An ultrasonic transducer that produces an output that is a symmetrical function comprises a piezoelectric crystal with several concentric ring electrodes on one side of the crystal. A resistor network applies different amplitudes of an ac source to each of the several electrodes. A plot of the different amplitudes from the outermost electrode to the innermost electrode is the first half of a Gaussian function. Consequently, the output of the crystal from the side opposite the electrodes has a Gaussian profile

Claus, R. O.

Zerwekh, P. S.

English

NASA Technical Reports Server

United States Patent 4,446,396 
Claw et al. [451 May 1,1984 
[54] ULTRASONIC TRANSDUCER WITH 
GAUSSIAN RADIAL PRESSURE 
DISTRIBUTION 
[561 References Cited 
U.S. PATENT DOCUMENTS 
[75] Inventors: 
[73] Assignee: 
[21] Appl. No.: 
[22] Filed: 
2,875,355 2/1959 Petermann .......................... 310/334 
3,090,030 5/1963 Schuck ............................ 310/334 X 
4,129,799 12/1978 Green ............................. 310/366 X 
4,155,259 5/1979 Engeler ........................... 310/334 X 
4,211,948 7/1980 Smith .............................. 310/334 X 
4,398,116 8/1983 Lewis .................................. 310/334 
Richard 0. Claus, Christiansburg, 
Va.; Paul S. Zerwekh, Palm Bay, Ha. 
The United States of America as 
represented by the Administrator of 
the ~ ~ t i ~ ~ d   t ti^ an  space 
Administration, Washington, D.C. 
Primary Examiner-Mark 0. Budd 
Attorney, Agent, or Firm-Howard J. Osborn; John R. 
Manning; William H. King 
414,107 
Sep. 2, 1982 
WI ABSTRArn 
A piezoelectric crystal with several concentric ring 
electrodes on one side of the crystal. A resistor network 
applies different amplitudes of an AC source to each of 
the several electrodes. A plot of the different ampli- 
tudes from the outermost electrode to the innermost 
electrode is the first half of a Gaussian function. Conse- 
quently, the output of the crystal from the side opposite 
[51] Int. Cl.3 ............................................. HOlL 41/08 
[52] U.S. Cl. .................................... 310/334; 310/317; 
310/366 
[58] Field of Search ................................ 310/33.4337, 
310/317, 366 
the electrodes has a Gaussian profile. 
7 Claims, 6 Drawing Figures 
18- 
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1 
ULTRASONIC TRANSDUCER WITH GAUSSIAN 
RADIAL PRESSURE DISTRIBUTION 
ORIGIN OF THE INVENTION 
The invention described herein was made in the per- 
formance of work under a NASA contract and is sub- 
ject to the provisions of Section 305 of the National 
Aeronautics and Space Act of 1958, Public Law 85-568 
(72 Stat. 435; 42 USC 2457). 
BACKGROUND O F  THE INVENTION 
The invention relates generally to an ultrasonic trans- 
ducer and more specifically concerns an ultrasonic 
transducer with a Gaussian radial pressure distribution. 
In materials evaluation applications requiring the 
interrogation of the modified far field pattern of an 
ultrasonic transducer it is desirable to use the transducer 
which produces a beam with a Gaussian profile. A 
simplified theoretical analysis of several bulk ultrasonic 
phenomenon require the consideration of bounded ul- 
trasonic beams having velocity distributions which are 
Gaussian as a function of radius. Additionally, since the 
beam profiles in the near field and far field regions are 
related by a Fourier transform operation, Gaussian 
profile beams are particularly useful in experimental 
situations in which a similarity between a near and far 
field pattern is desired. 
A standard prior art surface contact transducer typi- 
cally generates a field which is approximately uniform 
in the region near its contact surface (FIG. la) and 
negligible elsewhere. The resulting far field pattern thus 
contains significant sidelobe maxima, as shown in FIG. 
I&, which may be difficult to distinguish from the cen- 
tral beam in experiments involving beam translation and 
attenuation. Several transducer designs employing sin- 
gle electrodes of various shapes have been designed to 
provide a field which when averaged around the radii is 
a Gaussian function of radius. These electrode designs, 
however, introduce a distribution that is a function of 
angular displacement on the face of the transducer and 
not purely a function of radius. In the Journal of the 
Acoustical Society of America, vol. 49, pp 1668-1669, a 
method is described for generating a velocity distribu- 
tion which is Gaussian utilizing multiple linear elec- 
trodes. However, this Gaussian function is in one di- 
mension only. 
An object of this invention is to provide an ultrasonic 
transducer that produces an output having a Gaussian 
profrle. 
Another object of this invention is to provide an 
ultrasonic transducer that produces an output having a 
Gaussian profile as a function of radius. 
A further object of this invention is to provide an 
ultrasonic transducer that produces an output in which 
all cross-sections of the output through the center of the 
output is a Gaussian function. 
Still another object of this invention is to provide an 
ultrasonic transducer that produces an output having a 
Gaussian profile and in which a far field pattern of the 
output is similar to a near field pattern of the output. 
A still further object of this invention is to provide an 
ultrasonic transducer that produces an output that is a 
symmetrical function. Symmetrical function as used in 
this specification means a function such that the second 
half of the function if it were folded back on the first 
4,446,396 
half of the function there is a corresponding, equal am- 
plitude, equal distance from the center of the function, 
point on the second half of the function. 
Yet another object of this invention is to provide an 
5 ultrasonic transducer that produces an output such that 
any cross-section of the output through its center is a 
symmetrical function. 
Other objects and advantages of this invention will 
become apparent hereinafter in the specification and 
SUMMARY OF THE INVENTION 
The invention is an ultrasonic transducer consisting 
essentially of a piezoelectric crystal with several con- 
l5 centric circular ring electrodes on one side of the piezo- 
electric crystal. An AC source and a resistor network is 
provided for applying different amplitudes of the AC 
source to each of the electrodes. The amplitudes of the 
signal supplied to the different electrodes if plotted 
2o from the outermost to the innermost of the electrodes is 
a plot that fits one-half of a Gaussian function. Conse- 
quently, the output of the ultrasonic transducer is a 
signal having a profile corresponding to the Gaussian 
BRIEF DESCRIPTION OF THE DRAWINGS 
FIGS. la and lb are the near field and far field pro- 
FIG. 2 is a schematic drawing of the ultrasonic trans- 
FIG. 3 is a schematic drawing of the complete em- 
FIGS. 4a and 4b are profiles of the far field and near 
10 drawings. 
25 function. 
files of prior art ultrasonic transducers; 
30 ducer utilized in the invention; 
bodiment of the invention; and 
35 field output of the invention. 
DETAILED DESCRIPTION OF THE 
INVENTION 
Turning now to the embodiment of the invention 
40 selected for illustration in the drawings the number 11 
designates a circular, 19.1 mm diameter, 2.25 MHz 
X-cut quartz crystal. Several concentric circular ring 
electrodes 12 are formed on one side of the crystal 11. 
The innermost electrode can be in the shape of a small 
45 disc instead of a ring as shown. The electrode pattern is 
photo etched into a layer of chrome and gold on the 
quartz crystal. A wear plate 13 is attached to crystal 11 
on the side opposite the electrodes by means of a con- 
ductive adhesive. 
As shown in FIG. 3 the transducer disclosed in FIG. 
2 is designated as 14 and is connected to a network of 
resistors 15. A 2.25 MHz AC source 16 is connected to 
the resistor network by means of a coaxial cable 17. The 
junctions of the resistors 15 in the resistor network are 
55 connected to different ones of the electrodes 12 on 
transducer 14. Consequently, a different amplitude AC 
voltage is applied to each of the electrodes 12. 
Since different voltage amplitudes are applied to the 
electrodes 12, an electric field distribution which is 
60 exclusively a function of radius will be produced by the 
set of concentric ring electrodes 12. If the circumfer- 
ence of the rings is large with respect to the spacing 
between successive electrodes, the electric field in the 
gaps may be considered to be a linear function of radius. 
65 Placing the proper voltages on electrodes 12 by means 
of the different sizes of the resistors 15 in the resistor 
50 
half of the function would coincide with the first half of 
the function. In other words, for every point on the first 
network a piece-wise linear function which approxi- 
mates a Gaussian function may be generated on the face 
4,446,396 
3 4 
of the piezoelectric crystal 11. The degree to which this Even though this invention is disclosed as generating a 
function fits the desired Gaussian function is determined Gaussian function, it can be used to generate any sym- 
by the width of each electrode ring, the number of metrical function. That is, electrodes 12 can be placed 
electrodes, and the distribution of the electrode radii on and resistors 15 can be selected such that any cross-sec- 
the radius of the transducer crystal. Since the desired 5 tion of the output through the center of the output can 
Gaussian voltage function attains a particular value at be any symmetrical function. 
only one mathematical point on the radius, the elec- The advantages of this invention are that it provides 
trode width should be as small as possible. The photo- a simple inexpensive transducer that produces an output 
etching techniques used in the FIG. 1 transducer con- having a Gaussian or other symmetrical function pro- 
struction, however, required a minimum electrode 10 file. In addition, the near field and far field outputs of 
width of approximately 0.5 mm. The degree of fit to the the transducer are similar. 
desired Gaussian shape may be improved by using a 
large number of electrodes but this requires that the 
inner electrode spacing be small thereby increasing the 
possibility of electrical breakdown between adjacent 15 comprising: 
angular rings when high voltages are applied. Consider- means for supplying an AC voltage; 
ing these practical limitations in the present embodi- a piezoelectric crystal; 
ment of the invention it was found that with as few as several concentric circular ring electrodes attached 
five electrodes, the mean absolute fit error may be re- to one side of said piezoelectric crystal; and 
duced to less than 1.5% of the peak. means for applying a different amplitude of said AC 
Capacitance between electrodes and the wear plate voltage to each of said electrodes; 
ground plane was calculated and empirically verified to wherein a plot of said different amplitudes applied to 
be less than 2 picofarads, producing a negligible reac- said electrodes from the outermost to the inner- 
tive impedance at the 2.25 MHz operating frequency. most is a plot that fits one-half of said symmetrical 
Since this impedance is low, the simple resistive net- 25 function; 
work in FIG. 3 may be used to fix the desired set of whereby any cross-section through the center of the 
electrode voltages. ultrasonic signal emitted from the side of said pi- 
The leads of the resistive network are attached to ezoelectric crystal opposite said one side has a 
electrode 12 using a conductive adhesive and a dome of pressure distribution corresponding to said sym- 
epoxy 18 is applied to the electrode side of transducer 30 metrical function. 
14 to provide mechanical support for the leads and to 2. An ultrasonic transducer according to claim 1 
attenuate and disperse resonant surface wave modes. wherein said symmetrical function is a Gaussian func- 
Further damping is accomplished by a thin semi-viscous tion. 
layer of electrically conductive adhesive placed on the 3. An ultrasonic transducer according to claim 2 
opposite uncoated side of transducer 14 and under a thin 35 wherein a wear plate is attached to said opposite side of 
aluminum foil wear plate 13. The entire transducer said piezoelectric crystal. 
assembly is placed in a 1.3 cm diameter cylindrical PVC 4. An ultrasonic transducer according to claim 2 
case 19 and potted in filler-loaded epoxy 18. wherein said means for applying a different amplitude 
FIG. 4u shows the near field pressure distribution of said AC voltage to each of said electrodes is an impe- 
output of the transducer and FIG. 4b shows the far field 40 dance network. 
pressure distribution output of the transducer. As can be 5. An ultrasonic transducer according to claim 4 
noted the two are practically the same. including a housing for supporting said piezoelectric 
A Gaussian function is generated by transducer 14 by crystal and for housing said impedance network. 
applying different amplitude voltages to electrodes 12. 6. An ultrasonic transducer according to claim 4 
If these different amplitude voltages were plotted from 45 wherein said housing is filled with epoxy to provide 
the outermost electrode to the innermost electrode the support for the leads in the impedance network and to 
plot would be the first half of the Gaussian function. attenuate and disperse resonant surface wave modes. 
Hence, once the spacings between electrodes 12 are first 7. An ultrasonic transducer according to claim 1 
fixed, it is only necessary to select the sizes of resistors wherein the distance between any two adjacent said 
15 to apply the appropriate voltage amplitudes to the 50 ring electrodes is greater than the widths of either elec- 
electrodes. The appropriate voltage amplitudes are the trode in the plane of said electrodes. 
ones that will fit the first half of the Gaussian function. 
What is claimed is: 
1. An ultrasonic transducer having a radial pressure 
distribution corresponding to a symmetrical function 
20 
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55 
65 


Ultrasonic transducer with Gaussian radial pressure distribution

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