U.S. patent application number 12/208803 was filed with the patent office on 2010-03-11 for piezoelectric transducers and inertial sensors using piezoelectric transducers.
This patent application is currently assigned to ANALOG DEVICES, INC.. Invention is credited to William Albert Clark, John Albert Geen, Jinbo Kuang.
Application Number | 20100058861 12/208803 |
Document ID | / |
Family ID | 41278700 |
Filed Date | 2010-03-11 |
United States Patent
Application |
20100058861 |
Kind Code |
A1 |
Kuang; Jinbo ; et
al. |
March 11, 2010 |
Piezoelectric Transducers and Inertial Sensors using Piezoelectric
Transducers
Abstract
Transducers comprising a frame structure made of piezoelectric
material convert energy, through piezoelectric effect, between
electrostatic energy associated with voltage differential between
the electrodes sandwiching the frame structure and mechanical
energy associated with deformation of the frame structure. Inertial
sensors such as gyroscopes and accelerators, including inertial
sensors comprising ring resonators, utilize said transducers both
to generate oscillations of their resonators and to sense the
changes in such oscillations produced, in the sensors' frame of
reference, by Coriolis forces appearing due to the movement of the
sensors.
Inventors: |
Kuang; Jinbo; (Acton,
MA) ; Clark; William Albert; (Winchester, MA)
; Geen; John Albert; (Tewksbury, MA) |
Correspondence
Address: |
Sunstein Kann Murphy & Timbers LLP
125 SUMMER STREET
BOSTON
MA
02110-1618
US
|
Assignee: |
ANALOG DEVICES, INC.
Norwood
MA
|
Family ID: |
41278700 |
Appl. No.: |
12/208803 |
Filed: |
September 11, 2008 |
Current U.S.
Class: |
73/504.12 ;
73/514.34 |
Current CPC
Class: |
G01C 19/56 20130101;
G01P 15/09 20130101; G01C 19/5677 20130101; Y10T 29/42
20150115 |
Class at
Publication: |
73/504.12 ;
73/514.34 |
International
Class: |
G01C 19/56 20060101
G01C019/56; G01P 15/09 20060101 G01P015/09 |
Claims
1. A piezoelectric transducer comprising: a structure made of
piezoelectric material, the structure including: a set of
substantially flat concentric frames having a common top surface
and a common bottom surface and characterized by a direction of
elongation, the top and the bottom surfaces being substantially
parallel to a reference plane, and bridges connecting the frames,
the bridges disposed symmetrically about a plane of symmetry of the
structure so as to allow the frames to deform in the reference
plane; and a set of at least two top electrodes, disposed on the
top surface of the frames, and a set of at least two corresponding
bottom electrodes, disposed on the bottom surface of the frames,
the sets of top and bottom electrodes being substantially
equivalent and positioned opposite to each other, each of
corresponding top and bottom electrodes disposed on at least two
frames along a path that is symmetric about the plane of symmetry
and crosses some of the bridges, wherein the transducer transduces
energy, through piezoelectric effect, between electrostatic energy
associated with voltage differential between the corresponding top
and bottom electrodes and mechanical energy associated with
deformation of the frames.
2. A transducer according to claim 1, wherein the deformation of
the frames is reciprocating.
3. A transducer according to claim 1, wherein bridges crossed by
the path define a plurality of sections in the structure, the
plurality of sections including at least two peripheral sections
and a central section.
4. A transducer according to claim 3, wherein the central section
is longer than the at least two peripheral sections.
5. A transducer according to claim 3, wherein deformation of the
central section is characterized by higher amplitude than
deformations of peripheral sections.
6. A transducer according to claim 1, wherein the plane of symmetry
is perpendicular to the direction of elongation.
7. A transducer according to claim 1, wherein the transducer is
used for at least one of driving and sensing motion of a connected
mass.
8. A motion sensor comprising a body defining a local reference
system, the body including: a piezoelectric transducer including: a
set of substantially flat concentric frames having a common top
surface and a common bottom surface and characterized by a
direction of elongation, the top and the bottom surfaces being
substantially parallel to a reference plane; bridges connecting the
frames, the bridges disposed symmetrically about a plane of
symmetry of the transducer so as to allow the frames to deform in
the reference plane, the bridges and the frames made of
piezoelectric material; and a set of at least two top electrodes,
disposed on the top surface of the frames, and a set of at least
two corresponding bottom electrodes, disposed on the bottom surface
of the frames, the sets of top and bottom electrodes being
substantially equivalent and positioned opposite to each other,
each of corresponding top and bottom electrodes disposed on at
least two frames along a path that is symmetric about the plane of
symmetry and crosses some of the bridges, wherein the transducer
transduces energy, through piezoelectric effect, between
electrostatic energy associated with voltage differential between
the corresponding top and bottom electrodes and mechanical energy
associated with deformation of the frames; and a resonator coupled
to the piezoelectric transducer, the resonator characterized by a
motion that lies substantially in the reference plane.
9. A sensor according to claim 8, wherein the transducer causes,
through piezoelectric effect, the motion of the resonator.
10. A sensor according to claim 8, wherein the transducer senses,
through piezoelectric effect, the motion of the resonator.
11. A sensor according to claim 8, wherein the transducer is
configured to enable detection of changes in electric field
arising, through piezoelectric effect, from changes in the motion
of the resonator within the local reference system, the changes in
the motion associated with rotation of the body.
12. A sensor according to claim 8, wherein the motion of the
resonator is reciprocating.
13. A sensor according to claim 8, wherein the body is configured
to be reflectionally symmetric about a symmetry axis that is normal
to the reference plane.
14. A sensor according to claim 12, wherein the reciprocating
motion includes deformation of the frames perpendicularly to the
direction of elongation.
15. A sensor according to claim 8, further comprising a substrate,
wherein the body is affixed to the substrate using a set of anchors
for supporting the body above a surface of the substrate, at least
one anchor positioned proximate to the body's center of mass.
16. A sensor according to claim 15, wherein the body is affixed to
the substrate within a recess formed in the substrate.
17. A sensor according to claim 15, wherein the surface of the
substrate is leveled and the body is affixed to the substrate above
the leveled surface.
18. A sensor according to claim 15, wherein the set of anchors is
configured to allow movement of the body relative to the
substrate.
19. A sensor according to claim 15, wherein the set of anchors
includes multiple anchors positioned substantially symmetrically
about the body's center of mass.
20. A sensor according to claim 8, wherein the body further
comprises a hub portion.
21. A sensor according to claim 20, wherein the resonator comprises
a ring portion, the ring portion being supported by spoke
structures extending substantially in radial direction from the hub
portion.
22. A sensor according to claim 21, wherein the deformation of the
frames is transferred to the ring portion along the spoke
structures.
23. A sensor according to claim 21, wherein the top and the bottom
driving electrodes and the top and the bottom sensing electrodes at
least partially overlap with the spoke structures.
24. A sensor according to claim 21, wherein the hub portion and the
ring portion are circular.
25. A sensor according to claim 8, wherein the sensor is an
accelerometer.
26. A sensor according to claim 8, wherein the sensor is a
gyroscope.
27. A method of sensing a movement of an inertial sensor having a
body of piezoelectric material, the body characterized by
substantially constant thickness defined by two planes and also
having a set of top electrodes disposed on a top surface of the
body and a corresponding set of bottom electrodes disposed on a
bottom surface of the body, the sets of top and bottom electrodes
being opposite to one another, the sets of top and bottom
electrodes characterized by a pattern, the body defining a local
reference system, the method comprising: applying alternating
voltage differential between top driving electrodes from the top
set and corresponding bottom driving electrodes from the bottom set
so as to cause reciprocating motion, in the plane, of a portion of
the body through piezoelectric effect, wherein such reciprocating
motion changes, within the local reference system, upon the
movement of the inertial sensor; and sensing, through piezoelectric
effect, said changes to the reciprocating motion based on a voltage
differential arising between top sensing electrodes from the top
set and corresponding bottom sensing electrodes from the bottom
set.
28. A method according to claim 27, wherein the body is configured
to be reflectionally symmetric about a symmetry axis that is normal
to the plane.
29. A method according to claim 27, wherein the pattern is
configured to be reflectionally symmetric about the symmetry
axis.
30. A method according to claim 27, wherein the movement of the
inertial sensor is a rotation about an axis that is perpendicular
to the plane.
31. A method for modifying an oscillation of a resonator in an
inertial sensor, the inertial sensor comprising driving
piezoelectric transducers for enabling an oscillation of the
resonator and sensing piezoelectric transducers for enabling a
detection of a movement of the inertial sensor, the method
comprising: disposing piezoelectric compensating elements
substantially equidistantly among the driving and the sensing
piezoelectric transducers, the compensating elements and the
resonator forming corresponding capacitors having capacitive gaps;
during the oscillation of the resonator, measuring, with the
compensating elements, changes in electrostatic charges stored in
the capacitors, the changes in charges associated with changes in
the capacitive gaps due to the oscillation of the resonator; and
modifying the electrostatic charges stored in the capacitors so as
to modify the oscillation of the resonator.
32. A method according to claim 31, wherein the inertial sensor is
a gyroscope.
33. A method according to claim 31, wherein the resonator is a
frame.
34. A method according to claim 31, wherein the inertial sensor
further comprises a hub and the resonator is a ring connected to
the hub.
35. A method according to claim 31, wherein modifying the stored
electrostatic charges includes equalizing the changes in the stored
charges among the capacitors.
36. A method according to claim 31, wherein modifying the stored
electrostatic charges enables adjustment of a resonant frequency of
the resonator.
Description
TECHNICAL FIELD
[0001] The present invention relates generally to inertial sensors,
and more particularly to microelectromechanical inertial sensors
for measuring a rotational motion, such as ring gyroscopes.
BACKGROUND ART
[0002] It is known in the prior art to use inertial motion sensors
to track the position, orientation, and velocity (linear or
angular) of objects in the inertial reference frame, without the
need for external references. Inertial motion sensors generally
include gyroscopes, accelerators, and other motion-sensing devices.
Gyroscopes are well-known and used for measuring or maintaining
orientation based on the principles of conservation of angular
momentum. Vibrating structure gyroscopes, due to their simplicity
and low cost, gained popularity since 1980s over conventional,
rotating gyroscopes. The physical principle of a vibrating
structure gyroscope is very intelligible: a vibrating object tends
to keep vibrating in the same plane as its support is rotated. In
engineering literature, this type of device is also known as a
Coriolis vibratory gyro because, as the plane of oscillation is
rotated, the response detected by a transducer of the device
results from the Coriolis effect (as in a conventional rotating
gyroscope). The Coriolis effect is an apparent deflection of moving
objects from a straight path when they are viewed in a rotating
frame of reference, and is caused by the Coriolis force, which is
considered in the equation of motion of an object in a rotating
frame of reference and depends on the velocity of the moving
object, and centrifugal force. By determining the Coriolis force, a
rotation of the object can be described. Both the Coriolis force
and the Coriolis effect are well known in the art.
[0003] Some of vibrating gyroscopes utilize piezoelectric
oscillators to capture the rotational movements of objects, (see,
e.g., Ceramic Gyro.TM. devices by NEC-TOKIN Corporation of Japan,
www.nec-tokin.com). In such conventional, bulk piezoelectric
gyroscopes, used as, for example, angular velocity sensors, a
piezoelectric element torsionally vibrates a rod, which causes the
rod to work as a pendulum. Then, the value of the Coriolis force,
which occurs when the rod is rotated, is extracted after it is
converted into voltage by the piezoelectric element.
[0004] With material-micromachining becoming a rapidly developing
technology in recent years, silicon (Si) based
microelectromechanical systems (MEMS) and devices enriched the
field of inertial sensors by offering relatively inexpensive
vibrating structure gyroscopes. A general discussion of MEMS-based
gyroscopes is provided, for example, by Steven Nasiri, "A critical
review of MEMS gyroscopes technology and commercialization status",
ca. 2005, available at
http://www.invensense.com/shared/pdf/MEMSGyroComp.pdf
[0005] To date, MEMS-based gyroscopes have been implemented in
several embodiments. Some single-mass linear resonators, for
example, utilize a single mass oscillating to and fro along the
"sensitive" axis of the device, like a balance in a watch (see,
e.g., FIG. 1, illustrating a device by HSG-IMIT, Institut fur
Mikro- und Informationstechnik, or Institute for Micromachining and
Information Technology, of Germany,
http://www.hsg-imit.de/index.php?id=41&L=1). If such linear
device is rotated around an axis parallel to its sensitive axis,
Coriolis forces induce a second oscillation oriented perpendicular
to the direction of the (primary) oscillation of the mass.
[0006] Another variation of a linear-resonator gyroscope is based
on a tuning-fork idea, for example, as implemented by the Draper
Laboratory of Massachusetts, USA (www.draper.com), and described,
for example, in U.S. Pat. Nos. 5,767,405 and 7,043,985, each of
which is incorporated herein in its entirety by reference. An
example of a basic tuning fork MEMS gyroscope, shown in FIG. 2,
includes a pair of masses driven to oscillate with equal amplitudes
but in opposite directions. Rotation of the gyroscope about an
in-plane axis of sensitivity lifts the moving masses, which is
detected with capacitive electrodes positioned under the
masses.
[0007] Analog Devices Inc. of Norwood, Mass. offers a number of
integrated angular-rate sensing gyroscopes (see, for example, Geen
et al., "New iMEMS.RTM. Angular-Rate-Sensing Gyroscope", Analog
Dialog, Vol. 37, March 2003, available at
http://www.analog.com/library/analogDialogue/archives/37-03/gyro.html,
which is hereby incorporated herein by reference in its entirety).
Some exemplary MEMS gyroscopes are described in U.S. Pat. Nos.
6,877,374, 7,089,792, 7,032,451, 7,204,144, 7,357,025, and
7,216,539, each of which is hereby incorporated by reference in its
entirety. In such gyroscopes, capacitive silicon sensing elements
are interdigitated with stationary silicon beams attached to a
substrate that are used to measure a Coriolis-induced displacement
of a resonating mass.
[0008] Another family of MEMS-based inertial sensors known in the
art includes vibrating-wheel gyro structures, schematically
illustrated in FIG. 3. These structures generally have a wheel
driven to vibrate about its axis of symmetry, where rotation about
either in-plane axis results in the wheel's tilting, a change that
can be detected with capacitive electrodes under the wheel. Yet
another emerging MEMS-implementation is a ring gyroscope, where a
planar resonant Si-based ring structure is driven to resonance and
the position of its nodal points indicate the rotation angle. An
example of a ring gyroscope shown in FIG. 4 was developed at the
University of Michigan (see, e.g., F. Ayazi and K. Najafi, "Design
and Fabrication of A High-Performance Polysilicon Vibrating Ring
Gyroscope", Eleventh IEEE/ASME International Workshop on Micro
Electro Mechanical Systems, Heidelberg, Germany, Jan. 25-29, 1998;
F. Ayazi and K. Najafi, "High aspect-ratio combined poly and
single-crystal silicon (HARPSS) MEMS technology", J. of
Microelectromechanical Systems, v. 9, pp. 288-294, 2000; F. Ayazi
and K. Najafi, "A HARPSS Polysilicon Vibrating Ring Gyroscope",
Journal of Microelectromechanical Systems, Vol. 10, No. 2, June
2001). In such ring gyroscopes, a poly-Si ring resonator is driven
by drive and control electrodes to vibrate about its axis of
symmetry, and rotation of the chip that carries the gyroscope
results in a ring displacement that can be detected by
capacitance-sensing elements through the change in geometry of
capacitive air-gaps.
[0009] As would be appreciated by one skilled in the art, currently
employed micromachining processes are not particularly compatible
with widely used standard CMOS processes such as reactive-ion etch
(RIE) or electron-beam milling. Such incompatibility lengthens and
complicates fabrication cycles and increases the cost of the
resulting MEMS-based devices. In addition, current MEMS-based
solutions for inertial sensors quite often employ capacitive
driving and sensing structures, such as drive and control
electrodes of FIG. 4. The capacitive nature of operating a
conventional inertial sensor imposes, among other requirements, a
need for an air-gap between an oscillating mass (the ring in FIG.
4) and an electrode. The air-gaps of MEMS structures are clearly
susceptible to contamination with microparticles (during both the
manufacturing process and operation) that may permanently
incapacitate inertial sensors devices. Moreover, an
electrostatically driven mass or ring in such devices is
susceptible to anomalies in charge distribution across a set of
driving and sensing electrodes. In vibrating gyroscopes, the
non-uniform charge distribution can contribute to an offset drift
and reduce the accuracy and precision of these devices or even
nullify their performance.
SUMMARY OF THE INVENTION
[0010] Embodiments of a piezoelectric transducer of this invention
permit transferring energy, through piezoelectric effect, between
electrostatic energy associated with voltage differential between
the top and bottom electrodes of the transducer and mechanical
energy associated with deformation of frames of the transducer. In
one embodiment, the transducer of the invention comprises a
structure made of piezoelectric material that includes a set of
substantially flat elongated concentric frames connected by bridges
disposed symmetrically about a plane of symmetry of the structure.
Such bridges allow the frames to deform in a reference plane which
is substantially parallel to top and bottom surfaces of the frames.
A set of at least two top electrodes is disposed on the top
surfaces of the frames. A set of at least two corresponding bottom
electrodes is disposed on the bottom surface of the frames opposite
to the first set. Both the top and the bottom set of electrodes are
disposed on at least two frames along a path that is symmetric
about the plane of symmetry of the structure and crosses some of
the bridges. Some of these electrodes may be used to apply a
voltage differential between the top and bottom surfaces of the
piezoelectric transducer, while some of the electrodes may be
configured to sense the changes in motion of the frames of the
transducer based on a voltage differential associated with such
changes. In some embodiments, the deformation of the frames may be
reciprocating, and may be characterized by amplitude that is higher
in central portions of the frames than in peripheral portions of
the frames.
[0011] Related embodiments of the invention provide for a motion
sensor including the piezoelectric transducer of the invention
coupled with a resonator that may move substantially in the
reference plane. Such motion sensor may be used as an inertial
sensor, for example accelerometer or a gyroscope. In some
embodiments, the transducer may cause the motion of the resonator.
In alternative embodiments, the transducer may sense the motion of
the resonator. In addition, the transducer may be configured to
enable detection of charges in electric field arising, through
piezoelectric effect, from changes in the motion of the resonator
that are associated with rotation of the body of the motion sensor.
In related embodiments, the body of the transducer may be
reflectionally symmetric about the axis that is normal to the
reference plane and be affixed to and above a surface of a
substrate using a set of anchors, where at least one anchor may be
positioned proximate to the body's center of mass. Such anchors are
configured to allow movement of the body relative to the substrate.
Alternatively, the body of the transducer may be affixed to the
substrate within a recess formed in the substrate. In yet further
embodiments, the body of the sensor may comprise hub and ring
portions, where the ring portion may be supported by spokes
extending substantially in radial direction from the hub portion
and where the deformation of the frames of the piezoelectric
transducer may be transferred to the ring along the spokes. The hub
and the ring portions of the sensor may be circular or may be
generally shaped otherwise.
[0012] In addition, the invention provides a method of sensing a
movement of the embodiments of the inertial sensor of the invention
with the use of the piezoelectric effect by sensing changes, within
the local reference system, to the reciprocating motion of the
frames of the transducer based on a voltage differential arising
between the top and bottom sensing electrodes. Such changes in the
reciprocating motion are indicative of a rotation of the inertial
sensor about an axis that is perpendicular to the plane of motion
of the frames.
[0013] Furthermore, embodiments of the invention provide for method
for modifying an oscillation of a resonator in an inertial sensor.
Such modification includes disposing piezoelectric compensators
substantially equidistantly among the driving and the sensing
piezoelectric transducers of the inertial sensor so as to form gaps
between the corresponding compensators and the resonator of the
sensor, and measuring changes in charges stored in capacitors
associated with changes in capacitive gaps due to the oscillation
of the resonator. In addition, the method comprises a step of
modifying the stored electrostatic charges so as to affect the
oscillation of the resonator, for example, to adjust its resonant
frequency. In specific embodiments, such modification of charges
may include equalization of the changes in the stored charges among
the capacitors.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] The foregoing features of the invention will be more readily
understood by reference to the following detailed description,
taken with reference to the accompanying drawings, in which like
elements are annotated with like labels and numbers and in
which:
[0015] FIG. 1 shows a linear resonator gyroscope of the prior
art;
[0016] FIG. 2 shows a comb-drive tuning fork MEMS gyroscope of the
prior art;
[0017] FIG. 3 schematically illustrates a prior art concept of a
vibrating-wheel MEMS gyroscope;
[0018] FIG. 4 shows a poly-silicone ring gyroscope of the prior
art;
[0019] FIG. 5 illustrates a piezoelectric principle of general
operation of embodiments of the invention, wherein FIG. 5A shows a
top view and FIG. 5B shows a side view;
[0020] FIG. 6 schematically shows an inertial sensor having a ring
resonating structure attached to the central hub with the spokes in
accordance with an exemplary embodiment of the present invention,
wherein FIG. 6A shows a top view and FIG. 6B shows a side view;
[0021] FIG. 7 schematically depicts, in top view, two-fold-symmetry
modes of oscillation of an embodiment of a ring resonator. FIGS. 7A
shows deformations of the spoke-driven regions of the ring. FIG. 7B
shows deformations of the sensing regions of the ring located
between the driving spokes;
[0022] FIG. 8 schematically shows a MEMS-based inertial sensor
having two-fold symmetry in accordance with an exemplary embodiment
of the invention, wherein FIG. 8A shows a top view and FIG. 8B
shows a side view;
[0023] FIG. 9 depicts an exemplary frame structure of a
piezoelectric transducer in accordance with an exemplary embodiment
of the invention, wherein FIG. 9A shows a top view and FIG. 9B
shows a side view;
[0024] FIG. 10 depicts, in top view, an electrode pattern formed on
the frame structure of FIG. 9 including a close-up view of a
portion of the electrode pattern, in accordance with an exemplary
embodiment of the invention;
[0025] FIG. 11 shows a cross-section of the embodiment of FIG. 10
with an applied electric field E of a polarity that alternates
between the states of FIGS. 11A and 11B;
[0026] FIG. 12 schematically shows a deformation of the transducer
of FIG. 10 caused by the field of alternating polarity of FIG. 11
being applied to the frame structure of the transducer, wherein
FIG. 12A shows a view in which a spoke is pushed outward with
respect to the hub as a result of applying the field of FIG. 11A
and FIG. 12B shows a view in which the spoke is pulled towards the
hub as a result of applying the field of FIG. 11B;
[0027] FIG. 13 shows an exemplary embodiment of a MEMS-based
inertial sensor of the invention possessing three-fold
symmetry;
[0028] FIG. 14 schematically illustrates exemplary MEMS-based
devices comprising embodiments of inertial sensors of the
invention, wherein FIG. 14A shows an embodiment comprising an
inertial sensor anchored to the underlying leveled substrate and
FIG. 14B shows an embodiment comprising an inertial sensor anchored
within a recess in the underlying substrate; and
[0029] FIG. 15 shows an exemplary four-fold-symmetry oscillation
mode in accordance with an exemplary alternative embodiment of the
present invention.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
[0030] Embodiments of the present invention describe piezoelectric
transducers and inertial sensors such as gyroscopes and
accelerators utilizing such piezoelectric transducers. The
described embodiments utilize the piezoelectric effect both to
generate oscillations of their resonators and to sense the changes
in such oscillations produced, in the sensors' frames of reference,
by Coriolis forces appearing due to the movement of the sensors. In
specific embodiments, the movement may be a rotational
movement.
[0031] As used in this description and the accompanying claims, the
following terms shall have the meanings indicated, unless the
context otherwise requires:
[0032] A term "set" refers to either a unit or a combination of
multiple units.
[0033] "Electrostatic energy," as understood in the art, generally
refers to the potential energy which a collection of electric
charges possesses by virtue of their positions relative to each
other. For example, the energy, stored in an electric capacitor
after its separated conducting plates have been charged, is
electrostatic.
[0034] A "piezoelectric effect," conventionally related in the art
to generation of electric potential in response to mechanical
stresses applied to a piezoelectric material, and a "converse
piezoelectric effect," conventionally associated with formation of
material stresses or strains when an electric field is applied to
such material, are used interchangeably herein and should be
understood to generally refer to transduction between the
electrostatic energy and the mechanical energy in a piezoelectric
material subjected to either electrostatic or mechanical
influence.
[0035] "Body" refers to a representation of a physical structure
and material substance in a bodily form.
[0036] An electric field applied across a piezoelectric body is
considered to be "alternating" when the field is changed repeatedly
between two different states that generally manifest in different
effects on the shape of the piezoelectric body. Consequently,
reciprocating the applied electric field between the static vector
values of +E and -E (i.e., changing the field polarity with a use
of a switch, for example), which for some piezoelectric material
may correspond to expansion and contraction of the material, will
be understood as "alternating" the electrostatic field applied to
such material. Similarly, switching the static field applied to a
piezoelectric material between the values of E and zero (which may
respectively correspond to the state where the material experiences
mechanical stresses and the state in which material is not
piezoelectrically deformed) is also understood as "alternating" the
applied field.
[0037] FIG. 5 schematically illustrates, in top and side views, a
principle according to which an inertial piezoelectric sensor of
the present invention is realized. This principle applies equally
to a gyroscope, an accelerator, or any other type of inertial
sensor contemplated by the invention. As shown in FIG. 5A, two
electrodes--a driving electrode 10 and a sensing electrode 14--are
disposed on the top surface of a substantially flat body 18 having
substantially constant thickness of piezoelectric material. Another
pair of electrodes, comprising a driving electrode 12 and a sensing
electrode 16 that respectively correspond to the electrodes 10 and
14, is disposed on the bottom surface of the body 18 and is not
visible in the top view of FIG. 5A. For the sake of simplicity, the
side view of FIG. 5B shows only the driving electrodes 10 and 12.
When connected to a power supply, the driving electrodes create an
electric field E across the body 18 thus causing the body to expand
or contract through a well-understood in the art piezoelectric
effect. If the applied direct-current electric field E is
alternated, the resulting transduction of electrostatic energy to
mechanical energy of deformation of the body alternates as well. In
this case, the expansions and contractions of the body 18
reciprocally shift its boundary, e.g., by incremental amounts +dx
and -dx as indicated in FIG. 5, due to alternating mechanical
stresses generated across the body. As will be understood by one
skilled in the art, a detection of rotation--if present--of the
body 18 experiencing reciprocating mechanical expansion and
contraction can be enabled by the second pair of sensing electrodes
14 and 16, through the piezoelectric effect. An appropriate
measuring device such as voltmeter (not shown), for example,
connected to this second pair of electrodes 14 and 16 will register
a change in an electrostatic charge, generated in the vicinity of
the electrodes due to apparent variation in body's deformation
caused by rotation of the body, in accordance with the Coriolis
effect. Such registration of the change in the electrostatic charge
practically amounts to sensing the presence of and measuring the
Coriolis effect and, therefore, the rotational motion of the body
itself. The strength of the energy transduction, and therefore the
sensitivity of sensing the rotational motion, depends on physical
characteristics of the body 18, such as piezoelectric coefficients
and mass. It should be noted that, to this end, any pair of
electrodes--whether a pair (10,12) or a pair (14,16)--may be used
as either driving or sensing electrodes at the user's discretion,
in an exemplary embodiment.
[0038] In some related embodiments, to increase the sensitivity and
isotropy of sensing the rotational motion, the body of the
piezoelectric sensor may be configured in a circular fashion.
Moreover, in a specific embodiment, such as that shown in FIG. 6 in
top and side views, a body 20 of the sensor may feature a ring
resonating structure 24, suspended on the outer side of a centrally
positioned hub 26. (It should be noted that a different, internal
positioning of a ring resonating structure with respect to the
heavier, outer portion of the body 20 may also be realized.
However, as discussed below, such alternative positioning is likely
to subject the resulting piezoelectric sensor to errors during
performance due to structural offsets and variation of fabrication
processes.) As shown in FIG. 6, the hub 26 is connected to the ring
24 with spoke-like support structures 28 and 30. In this specific
embodiment, the body 20 is shown to be reflectionally symmetric
with respect to a normal 32 passing through a center of gravity G
of the body. However, such reflectional symmetry is not generally
required. The spokes 28 and 30 generally may be of any shape,
whether straight or curved, may be continuous, or may comprise
several pieces. It would be understood that reciprocating force
transferred to the ring 24 along the spokes 28 may generate a
vibrational in-plane oscillation of the ring (interchangeably
referred to herein as mode or resonating mode). For example,
periodic expansion and contraction of the ring forced by periodic
expansion and contraction of the spokes 28, operating
simultaneously along the x-axis, with the spokes 30 remaining idle,
will result in a substantially elliptical mode of the ring
oscillating along the x-axis. An out-of-phase addition of an
equivalent expansion and contraction of the spokes 30 to such
movements of the spokes 28 will extend the oscillation of the ring
to the y-axis as well, resulting in an oscillating mode possessing
a two-fold symmetry, as shown in FIG. 7A in top view. Here, a solid
line indicates the geometry of the ring 24 in its inactive state, a
dashed ellipse a corresponds to an extremal extension of the ring
along the x-axis, driven by the extension of the spokes 28 in the
x-axis and contraction of the spokes 30 in the y-axis of FIG. 6A,
and a dashed ellipse b illustrates an extremal extension of the
ring along the y-axis, driven by the extension of the spokes 30 in
the y-axis and contraction of the spokes 28 in the x-axis of FIG.
6A. In general, any reciprocating mechanical expansion and
contraction of the spokes 28 and 30 may be realized, according to
the embodiments of the invention, with the use of the piezoelectric
effect by applying an alternating electrostatic field to the
piezoelectric spokes 28 and 30 of the body 20.
[0039] As would be understood by a person skilled in the art, both
the deformation and the resulting oscillatory motion of
intermediate regions n, of the ring 24 of FIG. 6A, located between
the spoke-driven regions N (i.e., at substantially 45-degree angles
with respect to the x- and y-axes) are essentially out of phase
with respect to the deformation and the oscillatory motion of the
spoke-driven regions. The deformation of the spoke-driven regions N
would cause some deformation of the intermediate regions n whether
these intermediate regions are suspended, with respect to the hub
26 without any direct physical connection to the hub 26 or are
directly attached to it with another, intermediate set of
connectors (not shown in FIG. 6A). When such deformations of the
intermediate regions are periodic, they may be viewed as
oscillatory modes, schematically shown in FIG. 7B with arrows c and
d. Generally, the amplitude of deformation of the intermediate
regions may differ from that of the spoke-driven regions N. Such
deformation of the intermediate regions n will change, in the local
system of coordinates, should the body 20 be experiencing a
rotational motion. Therefore, certain embodiments of the current
invention utilize the change in oscillatory modes c and d of the
intermediate regions n of the ring for sensing a rotational motion,
experienced by the inertial sensor of the invention through
piezoelectric effect, as discussed below. In specific embodiments,
such sensing may be performed by sensors 29 connecting the hub 26
to the intermediate regions n of the ring 24 as shown in FIG.
6A.
[0040] FIG. 8 illustrates top and side views of a body 40 of a MEMS
embodiment of an exemplary inertial sensor system that possesses a
two-fold operational symmetry. Such inertial sensor may be a
gyroscope, an accelerometer, or another motion-sensing inertial
device. FIG. 8A shows detailed implementation of the embodiment of
FIG. 6A, in top view. The body 40 is made of piezoelectric material
such as, for example, aluminum nitride (AlN). Here, the
ring-resonator 24 is suspended with respect to the hub 26 of the
body 40 with a set of four spoke structures 42 and another set of
four spoke structures 56, each of which connects the hub and the
ring. All the spokes extend radially and outwardly with respect to
the hub and are disposed reflectionally symmetrically about a
symmetry axis 44, which is perpendicular to the body's top surface
46 and passes through the center of gravity G of the body. A set of
four transducers 50 discussed below may be integral with the
respective spokes 42 and, in combination with these spokes, may
form driving elements 52. Similarly, four sensing elements 54 are
symmetrically disposed in the areas intermediate to the driving
elements 52. Each of the sensing elements 54 comprises a spoke 56
and a transducer 58 that may be substantially equivalent to the
spoke 42 and transducer 50 of the driving elements 52.
[0041] Generally, an embodiment of a transducer of the invention
may be configured as a set of slabs or frames of piezoelectric
material sandwiched between appropriately structured pairs of
electrodes that are configured to either apply an electric field to
the material of the transducer or register the electrostatic charge
(accumulated on the opposite sides of the frames) and potential
(originating across the material). In some embodiments, the frames
of piezoelectric material comprising the transducer may be disposed
concentrically, as discussed below. When a periodically alternating
electric field is applied to the material of any transducer 50, the
transducer deforms, in oscillating fashion, and a corresponding
spoke 42 to which the transducer is connected. Consequently, the
regions of the ring 24 adjacent to the spokes 42 are spoke-driven
and periodically deformed, and the ring is engaged to oscillate in
a two-fold-symmetry resonating mode similar to that shown in FIGS.
7A and 7B. The intermediate regions of the ring, which are
connected to the hub 26 by the four sensing-element spokes 56,
transfer, in turn, such oscillating motion to the respective
sensing transducers 58 that register an electrostatic charge
accumulating at the opposite sides of the transducer material due
to the piezoelectric effect. If, in the process of
ring-oscillation, the body of the inertial sensor 40 is subjected
to a rotational motion, the Coriolis effect changes the modal shape
of the ring deformation in the local coordinate system associated
with the inertial sensor, and the sensing elements 54 register the
change in the electrostatic charge associated with the rotation. As
will be readily understood by a skilled artisan, both driving and
sensing elements of the embodiments of the present invention can be
structured substantially equivalently and, therefore, perform
either a driving or sensing role depending on the user's choice.
However, deliberate differences introduced between the embodiments
of a driving and sensing elements at user's discretion do not
affect the principle of operation of the embodiments and are within
the scope of the invention.
[0042] Configuration of transducers is further discussed with
reference to FIGS. 9 and 10, illustrating some exemplary
embodiments, with continuing reference to FIG. 8. Although the
transducer operation is described below with reference to the
driving transducers 50 of FIG. 8, the same description is equally
applicable to the sensing transducers 58. FIG. 9A shows, in top
view, a piezoelectric frame structure 60 of a transducer 50. As
shown, the piezoelectric frame structure is elongated along x-axis,
i.e. laterally with respect to a spoke 42 that connects the ring 24
of the gyroscope 40 to the hub 26. FIG. 9B offers a corresponding
side view. The structure 60 is characterized by a substantially
constant thickness t defined by the top and bottom substantially
flat surfaces 46 and 62 that are parallel to a reference plane (the
xy-plane in FIG. 9). Although the frame structure 60 is shown to
possess two-fold symmetry (about the yz- and xz-planes, each of
which is a plane of symmetry of the embodiment 60), it should be
appreciated that, in general, such symmetry is not required for
operation of the device. For example, an embodiment of a frame
structure may be configured to be symmetric only about a single
plane of symmetry of the structure. As shown in FIGS. 9A and 9B,
the frame structure 60 comprises a set of two frames--an outer
frame 64 and an inner frame 66--both of which have substantially
equal thicknesses t, are elongated along the x-axis, have a common
center O (i.e., are disposed concentrically with respect to the
center O), and are interconnected with piezoelectric bridges 68.
The frame configuration of FIGS. 9A and 9B may allow for a
selective and independent deformation in the xy-plane of at least
some portions of the frames 64 and 66. An example of such
deformation may be bending of at least a portion of a frame,
induced by the piezoelectric effect. As will be understood from the
following discussion, the bridges 68 facilitate flexing of the
frames. In an alternative embodiment, a frame structure may be
configured without at least some of gaps 70 between the frames, or
contain more than two frames. Neither variation, however, changes
the principle of operation of the device. An embodiment of the
frame structure such as the structure 60 of FIG. 9 is generally
fabricated from a piezoelectric material, for example AlN, with
conventional micromachining and lithographic methods used in
semiconductor industry such as, for example, reactive-ion etch
(RIE) or electron-beam milling. The use of conventional methods of
fabrication lends the resulting device to production on a mass,
cost-effective scale that is compatible with Si-integration
technologies. To complete the fabrication of a transducer, either
frames, or bridges, or both may contain through-hole vias for
appropriately providing electrical interconnections among the sets
of electrodes that are further deposited on the frame structure, as
shown in FIG. 10.
[0043] To utilize the piezoelectric principle of operation of the
transducer, two substantially equivalent sets of electrodes--a set
of top electrodes and a corresponding set of bottom electrodes,
each set including at least two electrodes--may be configured
opposite to one another on the top and bottom surfaces of the frame
structure, respectively, so as to facilitate the application of
electric field to the frame structure. Referring now to FIGS. 9 and
10, FIG. 10 displays an embodiment 80 of a transducer having a
two-frame structure 60 of FIG. 9. The embodiment 80 has a set of
two top electrodes 82 and 84, deposited on the top surface 46 of
the frame structure, and a corresponding set of two bottom
electrodes 82' and 84' (not shown) deposited on a bottom surface
62. Each of the top electrodes (and, respectively, each of the
bottom electrodes) is configured along a particular path that is
symmetric with respect to at least one plane of symmetry of the
frame structure and includes portions of both the frames 64 and 66
of FIG. 9A. It should be noted that in embodiments comprising more
than two frames, each of the electrode paths may be configured to
access at least two frames. To pass from one frame of the structure
to another, a corresponding electrode is configured to cross one of
the bridges 68 either along a corresponding surface (top or bottom)
of the frame structure or through a via created in that bridge. For
example, as shown in insert I of FIG. 10, the top electrode 84 may
be deposited over a central portion of a bridge 68 while the top
electrode 82 maintains its continuity through a via (not shown) in
the bridge 68. Both of the top electrodes are configured to at
least partially overlap with the top surface of the bridge 68,
keeping, at the same time, portions f of the bridge exposed. The
corresponding bottom electrodes are configured substantially
equivalently. The bridges of the transducer that are crossed by the
paths of electrodes generally define one central and several
peripheral transducing sections. Each of the transducing sections
may include one or more elements connecting the frames, such
elements not covered with electrodes. Such optional connecting
elements, which are shown in FIG. 9A as elements 69, are mainly
used for stiffening of the frame structure. Overall, the embodiment
60 of FIG. 9A comprises four bridges 68 and eight connecting
elements 69. Although, as shown in FIG. 10, regions L and M of the
transducer 80 (L being the outer region and M being the inner
region with respect to the hub 26) are characterized by three
sections--central section A and two peripheral sections B and
C--more than two peripheral sections may be formed at the user's
discretion. The electrodes may be fabricated of platinum (Pt) or
any other suitable material using appropriate lithographic methods
known in the art.
[0044] It should be appreciated that a transducer of the invention
can operate as part of either a driving element, generating an
in-plane mode of oscillation of the ring of the inertial sensor as
discussed above in reference to FIG. 7, or as part of a sensing
element. The operation of a driving transducer of the invention is
further discussed in reference to FIGS. 11 and 12, with continuing
reference to FIG. 10. FIGS. 11A and 11B schematically illustrate,
in side views, a cross-section of a portion of the frame of the
embodiment 80 of FIG. 10 with a an electric potential of cyclically
alternating polarity applied between the top electrode and the
corresponding bottom electrode (in this example, the electrodes 82
and 82') that sandwich the frame comprised of the piezoelectric
material. The instantaneous electrostatic field, associated with
the potential difference applied between the electrodes, is denoted
as E. It should be appreciated that, to enhance the driving
operation of the transducer 80, the polarity of a potential applied
to another electrode pair (84, 84') may be varied out-of-phase with
that applied to electrodes 82 and 82'.
[0045] To configure the transducer 80 as a driving transducer, in
the first half of the cycle, the polarity of electric field E
provided between the electrodes 82 and 82' may be chosen, for
example, to expand the piezoelectric material sandwiched between
the electrodes, as shown in FIG. 11A. At the same time, the
polarity of a non-zero field between the electrodes 84 and 84' may
be chosen to be out of phase with E to contract the corresponding
material. (Alternatively, no field may be applied between the
electrodes 84 and 84', in which case the portion of the material
sandwiched by these electrodes does not experience any externally
caused mechanical stress.) A cumulative piezoelectric effect
produced by the fields affecting the corresponding portions of the
frame structure as described will result in effective bowing of the
sections A, B, and C (in both the outer region L and the inner
region M of the transducer 80 of FIG. 10) outwardly with respect to
the center point O of the frame structure. In this deformation, the
bridges 68 connect sections B and A and sections C and A, so as to
effectively add the deformations of the sections B and C to the
deformation of the section A. Deformations of the sections
generally may be substantially equal and, when added together,
increase the overall outward/inward deformation. Consequently, the
amplitude of the deformation of the central section A is generally
higher than those of the peripheral sections. FIG. 12A illustrates
the described deformation of the frame structure of the transducer
80 that pushes a portion of the spoke 42 and, therefore, a rigidly
attached portion of the ring 24, outwards and away from the hub.
For the purposes of comparison, a neutral position and geometry
(i.e., the geometry corresponding to no field applied) of the frame
structure of the transducer is indicated with a dashed line.
[0046] In the second half of the cycle, the polarities of the
fields between the pairs of electrodes (82, 82') and (84, 84')
reverse, as shown in FIG. 11B for the pair of electrodes 82 and
82', and the frame structure of the transducer consequently bows
inward with respect to the center point O, as shown in FIG. 12B. As
a result, the bowing frame structure pulls the portion of the ring
24, to which it is attached by the spoke 42, towards the hub 26.
Accordingly, the appropriate periodic cycling through the change of
polarity of the potentials, applied out-of-phase to the
corresponding pairs of the top and the bottom electrodes of the
transducer 80, results in generating an in-plane oscillating mode,
of the ring 24 of the inertial sensor 40 of FIG. 8, similar to that
shown in FIGS. 7A and 7B. It would be understood, however, that the
out-of-phase application of the field (and, therefore, a potential
differential) between both abovementioned pairs of electrodes is
not generally required for the operation of the device. In a
related specific embodiment, for example, the ring 24 may be driven
by a potential reversal between only one pair of the
electrodes--either (82, 82') or (84, 84').
[0047] As would be understood by one skilled in the art, the same
transducer in an embodiment of the inertial sensor may operate as a
sensing transducer. Such sensing performance may be realized when a
difference of potentials between the electrodes of the transducer
(such as electrodes 82, 82' or 84, 84' of the embodiment 80 of FIG.
10) is piezoelectrically generated in response to the expansion and
contraction of the transducer's frame structure compelled by the
in-plane oscillation (indicated as a and b in FIGS. 7A and 7B) of
the ring 24. According to one embodiment of the invention, the user
has discretion to decide which transducers of the plurality of the
transducers of an embodiment will be assigned driving or sensing
functions. For example, as shown in FIG. 8, the transducers 50
operate as parts of the corresponding driving elements 52 of the
sensor 40, while the transducers 58 operate as parts of the
corresponding sensing elements 54 that are interleaved with or
disposed alternately and regularly between the driving elements 52.
The user may, for example, simply reverse the role of the
transducers or re-assign some of the transducers to function as
driving or sensing elements as desired for a particular
application. Although positional interleaving and regularity of the
driving and sensing elements of an embodiments of the inertial
sensor may increase the isotropy and sensitivity of sensing the
motion of a device comprising such embodiment (e.g., the rotational
motion of a MEMS-based gyroscope), such disposition of the driving
and sensing elements is not generally required for operation of the
embodiments of the inertial sensor of the invention.
[0048] It should be also appreciated that normal variations in
fabrication processes may result in certain deviations of both the
structure and uniformity of the embodiments of invention such as,
for example, the degree of circularity of the ring or the
uniformity of dimensions throughout the frames. As a result, such
characteristics of the transducer as mass, geometry, and
lever-stiffness may deviate from the expected. If not compensated,
such deviations may affect the nature and changes of the
ring-oscillation mode and lead to erroneous measurement of the
motion of the inertial sensor. To provide for active balancing and
compensation of manufacturing defects as well as operational
self-calibration of the inertial sensor embodiments, some
embodiments may include additional compensating elements designated
as 90 in the example of the sensor 40 of FIGS. 8. The compensating
elements 90 may be configured as metal-piezoelectric-metal layered
structures and be electrostatically coupled with the ring 24
through the capacitive gaps between the elements 90 and the ring,
may be concentric with the ring, and may be fabricated in a fashion
similar to that of the transducers of the invention. It should be
understood that, by applying a voltage differential to the
compensating elements 90 with respect to the ring, the compensating
elements may be used to effectively modify a spring constant of the
ring 24, for example, to adjust the resonant frequency of or change
the mode of oscillation of the ring. Alternatively, the
compensators 90 may also be used to equalize resonant frequencies
of the drivers 50 and the sensors 58. In a specific embodiment, the
sensitivity of the inertial sensor device 40 of FIG. 8 may be
enhanced by interleaving the compensating elements 90 with the
drivers 50 and the sensors 58 so as to preserve the symmetry of the
device. In general, however, different patterns of disposing the
compensating elements among the driving and the sensing elements of
an embodiment do not change the principle of operation of the
embodiment and are within the scope of the invention. It will be
also understood that the described principle of using compensating
elements, which allow for adjustment of the resonant frequency of
the inertial sensor that has a ring resonator, may be equally
applied to any other type of a resonator, such as a linear
resonator or a resonator generally shaped as a frame.
[0049] As described, embodiments of the invention employ
piezoelectric drivers and/or sensors that are mechanically (as
opposed to electrostatically) coupled to the resonating mass for
respectively driving or sensing the movement of the mass. The
piezoelectric principle of operation provides the inertial sensors
of the invention with important advantages. First, lateral
capacitive coupling to the fixed structural elements of the
capacitive-type ring-gyroscopes of prior art is essentially
eliminated, and the interaction with the substrate is mechanical
and through the anchors. Additionally, the errors, introduced to
the performance of the sensor by thermal and external-packaging
stresses through unaccounted variations in capacitive gaps, are
essentially eliminated. Also, the damping effect is substantially
reduced, so a higher quality-factor (Q) can be achieved. Moreover,
elimination of the capacitive air-gap also increases tolerance of
the ring gyroscope to external vibrations.
[0050] As is known in the art, MEMS-based embodiments of inertial
sensors are often susceptible to offsets arising from stresses in
the chip due to thermal variations or assembly processes. To reduce
such offsets, the support of the body 40 of FIG. 8 (or any other
embodiment of the invention) above the underlying substrate may be
arranged by affixing, within an inner periphery of the body, a
single anchor or multiple anchors 92 (not shown in side view)
positioned closely together and near the center of mass of the body
40. Such an exemplary solution was previously disclosed in a
commonly assigned U.S. Pat. No. 6,892,576, which is incorporated
herein in its entirety by reference. Positioning of the body of the
inertial sensor of the invention with respect to the substrate may
vary and includes, for example, the affixation of the body above a
leveled substrate, as shown in FIG. 14A, or within a recess of a
substrate, as shown in FIG. 14B.
[0051] The embodiments of the invention described above are
intended to be merely exemplary; numerous variations and
modifications will be apparent to those skilled in the art based on
the teachings of this disclosure. Piezoelectric drivers and/or
sensors of the type described above (e.g., with reference to FIGS.
6,8-10,13) can be used in other types of inertial sensors and are
not limited to ring gyroscopes. For example, piezoelectric
transducers of the invention may be used in linearly resonating
MEMS-based structures such as linear resonator gyroscopes. Although
the operation of the inertial sensor of the invention was described
in reference to an embodiment of FIG. 8 containing four driving
elements 52 and four sensing elements 54, it should be understood
that there is no theoretical limitation on the number of driving
and sensing elements or a particular fashion in which the driving
elements operate. For example, in reference to FIG. 8, the ring 24
of the inertial sensor may be driven by the four driving elements
52 that are paired (thus forming one pair of driving elements
operating along the x-axis and another pair of driving elements
operating along the y-axis) to generate a fundamental mode of
in-plane oscillation similar to that of FIG. 7A or FIG. 7B, where
the driving elements that are disposed parallel to the x-axis
operate with a 180-degree phase shift with respect to the driving
elements disposed parallel to the y-axis. The driving elements of
the embodiments of the inertial sensor may be generally caused to
operate in any desired order with any desired phase shift to put a
resonator of the sensor into a mode of oscillation a change to
which, produced by the movement of the sensor, may be detected
using the piezoelectric effect as discussed. Furthermore, it should
be appreciated that a particular degree of symmetry of an
embodiment of the invention is not generally required, and that the
regularity of form or arrangement in terms of like, reciprocal, or
corresponding parts of the embodiments can be chosen as desired for
a particular application. For example, a ring embodiment of a
transducer of the invention may possess an odd-number operational
symmetry, such as an embodiment 110 of FIG. 13, illustrating a
variation of a ring-gyroscope with a three-fold symmetry determined
by the six driving elements 50, six corresponding sensing elements
58, and twelve compensating elements 90. Electrical circuitry
between the transducers and compensating elements of an embodiment
and the substrate may be generally established through the anchors
92 via conductors 94 that are deposited on the top or bottom
surfaces of the hub, for example, or through vias in the body of
the inertial sensor so as to connect the electrodes of the
transducers and compensating elements with the anchors 92.
[0052] While exemplary embodiments using two-fold and three-fold
oscillation modes are described above, it should be noted that
various alternative embodiments may use four-fold, five-fold, and
higher oscillation modes with appropriate numbers of driving
elements and sensing elements. FIG. 15 depicts a four-fold
oscillation mode in accordance with an exemplary embodiment of the
invention, which may employ, for example, eight driving elements
arranged at 45 degree intervals and eight sensing elements
interspersed between the driving elements. The oscillation modes
are depicted as curve e (i.e., the solid curve) and curve f (i.e.,
the dashed curve) in FIG. 15. It will be apparent to the skilled
artisan, based on the teachings of this disclosure, how driving
elements and sensing elements may be arranged for this and other
oscillation modes.
[0053] Additionally, the distribution of driving and sensing roles
among the transducers (which are capable of performing in either
role, as discussed above) as well as activation of the compensating
elements in a particular embodiment may be, for example,
pre-programmed and controlled with a processor. In this case, the
computer may automatically adjust the performance of a transducer
of the invention in response to a feedback signal provided by the
compensating elements.
[0054] The embodiments of the invention described above are
intended to be merely exemplary; numerous variations and
modifications will be apparent to those skilled in the art. All
such variations and modifications are intended to be within the
scope of the present invention as defined in any appended
claims.
* * * * *
References