U.S. patent number 3,879,698 [Application Number 05/354,519] was granted by the patent office on 1975-04-22 for unipolar acoustic pulse generator apparatus.
This patent grant is currently assigned to Edo Corporation. Invention is credited to Perry Arnold Pepper.
United States Patent |
3,879,698 |
Pepper |
April 22, 1975 |
UNIPOLAR ACOUSTIC PULSE GENERATOR APPARATUS
Abstract
In apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to generate
unipolar accoustic pulses in an acoustic medium, the dimensions of
the radiating face of the transducer or of an array of radiating
transducer faces are chosen to simplify the response of the
transducers, thereby simplifying the required transducer driving
signals and the apparatus required to generate those signals.
Inventors: |
Pepper; Perry Arnold (Great
Neck, NY) |
Assignee: |
Edo Corporation (College Point,
NY)
|
Family
ID: |
23393697 |
Appl.
No.: |
05/354,519 |
Filed: |
April 26, 1973 |
Current U.S.
Class: |
367/137; 310/334;
310/317 |
Current CPC
Class: |
G10K
15/043 (20130101); B06B 1/0215 (20130101); B06B
2201/55 (20130101) |
Current International
Class: |
B06B
1/02 (20060101); G10K 15/04 (20060101); H04b
011/00 () |
Field of
Search: |
;340/3A,5R,10,15
;310/8.1,8.2,9.5,9.6 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Farley; Richard A.
Attorney, Agent or Firm: Steidl; Daniel H.
Claims
What is claimed is:
1. Apparatus for producing a unipolar displacement of the radiating
face of an electroacoustic transducer to produce an acoustic signal
in a medium having an acoustic velocity c.sub.w, said unipolar
displacement having a half pulse duration time parameter t.sub.o
and said radiating face having maximum dimenion z, characterized in
that t.sub.o is substantially equal to the quotient (z/c.sub.w),
means for generating a signal waveform, and means for applying said
signal waveform to said transducer.
2. Apparatus for producing a unipolar displacement of the radiating
face of an electroacoustic transducer to produce an acoustic signal
in a medium having an acoustic velocity c.sub.w, said unipolar
displacement having a half pulse duration time parameter t.sub.o
and said radiating face having maximum dimension z, characterized
in that t.sub.o is substantially equal to the quotient (z/c.sub.w),
said radiating face of said transducer displacing from a rest
position to maximum displacement during during a first interval of
time t.sub.o and returning from maximum displacement to said rest
position during a second subsequent interval of time t.sub.o, and
means for applying to said transducer an electrical signal
including a signal component characterized by a first signal pulse
at the start of said first time interval and a second signal pulse
at the end of said second time interval.
3. The apparatus defined in claim 2 wherein each of said signal
pulses is characterized by a substantially instantaneous rise time
followed by gradual decay.
4. The apparatus defined in claim 3 wherein the rise time of said
first signal pulse is substantially concurrent with the start of
said first time interval and the rise time of said second signal
pulse is substantially concurrent with the end of said second time
interval.
5. The apparatus defined in claim 4 wherein the duration of each of
said signal pulses is substantially equal to t.sub.o.
6. The apparatus defined in claim 5 wherein said electrical signal
component is further characterized by a predetermined reference
signal level before said first signal pulse and after said second
signal pulse.
7. The apparatus defined in claim 6 wherein the peaks of both of
said signal pulses are of a first polarity relative to said
predetermined reference signal level.
8. The apparatus defined in claim 7 wherein said electrical signal
component is further characterized by a polarity opposite said
first polarity during the interval of time between said first and
second signal pulses.
9. The apparatus defined in claim 8 wherein the radiating face of
said transducer is a circular surface of diameter z.
10. The apparatus defined in claim 9 wherein said transducer is a
cylinder, one end of which is the radiating face of said
transducer.
11. The apparatus defined in claim 8 wherein the radiating face of
said transducer is a rectangle of diagonal z.
12. The apparatus defined in claim 8 wherein the radiating face of
said transducer is a triangle having longest side z.
13. The apparatus defined in claim 8 wherein the radiating face of
said transducer is an ellipse having major axis z.
14. The apparatus defined in claim 2 wherein said means for
applying comprises:
means for generating a trigger signal;
a plurality of shaped pulse generating channels responsive to said
trigger signal, each of said channels comprising means for delaying
said trigger signal, means responsive to the delayed trigger signal
for generating a rectangular pulse of predetermined amplitude and
duration, and means for shaping said rectangular pulse to produce a
shaped output pulse; and
means for summing the shaped output pulses of each of said channels
to produce said electrical signal.
15. Apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to produce an
acoustic signal in a medium having an acoustic velocity c.sub.w,
said unipolar displacement having a half pulse duration time
parameter t.sub.o and said radiating face having a maximum
dimension z, characterized in that t.sub.o is substantially equal
to the quotient (z/cw), said transducer being characterized by an
acoustic velocity c, wherein the dimension L of said transducer
normal to said radiating face bears substantially the same
proportional relation to c as z bears to c.sub.w, and wherein the
radiating face of said transducer displaces from a rest position to
maximum displacement during a first interval of time t.sub.o and
returns from maximum displacement to said rest during a second
subsequent interval of time t.sub.o, means for applying to said
transducer an electrical signal including a signal component
characterized by a first signal pulse at the start of said first
time interval and a second signal pulse at the end of said second
time interval.
16. The apparatus defined in claim 15 wherein each of said signal
pulses is characterized by a substantially instantaneous rise time
followed by gradual decay.
17. The apparatus defined in claim 16 wherein the rise time of said
first pulse is substantially concurrent with the start of said
first time interval and the rise time of said second signal pulse
is substantially concurrent with the end of said second time
interval.
18. The apparatus defined in claim 17 wherein the duration of each
of said signal pulses is substantially equal to t.sub.o.
19. The apparatus defined in claim 18 wherein said electrical
signal component is further characterized by a predetermined
reference signal level before said first signal pulse and after
said second signal pulse.
20. The apparatus defined in claim 19 wherein the peaks of both of
said signal pulses are the first polarity relative to said
predetermined reference signal level.
21. The apparatus defined in claim 20 wherein said electrical
signal component is further characterized by a polarity opposite
said first polarity during the interval of time between said first
and second signal pulses.
22. The apparatus defined in claim 21 wherein the radiating face of
said transducer is a circular surface of diameter z.
23. The apparatus defined in claim 22 wherein said transducer is a
cylinder of length L, one end of which is the radiating face of
said transducer.
24. The apparatus defined in claim 15 wherein said means for
applying comprises:
means for generating a trigger signal;
a plurality of shaped pulse generating channels responsive to said
trigger signal, each of said channels comprising means for delaying
said trigger signal, means responsive to the delayed trigger signal
for generating a rectangular pulse of predetermined amplitude and
duration, and means for shaping said rectangular pulse to produce a
shaped output pulse; and
means for summing the shaped output pulses of each of said channels
to produce said electrical signal.
25. Apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to produce an
acoustic signal in a medium having an acoustic velocity c.sub.w,
the radiating face of said transducer having maximum dimension z
and said transducer having an acoustic velocity c and a dimension L
normal to said radiating face, wherein the ratio of z to c.sub.w is
substantially equal to the ratio of L to c, means for generating a
signal waveform, and means for applying said signal waveform to
said transducer.
26. Apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to produce an
acoustic signal in a medium characterized by an acoustic velocity
c.sub.w, said unipolar displacement having a half pulse duration
time parameter t.sub.o, the radiating face of said transducer
having maximum dimension z, and said transducer having an acoustic
velocity c and a dimension L normal to said radiating face, wherein
t.sub.o is substantially equal to the quotient (L/c) and to the
quotient (z/c.sub.w), means for generating a signal waveform, and
means for applying said signal waveform to said transducer.
27. Apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to produce an
acoustic signal in an acoustic medium, said unipolar displacement
having a half pulse duration time parameter t.sub.o, characterized
in that t.sub.o is substantially equal to the time required for an
acoustic wave to traverse the maximum dimension of the radiating
face through the acoustic medium, means for generating a signal
waveform, and means for applying said signal waveform to said
transducer.
28. Apparatus for producing a unipolar displacement of the
radiating face of an electroacoustic transducer to produce an
acoustic signal in an acoustic medium, said transducer having a
non-radiating face opposite said radiating face, said unipolar
displacement having a half pulse duration time parameter t.sub.o,
characterized in that t.sub.o is substantially equal to the time
required for an acoustic wave to travel through the transducer from
one face to the other and further characterized in that t.sub.o is
substantially equal to the time required for an acoustic wave to
traverse the maximum dimension of the radiating face through the
acoustic medium, means for generating a signal waveform, and means
for applying said signal waveform to said transducer.
29. Apparatus for generating a unipolar displacement of the
radiating faces of a plurality of electroacoustic transducers to
produce an acoustic signal in a medium having an acoustic velocity
c.sub.w, said unipolar displacement having a half pulse duration
time parameter t.sub.o, the radiating faces of said transducers
forming a coplanar array having a maximum dimension z characterized
in that t.sub.o is substantially equal to the quotient (z/c.sub.w),
means for generating a signal waveform, and means for applying said
signal waveform to said transducers.
30. The apparatus defined in claim 29 wherein the radiating faces
of said transducers displace from a rest position to maximum
displacement during a first interval of time t.sub.o and return
from maximum displacement to said rest position during a second
subsequent interval of time t.sub.o.
31. The apparatus defined in claim 29 wherein each of said
transducers is characterized by an acoustic velocity c and wherein
the dimension L of each of said transducers normal to its radiating
face bears substantially the same proportional relation to c as z
bears to c.sub.w.
32. The apparatus defined in claim 31 wherein the radiating faces
of said transducers displace from a rest position to maximum
displacement during a first interval of time t.sub.o and return
from maximum displacement to said rest position during a second
subsequent interval of time t.sub.o.
33. The apparatus defined in claim 32 comprising means for applying
to said transducers an electrical signal including a signal
component characterized by a first signal pulse at the start of
said first time interval and a second signal pulse at the end of
said second time interval.
34. The apparatus defined in claim 33 wherein each of said signal
pulses is characterized by a substantially instantaneous rise time
followed by gradual decay.
35. The apparatus defined in claim 34 wherein the rise time of said
first signal pulse is substantially concurrent with the start of
said first time interval and the rise time of said second signal
pulse is substantially concurrent with the end of said second time
interval.
36. The apparatus defined in claim 35 wherein the duration of each
of said signal pulses is substantially equal to t.sub.o.
37. The apparatus defined in claim 36 wherein said electrical
signal component is further characterized by a predetermined
reference signal level before said first signal pulse and after
said second signal pulse.
38. The apparatus defined in claim 37 wherein the peaks of both of
said signal pulses are of a first polarity relative to said
predetermined reference signal level.
39. The apparatus defined in claim 38 wherein said electrical
signal component is further characterized by a polarity opposite
said first polarity during the interval of time between said first
and second signal pulses.
40. The apparatus defined in claim 33 wherein said means for
applying comprises:
means for generating a trigger signal;
a plurality of shaped pulse generating channels responsive to said
trigger signal, each of said channels comprising means for delaying
said trigger signal for generating a rectangular pulse of
predetermined amplitude and duration, and means for shaping said
rectangular pulse to produce a shaped output pulse; and
means for summing the shaped output pulses of each of said channels
to produce said electrical signal.
41. Apparatus for producing a unipolar displacement of the
radiating faces of a plurality of electroacoustic transducers to
produce an acoustic signal in a medium having an acoustic velocity
c.sub.w, said unipolar displacement having a half pulse duration
time parameter t.sub.o, the radiating faces of said transducers
forming a coplanar array having a maximum dimension z, each of said
transducers having an acoustic velocity c and a dimension L
perpendicular to its radiating face, wherein t.sub.o is
substantially equal to the quotient (L/c) and to the quotient
(z/c.sub.w), means for generating a signal waveform, and means for
applying said signal waveform to said transducers.
42. Apparatus for producing a unipolar displacement of the
radiating faces of a plurality of electroacoustic transducers to
produce an acoustic signal in an acoustic medium, said unipolar
displacement having a half pulse duration time parameter t.sub.o,
the radiating faces of said transducers forming a coplanar array
having a maximum dimension z, each of said transducers having a
non-radiating face opposite said radiating face, characterized in
that t.sub.o is substantially equal to the time required for an
acoustic wave to propagate through each of said transducers from
one of its faces to the other and further characterized in that
t.sub.o is substantially equal to the time required for an acoustic
wave to propagate a distance z in the acoustic medium, means for
generating a signal waveform, and means for applying said signal
waveform to said transducers.
43. Apparatus for generating a unipolar acoustic displacement of
the radiating faces of a plurality of electroacoustic transducers,
to produce an acoustic signal in a medium having an acoustic
velocity c.sub.w, said unipolar displacement having a half pulse
duration time parameter t.sub.o, the radiating faces of said
transducers forming a coplanar array having a maximum dimension z
characterized in that t.sub.o is substantially equal to the
quotient (z/c.sub.w), the radiating faces of said transducers
displacing from a rest position to maximum displacement during a
first interval of time t.sub.o and returning from maximum
displacement to said rest position during a second subsequent
interval of time t.sub.o, and means for applying to said
transducers an electrical signal including a signal component
characterized by a first signal pulse at the start of said first
time interval and a second signal pulse at the end of said second
time interval.
44. The apparatus defined in claim 43 wherein each of said signal
pulses is characterized by a substantially instantaneous rise time
followed by gradual decay.
45. The apparatus defined in claim 44 wherein the rise time of said
first signal pulse is substantially concurrent with the start of
said first time interval and the rise time of said second signal
pulse is substantially concurrent with the end of said second time
interval.
46. The apparatus defined in claim 45 wherein the duration of each
of said signal pulses is substantially equal to t.sub.o.
47. The apparatus defined in claim 46 wherein said electrical
signal component is further characterized by a predetermined
reference signal level before said first signal pulse and after
said second signal pulse.
48. The apparatus defined in claim 47 wherein the peaks of both of
said signal pulses are of a first polarity relative to said
predetermined reference signal level.
49. The apparatus defined in claim 48 wherein said electrical
signal component is further characterized by a polarity opposite
said first polarity during the interval of time between said first
and second signal pulses.
50. The apparatus defined in claim 43 wherein said means for
applying comprises:
means for generating a trigger signal;
a plurality of shaped pulse generating channels responsive to said
trigger signal, each of said channels comprising means for delaying
said trigger signal, means responsive to the delayed trigger signal
for generating a rectangular pulse of predetermined amplitude and
duration, and means for shaping said rectangular pulse to produce a
shaped output pulse; and
means for summing the shaped output pulses of each of said channels
to produce said electrical signal.
Description
BACKGROUND OF THE INVENTION
This invention relates to electroacoustic transducer apparatus and,
more particularly, to electroacoustic transducer apparatus for
producing high energy unipolar pressure pulses in an acoustic
medium of relatively high specific impedance (e.g., water).
Unipolar acoustic pulses are useful in a wide variety of
applications. In underwater sonar, for example, unipolar acoustic
pulses radiating from a transducer can be used for high resolution
object detection, identification, and the like. Unipolar acoustic
pulses are typically generated by producing a unipolar displacement
of the radiating face of a transducer device (e.g., an
electroacoustic transducer device) which is immersed in or
otherwise contiguous with an acoustic medium. In general, the
unipolar displacement of the radiating transducer face (sometimes
referred to herein as a unipolar transducer displacement or
unipolar transducer response) results in a sequence of unipolar
acoustic pulses in the acoustic medium. The individual pulses in
such a sequence do not generally correspond to the amplitude and
duration of the unipolar transducer displacement. Rather, the
sequence of the acoustic pulses usually corresponds more nearly to
the second derivative of the displacement of the radiating
transducer face (i.e., the acceleration history of the radiating
transducer face). Unipolar transducer displacements are emdployed
not because they uniquely result in unipolar acoustic pulses, but
because the acoustic pulse sequences produced are relatively
uncomplicated and of short duration (i.e., not substantially longer
than the transducer displacement pulse). This latter feature is
particularly desirable for pulse repetition purposes. In reading
this specification, the distinction between unipolar transducer
displacement and unipolar acoustic pulses must be kept clearly in
mind.
In copending U.S. patent application Ser. No. 92,798 now U.S. Pat.
No. 3,715,710, J. Bernstein, et al., disclose apparatus for
producing unipolar displacement of the radiating face of an
electro-acoustic transducer. In accordance with the principles of
that invention, a transducer (e..g., a cylindrical piezo-electric
transducer) is driven by an electrical signal having
discontinuities in amplitude which initially stimulate vibration or
mechanical oscillation of the transducer and then, after a half
cycle of transducer oscillation in the fundamental mode,
substantially dampen the oscillations of the transducer. Transducer
oscillations are damped by applying signal discontinuities to the
transducer which would produce oscillations of the same amplitude
as the oscillations to be damped, but in phase opposition thereto,
thereby interfering with and tending to cancel out the undesired
oscillations. Since transducers of the type described may exhibit
more than one mode of vibration in each physical direction, it is
appropriate to provide a driving signal having discontinuities for
damping oscillation in several of the more significant modes in
order to produce a "clean" (i.e., sharply defined) unipolar
transducer response. In general, even for very simply shaped
transducer responses, the required driving voltage waveforms are
quite complex and so will be the electrical or electronic apparatus
used to generate these waveforms.
In my concurrently filed application Ser. No. 354,518, it is shown
that for certain types of transducer responses, the transducer
driving signal can be considerably simplified by relating the time
parameter of the desired transducer response to the longitudinal
dimension of the transducer.
In certain situations it becomes necessary to consider the pressure
of the acoustic medium on the radiating face of the transducer.
This is particularly true when the acoustic medium has a relatively
high value of specific impedance, as is true, for example, in the
case of water. In that event, an additional driving signal
component must be provided to account for the interaction of the
transducer and the acoustic medium.
It is therefore an object of this invention to improve and simplify
unipolar acoustic pulse generating apparatus for use with acoustic
media of relatively high specific impedance.
It is a more particular object of this invention to provide
unipolar acoustic pulse generating apparatus in which the
additional transducer driving signal component required to account
for the pressure of the acoustic medium on the radiating face of
the transducer is simplified and the driving signal generating
apparatus is also accordingly simplified.
SUMMARY OF THE INVENTION
These and other objects of the invention are accomplished in
accordance with the principles of the invention by unipolar
acoustic pulse generator apparatus in which a certain dimension of
the radiating face of the transducer or of the several radiating
faces of an array of transducers is chosen to simplify the response
of the transducers, thereby simplifying the required driving
signals and the apparatus required to generate those signals. More
particularly, the greatest or principal dimension z of the
radiating transducer face or array of faces is chosen so that a
time parameter t.sub.o of the desired unipolar acoustic output
pulse is substantially equal to the quotient z/c.sub.w, where
c.sub.w is the acoustic velocity of the ensonified acoustic
medium.
Further features and objects of the invention, its nature and
various advantages will be more apparent upon consideration of the
attached drawing and the following detailed description of the
invention.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1A is a side view of a piezoelectric transducer of the type
used for generating unipolar acoustic pulses in an acoustic
medium;
FIG. 1B is an end view of the transducer of FIG. 1A;
FIG. 2A is a diagram of an idealized unipolar displacement of the
radiating face of the transducer of FIG. 1 plotted against
time;
FIG. 2B is a diagram of the additional transducer driving signal
component required to account for the pressure of the acoustic
medium on the radiating face of the transducer in unipolar acoustic
pulse generator apparatus constructed in accordance with the
principles of this invention;
FIG. 3 is a schematic block diagram of apparatus for generating
transducer driving signals of the type shown in FIG. 2B; and
FIG. 4 is an end view of an array of transducers useful in
understanding the application of the principles of this invention
to transducer arrays.
DETAILED DESCRIPTION OF THE INVENTION
As shown in FIGS. 1A and 1B, a typical cylindrical electroacoustic
transducer 10 is made up of a plurality of discs 12 interspersed
with electrodes 14 and bonded together with adhesives or the like.
Discs 12 are a piezoelectric material (e.g., barium titanate or
lead zirconate titanate) polarized to operate in the "33 mode"
wherein the mechanical stresses in the transducer material are
parallel to the longitudinal axis 16 of the transducer and
perpendicular to the electrodes. Electrodes 14 are interconnected
by wellknown wiring arrangements (not shown).
Transducer 10 has a radiating face 18 contiguous with an acoustic
medium (e.g., air or water) and an opposite non-radiating face 20.
The non-radiating face of transducer 10 is shown as free, but it
may be clamped, attached to springs, or otherwise restrained in any
manner.
When transducer 10 is energized by a suitable driving signal
applied to electrodes 14, radiating face 18 displaces, thereby
projecting an acoustic signal into the surrounding acoustic medium.
In many applications, the most desirable acoustic signal is a
unipolar pulse. As is discussed in greater detail in my
above-mentioned concurrently filed application, unipolar acoustic
pulses are most readily generated by producing a unipolar
displacement of the radiating face of the transducer, as
illustrated, for example, by the displacement history of FIG. 2A.
Although the particular displacement history shown in FIG. 2A is
not necessarily the most desirable in all applications and although
the principles of this invention are equally applicable to
generating a wide variety of other unipolar transducer responses,
the present invention will be readily understood from an
explanation of its application to generating a transducer response
of the type shown in FIG. 2A.
Apparatus for producing displacement of the radiating face of a
transducer of the type shown in FIG. 1 is disclosed in the
above-mentioned application of Bernstein, et al., and in my
above-mentioned concurrently filed application. The required
transducer driving signal is typically a curved waveform having a
number of discontinuities for initially stimulating and then
damping oscillation of the transducer. A driving signal of this
type is conveniently generated by summing a plurality of
appropriately shaped and timed signal pulses. Apparatus for
generating a signal of this type is shown in FIG. 3. In the
apparatus of FIG. 3, rep-rate signal generator 30 and
differentiator 32 produce a trigger signal whenever an acoustic
output pulse is required. This trigger signal is applied to each of
a plurality of pulse generating signal channels, respectively
represented by pulse generators 40-1 through 40-n. Each of pulse
generators 40 produces an appropriately shaped and timed output
signal pulse. The signal pulses produced by pulse generators 40 are
scaled and summed by potentiometers 50 and operational amplifier 52
to produce a driving signal waveform applied to transducer 70. If
desired, the output signal of amplifier 52 may be filtered by low
pass filter 60 before being applied to transducer 70. Signal
generating apparatus of the type shown in FIG. 3, is described in
greater detail, for example, in my concurrently filed
application.
As a rule, if the response of the transducer to driving signal
discontinuities can be simplified, the quality of the acoustic
output pulse is improved and the number of modes of transducer
oscillation requiring damping is reduced. This results in
simplification of the required transducer driving signal and of the
apparatus required to generate that signal. As described in my
concurrently filed application, a considerable simplification in
the driving voltage waveform is achieved by designing the
transducer so that the half pulse duration time parameter t.sub.o
of the desired output pulse is an integer multiple of the quotient
L/c, where L is the longitudinal dimension of the transducer and c
is the acoustic velocity of the material of the transducer. The
quotient L/c is a time parameter which corresponds to the time
required for an acoustic wave to propagate through the transducer
along its length L.
In certain applications, interaction between the ensonified
acoustic medium and the transducer becomes a significant factor in
transducer response. This is particularly true when acoustic pulses
are to be transmitted into a medium, such as water, which has a
relatively high specific impedance value, this value being the
product of the mass density of the medium and its acoustic velocity
c.sub.w. In that event, an additional transducer driving signal
component is required to account for the pressure of the medium on
the radiating face of the transducer. While this additional signal
component will in general have a distinctly smaller amplitude than
those signal components considered, for example, in my concurrently
filed application, it must still be present in the driving signal
waveform for accurate output pulse generation.
In general, the nature and complexity of the additional signal
component referred to above depends on three time parameters: the
half pulse duration time parameter t.sub.o, the time required for
an acoustic pulse to travel the length of the transducer (e.g., the
quotient L/c); and the time required for an acoustic wave in the
ensonified medium to traverse the greatest or principal dimension
of the radiating face of the transducer. The last of these
parameters is given by the quotient z/c.sub.w, where z is the
maximum dimension of the radiating face of the transducer and
c.sub.w is as defined above. As in my concurrently filed
application, it is desirable for the purpose of simplifying this
additional signal component to design the transducer so that
t.sub.o is an interger multiple of the quotient L/c, the
relationship t.sub.o = L/c being the most desirable. In accordance
with the principles of the instant invention, it is also desirable
for this purpose to design the transducer so that t.sub.o =
(z/c.sub. w). The simplest additional signal component is required
when both of these conditions are met, i.e., when t.sub.o = (L/c )
= (Z/c.sub.w).
In the case of the cylindrical transducer of FIG. 1, z is the
diameter of radiating face 18. Assuming that t.sub.o = (L/c) =
(z/c.sub.w) for the transducer of FIG. 1 and that non-radiating
face 20 is not constrained, the additional transducer driving
signal component required for the generation of the output pulse
shown in FIG. 2A takes the form shown in FIG. 2B. This waveform
includes two pulses, each of duration t.sub.o beginning
respectively at t = 0 and t = 2t.sub.o. Each of these pulses
includes an initial discontinuity followed by gradual decay.
Between these two pulses, the signal waveform has a polarity
opposite that of the peaks of pulses. Like the other components of
the transducer driving signal, this additional driving signal
component may be generated by one or more channels of the apparatus
of FIG. 3, i.e., by one or more of pulse generators 40.
The principles discussed above in connection with cylindrical
transducer of FIG. 1 are equally applicable in a wide variety of
other situations. In the case of an isolated cylindrical transducer
of basic diameter d operating in the 33 mode and employing a
circular radiating face of diameter d', it is d' rather than d
which should be used for z in the preceding relationships. This
situation is exemplified by many practical transducer designs
employing end masses.
For an isolated prismatic transducer of any general cross sectional
shape operating in the 33 mode, z is the maximum or greatest
dimension of the radiating face. In the case of a transducer having
a square or rectangular radiating face, for example, z is the
diagonal of the square or rectangle. In the case of a transducer
having a triangular radiating face, z is the longest side of the
triangle. In the case of a transducer having an elliptical
radiating face, z is the major axis of the ellipse.
In certain applications, it may be desired to produce transducer
responses having different durations. For example, such responses
may all have the form shown in FIG. 2A, but with different values
of t.sub.o, as well as different amplitudes. In accordance with the
foregoing principles of this invention, this capability is best
achieved by use of a single transducer for each different response
duration. Each transducer would then have a different radiating
face dimension, z, in accordance with the optimizing principle, z =
c.sub.w t.sub.o, and, in accordance with the optimizing principle
disclosed in my above-mentioned concurrently filed application,
i.e., L = ct.sub.o, would have a different length, L.
The principles of this invention are also applicable to arrays of
transducers having multiple radiating faces in a common plane. In
the case of such an array, the maximum dimension of the array of
radiating faces corresponds to the maximum dimension of the
radiating face of an isolated transducer and is the value of z in
the relationships above. For the rectangular array of radiating
faces 80 shown in FIG. 4, z is the diagonal of the array as
indicated by the segment a -b. As is evident from this example, the
intervening portions of the non-radiating interstices 82 between
the radiating faces 80 must be included in determining the distance
z.
* * * * *