- Email: [email protected]
Broad-band driving of echographic arrays using 10 ns-500 V efficient pulse generators
Broad-band driving of echographic arrays using 10 ns-500 V efficient pulse
generators A. Ramos-FernSndez, P.T. Sanz-Sanchez and F.R. Montero de Espinosa UEI Ultrasonidos, Instituto de Acustica del CSIC, Serrano 144, 2 8 0 0 6 Madrid, Spain Received 10 June 1986; revised28 October 1986
To obtain a good dynamic range on echographic signals produced by broad-band piezoelectric arrays with frequencies > 4 M Hz, it is necessary to excite each of the array elements with very fast electric spikes. Therefore, for most depths used in medical echographic visualization, or NDT applications, electric pulses of some hundreds of volts with a rise-time of < 30 ns are required. This Paper outlines an analysis of the required characteristics of the high voltage excitation stages for each of the elements of a linear piezoelectric array designed for scanning and electronic focussing. An efficient basic unit for multichannel pulse generation up to 5 0 0 V with a rise-time of 10 ns is described. This unit has been especially designed for the impulsional driving of broadband piezoelectric array elements in the frequency range 1-30 M Hz. The generated electric pulse shape is studied as a function of the generator internal parameters and its external load, and some experimental results for different real transduction conditions are presented. Keywords: echography; pulse generation; excitation systems
Suitable shock excitation of individual elements from piezoelectric arrays designed for frequency bands centered above 4 MHZ, has to be made through high voltage electric pulses (350-400 V minimum) with a rise-time of < 30 ns. These conditions are required if a good dynamic range is wanted in echographic signals obtained from the depths usually handled in biological tissues and some special N D T applications. These extreme conditions, compared with the corresponding simpler cases at lower frequencies, are necessary because of the sharp increase in attenuation with increasing frequency and the high electric impedance of the piezoelectric array elements at those frequencies. This high impedance is a consequence of the geometry imposed on the array elements by the work frequency and acoustic field theory ~,6. There are several different ways to obtain high voltage pulses with short rise-times. In References 2 and 3 two different circuits are shown which reach electrical pulses with amplitudes > 220 V. The first circuit, using a SRC device for the high voltage switching 2,3, has a rise-time between 150-250 ns; this is too high for applications above 2 MHz, The second circuiP can generate 240 V amplitude pulses over a damping resistance of 300 ~ with a rise-time of ~ 100 ns using a MOSFET MTP 474 transistor. This pulse can be used to drive transducers at frequencies < 3.5 MHz. These nominal circuit performances can be severely impaired in real load work conditions due to the influence of the high electrical clamped capacitances of the piezoelectric elements. 0041-624X/87/040221-08 $03.00 © 1987 Butterworth Et Co (Publishers) Ltd
M u l t i c h a n n e l g e n e r a t i o n of h i g h v o l t a g e p u l s e s t o drive h i g h f r e q u e n c y e c h o g r a p h t c ° arrays
Preliminary considerations We have mentioned above some general requirements for the excitation of each of the individual elements in piezoelectric arrays used for echographic purposes. Moreover, if fast variable electronic focussing is required, the emission/reception process must have a number of channels working in parallel equal to the number, n, of individual electric elements used as the array aperture. With a system as indicated in Figure 1, it is possible to drive the aperture elements with a focal distribution that can vary according to time, being able to delay the received echoes at each aperture channel synchronizing with the corresponding exciting distribution. The implementation of this variable focussing implies some special requirements in the spike stage design. The first requirement is a consequence of the short time difference between the excitation of two consecutive elements, which can be as short as a few nanoseconds. Such a short time makes it impossible to share only one generator between all the aperture elements. The second requirement deals with the number of spike generators, this is dependent on the type of focussing and, more importantly, on the scanning used in each, case. This n u m b e r varies between n/2 and the total number of array
Ultrasonics 1987 Vol 25 July
221
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. Figure 2 shows the circuit diagram of a pulser developed for the excitation of each array element, valid for a frequency range up to 25-30 MHz. This circuit, widely applied to different piezoelectric transducers, can furnish pulses with the voltage and rise-time requirements mentioned above.
Array ~ e ]
~.,/]-
~
.nJ
.,.~,,,~t~. ~ . ~ ~ . ~
~:::
I I
s' I '
e.rt~ 1 / ~lticha pu Ise
Pr°grarr and col
•
I °~;"'°°'
-
'
I
1
I
-
Focal zones
Wide-band preamplifiers
Figure 1 Simplifiedblockdiagramof a multichannelemission/ variablefocussingof the arrayaperture
reception system for
elements, m. Each of these spike generators will excite one or more piezoelectric elements (co-phasing) depending on the array design. As simple a design as possible is needed for the excitation basic unit as the number of electric elements on a linear array, m, can be ~ 100. The same criteria of simplicity also applies to the reception unit, mainly at the nearest array stages: 'emission/ reception' uncoupling and signal preamplification.
Circuit design In the design of this circuit we have optimized switching of the high voltage device used (power MOSFET, series IRF 840) and its correct coupling to the transducer device. In the first part of the circuit, complementary transistors T2 and/'3 supply and absorb, respectively, the high level gate currents needed for fast switching of transistor Tmf. A Zener diode, Z (4 V 7), has been included between the drain of Tmf and the discharge capacitor C; the more important effect of this Zener diode is to protect the positive half-cycles corresponding to the initial part of the radiofrequency echographic signals (normally < 4 V). If the Zener diode is not used, these positive half-cycles will go to ground through D1, C and Tmf, distorting the complete signal. The circuit also includes an adjustable inductance, Lo, in parallel with the damping resistance, RD, which allows modification of the temporal evolution of the exciting signal. Diodes DI and D2 prevent the formation of the typical damped oscillatory signal originating from the C-Lo series circuit, allowing only the first negative halfcycle to pass to the transducer, as shown in Figure 2. The Lo-D~-D 2 network can improve the amplitude and shape of the generated pulse due to the following: this network can substitute the resistance RD advantageously to produce a fast electric damping without losing pulse amplitude: and it can facilitate the generation of driving pulses with a trailing edge slope independent of the MOSFET cut-off, which can be useful in reducing the temporal dispersion of the pulse widths for all the individual array elements. This dispersion problem is a consequence of the wide cut-off time tolerances on the switching devices normally used and has motivated the
18vI l°v e t tw(min=) 60ns ilrisetime<5ns F[1 --I ~-tw
--d
/
--
J IT Rc C313!Tm~+11
~ [ ~~_1
R~~,~"_v~~~~ ' ~ ~V(~
)i FromtransmittingBSX ] T3J electroniclens ul-~ ~ N 2 2 1 9
222
I ] I-J~/~/~J~ ) ~ i e r
l':°rterCe:"e°s / D2 x5 Z ~ ~ ~
Ix ] Ix ~ "~" L1A"~;~ RD ~ ?L°--l~ZT~!t2[
Pulser Figure 2
~
!Bipolarlimiteri Receiver
-[--
Circuitdiagramof the highvoltagepulsegeneratorandthe limiterstagecorrespondingto eachof thechannelsin Ultrasonics 1987 Vol 25 July
Figure1
Broad-band driving of echographic arrays: .4. Ramos-Fernandez et al.
(RD//RT//Rr),
IfR L whereRr is the input resistance at the reception stage, it is possible to establish the following relationship =
-v0 R L C [1 - exp(-t/RLC)];Vt/(O < t < ton)
V'o(t ) = - ton
(1)
Figure 3 Leadingedge of the output pulse, V~, obtained from the circuitdescribed in Figure 2. Vo = 400 V, Rc = 18 k~, C = 2.2 nF, R1=4.7 n , R D = 2 7 0
use, for other workersL of feedback systems to control the pulse width. With regard to the received echo signals produced at the explored field, we include in Figure 2 the first two stages corresponding to each of the individual array elements. These stages consist of a bipolar limiter (_+ 5.4 V) and a broad-band signal preamplifier. Figure 3 shows in detail the leading edge of the output pulse, V 0, generated by the circuit shown in Figure 2. Circuit parameters similar to those typical in echographic array applications were used: V0 = 400 V, Rc = 18 k~, ('7 = 2.2 nF, Ri = 4.7 ~ and RD = 270 ~. The pulse rise-time, ~ 10 ns, reached the optimal amplitude value, Vo, which in this case is 400 V. If low impedance transducers are connected, these optimal characteristics can become slightly worse. Nevertheless, by fitting the parameters Re, C, Ri and RD, these problems can be minimized.
This expression agrees with that proposed in Reference 2. The values of V'o(t) are only valid during the pulse leading edge, consequently it would be inappropriate to try to deduce anything beyond that time. To avoid this problem we can approximate Tmr switching with a decreasing exponential function which, being valid after ton(Vt> 0). is in better agreement with the real behaviour of the transistor saturation. Using this kind of function, the expression for V'o(t) is
CR L V'o(t) = - V o C R L _ r
[exp(-t/C R L) -- exp(--t/T)];
Vt>0
(2) As can be seen above, V'o(t) is composed of two decreasing exponential functions, both having the same initial amplitude, Vo CRL/(CRL--r), but with opposite sign.
a Vo
t~ o n
t
+ V0
Temporal analysis of the output pulse shape The time evolution of the output pulse produced by the proposed circuit can be approximately predicted knowing the values corresponding to Vo, C, RD, Lo and ZT (in resonance conditions) in each application. The circuit behaviour was analysed for three different load conditions: 1 inductance, L0, disconnected and the transducer considered as a pure resistive load RT, at excitation time, (this condition is proposed in Reference 2); 2 inductance, Lo, disconnected and the transducer modelled as a parallel electrical equivalent network, RTCT; and 3 inductance, L0, connected with the transducer considered as a parallel electrical network, RTCT.
b V° IVDVl~
+Vo ,4
Voi Voexp(-t/r) [ V t > 0]
C +Vo
Case 1 If we suppose that the drain voltage of the MOSFET transistor during switching decreases linearly with time from V = Iio at t = 0 to V = 0 at t = ton, the circuit from Figure 2 can be modelled using the equivalent circuit shown in Figure 4a. The effects produced by RI(RI~RT) and the diode network, D1 -- D> have only a slight effect on V 0 and, therefore, can be neglected.
i< +tl i
VD VD = Vo e x p ( - t / r )
[Vt>0]
D
RL
CT
L0
Vo
=
Figure 4 Simplified equivalent circuits of the MOSFET pulse generator. (a) Case 1; (b) case 2; (c) case 3
Ultrasonics 1 9 8 7 Vol 25 July
223
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. Case 2 If we maintain the hypothesis of an exponential type function for Tmf switching, the approximated equivalent circuit is as shown in Figure 4b. The transducer clamped capacity, Cx, has been included because it exerts a direct influence over the V'o(t) shape from the beginning of the electric excitation due to the static characteristic of that capacity. The expression for V~ in this case is
VoCRL V;(t)
=-
(C+CT)R
L -1"
× [exp(-t/(C + CT)RL) -- exp(-t/r)]
(3)
From this expression it can be seen that the maximum peak value expected for Vh (given ideal conditions, (C + Ca-)RL >>r) depends strongly on the transducer static capacity, CT, in such a way that it only reaches the optimal value ( ~ - V 0 ) when CT
Case 3 Figure 4c shows the simplified equivalent circuit corresponding to the assumptions made in the third case, as cited above. A diode, D, has been included in parallel with the output terminals; this represents the series connected diode sets D t and D2 shown in Figure 2. With the present load conditions, the expression for V 0 is
VoC RL
v'o(t)
=
(C +CT) R c
--
r +7"2RIJLo
× exp(-t/r) - A e x p ( - a t ) cos(/3t + ~J)
(4)
where 1
= L~L(C + CT)
and
=
['
Lo(C¥CT)
(')1
Experimental results The pulse generator, as outlined above, can be adapted to a wide variety of echographic transducers, with different working frequency bands and electrical impedances, to produce broad-band ultrasonic pulses with very good electric device-transducer coupling. Some experimental results are presented below for the electric driving spike and the corresponding ultrasonic echographic pulse for transducers with both high (similar to the individual elements from a high frequency array) and low electrical impedance (< 5 f~). Figure 5 shows the generated output pulse without load (transducer and inductance, L0, disconnected) and with R D = 100 ['L It can be seen that the spike has an amplitude of ~ 400 V with a shape similar to those shown in References 2 and 3, but with a faster leading edge ( ~ 10 ns). Moreover, [V'olmax/Vo is very close to unity, enabling pulse generation with a high overall efficiency. Nevertheless, this pulse shape is not the best one to drive piezoelectric transducers as the rising slope can excite low frequency modes in the transducer. To minimize these undesirable effects, very low values Of RD must be used, consequently the pulse amplitude will be reduced, decreasing the dynamic range of the echographic signals. If a suitable inductance, L0, is connected in parallel with the damping resistance, RD, it is possible to eliminate the undesired influence of the low frequency modes without greatly loweringRD. At the same time, this inductance can be used to control the total pulse width as shown below. The experiments were carried out with transducers of
2 1/2
28L(~7+ CT)
A and ~pare integration constants dependent on C, Vo, CT, r, RL and Lo. Equation (4) is compounded by two terms. The first is exponential, decreasing according to r, and for v < ( C + CT) RL it is practically equal to the second term of Equation (3). The second term is oscillatory with angular frequency /3, exponentially damped with a constant or. Diode D was not included in Equation (4) and it will cancel the function cos(/3t + ~) after the first zerocrossing, preventing an undesired lengthening on the output pulse. This cosine function makes the positive edge start with a slope smoother than in the pure exponential case but allowing the total pulse rise toward zero to be produced in a shorter time. This effect enables the driving pulses to be obtained with relatively short total widths and without involving significant attenuation on the resultant amplitude. This can be seen in Figure 6 where V0 has a width -~100 ns and a peak amplitude very near to V 0 = 400 V. To obtain a pulse with a similar width but without the
224
inductance, L 0, it would be necessary to reduce the value of C RD greatly, or to make Rc < 500 fl. The first possibility would notably reduce the peak amplitude, whereas the second would involve the use of a source, V0, with high peak current making this solution prohibitive for multi-channel excitation. Therefore, it seems that the use of a parallel inductance, L0, connected at the output terminals of the pulse generator is the most useful way to attain narrow output pulses with high efficiency. Moreover, this inductance produces other advantageous effects, such as 'selective damping' of the secondary oscillating modes and cancellation of the static transducer capacity when required.
Ultrasonics 1987 Vol 25 July
Figure 5 Pulse shape at V 'o of the circuit shown in Figure 21oaded with: RD= 100 •,Rc= 18 kl~, Vo= 400 V, R== 4.7 N , C = 1.5 nF and with repetition frequency = 5 kHz
Broad-band driving of echographic arrays: A Rarnos-Fernandez et al.
Figure 6 Pulse shape at V~) when the generator is loaded with a 5 M Hz minitransducer (radiant area ~ 4 mm 2) connected in parallel with L o = 3.5/zH and R D= 1 5 0 0 ~. Other circuit parameters are the same as in Figure 5
Figure 7
as nearly a half-cycle at the transducer resonant frequency. Consequently it is possible to take echographic signals with high amplitudes. Figure 7 shows the echo (7 V peak to peak) obtained with the transducer and circuit characteristics mentioned above. This high echo amplitude can be justified because, together with all the effects mentioned, the inductance, L0, can produce a movement on the transducer reception band towards the emission band, consequently increasing the echographic efficiency. Non-correspondence between emission and reception bands can happen in transducers with high coupling factors driven with generators having different terminal impedances at emission and reception s. Figures 8 and 9 correspond to Figures 6 and 7, respectively, but a low damping resistance, instead of an inductance, L0, has been used to reduce the low parasite frequency oscillations. These figures clearly show how the echographic signals decrease by ~ 17 dB. Figure 11 shows the frequency spectra corresponding to the signals in Figures 7 and 9. The second transducer is formed by a 10 M H z PZT-5A ceramic (Vernitron) 10 x 10 m m in size, backed with a loaded epoxy resin of specific impedanceZB ----12 x 10~ k g m -2 s -~ and one matching layer adapted to water
Echographic response obtained in t l - t 2 with the driving
pulse shown in Figure 6
various frequencies specially designed and constructed in our laboratory to show the performances of the spike generator presented in this Paper. The pulse-echo measurements were made using a steel target situated at the far-field transition in each case; the frequency spectra were obtained using a Data 6000 waveform analyser. Figure 6 shows the output pulse shape of the proposed circuit when driving a 5 M H z transducer of similar dimensions to the individual elements of an echographic array. This transducer has a PZT-SA piezoelectric ceramic (1.6 x 2.3 mm, Vernitron) with a backing made of a loaded epoxy resin with specific impedance ZB --- 7 x l0 ~ kg m -2 s -~ and without matching layers 7. In Figure 10 the input electric impedance (modulus) and conductance versus the frequency corresponding to the above transducers are shown. These functions were measured under the following transducer work conditions: the transducer was mechanically loaded with water and electrically loaded with a shielded cable RG-174/U type, 110 cm long. The circuit parameters used in this case were: R D = 1500 f'l, R C = 18 kFl, Vo = 400 V, Rl ----4.7 N, C = 1.5 nF and Lo = 3.5 /xH. The inductance, Lo, in addition to the filtering effects ('selective damping') mentioned above, enables the pulse shape to be modelled
Figure 8 V~ pulse for the same transducer shown in Figure 6, without the inductance, L 0, and with R o = 120 ~. Other circuit parameters are the same as in Figure 5
Figure 9 Echographic response in tl--t 2 corresponding to the excitation conditions in Figure 8
Ultrasonics 1987 Vol 25 July
225
Broad-band driving of echographic arrays." ,a Ramos-Fernandez et al. 300-
a
~n
E a= o
•"%.•
200-
'%
E
''....,,
E
• '.,.. ..........
..., ..... ..• "'•
I00 2.5
I
I
I
4
5
6
6.5
Frequency (MHz)
b
e m i s s i o n (also m a d e with a loaded epoxy)• The echo from this transducer driven with our spike generator is shown in Figure 12. The circuit parameters were: V0 = 400 V, Rc = 18 k ~ , C = 0.68 nF, Rl = 1 1"), RD = 22 ~ and L0 = 2.2 fill. As expected, the ultrasonic pulse is very short and the amplitude is less than the first case detailed above• This is due to greater electrical and mechanical damping. Figure 13 shows the input electrical i m p e d a n c e corresponding to the above transducer under the following work conditions: water loaded and with a shielded cable (RG-58 A / U type, 20 c m long). The echographic signal in Figure 12 shows that the spike generator can be used to drive both high and low i m p e d a n c e transducers, but with less efficiency in the second case. The frequency spectrum corresponding to the pulse signal of Figure I2 is shown in
Figure 14. Finally, we include s o m e experimental results related to a minitransducer 1.5 m m in radius constructed from a 10 M H z PZT-5A ceramic (Vernitron), backed with a loaded epoxy resin with specific i m p e d a n c e ZB = 18 × 106 kg m -2 s -1 and without m a t c h i n g layers. In Figure 15 the input electric i m p e d a n c e and conductance of this transducer are shown. The transducer was loaded with water and had a shielded cable (RG-58 A / U type, 120 c m long). Figure 16 shows the pulse-echo signal obtained w h e n
•.....•
2-
6
._x
E a= o (.9
g
I-
0 (.)
o
I 4
I
2.5
3
I ,5
Frequency
6..5
(MHz)
Figure 1 0 (a) Measured electrical input impedance, I ZI, and (b) conductance, G, of the 5 M H z minitransducer used for the echographic responses shown in Figures 7 and 9
O
fib
o.
E
°20
-40 2.5
I
I
i
!
3
4
5
6
6.5
Frequency (MHz) Figure 11 Spectrum analysis of the echographic signals shown in: a, Figure 7; b, Figure 9. The amplitude scale is relative to the maximum amplitude of a
226
Ultrasonics 1 9 8 7 Vol 25 July
Figure 1 2 Echographic signal obtained from a low impedance transducer ( 1 0 x 1 0 mm) with the following parameters: V 0 = 4 0 0 V, R c = 18 k~, C = 0 . 6 8 nF, R I = 11~, R o = 2 2 and L o = 2.2 #H. (a) First echo; (b) echo in more detail
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. 150
10
a
% °
"~ IO0" ,.,.°",• .,
°
E o
"',
• °°
.
J=
°.
N.~ ,°
°,. %, • ,..
5
• ....,...,
o I
.
.
,,....... . .
,...... .
',,,,••
"',,,.
_E 5 0 -
E
••
,,
•° •, .
•°" • •, •°.
12 Frequency(MHz] 0 4.5
I
I
I
5
6
7
I
I
I
8
9
I0
lOb
,.'.,, .,°
K
Frequency (MHz)
T. E
",..,
Figure 1 3 Measured electrical input impedance, IZ~ of the 10 x 1 0 mm transducer considered in Figure 12
%.-,,,, c O
5-
.¢j c o (J
,,.•'
o
-I0.
i
6
4
8
E <~
I=0
12
Frequency (MHz) Figure 1 5 Measured electrical input impedance, JZl, and conductance, G, of a circular minitransducer 1.5 mm radius, 10 M H z frequency and backed with Z = 18 x 108 kg m -2 s-1
-20
I 5
3
~ 7
9
II
Frequency ( MHz} Figure 1 4
Spectrum analysis of the echographic signal shown in
Figure 12. The amplitude scale is relative to the maximum value
driving this transducer with the spike generator outlined in this Paper. The following circuit parameters were used: 1Io= 475 V, Rc = 18 kl), C = 2.2 nF, R1 = 4.712, RD = 200 f~ and Lo = 1.3 ktH. The signal character.istics can also be seen in Figure 17 where the corresponding frequency spectrum is shown. Conclusions In this Paper we have outlined the basic unit of a multichannel pulse generator designed to drive broadband piezoelectric arrays with output spikes of up to 500 V and a rise-time of ~ 10 ns. This circuit includes a 'selective damping' network to control the rising edge of the generated electric pulse independently of the cut-off of the commutation device used. This characteristic allowed us to obtain relatively narrow pulses without needing very
0
"'
-2"
--4
,
o
i
]
i
i
I
05 Seconds (xlO -6)
Figure 1 6 Echographic response transducer considered in Figure generator parameters: V o = 4 7 5 Rp=4.7 ~,R o=200~andL 0=
in t 1 - t 2 corresponding to the
15, with the following pulse V, R C = 18 k~, C = 2.2 nF, 1.3/~H
low damping resistance or expensive high voltage sources with elevated peak current. We have obtained some approximate analytical expressions to study the time evolution of the output electric pulse as a function of the generator parameters
Ultrasonics 1 9 8 7 Vol 2 5 July
227
Broad-band driving of echographic arrays." A Ramos-Fernandez et al.
Acknowledgements
J
We would like to thank Dr E. D'Ottavi from the Acoustic Institute "O.M. Corbino', Italy, for the information provided at the beginning of this work, and M.A. GarciaOlias and J. Garcia-Vegas for their assistance in the development of prototypes. This work was supported by the CAICYT, research programme no. PR84-0193-C02-01.
rm
a) "0
-to Q.
E
References I 2 -20 4
i 6
] 8
I
[O
12
Frequency (MHz)
3 4
1 7 Spectrum analysis of the echographic signal shown in Figure 16. The amplitude s c a l e is relative to the maximum value Figure
5
and the transducer impedance. In particular, the influence of the damping resistance, the static transducer capacitance and the compensating inductance, L0, on the generator transient response have been studied. Finally, we have shown some output electric pulses and various measured echographic responses from different specially designed transducers (5-[0 MHz) driven with the generator presented in this Paper.
228
Ultrasonics 1987 Vol 25 July
6
7
Kino, G.S. and DeSilets, Ch.S. Design or" slotted transducer arrays with matched backing Ultrasonic Imaging (1979) I 189209 Okyere, J.G. and Cousin, A.J. The design of a high ~oltage SCR pulse generator for ultrasonic pulse-echo applications Ultrasonic~ (1979) 17 81-84 Mattila, P. and Luukkala, M. FET pulse generator fi)r ultrasonic pulse-echo applications Ultrasonics (1981) 19 235-236 Certo, M., Dotti, D. and Vidali, P. A programmable pulse generator for piezoelectric multielement transducers Ultrasonk's (1984) 22 163-166 Sanz, P.T., Ramos, A. lnfluencia de la capacidad negativa del circuito equivalente de Mason para transductores piezoelectricos en modo thickness, sobre la frecuencia de mfixima cficicncia ecogrilfica Proc XX Bicnal dc la RSEF Barcelona. Spain (September 1985) 349 Montero de Espinosa, F., Ramos-Fernandez, A. and Pappalardo, M. Array lineal de banda ancha para visualizacion ultras6nica Diseno y caracterizacion de un prototipo experimental (2.254.25 MHz) Mundo Electr&nico (1985) 154 119-126 Montero de Espinosa, F. Two-phase alumina epoxy resin material for multilayer ultrasonic transducers Proc UI 85 Butterworths, Guildford. UK (1985) 857-862
generators A. Ramos-FernSndez, P.T. Sanz-Sanchez and F.R. Montero de Espinosa UEI Ultrasonidos, Instituto de Acustica del CSIC, Serrano 144, 2 8 0 0 6 Madrid, Spain Received 10 June 1986; revised28 October 1986
To obtain a good dynamic range on echographic signals produced by broad-band piezoelectric arrays with frequencies > 4 M Hz, it is necessary to excite each of the array elements with very fast electric spikes. Therefore, for most depths used in medical echographic visualization, or NDT applications, electric pulses of some hundreds of volts with a rise-time of < 30 ns are required. This Paper outlines an analysis of the required characteristics of the high voltage excitation stages for each of the elements of a linear piezoelectric array designed for scanning and electronic focussing. An efficient basic unit for multichannel pulse generation up to 5 0 0 V with a rise-time of 10 ns is described. This unit has been especially designed for the impulsional driving of broadband piezoelectric array elements in the frequency range 1-30 M Hz. The generated electric pulse shape is studied as a function of the generator internal parameters and its external load, and some experimental results for different real transduction conditions are presented. Keywords: echography; pulse generation; excitation systems
Suitable shock excitation of individual elements from piezoelectric arrays designed for frequency bands centered above 4 MHZ, has to be made through high voltage electric pulses (350-400 V minimum) with a rise-time of < 30 ns. These conditions are required if a good dynamic range is wanted in echographic signals obtained from the depths usually handled in biological tissues and some special N D T applications. These extreme conditions, compared with the corresponding simpler cases at lower frequencies, are necessary because of the sharp increase in attenuation with increasing frequency and the high electric impedance of the piezoelectric array elements at those frequencies. This high impedance is a consequence of the geometry imposed on the array elements by the work frequency and acoustic field theory ~,6. There are several different ways to obtain high voltage pulses with short rise-times. In References 2 and 3 two different circuits are shown which reach electrical pulses with amplitudes > 220 V. The first circuit, using a SRC device for the high voltage switching 2,3, has a rise-time between 150-250 ns; this is too high for applications above 2 MHz, The second circuiP can generate 240 V amplitude pulses over a damping resistance of 300 ~ with a rise-time of ~ 100 ns using a MOSFET MTP 474 transistor. This pulse can be used to drive transducers at frequencies < 3.5 MHz. These nominal circuit performances can be severely impaired in real load work conditions due to the influence of the high electrical clamped capacitances of the piezoelectric elements. 0041-624X/87/040221-08 $03.00 © 1987 Butterworth Et Co (Publishers) Ltd
M u l t i c h a n n e l g e n e r a t i o n of h i g h v o l t a g e p u l s e s t o drive h i g h f r e q u e n c y e c h o g r a p h t c ° arrays
Preliminary considerations We have mentioned above some general requirements for the excitation of each of the individual elements in piezoelectric arrays used for echographic purposes. Moreover, if fast variable electronic focussing is required, the emission/reception process must have a number of channels working in parallel equal to the number, n, of individual electric elements used as the array aperture. With a system as indicated in Figure 1, it is possible to drive the aperture elements with a focal distribution that can vary according to time, being able to delay the received echoes at each aperture channel synchronizing with the corresponding exciting distribution. The implementation of this variable focussing implies some special requirements in the spike stage design. The first requirement is a consequence of the short time difference between the excitation of two consecutive elements, which can be as short as a few nanoseconds. Such a short time makes it impossible to share only one generator between all the aperture elements. The second requirement deals with the number of spike generators, this is dependent on the type of focussing and, more importantly, on the scanning used in each, case. This n u m b e r varies between n/2 and the total number of array
Ultrasonics 1987 Vol 25 July
221
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. Figure 2 shows the circuit diagram of a pulser developed for the excitation of each array element, valid for a frequency range up to 25-30 MHz. This circuit, widely applied to different piezoelectric transducers, can furnish pulses with the voltage and rise-time requirements mentioned above.
Array ~ e ]
~.,/]-
~
.nJ
.,.~,,,~t~. ~ . ~ ~ . ~
~:::
I I
s' I '
e.rt~ 1 / ~lticha pu Ise
Pr°grarr and col
•
I °~;"'°°'
-
'
I
1
I
-
Focal zones
Wide-band preamplifiers
Figure 1 Simplifiedblockdiagramof a multichannelemission/ variablefocussingof the arrayaperture
reception system for
elements, m. Each of these spike generators will excite one or more piezoelectric elements (co-phasing) depending on the array design. As simple a design as possible is needed for the excitation basic unit as the number of electric elements on a linear array, m, can be ~ 100. The same criteria of simplicity also applies to the reception unit, mainly at the nearest array stages: 'emission/ reception' uncoupling and signal preamplification.
Circuit design In the design of this circuit we have optimized switching of the high voltage device used (power MOSFET, series IRF 840) and its correct coupling to the transducer device. In the first part of the circuit, complementary transistors T2 and/'3 supply and absorb, respectively, the high level gate currents needed for fast switching of transistor Tmf. A Zener diode, Z (4 V 7), has been included between the drain of Tmf and the discharge capacitor C; the more important effect of this Zener diode is to protect the positive half-cycles corresponding to the initial part of the radiofrequency echographic signals (normally < 4 V). If the Zener diode is not used, these positive half-cycles will go to ground through D1, C and Tmf, distorting the complete signal. The circuit also includes an adjustable inductance, Lo, in parallel with the damping resistance, RD, which allows modification of the temporal evolution of the exciting signal. Diodes DI and D2 prevent the formation of the typical damped oscillatory signal originating from the C-Lo series circuit, allowing only the first negative halfcycle to pass to the transducer, as shown in Figure 2. The Lo-D~-D 2 network can improve the amplitude and shape of the generated pulse due to the following: this network can substitute the resistance RD advantageously to produce a fast electric damping without losing pulse amplitude: and it can facilitate the generation of driving pulses with a trailing edge slope independent of the MOSFET cut-off, which can be useful in reducing the temporal dispersion of the pulse widths for all the individual array elements. This dispersion problem is a consequence of the wide cut-off time tolerances on the switching devices normally used and has motivated the
18vI l°v e t tw(min=) 60ns ilrisetime<5ns F[1 --I ~-tw
--d
/
--
J IT Rc C313!Tm~+11
~ [ ~~_1
R~~,~"_v~~~~ ' ~ ~V(~
)i FromtransmittingBSX ] T3J electroniclens ul-~ ~ N 2 2 1 9
222
I ] I-J~/~/~J~ ) ~ i e r
l':°rterCe:"e°s / D2 x5 Z ~ ~ ~
Ix ] Ix ~ "~" L1A"~;~ RD ~ ?L°--l~ZT~!t2[
Pulser Figure 2
~
!Bipolarlimiteri Receiver
-[--
Circuitdiagramof the highvoltagepulsegeneratorandthe limiterstagecorrespondingto eachof thechannelsin Ultrasonics 1987 Vol 25 July
Figure1
Broad-band driving of echographic arrays: .4. Ramos-Fernandez et al.
(RD//RT//Rr),
IfR L whereRr is the input resistance at the reception stage, it is possible to establish the following relationship =
-v0 R L C [1 - exp(-t/RLC)];Vt/(O < t < ton)
V'o(t ) = - ton
(1)
Figure 3 Leadingedge of the output pulse, V~, obtained from the circuitdescribed in Figure 2. Vo = 400 V, Rc = 18 k~, C = 2.2 nF, R1=4.7 n , R D = 2 7 0
use, for other workersL of feedback systems to control the pulse width. With regard to the received echo signals produced at the explored field, we include in Figure 2 the first two stages corresponding to each of the individual array elements. These stages consist of a bipolar limiter (_+ 5.4 V) and a broad-band signal preamplifier. Figure 3 shows in detail the leading edge of the output pulse, V 0, generated by the circuit shown in Figure 2. Circuit parameters similar to those typical in echographic array applications were used: V0 = 400 V, Rc = 18 k~, ('7 = 2.2 nF, Ri = 4.7 ~ and RD = 270 ~. The pulse rise-time, ~ 10 ns, reached the optimal amplitude value, Vo, which in this case is 400 V. If low impedance transducers are connected, these optimal characteristics can become slightly worse. Nevertheless, by fitting the parameters Re, C, Ri and RD, these problems can be minimized.
This expression agrees with that proposed in Reference 2. The values of V'o(t) are only valid during the pulse leading edge, consequently it would be inappropriate to try to deduce anything beyond that time. To avoid this problem we can approximate Tmr switching with a decreasing exponential function which, being valid after ton(Vt> 0). is in better agreement with the real behaviour of the transistor saturation. Using this kind of function, the expression for V'o(t) is
CR L V'o(t) = - V o C R L _ r
[exp(-t/C R L) -- exp(--t/T)];
Vt>0
(2) As can be seen above, V'o(t) is composed of two decreasing exponential functions, both having the same initial amplitude, Vo CRL/(CRL--r), but with opposite sign.
a Vo
t~ o n
t
+ V0
Temporal analysis of the output pulse shape The time evolution of the output pulse produced by the proposed circuit can be approximately predicted knowing the values corresponding to Vo, C, RD, Lo and ZT (in resonance conditions) in each application. The circuit behaviour was analysed for three different load conditions: 1 inductance, L0, disconnected and the transducer considered as a pure resistive load RT, at excitation time, (this condition is proposed in Reference 2); 2 inductance, Lo, disconnected and the transducer modelled as a parallel electrical equivalent network, RTCT; and 3 inductance, L0, connected with the transducer considered as a parallel electrical network, RTCT.
b V° IVDVl~
+Vo ,4
Voi Voexp(-t/r) [ V t > 0]
C +Vo
Case 1 If we suppose that the drain voltage of the MOSFET transistor during switching decreases linearly with time from V = Iio at t = 0 to V = 0 at t = ton, the circuit from Figure 2 can be modelled using the equivalent circuit shown in Figure 4a. The effects produced by RI(RI~RT) and the diode network, D1 -- D> have only a slight effect on V 0 and, therefore, can be neglected.
i< +tl i
VD VD = Vo e x p ( - t / r )
[Vt>0]
D
RL
CT
L0
Vo
=
Figure 4 Simplified equivalent circuits of the MOSFET pulse generator. (a) Case 1; (b) case 2; (c) case 3
Ultrasonics 1 9 8 7 Vol 25 July
223
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. Case 2 If we maintain the hypothesis of an exponential type function for Tmf switching, the approximated equivalent circuit is as shown in Figure 4b. The transducer clamped capacity, Cx, has been included because it exerts a direct influence over the V'o(t) shape from the beginning of the electric excitation due to the static characteristic of that capacity. The expression for V~ in this case is
VoCRL V;(t)
=-
(C+CT)R
L -1"
× [exp(-t/(C + CT)RL) -- exp(-t/r)]
(3)
From this expression it can be seen that the maximum peak value expected for Vh (given ideal conditions, (C + Ca-)RL >>r) depends strongly on the transducer static capacity, CT, in such a way that it only reaches the optimal value ( ~ - V 0 ) when CT
Case 3 Figure 4c shows the simplified equivalent circuit corresponding to the assumptions made in the third case, as cited above. A diode, D, has been included in parallel with the output terminals; this represents the series connected diode sets D t and D2 shown in Figure 2. With the present load conditions, the expression for V 0 is
VoC RL
v'o(t)
=
(C +CT) R c
--
r +7"2RIJLo
× exp(-t/r) - A e x p ( - a t ) cos(/3t + ~J)
(4)
where 1
= L~L(C + CT)
and
=
['
Lo(C¥CT)
(')1
Experimental results The pulse generator, as outlined above, can be adapted to a wide variety of echographic transducers, with different working frequency bands and electrical impedances, to produce broad-band ultrasonic pulses with very good electric device-transducer coupling. Some experimental results are presented below for the electric driving spike and the corresponding ultrasonic echographic pulse for transducers with both high (similar to the individual elements from a high frequency array) and low electrical impedance (< 5 f~). Figure 5 shows the generated output pulse without load (transducer and inductance, L0, disconnected) and with R D = 100 ['L It can be seen that the spike has an amplitude of ~ 400 V with a shape similar to those shown in References 2 and 3, but with a faster leading edge ( ~ 10 ns). Moreover, [V'olmax/Vo is very close to unity, enabling pulse generation with a high overall efficiency. Nevertheless, this pulse shape is not the best one to drive piezoelectric transducers as the rising slope can excite low frequency modes in the transducer. To minimize these undesirable effects, very low values Of RD must be used, consequently the pulse amplitude will be reduced, decreasing the dynamic range of the echographic signals. If a suitable inductance, L0, is connected in parallel with the damping resistance, RD, it is possible to eliminate the undesired influence of the low frequency modes without greatly loweringRD. At the same time, this inductance can be used to control the total pulse width as shown below. The experiments were carried out with transducers of
2 1/2
28L(~7+ CT)
A and ~pare integration constants dependent on C, Vo, CT, r, RL and Lo. Equation (4) is compounded by two terms. The first is exponential, decreasing according to r, and for v < ( C + CT) RL it is practically equal to the second term of Equation (3). The second term is oscillatory with angular frequency /3, exponentially damped with a constant or. Diode D was not included in Equation (4) and it will cancel the function cos(/3t + ~) after the first zerocrossing, preventing an undesired lengthening on the output pulse. This cosine function makes the positive edge start with a slope smoother than in the pure exponential case but allowing the total pulse rise toward zero to be produced in a shorter time. This effect enables the driving pulses to be obtained with relatively short total widths and without involving significant attenuation on the resultant amplitude. This can be seen in Figure 6 where V0 has a width -~100 ns and a peak amplitude very near to V 0 = 400 V. To obtain a pulse with a similar width but without the
224
inductance, L 0, it would be necessary to reduce the value of C RD greatly, or to make Rc < 500 fl. The first possibility would notably reduce the peak amplitude, whereas the second would involve the use of a source, V0, with high peak current making this solution prohibitive for multi-channel excitation. Therefore, it seems that the use of a parallel inductance, L0, connected at the output terminals of the pulse generator is the most useful way to attain narrow output pulses with high efficiency. Moreover, this inductance produces other advantageous effects, such as 'selective damping' of the secondary oscillating modes and cancellation of the static transducer capacity when required.
Ultrasonics 1987 Vol 25 July
Figure 5 Pulse shape at V 'o of the circuit shown in Figure 21oaded with: RD= 100 •,Rc= 18 kl~, Vo= 400 V, R== 4.7 N , C = 1.5 nF and with repetition frequency = 5 kHz
Broad-band driving of echographic arrays: A Rarnos-Fernandez et al.
Figure 6 Pulse shape at V~) when the generator is loaded with a 5 M Hz minitransducer (radiant area ~ 4 mm 2) connected in parallel with L o = 3.5/zH and R D= 1 5 0 0 ~. Other circuit parameters are the same as in Figure 5
Figure 7
as nearly a half-cycle at the transducer resonant frequency. Consequently it is possible to take echographic signals with high amplitudes. Figure 7 shows the echo (7 V peak to peak) obtained with the transducer and circuit characteristics mentioned above. This high echo amplitude can be justified because, together with all the effects mentioned, the inductance, L0, can produce a movement on the transducer reception band towards the emission band, consequently increasing the echographic efficiency. Non-correspondence between emission and reception bands can happen in transducers with high coupling factors driven with generators having different terminal impedances at emission and reception s. Figures 8 and 9 correspond to Figures 6 and 7, respectively, but a low damping resistance, instead of an inductance, L0, has been used to reduce the low parasite frequency oscillations. These figures clearly show how the echographic signals decrease by ~ 17 dB. Figure 11 shows the frequency spectra corresponding to the signals in Figures 7 and 9. The second transducer is formed by a 10 M H z PZT-5A ceramic (Vernitron) 10 x 10 m m in size, backed with a loaded epoxy resin of specific impedanceZB ----12 x 10~ k g m -2 s -~ and one matching layer adapted to water
Echographic response obtained in t l - t 2 with the driving
pulse shown in Figure 6
various frequencies specially designed and constructed in our laboratory to show the performances of the spike generator presented in this Paper. The pulse-echo measurements were made using a steel target situated at the far-field transition in each case; the frequency spectra were obtained using a Data 6000 waveform analyser. Figure 6 shows the output pulse shape of the proposed circuit when driving a 5 M H z transducer of similar dimensions to the individual elements of an echographic array. This transducer has a PZT-SA piezoelectric ceramic (1.6 x 2.3 mm, Vernitron) with a backing made of a loaded epoxy resin with specific impedance ZB --- 7 x l0 ~ kg m -2 s -~ and without matching layers 7. In Figure 10 the input electric impedance (modulus) and conductance versus the frequency corresponding to the above transducers are shown. These functions were measured under the following transducer work conditions: the transducer was mechanically loaded with water and electrically loaded with a shielded cable RG-174/U type, 110 cm long. The circuit parameters used in this case were: R D = 1500 f'l, R C = 18 kFl, Vo = 400 V, Rl ----4.7 N, C = 1.5 nF and Lo = 3.5 /xH. The inductance, Lo, in addition to the filtering effects ('selective damping') mentioned above, enables the pulse shape to be modelled
Figure 8 V~ pulse for the same transducer shown in Figure 6, without the inductance, L 0, and with R o = 120 ~. Other circuit parameters are the same as in Figure 5
Figure 9 Echographic response in tl--t 2 corresponding to the excitation conditions in Figure 8
Ultrasonics 1987 Vol 25 July
225
Broad-band driving of echographic arrays." ,a Ramos-Fernandez et al. 300-
a
~n
E a= o
•"%.•
200-
'%
E
''....,,
E
• '.,.. ..........
..., ..... ..• "'•
I00 2.5
I
I
I
4
5
6
6.5
Frequency (MHz)
b
e m i s s i o n (also m a d e with a loaded epoxy)• The echo from this transducer driven with our spike generator is shown in Figure 12. The circuit parameters were: V0 = 400 V, Rc = 18 k ~ , C = 0.68 nF, Rl = 1 1"), RD = 22 ~ and L0 = 2.2 fill. As expected, the ultrasonic pulse is very short and the amplitude is less than the first case detailed above• This is due to greater electrical and mechanical damping. Figure 13 shows the input electrical i m p e d a n c e corresponding to the above transducer under the following work conditions: water loaded and with a shielded cable (RG-58 A / U type, 20 c m long). The echographic signal in Figure 12 shows that the spike generator can be used to drive both high and low i m p e d a n c e transducers, but with less efficiency in the second case. The frequency spectrum corresponding to the pulse signal of Figure I2 is shown in
Figure 14. Finally, we include s o m e experimental results related to a minitransducer 1.5 m m in radius constructed from a 10 M H z PZT-5A ceramic (Vernitron), backed with a loaded epoxy resin with specific i m p e d a n c e ZB = 18 × 106 kg m -2 s -1 and without m a t c h i n g layers. In Figure 15 the input electric i m p e d a n c e and conductance of this transducer are shown. The transducer was loaded with water and had a shielded cable (RG-58 A / U type, 120 c m long). Figure 16 shows the pulse-echo signal obtained w h e n
•.....•
2-
6
._x
E a= o (.9
g
I-
0 (.)
o
I 4
I
2.5
3
I ,5
Frequency
6..5
(MHz)
Figure 1 0 (a) Measured electrical input impedance, I ZI, and (b) conductance, G, of the 5 M H z minitransducer used for the echographic responses shown in Figures 7 and 9
O
fib
o.
E
°20
-40 2.5
I
I
i
!
3
4
5
6
6.5
Frequency (MHz) Figure 11 Spectrum analysis of the echographic signals shown in: a, Figure 7; b, Figure 9. The amplitude scale is relative to the maximum amplitude of a
226
Ultrasonics 1 9 8 7 Vol 25 July
Figure 1 2 Echographic signal obtained from a low impedance transducer ( 1 0 x 1 0 mm) with the following parameters: V 0 = 4 0 0 V, R c = 18 k~, C = 0 . 6 8 nF, R I = 11~, R o = 2 2 and L o = 2.2 #H. (a) First echo; (b) echo in more detail
Broad-band driving of echographic arrays: A Ramos-Fernandez et al. 150
10
a
% °
"~ IO0" ,.,.°",• .,
°
E o
"',
• °°
.
J=
°.
N.~ ,°
°,. %, • ,..
5
• ....,...,
o I
.
.
,,....... . .
,...... .
',,,,••
"',,,.
_E 5 0 -
E
••
,,
•° •, .
•°" • •, •°.
12 Frequency(MHz] 0 4.5
I
I
I
5
6
7
I
I
I
8
9
I0
lOb
,.'.,, .,°
K
Frequency (MHz)
T. E
",..,
Figure 1 3 Measured electrical input impedance, IZ~ of the 10 x 1 0 mm transducer considered in Figure 12
%.-,,,, c O
5-
.¢j c o (J
,,.•'
o
-I0.
i
6
4
8
E <~
I=0
12
Frequency (MHz) Figure 1 5 Measured electrical input impedance, JZl, and conductance, G, of a circular minitransducer 1.5 mm radius, 10 M H z frequency and backed with Z = 18 x 108 kg m -2 s-1
-20
I 5
3
~ 7
9
II
Frequency ( MHz} Figure 1 4
Spectrum analysis of the echographic signal shown in
Figure 12. The amplitude scale is relative to the maximum value
driving this transducer with the spike generator outlined in this Paper. The following circuit parameters were used: 1Io= 475 V, Rc = 18 kl), C = 2.2 nF, R1 = 4.712, RD = 200 f~ and Lo = 1.3 ktH. The signal character.istics can also be seen in Figure 17 where the corresponding frequency spectrum is shown. Conclusions In this Paper we have outlined the basic unit of a multichannel pulse generator designed to drive broadband piezoelectric arrays with output spikes of up to 500 V and a rise-time of ~ 10 ns. This circuit includes a 'selective damping' network to control the rising edge of the generated electric pulse independently of the cut-off of the commutation device used. This characteristic allowed us to obtain relatively narrow pulses without needing very
0
"'
-2"
--4
,
o
i
]
i
i
I
05 Seconds (xlO -6)
Figure 1 6 Echographic response transducer considered in Figure generator parameters: V o = 4 7 5 Rp=4.7 ~,R o=200~andL 0=
in t 1 - t 2 corresponding to the
15, with the following pulse V, R C = 18 k~, C = 2.2 nF, 1.3/~H
low damping resistance or expensive high voltage sources with elevated peak current. We have obtained some approximate analytical expressions to study the time evolution of the output electric pulse as a function of the generator parameters
Ultrasonics 1 9 8 7 Vol 2 5 July
227
Broad-band driving of echographic arrays." A Ramos-Fernandez et al.
Acknowledgements
J
We would like to thank Dr E. D'Ottavi from the Acoustic Institute "O.M. Corbino', Italy, for the information provided at the beginning of this work, and M.A. GarciaOlias and J. Garcia-Vegas for their assistance in the development of prototypes. This work was supported by the CAICYT, research programme no. PR84-0193-C02-01.
rm
a) "0
-to Q.
E
References I 2 -20 4
i 6
] 8
I
[O
12
Frequency (MHz)
3 4
1 7 Spectrum analysis of the echographic signal shown in Figure 16. The amplitude s c a l e is relative to the maximum value Figure
5
and the transducer impedance. In particular, the influence of the damping resistance, the static transducer capacitance and the compensating inductance, L0, on the generator transient response have been studied. Finally, we have shown some output electric pulses and various measured echographic responses from different specially designed transducers (5-[0 MHz) driven with the generator presented in this Paper.
228
Ultrasonics 1987 Vol 25 July
6
7
Kino, G.S. and DeSilets, Ch.S. Design or" slotted transducer arrays with matched backing Ultrasonic Imaging (1979) I 189209 Okyere, J.G. and Cousin, A.J. The design of a high ~oltage SCR pulse generator for ultrasonic pulse-echo applications Ultrasonic~ (1979) 17 81-84 Mattila, P. and Luukkala, M. FET pulse generator fi)r ultrasonic pulse-echo applications Ultrasonics (1981) 19 235-236 Certo, M., Dotti, D. and Vidali, P. A programmable pulse generator for piezoelectric multielement transducers Ultrasonk's (1984) 22 163-166 Sanz, P.T., Ramos, A. lnfluencia de la capacidad negativa del circuito equivalente de Mason para transductores piezoelectricos en modo thickness, sobre la frecuencia de mfixima cficicncia ecogrilfica Proc XX Bicnal dc la RSEF Barcelona. Spain (September 1985) 349 Montero de Espinosa, F., Ramos-Fernandez, A. and Pappalardo, M. Array lineal de banda ancha para visualizacion ultras6nica Diseno y caracterizacion de un prototipo experimental (2.254.25 MHz) Mundo Electr&nico (1985) 154 119-126 Montero de Espinosa, F. Two-phase alumina epoxy resin material for multilayer ultrasonic transducers Proc UI 85 Butterworths, Guildford. UK (1985) 857-862