CB + c,)
~CO 64F12)
The influence of pulser turn on time
Consider the transmitter configuration outlined in Fig. 4. in which the pulser has a uniform turn-on characteristic of duration t,,. For this case, the input voltage may be expressed by the following transform equation.
(11)
F = - HT( 1 - emfio )/s2 to
k2 (TF/~ + TB/2)t/T
(10) I
for
In this analysis, it is assumed that pulser ‘on’ resistance may be ignored and that an inductive matching section with resistive damping is connected across the transducer. The voltage applied to the device is thus given by
O
(12)
Under conditions of no secondary action (for example, k = 0), the output force over this time interval is a step function of amplitude P
where fI
= s2 RELECB/
(s2 RELE(Co
•t C,) + SLE + RE ) (13)
The exponential term in (10) describes secondary piezoelectric action and is a function of the piezoelectric. electrical and mechanical properties of the system. As expected both primary and secondary action are maximized under the condition Ca > C,,.
Equation I_ nY
+ Cr.,) = 0.9,
R.
= 5 f&R0
C,/(C,
+ C,)
Ro = 5 !A
V*(t) = -+
given
( sin j?t - eearo sin/3 (t - to) )
(14)
where
= 100 52
Q =
The transducer is subject to conditions damping and step voltage excitation.
transform
0
(2 = (CO +
= 0.1,
inverse
-cut
To illustrate the effects of pulser impedance, consider Fig. 7. which depicts the output force profiles in the time domain for the following three conditions: C,/(C,
(12) has a standard
cB)/c,
( 2RE(COtc,))-’
(15)
of light P = (l/L&CO
The influence of secondary piezoelectric action is readily apparent for the higher value of blocking capacitance. as indicated by the strong positive exponentials. A reduction in secondary action and output force magnitude with increasing ‘on’ resistance may also be observed. For the smaller value of blocking capacitance, little secondary action is evident and there is a considerable reduction in response magnitude.
+Cg)-
l/4R&(Co
+C&’
Equation (14) represents the actual voltage developed across the transducer static capacitance, in the absence, of secondary piezoelectric action. At t = t,,, this voltage is given by
V*(t) =
- HT ema* CB (CO +c,)
(16)
For to equal to zero. the switch is ideal and
020
0.15
vt(t)
= -HTCB/(Co
t=ro -0
0.10
+ c,) (17)
$ g
This is the maximum value of voltage which may be applied to the transducer, for fixed values of C,, and Cu. A comparison between (16) and (17) indicates that increasing t,, serves to reduce the efficiency of the transmitting configuration.
005
$ 0
g S
z -0.05 ‘Z _o d -0.10 -015 -Ox,
0
I
I
I
I
I
I
I
I
I
05
IO
I5
2.0
25
30
3.5
4.0
4.5
Time [ps] Fig. 7 Output force temporal characteristics for a lightly damped transducer subject to variations in pulser impedance
ULTRASONICS.
MAY 1985
5.0
Turn-on time can also have a marked influence on the output wave characteristics. This may readily be observed from Fig 8, which depicts the output force spectra for two different values of turn-on time (to = T/10 and to = 27). In the figure, a lightly damped transducer is assumed, in conjunction with a pulser ‘on’ resistance of 1 s1 and a blocking capacitor of 1 nF. The corresponding time domain waveforms are shown in Fig. 9. Differences in the magnitude and form of the
107
018
However. care must be taken with some of the higher frequency ceramic and polymer film devices which possess transit times in the region of 10 ns - 50 ns. For such cases. the appropriate switching device should be carefully selected for the required system efficiency and pulse characteristics. Variations in pulser turn-on time also have a more marked influence on the output response than in the lower frequency devices. Avalanche transistors have potential switching times of under 5 ns’ and despite relatively low blocking voltages and shorter lifetimes, they are often the most suitable switches for driving polymer film and high frequency ceramic transducers.
016
The influence 0
Ftg. 8
05
Output
damped
IO
force
transducer
15
spectral subject
20
25
30
Frequency
[MHZ]
magnwde
35
characterlstlcs
to different
conditions
40
45
50
for a lightly
of pulser
turn-on
time
of the matching
network
A matching or pulse shaping network in the form of a resistor or the parallel combination of a resistor and an inductor is often connected across the transducer electrodes. The network is usually incorporated to maximize the system sensitivity and/or optimize the pulse width to meet resolution requirements. Although narrowband excitation systems. utilizing low efficiency transduction devices. have received much attention in the literature. (see for example Ref. 8) little data are available on practical pulser matching configurations. It is the purpose of the present section to examine the influence of the matching network on an efficient piezoelectric transducer system driven under the practical transient conditions commonly encountered in ndt and biomedical applications. Consider firstly a purely resistive element connected across the transducer which is driven via a blocking capacitor and an ideal pulser.
-0.08
I 0
I
I
1
I
I
I
I
I
I
05
IO
15
20
25
30
35
40
45
Time Fig. 9
Output
transducer
force
subject
temporal
to different
characteristics conditions
50
For the majority of piezoceramic devices. this condition is approximated very closely by the use of a switching MOSFET. For such a configuration.
[ps] for a lightly of pulser
turn-on
damped
Yr = SC&E/(1 r,
output wave profiles are clearly evident, with the higher value of to giving rise to a reduction in magnitude and increase in pulse rise-time. It should be noted that the extensive ringing normally associated with a lightly damped system has been substantially reduced by increasing the turn-on time. This serves to illustrate a simple method of electrically controlling transducer response and a variety of output spectra may be achieved by varying turn-on times in this fashion. Switching MOSFET devices lend themselves to such an application. as their switching characteristics may be varied by suitably adjusting the driving circuitry. In general, if r, < T/10. the driving waveshape may be considered ‘ideal’, and the input approximated very closely by a step function. This condition applies to most of the piezoceramic transducers used in nondestructive testing and biomedical applications. where transit times of 100 ns - 250 ns are commonly encountered. Avalanche transistors and switching MOSFET devices possess turn-on times well within this range and so do some thyristors and valves. Consequently, pulsers with turn-on times in the range IO ns - 20 ns would serve to maximize the system efficiency. if operated in the correct manner.
108
+ s (C, + Cu)R=)
(18)
time
= (1 + SC&E)/(
1 •t s (C, + CB)RE)
(19)
That is. as RE is reduced. the transmission efliciency lowered and the amount of secondary action is increased. Alternatively.
is
YF -+ 1 and Yr -+ 0
RE
+
0,
RE
+
O"> YF>YI
-+ cB/(cfl +cB)
The influence of RE on both primary and secondary piezoelectric action may be neglected if MC’,,+ CB)RE > I. For most piezoceramic devices operating under lightly damped conditions. this condition is satisfied if w (Co + CB)RE 2 20
(20)
This criterion may of course be relaxed with respect to secondary action under conditions of increased mechanical damping increased frequency of operation or when using reduced efficiency polymer-film devices. The time constant (Cb + CB)Rk is also mainly responsible for determining the width of the voltage pulse applied to the transducer and hence the bandwidth of the transmitted force waveform. From (18). the voltage developed across the transducer static capacitance under ideal pulsed conditions is given by.
ULTRASONICS.
MAY 1985
V,(t)
= -HT
CB (CO
+CBjRE)
exp(-r/(CO
(2l)
+cB)
Consequently. for wideband operation, a low value of R, (or Ca) is often required. reducing the overall transmission efficiency of the system. The addition of further R-C differentiating networks to approximate impulse excitation will also reduce overall system sensitivity. To illustrate some of these factors. consider Fig. 10. which depicts the normalized force magnitude frequency response for three different values of load resistor. Other parameters used in the simulation are to = 20 ns. R, = 1 s1. c‘a = 2.2 nF, under conditions of heavy damping. It,may be observed that a reduction in R, serves to reduceethe transmission efficiency and broaden the pulse bandwidth. Fig. 11 shows the corresponding spectra under conditions of light damping. It should be noted that for this case, the influence of RE is considerably reduced. The response is in fact dominated by the external mechanical load conditions. A tuning network invariably the parallel combination of a resistor and an inductor. is often employed to increase the efficiency of a pulser configuration, usually at the expense of the system bandwidth. For the ‘ideal’ pulser. three possible conditions arise. From (15)
In this case fi is imaginary, giving rise to an overdamped system. This results in a wide. smooth voltage waveform developed across the transducer static capacitance and is not normally encountered practice. (b)LE
= 4Rg(Co
In this case /3 is real. corresponding to an underdamped system. It gives rise to an oscillatory voltage waveform developed across the static capacitance, the frequency of which is determined by (15). This is a necessary condition for inductive tuning under pulsed conditions. In practice. L, is selected to tune with C,, at the transducer resonance and RE is chosen to produce the required degree of damping compatible with the system resolution requirements. However, because of the complex electromechanical interaction associated with high efficiency transducers, such a technique is really only applicable under certain rigid circumstances. To illustrate this, consider a feedback model of the tuned system driven under ideal pulsed conditions. That is
?I = s~LERECB/(S~LERE(CO +CB)
+sLE +REj
or
+ (oLE/RE)~
1%
(22)
and fF
= (s~LERECB +sLE +RE)/{
s~LERE(CO
+CB)
or 1YF 1 = [ ((1 - ‘d2LECB)’
+ (WLE/RE)2 )/
in
+Cu)
In this case /3 is zero, corresponding to a condition of critical damping. It is a condition difficult to achieve in practice. as some degree of overshoot or undershoot usually results.
)] ’
(( 1 - o~LE(CO + CB))~ + (wLE/RE)~
(23)
It is apparent from (22) and (23) that both primary and secondary piezoelectric actions are maximized at a tuned frequency given by f,,,
=
+cB)LE
1/277((c0
1"
(24)
“.L”
024
-
0.22 -
-
R,
= IO ka
0.20-
-.-
R,
= 220
-o-RE= 018 ’.z
n
500.
-
0.16 -
6 0.14 -
z gOl2,b 0.10-
0 Frequency Fig. 10 damped
Output
force
transducer
spectral
subject
magnnude
to different
resistance
ULTRASONICS.
[MHz
characteristics conditions
0.5
IO
1.5
2.0
2.5
Frequency
] for a heavily
of parallel
load
Fig. 1 1 damped
Output transducer
force
spectral
subject
magmtude
to different
30
35
40
45
50
[MHz] characterlstlcs
conditions
for a lightly
of parallel
load
resistance
MAY 1985
109
which is subject to light mechanical loading All other parameters arc as in the previous example. A distinct minimum may be observed in the vicinity of tuned resonance the extent of which varies inversely with the degree of electrical damping. Note that for R, = 50 CR. the response is dominated by the damping component and the inductor has little or no influence. The damping resistor has little or no influence on the system performance if the condition R, > wLFi is valid. This requirement is fulfilled for lightly damped, piezoceramic transducers if R, 2 20 wLk.
-
RE = IO k.Q -.RE = 220 a -o-RR,=50R $
07
1 C
6 0.6 z Ql 05 2 P 2 0.4 .B G 03
.~L__&
02 01
0
Fig.
12
force
transducer
parallel
tuned
1.5
IO
Output
damped
1.8
05
spectral
subject
20
25
30
Frequency
[MHz]
magmtude
to variations
35
charactertstics in the dampmg
40
45
50
for a lightly resistance
of a
network
,
I -RE=IOkLL
RE 220 J-l RE = 50 0.
-o-
q
-o-
0
05
15
IO
20
2.5
Frequency Fig. 13 damped parallel
Output transducer tuned
force
spectral
subject
magnitude
to variations
30
35
40
45
50
[MHz] characteristics
I” the damplng
for a medium resistance
of a
network
The influence of the damping resistor on primary and secondary action is also evident from (22) and (23). For example, in the absence of a damping component. both Yt and YF are in theory infinite at the tuned resonant frequency. In addition, it may also be observed that the amount of feedback is minimized at a frequency of I127r(L&‘t9”Z Hz. In the absence of RE, the amount of secondary is zero at this particular frequency.
The twin peaks on either side of tuned resonance arise directly from the strong secondary interaction within the system. As a result, they are reduced by: increasing the mechanical and/or the electrical damping: operation at higher frequencies, where secondary effects are reduced: or use of a transducer with a lower value of coupling coefficient. For example, Fig. 13 shows the same three responses under conditions of medium mechanical damping (RF = RB = 0.5). In this case, secondary action is sufficiently reduced to permit a degree of electrical tuning at the required frequency. Similar effects occur for other situations in which the total amount of secondary action is reduced. As an example. Fig. 14 shows the frequency response for the same transducer system tuned to the third harmonic of mechanical resonance. The transducer is subject to light mechanical loading and a damping component of 10 kR was selected to maximize the tuning effect. Although a distinct minimum may be observed, a comparison with Fig. 12 indicates a significant reduction in the intluence of secondary piezoelectric action. The time domain responses corresponding to light and medium damping are shown in Fig. 15. (All other parameters are as in the previous examples.) The enhanced response under conditions of reduced secondary action is readily apparent. Dual frequency components in the lightly damped output may also be observed. In fact, under conditions of heavy damping. the response may be shown to approximate closely to the open loop case, and a significant improvement in system efficiency may be obtained by an appropriate tuning network (at the expense of system bandwidth).
action
At the frequency of tuned resonance. primary and secondary action is maximized and it may be expected that maximum system efficiency occurs under such conditions. However, because of phase changes within the feedback loops, there is no guarantee that the input and feedback currents sum in a constructive marine?**** In fact_ the feedback is often negative at particular frequencies. resulting in a considerable reduction in the total input current. Furthermore, such effects are often compounded under complex electrical load conditions. This may be illustrated by considering Fig. 12, which depicts the frequency response of a parallel tuned system for three different values of damping resistance. The inductance was selected to resonate with (CO + C,) at the mechanical resonant frequency of the transducer.
110
0
05
IO
15
20
25
30
Frequency Fig.
14
damped
Output transducer
force
spectral
tuned
magnitude
to the third
35
characterwlcs
harmomc
40
45
[MHz] for a lightly
of mechanical
ULTRASONICS.
resonance
MAY 1985
50
they are still used in some high intensity applications where high voltages and fast turn-on times are required. For example, the Krytron KN-22” can switch in excess of 2.5 kV in under 50 ns and is comparable in size with most commercially available solid state devices. However, they are relatively expensive. require additional driving circuitry for optimum switching and possess relatively low lifetimes. Thyristors These devices are commonly used in ultrasonic pulser applications where energy and reliability are a primary requirement. However, as ultrasonic transmitters, they suffer from the following disadvantages. 0
05
IO
15
20
25 Time
Fig. 15
Output
subject
to different
force
temporal
condltlons
30
40
45
tuned
system
50
1~~1
characteristics of mechanlcal
35
for a pulsed
Commercially available thyristors are limited in speed and there is invariably a trade-off between HT voltage and turn-on time. Thyristors with turn-on times less than 100 ns tend to be relatively expensive.
damping
The ‘on’ resistance is relatively 20 Cl for many devices. In general, this form of electrical tuning under pulsed conditions is advantageous only if secondary piezoelectric effects are reduced. This is in agreement with the work performed by Legge’O. who used a narrowband model to illustrate some of the concepts. For the majority of piezoceramic devices, a reduction in the amount of feedback by a factor of 20 is generally sufficient to permit electrical tuning at a single frequency. However, for polymer film devices, which are not only less efficient in transmission but are relatively straightforward to damp mechanically, inductive tuning of this type may be performed without unexpected distortion of the output response.
Conclusion Some of the electrical variables associated with transient piezoelectric transmission have been investigated. Characteristics of practical switching devices have been included in the model and their influence on transducer response evaluated by means of the systems approach. The effect of pulser ‘on’ resistance, turn-on time and matching circuitry have been modelled for a variety of transducer and mechanical load conditions. It is anticipated that this work will eventually lead to more realistic transducer assessment under pulsed conditions. Similar studies have been made on the spatial field characteristics and also on the piezoelectric receiver. This will be reported at a later date.
Appendix Characteristics
of some common
pulser
devices
Practical excitation devices include valves. thyristors, avalanche transistors and switching MOSFETs. Their relevant characteristics are broadly outlined in this section. Note that no attempt is made to discuss the theoretical operation of the devices: such information may readily be obtained from an appropriate reference manual.
Although capable of handling large amounts of current and, in some instances, possessing fast switching times, valves have been largely superseded by solid state devices in pulsed ultrasonic applications. However,
ULTRASONICS.
MAY 1985
high, in the region of
Thyristors are difficult to switch off, limiting the maximum pulse repetition frequency. Although gatecontrolled devices are available. their switching times are still relatively slow when compared with avalanche transistors and switching MOSFETs. Avalanche transistors Bipolar transistors operating in the avalanche moder2 are characterized by fast switching times (0.1-100 ns) and low values on ‘on’ resistance (less than 10 Sz typically, although the value is a function of current). However, the maximum HT voltage on commercial devices is limited to approximately 300 V. Although higher voltages are possible by cascading devices, the associated driving circuitry becomes more complex in order that simultaneous conduction is ensured13. Switching M0SFET.s These devices possess high operating voltages (1 kV), very fast switching times (10 ns) and low ‘on’ resistances (0.3 a)“. Such characteristics render them ideal for ultrasonic transducer drive circuits and they are already superseding thyristors and avalanche transistors in the majority of cases. A typical example outlining the performance characteristics of the devices is the IRFS30i4, which is capable of handling peak currents of 7 A (3 A continuous) and operates up to 500 V with a rated switching time of 30 ns. The resistance in the conducting state is only 1.3 Sz and consequently. the switch approximates closely to the ideal situation. It should be noted however, that the driving circuitry must be carefully designed to produce optimum switching performance and avoid damage to the device.
Acknowledgements The author wishes to express gratitude to the UKSERC Marine Technology Directorate for funding the research programme from which the present work developed; also to Mr M. Jackson, for his assistance with the simulation diagrams.
References I
Erikson, E.K. Tone-Burst Testing of I!XE Tmn.\: Sonicr (ilrrasonics, W-26
Pulse Echo Transducers. (I) (1979) 7-14
111
7
3 4
S
6
7
112
Carson, D.L. What a Hospital Physicist Needs in a Transducer Characterisation Standard: Arc Tissue Equivalent Test Objects Necessary? IEb::‘ETTrtrt7.,. Sorlia U/rru.\onic.~, SU-26 ( I ) ( 1979) I-h Hayward, G., MacLeod, C.J., Durrani, T.S. A Systems Model of the Thickness - Mode Piezoelectric Transducer. JI /Icou.\r sot Am. (1984) Hayward, G. A Systems Feedback Representation ol Piezoelectric Transducer Operational Impedancs. Ulrvcwr~ict 22(4)(19X4) 1.53-162 Hayward, G., Jackson, M.N. The IJac of I’ - Transforms in Modelling Piezoelectric Transducers. IEEE Illtrasonics Symposium, Atlanta, (Nov. 19X3) Hayward, G., Jackson, M.N. Discrete-Time Modclling of the Thickness-Mode Piezoelectric Transducer. Il;b1b: Tram S0nic.r Ultrasonics SU-31 (3) (19X4) 137-120 Hansen, J.P., Schmidt, W.A. A I,ast Risctimc Awlanchc
X
9 IO
11 I? I3 14
Transistor Pulse Generator for Driving Injection Lasers. Proc. IEm: (Lett) 55 ( 1967) 2 lb-2 I7 Thurston, R.N. Effect of Electrical and Mechanical Terminating Resistancca on Los> and Bandwidth According to the Conventional Equivalent Circuit of a Pieroclcctric Transducer. IRE Trmu. L’/trrr.sor~ic:cEngg (1960) I h-25 Brown, A.F., Weight, J.P. Generation and Rcccption 01 Wideband Illtrasound. Cbwwnicv 12 (1974) 161-167 Legge, R.D. The Effect5 of Tuning Inductance on the Performance of Ultrasonic Probes Used for Non-Destructive Testing, CEGB Report No. NW/SSD/RRIj4/79, (Jan. 19x0) EG and G (ElectrtrOptics Division) Data Sheet K55OOB-2 Fcrranti Semiconductors Ltd: The USC of Transistors in the Avalanche Mode Prince, P.R. Paralleling Avalanche Transistors. pr/‘roc:fl_E:‘E (correspondence). 53 (March 1‘965) 303 Mospower Design Catalog. Siliconix Inc (Jan. ISXi)
ULTRASONICS.
MAY 1985