U.S. patent application number 14/924085 was filed with the patent office on 2016-12-01 for micromachined resonating beam gyroscopes.
The applicant listed for this patent is Analog Devices, Inc.. Invention is credited to Sunil Ashok Bhave, Eugene Oh Hwang.
Application Number | 20160349053 14/924085 |
Document ID | / |
Family ID | 57398350 |
Filed Date | 2016-12-01 |
United States Patent
Application |
20160349053 |
Kind Code |
A1 |
Hwang; Eugene Oh ; et
al. |
December 1, 2016 |
Micromachined Resonating Beam Gyroscopes
Abstract
A single-axis resonating beam gyroscope uses a special
arrangement of support tethers that maximizes the Q (quality
factor) and minimizes stress sensitivity. The tethers are located
at the nodal points of the beam with respect to a predetermined
drive mode and are approximately one-fourth the length of the beam.
Also, the tethers do not extend above or through the nodal points
of the beam, which would be difficult to produce in typical MEMS
fabrication processes. Embodiments typically use electrostatic
drive and sense transduction. Trim electrodes may be used to
compensate for any erroneous modal coupling.
Inventors: |
Hwang; Eugene Oh; (Melrose,
MA) ; Bhave; Sunil Ashok; (West Lafayette,
IN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Analog Devices, Inc. |
Norwood |
MA |
US |
|
|
Family ID: |
57398350 |
Appl. No.: |
14/924085 |
Filed: |
October 27, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62169547 |
Jun 1, 2015 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01C 19/5656 20130101;
G01C 19/5649 20130101 |
International
Class: |
G01C 19/5656 20060101
G01C019/5656 |
Claims
1. A resonating beam gyroscope comprising: a rectangular beam
arranged along a longitudinal axis in a device plane, the
rectangular beam having a plurality of nodal points on both sides
of the beam in the device plane with respect to a fundamental or
higher order flexural drive mode, said nodal points being remote
from the ends of said beam such that said beam includes a tail
portion at each end of said beam; a set of tethers in the device
plane, each tether coupled to the beam at a distinct nodal point,
wherein a top edge of each tether is at or below a top edge of the
beam ; a set of drive electrodes configured for driving the beam to
resonate in the drive mode; and a set of sense electrodes
configured for sensing deflections of the beam caused by rotation
of the gyroscope about the longitudinal axis.
2. A gyroscope according to claim 1, wherein the drive mode is
out-of-plane and the deflections are in-plane.
3. A gyroscope according to claim 1, wherein the drive mode is
in-plane and the deflections are out-of-plane.
4. A gyroscope according to claim 1, wherein the relative length of
the tail portions are characterized by a node ratio of the beam
Lnode/L approximately equal to X/(2*(X+1)), where Lnode is the
length from the center of the beam to a nodal point, L is the total
length of the beam, and X is the order of the flexural drive mode
for the beam.
5. A gyroscope according to claim 1, wherein the tethers are
configured to maximize a quality factor of the beam.
6. A gyroscope according to claim 1, wherein the electrodes are
electrostatically coupled with the beam.
7. A gyroscope according to claim 1, further comprising: a first
set of variable-overlap trim electrodes; and a second set of
variable-overlap trim electrodes opposing the first set of
variable-overlap trim electrodes, wherein the first and second sets
of variable-overlap trim electrodes are configured to produce
forces in the direction of such deflections to compensate for
erroneous beam deflections in the direction of such
deflections.
8. A gyroscope according to claim 1, wherein the erroneous beam
deflections are in proportion to resonation of the beam in the
drive mode.
9. A method of operating a resonating beam gyroscope, the method
comprising: driving a rectangular beam to resonate in a fundamental
or higher order flexural drive mode, the beam arranged along a
longitudinal axis in a device plane, the beam supported by a set of
tethers coupled to the beam at nodal points on both sides of the
beam in the device plane with respect to the fundamental or higher
order flexural drive mode, said nodal points being remote from the
ends of said beam such that said beam includes a tail portion at
each end of said beam, wherein a top edge of each tether is at or
below a top edge of the beam; and sensing deflections of the beam
caused by rotation of the gyroscope about the longitudinal
axis.
10. A method according to claim 9, wherein the drive mode is
out-of-plane and the deflections are in-plane.
11. A method according to claim 9, wherein the drive mode is
in-plane and the deflections are out-of-plane.
12. A method according to claim 9, wherein the relative length of
the tail portions are characterized by a node ratio of the beam
Lnode/L approximately equal to X/(2*(X+1)), where Lnode is the
length from the center of the beam to a nodal point, L is the total
length of the beam, and X is the order of the flexural drive mode
for the beam.
13. A method according to claim 9, further comprising: providing
compensation signals to sets of variable-overlap trim electrodes to
produce forces in the direction of such deflections to compensate
for erroneous beam deflections in the direction of such
deflections.
14. A method according to claim 13, wherein providing compensation
signals to sets of variable-overlap trim electrodes comprises:
providing compensation signals to a first set of trim electrodes
including at least one electrode placed along a center portion on
one side of the beam and at least one electrode placed along each
tail section on the other side of the beam; and providing
compensation signals to a second set of trim electrodes opposing
the first set of trim electrodes, wherein the trim electrodes
variably overlap the beam with respect to a direction of such
deflections and are configured to produce forces in the direction
of such deflections to compensate for erroneous beam deflections in
the direction of such deflections.
15. A gyroscope comprising: a resonator means including a
rectangular beam arranged along a longitudinal axis in a device
plane and a set of tethers coupled to the beam at nodal points on
both sides of the beam in the device plane with respect to a
fundamental or higher order flexural drive mode, said nodal points
being remote from the ends of said beam such that said beam
includes a tail portion at each end of said beam, wherein a top
edge of each tether is at or below a top edge of the beam; means
for driving the beam to resonate in the drive mode; and means for
sensing deflections of the beam caused by rotation of the gyroscope
about the longitudinal axis.
16. A gyroscope according to claim 15, wherein the drive mode is
out-of-plane and the deflections are in-plane.
17. A gyroscope according to claim 15, wherein the drive mode is
in-plane and the deflections are out-of-plane.
18. A gyroscope according to claim 15, wherein the relative length
of the tail portions are characterized by a node ratio of the beam
Lnode/L approximately equal to X/(2*(X+1)), where Lnode is the
length from the center of the beam to a nodal point, L is the total
length of the beam, and X is the order of the flexural drive mode
for the beam.
19. A gyroscope according to claim 15, wherein the tethers are
configured to maximize a quality factor of the beam.
20. A gyroscope according to claim 15, further comprising: means
for providing compensation signals to sets of variable-overlap trim
electrodes to produce forces in the direction of such deflections
to compensate for erroneous beam deflections in the direction of
such deflections.
Description
CROSS-REFERENCE TO RELATED APPLICATION(S)
[0001] This patent application claims the benefit of U.S.
Provisional Patent Application No. 62/169,547 entitled
MICROMACHINED GYROSCOPES filed on Jun. 1, 2015, which is hereby
incorporated herein by reference in its entirety.
[0002] The subject matter of this patent application may be related
to the subject matter of commonly-owned U.S. patent application
Ser. No. ______ entitled MICROMACHINED CROSS-HATCH VIBRATORY
GYROSCOPES filed on even date herewith, which is hereby
incorporated herein by reference in its entirety.
FIELD OF THE INVENTION
[0003] The present invention relates generally to micromachined
gyroscopes.
BACKGROUND OF THE INVENTION
[0004] Micromachined (MEMS) gyroscopes have become established as
useful commercial items. Generally speaking, a MEMS gyroscope
incorporates two high-performing MEMS devices, specifically a
self-tuned resonator in the drive axis and a micro-acceleration
sensor in the sensing axis. Gyroscope performance is very sensitive
to such things as manufacturing variations, errors in packaging,
driving, linear acceleration, and temperature, among other things.
Basic principles of operation of angular-rate sensing gyroscopes
are well understood and described in the prior art.
[0005] The principles of vibratory sensing angular rate gyroscopes
with discrete masses are long-established. Generally speaking, a
vibratory rate gyroscope works by oscillating a proof mass (also
referred to herein as a "shuttle" or "resonator"). The oscillation
is generated with a periodic force applied to a spring-mass-damper
system at the resonant frequency. Operating at resonance allows the
oscillation amplitude to be large relative to the force applied.
When the gyroscope is rotated, Coriolis acceleration is generated
on the oscillating proof mass in a direction orthogonal to both the
driven oscillation and the rotation. The magnitude of Coriolis
acceleration is proportional to both the velocity of the
oscillating proof mass and the rotation rate. The resulting
Coriolis acceleration can be measured by sensing the deflections of
the proof mass. The electrical and mechanical structures used to
sense such deflections of the proof mass are referred to generally
as the accelerometer.
SUMMARY OF EXEMPLARY EMBODIMENTS
[0006] In certain embodiments there is provided a vibrating beam
gyroscope comprising a rectangular beam arranged along a
longitudinal axis in a device plane, the rectangular beam having a
plurality of nodal points on both sides of the beam in the device
plane with respect to a fundamental or higher order flexural drive
mode, said nodal points being remote from the ends of said beam
such that said beam includes a tail portion at each end of said
beam; a set of tethers in the device plane, each tether coupled to
the beam at a distinct nodal point, wherein a top edge of each
tether is at or below a top edge of the beam; a set of drive
electrodes configured for driving the beam to resonate in the drive
mode; and a set of sense electrodes configured for sensing
deflections of the beam caused by rotation of the gyroscope about
the longitudinal axis.
[0007] In certain other embodiments there is provided a method of
operating a resonating beam gyroscope, comprising driving for
driving a rectangular beam to resonate in a fundamental or higher
order flexural drive mode, the beam arranged along a longitudinal
axis in a device plane, the beam supported by a set of tethers
coupled to the beam at nodal points on both sides of the beam in
the device plane with respect to the fundamental or higher order
flexural drive mode, said nodal points being remote from the ends
of said beam such that said beam includes a tail portion at each
end of said beam, wherein a top edge of each tether is at or below
a top edge of the beam; and sensing deflections of the beam caused
by rotation of the gyroscope about the longitudinal axis.
[0008] In certain other embodiments there is provided a gyroscope
comprising a resonator means including a rectangular beam arranged
along a longitudinal axis in a device plane and a set of tethers
coupled to the beam at nodal points on both sides of the beam in
the device plane with respect to a fundamental or higher order
flexural drive mode, said nodal points being remote from the ends
of said beam such that said beam includes a tail portion at each
end of said beam, wherein a top edge of each tether is at or below
a top edge of the beam; means for driving the beam to resonate in
the drive mode; and means for sensing deflections of the beam
caused by rotation of the gyroscope about the longitudinal axis. In
various alternative embodiments, the drive mode may be out-of-plane
and the deflections may be in-plane, or the drive mode may be
in-plane and the deflections may be out-of-plane. The relative
length of the tail portions may be characterized by a node ratio of
the beam Lnode/L approximately equal to X/(2*(X+1)), where Lnode is
the length from the center of the beam to a nodal point, L is the
total length of the beam, and X is the order of the flexural drive
mode for the beam. Devices may be fabricated such that the tethers
are configured to maximize a quality factor of the beam. The
electrodes may be electrostatically coupled with the beam.
[0009] In any of the above-described embodiments, modal coupling
may be mitigated by providing compensation signals to sets of
variable-overlap trim electrodes to produce forces that reduce
erroneous beam deflections. For example, the sets of
variable-overlap trim electrodes may include a first set of trim
electrodes including at least one electrode placed along a center
portion on one side of the beam and at least one electrode placed
along each tail section on the other side of the beam, and a second
set of trim electrodes opposing the first set of trim electrodes,
wherein the trim electrodes variably overlap the beam with respect
to a direction of such deflections and are configured to produce
forces in the direction of such deflections to compensate for
erroneous beam deflections in the direction of such deflections.
The erroneous beam deflections may be in proportion to resonation
of the beam in the drive mode.
[0010] Additional embodiments may be disclosed and claimed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The foregoing features of embodiments will be more readily
understood by reference to the following detailed description,
taken with reference to the accompanying drawings, in which:
[0012] FIG. 1 is a schematic diagram showing a top view of the
resonator and support tethers for a single-axis resonating beam
gyroscope, in accordance with certain exemplary embodiments;
[0013] FIG. 2 is a schematic diagram showing conceptual components
of a resonant beam of the resonator shown in FIG. 1, in accordance
with exemplary embodiments of the invention;
[0014] FIG. 3 is a schematic diagram depicting two parameters for
determining the node ratio of a resonant beam, in accordance with
one exemplary embodiment;
[0015] FIG. 4 schematically shows a first possible drive mode and
corresponding sense mode for a single-axis gyroscope of the type
shown in FIG. 1, in accordance with one exemplary embodiment;
[0016] FIG. 5 schematically shows one possible arrangement of drive
and sense electrodes to support the mode shapes shown in FIG. 4, in
accordance with one exemplary embodiment;
[0017] FIG. 6 is a schematic diagram for an exemplary gyroscope
drive and sense circuit for the gyroscope arrangement shown in FIG.
5, in accordance with one exemplary embodiment;
[0018] FIG. 7 schematically shows a set of optional electrodes
placed adjacent to the tail ends of the beam for driving, sensing,
or adjusting motion of the beam, in accordance with one exemplary
embodiment; and
[0019] FIG. 8 is a schematic diagram showing an arrangement of
split electrodes for reducing modal coupling, in accordance with
one exemplary embodiment.
[0020] It should be noted that the foregoing figures and the
elements depicted therein are not necessarily drawn to consistent
scale or to any scale. Unless the context otherwise suggests, like
elements are indicated by like numerals.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
[0021] In embodiments of the present invention, a single-axis
resonating beam gyroscope uses a special arrangement of support
tethers that maximizes the Q (quality factor) while limiting stress
sensitivity.
[0022] For purposes of the following description and the
accompanying claims, a "set" includes one or more members, the
"mode" of a resonating body is the shape of motion of the body at
resonance, the term "anti-phase" with respect to the resonant modes
(i.e., displacement) of two resonating bodies means that the
resonating bodies resonate with the same mode shape but 180 degrees
out-of-phase, the term "in-plane" with respect to a resonant mode
means resonance predominately in the plane of the resonator
structure(s), the term "out-of-plane" with respect to a resonant
mode means resonance predominately normal to the plane of the
resonator structure(s), a "node" or "nodal point" with respect to a
resonating body is a point or area of the resonant motion having
zero or near zero displacement, an "anti-node" with respect to a
resonating body is a point or area of the resonant motion having
the largest displacement, and an "electrode" is a structure through
which an electrical or electromechanical effect is applied and/or
sensed. In exemplary embodiments, various electrodes are used for
driving resonators into their targeted mode shape at the designed
frequency and/or sensing electrical or electromechanical effects
through capacitive coupling (e.g., between a resonator mass and one
or more adjacent structures), although it should be noted that
other types of electrodes and couplings may be used (e.g.,
piezoelectric). Thus, in exemplary embodiments, electrodes may
include a resonator mass and one or more structures for driving
and/or sensing movement of the resonator mass.
[0023] FIG. 1 is a schematic diagram showing a top view of the
resonator and support tethers for a single-axis resonating beam
gyroscope 100, in accordance with certain exemplary embodiments.
Among other things, the gyroscope 100 includes a single resonant
beam 102 supported at its nodal points with respect to a
predetermined resonant mode by four thin tethers 104 that allow the
beam 102 to freely resonate both in-plane and out-of-plane. The
tethers 104 are anchored to an underlying substrate and suspend the
beam 102 above the substrate so that the beam 102 is free to
resonate both in-plane and out-of-plane. For sensing rotations
about the axis of sensitivity "a", the gyroscope 100 may be
configured such that beam 102 is driven to resonate out-of-plane by
a set of drive electrodes (discussed below) and to deflect in-plane
when the gyroscope is rotated about the axis of sensitivity a,
where such deflections can be sensed by a set of sense electrodes
(discussed below). Alternatively, the gyroscope 100 may be
configured such that the beam 102 is driven to resonate in-plane
and to deflect out-of-plane when the gyroscope is rotated about the
axis of sensitivity "a".
[0024] Importantly, the tethers 104 do not extend above or through
the nodal points of the beam 102 (i.e., the top edge of the tethers
is at or below the top edge of the beam), which, among other
things, facilitates fabrication of the accelerometer compared to
support structures that extend above and/or through the beam. The
tethers 104 preferably are configured to maximize the Q (quality
factor) of the resonating beam. Generally speaking, the tethers are
as thin as possible (e.g., approximately 5 um in one exemplary
embodiment) and the length of the tethers depends at least
partially on the dimensions of the beam (e.g., approximately 30 um
length in one exemplary embodiment having a beam that is 450 um in
length and 50 um in height and width). The beam 102 and the tethers
104 may be formed from a unitary layer of material.
[0025] FIG. 2 is a schematic diagram showing conceptual components
of the resonant beam 102, in accordance with exemplary embodiments
of the invention. The beam's attachment to the tethers 104 on
opposite sides of the beam 102 at locations 204 and 208
conceptually divides the resonant beam 102 into a central section
206 and two tail sections 202 and 210. The locations 204 and 208
are preferably at nodal points of the resonant beam with respect to
both the drive mode shape and the sense mode shape of the resonant
beam for the resonant mode in which the resonator 100 is configured
to operate.
[0026] It is important to note that the tail sections of each beam
202 and 210 are very important for allowing the drive mode shape
and the sense mode shape to be carefully configured. In this
respect, the resonant beam 102 can be characterized by a node
ratio, which is a parameter quantifying how long the tail portion
is relative to the length of the beam. FIG. 3 is a schematic
diagram depicting two parameters, Lnode and L, for determining the
node ratio of a resonant beam 102, in accordance with one exemplary
embodiment, where Lnode is the length of the portion of the
resonant beam 102 from the center point to the nominal nodal point,
L is the length of the resonant beam 102, and the node
ratio=Lnode/L. In exemplary embodiments, the target node ratio can
be approximated by node ratio=Lnode/L=X/(2*(X+1)), where X is the
order of the flexural mode for the beam. For example, the Lnode/L
target node ratio for a fundamental (first order) flexural mode is
approximately 1/4=0.25 (actually 0.275 in certain specific
exemplary embodiments, the Lnode/L target node ratio for a second
order flexural mode is approximately 2/6=0.33, etc. Of course, an
alternative node ratio value could be based on the length of the
tail portion (e.g., Ltail=L-Lnode, alternative node
ratio=Ltail/L).
[0027] FIG. 4 schematically shows a first possible drive mode and
corresponding sense mode for a single-axis gyroscope of the type
shown in FIG. 1. In this exemplary embodiment, the beam 102 is
driven in an out-of-plane fundamental (first harmonic) flexural
resonant mode, as depicted in FIG. 4(A), and the beam 102 deflects
in-plane in a fundamental (first harmonic) flexural mode due to
Coriolis forces when the gyroscope is rotated about the axis of
sensitivity a, as depicted in FIG. 4(B). The tethers 104 are
located at the nodal points of the beam 102 with respect to the
drive and sense modes.
[0028] Furthermore, typical embodiments of the gyroscope shown in
FIG. 1 use electrostatic drive and sense transduction, as opposed
to piezoelectric transduction.
[0029] FIG. 5 schematically shows a first possible arrangement of
electrostatic drive and sense electrodes to support the drive and
sense mode shapes shown in FIG. 4. Here, the beam 102 is flanked by
two in-plane sense electrodes S102a and S102b, one on each side of
the central section, while a single out-of-plane drive electrode
D102 is underlying the beam 102. The electrodes are typically
placed at the anti-nodes of the respective mode shapes. The drive
electrode D102 is shown with broken lines to indicate that it is
underlying the beam 102, e.g., on a substrate underlying the beam
102.
[0030] During operation of the gyroscope, an alternating drive
signal is applied to the drive electrode D102 to cause the beam 102
to resonate out-of-plane. In this exemplary embodiment, a
differential gyroscope output signal is produced from the sense
electrodes S102a and S102b [i.e., Output=S102a-S102b].
Conceptually, when there is no rotation about the axis of
sensitivity, the beam 102 will be equidistant from both sense
electrodes and therefore the capacitances between each of the sense
electrodes and the beam 102 will be the same and hence the
differential gyroscope output will be zero. However, when there is
rotation about the axis of sensitivity causing the beam to deflect
in-plane, the beam 102 will move closer to one sense electrode
while moving further from the other sense electrode and therefore
the capacitances between each of the sense electrodes and the beam
102 will be different and hence the differential gyroscope output
will be non-zero and in proportion to the rate of rotation.
[0031] FIG. 6 is a schematic diagram for an exemplary gyroscope
drive and sense circuit 600 for the gyroscope arrangement shown in
FIG. 5. Among other things, the gyroscope drive and sense circuit
600 includes a drive circuit 602 and a sense circuit 604. The drive
circuit 602 provides alternating drive signals to the drive
electrode 102 at a nominal drive frequency fo. The sense circuit
604 receives the differential sense signals from the opposing sense
electrodes S104a and S104b and demodulates the signals at the drive
frequency fo and combines the demodulated signals differentially to
produce the output signal.
[0032] In the exemplary embodiment described above with reference
to FIGS. 4 and 5, the gyroscope is configured to operate with an
out-of-plane drive mode and an in-plane sense mode, although it
should be noted that in various alternative embodiments, the
gyroscope may be configured to operate with an in-plane drive mode
and an out-of-plane sense mode. Thus, for example, the gyroscope
100 could be configured to operate with an out-of-plane drive mode
depicted in FIG. 4(B) and an in-plane sense mode depicted in FIG.
4(A).
[0033] In the exemplary embodiment described above with reference
to FIGS. 4 and 5, the gyroscope is configured to operate in its
fundamental (first harmonic) mode, although it should be noted that
in various alternative embodiments, the gyroscope may be configured
to operate in a higher-order mode. When a higher-order mode is
used, additional tethers may be placed at the additional nodal
points.
[0034] It also should be noted that electrodes additionally or
alternatively may be placed adjacent to the tail ends of the beams
in-plane and/or out-of-plane, e.g., to drive, sense, and/or adjust
motion of the beam 102. FIG. 7 schematically shows an alternate
arrangement of electrodes including a set of optional electrodes
placed adjacent to the tail ends of the beam for driving, sensing,
or adjusting motion of the beam including both in-plane and
out-of-plane electrodes. Here, compared to the arrangement of
electrostatic drive and sense electrodes shown in FIG. 5, the beam
102 is flanked by additional in-plane sense electrodes S112a and
S112b on opposite sides of the tail ends, and additional
out-of-plane drive electrodes D102b are underlying the tail ends.
The additional drive electrodes D102b are shown with broken lines
to indicate that they are underlying the beam 102, e.g., on a
substrate underlying the beam 102.
[0035] During operation of the gyroscope, alternating drive signals
can be applied to the drive electrodes D102a and D102b to cause the
beam 102 to resonate out-of-plane, with the drive electrodes D102b
driven in anti-phase to the drive electrode D102a. In this
exemplary embodiment, a differential gyroscope output signal is
produced from the sense electrodes [i.e.,
Output=(S102a+S112a)-(S102b+S112b)]. It is important to note that
the additional sense electrodes S112a are on the opposite side of
the beam 102 from sense electrode S102a, while the additional sense
electrodes S112b are on the opposite side of the beam 102 from
sense electrode S102b.
[0036] When there is no rotation about the axis of sensitivity, the
beam 102 is nominally equidistant from all of the sense electrodes
and therefore the differential gyroscope output is nominally zero.
However, when there is rotation about the axis of sensitivity
causing the beam to deflect in-plane, the beam 102 will move closer
to one set of sense electrodes (e.g., sense electrodes S102a and
S112a) while moving further from the other set of sense electrodes
(e.g., sense electrodes S102b and S112b) and therefore the
differential gyroscope output will be non-zero and in proportion to
the rate of rotation.
[0037] In various alternative embodiments, the additional
electrodes can be used for other purposes. For example, rather than
using the additional electrodes D102b for driving resonance of the
beam 102, these electrodes could be used to sense resonance of the
beam 102, e.g., to provide a feedback signal for a PLL-based drive
circuit. Similarly, rather than using the additional electrodes
S112a and S112b for sensing in-plane deflections of the beam 102,
these electrodes could be used to compensate for erroneous in-plane
movements of the beam 102 such as from manufacturing or other
imbalances.
[0038] It should be noted that, in various alternative embodiments,
the gyroscope of the type described above may be operate inversely,
i.e., driven in-plane with out-of-plane sensing.
[0039] One potential problem with operation of a resonating beam
gyroscope of the type discussed above is that the driven motion of
the beam 102 (e.g., out-of-plane in the exemplary embodiments
described above) can include off-axis movements of the beam 102
(e.g., sense-axis movements) that can cause erroneous non-zero
differential output signals (often referred to as quadrature
error). Such off-axis movements (often referred to as modal
coupling) can be caused from various sources typically associated
with fabrication imperfections in typical MEMS fabrication
processes, such as unequal spring constants of the tethers 104,
differences in the dimensions of the drive electrodes, differences
in the gaps between the drive electrodes and the beam 102, and
imperfections in the dimensions of the beam 102 (e.g., side wall
angle). The manifestation of this problem is as follows: typically
in response to an in-plane force, only in-plane displacement is
desired; when modal coupling occurs, an in-plane force causes both
the desired in-plane displacement in addition to some amount of
out-of-plane displacement dependent upon the degree of the
fabrication imperfection causing it. The opposite is also true: a
purely out-of-plane force will result in both out-of-plane and
in-plane displacements. In both cases, the undesired displacement
is proportional to both the desired displacement and the degree of
imperfection.
[0040] One way to reduce or "trim" this error source is to apply an
electrostatic force which applies a force in the opposite direction
of the undesired displacement in such a manner to null the
displacement in the undesired direction. This can be done by having
split electrodes on top or bottom of the device at locations of
maximum displacement of the mode shape. A differential DC voltage
applied to each electrode (Vbias +/- Vtune) can provide the
required opposite force to null the undesired displacement.
[0041] FIG. 8 is a schematic diagram showing an arrangement of
split electrodes for reducing modal coupling, in accordance with
one exemplary embodiment. Specifically, as shown in FIG. 8(A), in
this example, the arrangement of split electrodes includes two
opposing sets of trim electrodes 802 and 804 placed above the beam
102 (referred to as QTRM- and QTRM+), each having four trim
electrodes, two placed along the center section on one side of the
beam 102 and one placed along each tail section on the other side
of the beam 102. Such placement of the trim electrodes is due to
the resonant mode of the beam 102, i.e., when the center section of
the beam 102 moves in one in-plane (y-axis) direction, the tail
sections of the beam 102 move in the other direction. This
arrangement of trim electrodes placed above the beam 102 generally
would be appropriate for an out-of-plane drive mode (i.e., in the
x-axis direction shown in FIG. 8) although such arrangement also
can be used for an in-plane drive mode; similar trim electrodes
placed on the side(s) of the beam 102 generally would be
appropriate for an in-plane drive mode (i.e., in the y-axis
direction shown in FIG. 8) although such arrangement also can be
used for an out-of-plane drive mode.
[0042] FIG. 8(B) is a cross-sectional view of a beam 102 having a
width "W" and pair of opposing trim electrodes 802 and 804, which
are spaced from the beam 102 by a gap "g". Here, the trim electrode
802 is a member of the QTRM- set of trim electrodes and receives a
compensating voltage signal VQ- while the trim electrode 804 is a
member of the QTRM+ set of trim electrodes and receives a
compensating voltage signal VQ+. As shown in FIG. 8(B), the trim
electrodes are "partial-overlap" electrodes, i.e., when the beam
102 is at its nominal (center) position along the y-axis, only part
of the width of each trim electrode (represented by "y.sub.o")
overlaps with the beam 102, and the amount of overlap is the same
for the trim electrodes on both sides of the beam 102. When the
beam 102 experiences displacement in-plane in the y-axis, the
amount of overlap between each trim electrode and the beam 102
changes and hence any force produced on the beam 102 by a
particular trim electrode varies in proportion to the amount of
displacement. Thus, for example, with reference again to FIG. 8(B),
if the beam 102 were to move toward the left in the y-axis
direction, then the amount of overlap between the trim electrode
802 and the beam 102 would increase and correspondingly the amount
of overlap between the trim electrode 804 and the beam 102 would
decrease.
[0043] In the example shown in FIG. 8, the capacitance between each
trim electrode and the beam 102 depends on the nominal gap "g" as
well as the x-axis displacement (x.sub.disp) of the beam 102 from
its nominal x-axis position (i.e., capacitance increases as the
beam moves toward the trim electrode and decreases as the beam
moves away from the trim electrode). Also, because the trim
electrodes are variable overlap electrodes, the capacitance between
each trim electrode and the beam 102 also depends on the y-axis
displacement "y" of the beam 102 relative to the nominal y-axis
position "y.sub.o" of the beam 102 (i.e., capacitance increases as
the overlap increases and decreases as the overlap decreases). The
differential capacitances dC- and dC+ per unit length of the beam
102 with respect to the QTRM- and QTRM+ electrodes, respectively,
can be represented as follows:
dC - = .epsilon. 0 dl ( y 0 - y ) g - x disp ##EQU00001## dC + =
.epsilon. 0 dl ( y 0 + y ) g - x disp ##EQU00001.2##
[0044] As discussed above, even when there is no rotation of the
gyroscope, the driven motion of the beam 102 can cause erroneous
sense-axis displacements of the beam 102 through modal coupling,
and such erroneous sense-axis displacements of the beam 102 are
generally proportional to the drive-axis displacement of the beam.
Therefore, in order to compensate for such modal coupling, a
quadrature cancellation circuit provides correcting voltage signals
VQ- and VQ+ on the QTRM- and QTRM+ electrodes, respectively, to
produce correcting forces in the sense-axis that substantially
cancel the unwanted sense-axis displacements. Thus, the effective
y-axis correcting force Fy in this example can be characterized
by:
F y = 1 2 .differential. C .differential. y V 2 ##EQU00002##
and consequently:
dF y = 1 2 .epsilon. 0 dl g - x disp ( VQ + 2 - VQ - 2 )
##EQU00003##
[0045] The effective force per trim electrode can be characterized
by:
dF y . QTRM ~ 1 2 .epsilon. 0 dl g ( 1 + x disp g ) ( VQ + 2 - VQ -
2 ) ##EQU00004##
[0046] For a single QTRM electrode pair, the part of the force that
is linearly proportional to the x-axis drive force can be
characterized by:
k xy , QTRM ~ 1 2 .epsilon. 0 g 2 ( VQ + 2 - VQ - 2 ) .intg. .phi.
mode l ##EQU00005##
[0047] where the integral component of the equation allows for
weighting by mode shape.
[0048] It should be noted that trim electrodes of the type shown in
FIG. 8 can be placed above and/or below the beam. Electrodes can be
placed above the beam, for example, by including the electrodes on
a cap wafer that is attached to the device wafer containing the
beam. Alternatively, the electrodes can be formed in situ with the
beam and tethers, for example, by depositing and patterning
additional material layers above device layer containing the beam
and tethers. In addition to, or in lieu of, the variable-overlap
electrodes placed above the beam, similar variable-overlap
electrode can be placed below the beam, for example, supported
directly or indirectly by a substrate underlying the beam. Thus, in
certain embodiments, variable-overlap electrodes may be placed both
above and below the beam. Similar trim electrodes additionally or
alternatively may be placed at the side(s) of the beam 102.
[0049] It should be noted that embodiments of the present invention
may use any of a variety of transduction methods for driving and/or
sensing, including, but not limited to, electrostatic transduction
or piezoelectric transduction.
[0050] The present invention may be embodied in other specific
forms without departing from the true scope of the invention, and
numerous variations and modifications will be apparent to those
skilled in the art based on the teachings herein. Any references to
the "invention" are intended to refer to exemplary embodiments of
the invention and should not be construed to refer to all
embodiments of the invention unless the context otherwise requires.
The described embodiments are to be considered in all respects only
as illustrative and not restrictive.
* * * * *