Multi-axis resonant accelerometer

Abstract

The present invention relates to a multi-axis resonant accelerometer. The multi-axis resonant accelerometer is based on detecting changes in the resonant frequency of one or more electrostatically driven resonator masses due to changes in the electrostatic gap under acceleration. Specifically, one or more resonator masses are configured to resonate simultaneously in different directions associated with different sensitivity axes (e.g., X, Y, and / or Z axes). The movement of each resonator mass is monitored by one or more electrostatically coupled sensing electrodes. Acceleration along a particular sensitivity axis causes small changes in the electrostatic gap between the corresponding resonator mass and the sensing electrode associated with that sensitivity axis, and this change in the electrostatic gap manifests as a small change in the resonator resonant frequency, from which an accelerometer output signal can be generated.

Description

[0001] This application is a divisional application of an application filed on October 14, 2016, with application number 201680069861.2 and invention name “Multi-axis resonant accelerometer”.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This patent application claims priority to U.S. Patent Application No. 14 / 887,973, filed on October 20, 2015, entitled Multi-Axis Resonant Accelerometer, the entire contents of which are incorporated herein by reference. Technical Field

[0004] The present invention relates generally to resonant accelerometers and, more particularly, to multi-axis resonant accelerometers based on detecting changes in the resonant frequency of one or more electrostatically driven resonator masses due to changes in an electrostatic gap under acceleration. Background Art

[0005] An accelerometer is a sensor that converts acceleration forces into an electronic signal. Accelerometers are used in a wide variety of devices and applications. For example, accelerometers are commonly found in various automotive systems, such as airbag deployment and rollover detection. Accelerometers are also commonly found in many computer devices, for example, for motion-based sensing (e.g., fall detection) and control (e.g., motion-based controls for gaming).

[0006] Generally speaking, a MEMS (microelectromechanical system) accelerometer typically includes a proof mass and one or more sensors for sensing movement or position changes of the proof mass caused by external acceleration. Accelerometers can be configured to sense one, two, or three axes of acceleration. Typically, the proof mass is configured in a predetermined device plane, and the sensitivity axis is generally referenced to the device plane. For example, acceleration sensed along an axis parallel to the device plane is typically referred to as X- or Y-axis acceleration, while acceleration sensed along an axis perpendicular to the device plane is typically referred to as Z-axis acceleration. A uniaxial accelerometer may be configured to detect only X- or Y-axis acceleration or only Z-axis acceleration. A dual-axis accelerometer may be configured to detect both X- and Y-axis acceleration, or may be configured to detect both X- and Z-axis acceleration. A triaxial accelerometer may be configured to detect X-, Y-, and Z-axis acceleration. Summary of the Invention

[0007] In certain embodiments, a multi-axis resonant accelerometer is provided, comprising: a resonator including at least one resonator mass configured in a device plane; a set of x-axis drive electrodes configured to drive x-axis motion of the at least one resonator mass in the device plane; a set of y-axis drive electrodes configured to drive y-axis motion of the at least one resonator mass in the device plane; a set of x-axis sense electrodes configured to sense a change in x-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of x-axis acceleration; and a set of y-axis sense electrodes configured to sense a change in y-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of y-axis acceleration.

[0008] In certain other embodiments, a method of operating a multi-axis resonant accelerometer having a resonator including at least one resonator mass disposed in a device plane is provided. The method includes: driving the at least one resonator mass to resonate with x-axis motion and y-axis motion in the device plane; sensing a change in an x-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of x-axis acceleration; and sensing a change in a y-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of y-axis acceleration.

[0009] In certain other embodiments, a multi-axis resonant accelerometer is provided, comprising: a resonator including at least one resonator mass configured in a device plane; means for driving the at least one resonator mass into resonance with x-axis motion and y-axis motion in the device plane; means for sensing a change in an x-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of an x-axis acceleration; and means for sensing a change in a y-axis resonant frequency of the at least one resonator mass based on electrostatic spring tuning in the presence of a y-axis acceleration.

[0010] In various alternative embodiments, at least one resonator mass can include multiple resonator masses coupled to operate as a single resonator, and each set of sensing electrodes can be configured for single-ended sensing of changes in resonant frequency. Alternatively, at least one resonator mass can include multiple resonator masses, each set of drive electrodes can be configured to drive a first subset of the resonator masses to resonate in antiphase with a second subset of the resonator masses, and each set of sensing electrodes can be configured for differential sensing of changes in resonant frequency. The x-axis motion and the y-axis motion can be driven at the same resonant frequency, or at different resonant frequencies. The change in resonant frequency of a given axis can be based on a voltage difference between a drive electrode associated with the given axis and a sense electrode associated with the given axis.

[0011] Various alternative embodiments may additionally include z-axis sensing, such that the resonator further includes at least one z-axis sensor element configured to resonate with z-axis motion perpendicular to the device plane, wherein each z-axis sensor element is part of a unique resonator mass. Z-axis motion of the at least one z-axis sensor element is driven, for example, by a set of z-axis drive electrodes. Changes in the z-axis resonant frequency of the at least one z-axis sensor element in the presence of z-axis acceleration are sensed, for example, by a configured set of z-axis sense electrodes based on electrostatic spring tuning. Each z-axis sensor element may comprise a seesaw sensor element.

[0012] Other embodiments may be disclosed and claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The above-described features of the embodiments will be more readily understood by referring to the following detailed description with reference to the accompanying drawings, in which:

[0014] Figure 1 is a schematic top view of a device layer structure for an XY-axis resonant accelerometer using differential X / Y-axis sensing with a weak resonator mass or no resonator coupling according to an exemplary embodiment of the present invention;

[0015] Figure 2 is an illustration of an acceleration in the −X direction (ie, −Ax) for causing a corresponding displacement of the resonator mass in the +X direction in differential sensing according to an exemplary embodiment;

[0016] Figure 3 is a schematic block diagram of an accelerometer control circuit for a single axis for differential sensing according to an exemplary embodiment;

[0017] Figure 4 is a schematic top view of a device layer structure for an XY-axis resonant accelerometer using strongly coupled anti-phase drive and single-ended X / Y-axis sensing of a resonator mass according to an exemplary embodiment of the present invention;

[0018] Figure 5 is based on Figure 4 An exemplary embodiment of the present invention is a schematic diagram illustrating the frequency pulling effect of an acceleration in the -X direction (i.e., -Ax) on a resonator mass with a corresponding displacement in the +X direction for single-ended sensing;

[0019] Figure 6 is a schematic block diagram of a single-axis accelerometer control circuit 800 for single-ended sensing according to an exemplary embodiment;

[0020] Figure 7is a schematic top view of a device layer structure of an XY-axis resonant accelerometer for strongly coupled in-phase driving and single-ended X / Y-axis sensing using a resonator mass according to an exemplary embodiment of the present invention;

[0021] Figure 8 is based on Figure 7 An exemplary embodiment of the present invention is a schematic diagram illustrating the frequency pulling effect of an acceleration in the -X direction (i.e., -Ax) on a resonator mass with a corresponding displacement in the +X direction for single-ended sensing;

[0022] Figure 9 is a schematic top view of a device layer structure for a triaxial resonant accelerometer according to another exemplary embodiment of the present invention;

[0023] Figure 10 Shown according to Figure 9 Details of the seesaw element of an embodiment;

[0024] Figure 11 is a schematic diagram illustrating relative positions of a driving circuit and a sensing electrode under a seesaw element according to an exemplary embodiment;

[0025] It should be noted that the foregoing figures and the elements depicted therein are not necessarily drawn to consistent scale or any scale. Unless the context dictates otherwise, like numbers refer to like elements. DETAILED DESCRIPTION

[0026] A multi-axis resonant accelerometer (RXL) is based on detecting changes in the resonant frequency of one or more electrostatically driven resonator masses due to changes in the electrostatic gap under acceleration. Specifically, one or more resonator masses are configured to resonate simultaneously in different directions associated with one or more axes of sensitivity (e.g., X, Y, and / or Z axes). The motion of each resonator mass is monitored via one or more electrostatically coupled sense electrodes. Acceleration along a particular axis of sensitivity causes displacement of the resonator mass in the opposite direction, which effectively changes the electrostatic gap between the mass and the corresponding drive / sense electrode associated with that particular axis of sensitivity, thereby effectively changing the electrostatic spring stiffness of the resonator mass and, in turn, the resonant frequency of the resonator mass. This change in resonant frequency (sometimes referred to herein as "frequency pulling" or "electrostatic spring tuning") can be sensed, and an output signal can be generated based on the amount of change in resonant frequency. While a common resonant frequency can be used, the resonant frequency can be substantially different for each axis of sensitivity (e.g., to help mitigate mode injection and locking issues).

[0027] For purposes of the following description and the appended claims, a "kit" includes one or more components, a "mode" of a resonant body is the shape of motion of the body when resonating, the term "anti-phase" with respect to the resonant modes (i.e., displacements) of two resonant bodies means that the resonants resonate with the same mode shape but 180 degrees out of phase, the term "in-plane" with respect to a resonant mode means that the resonance is primarily in the plane of the resonator structure, the term "out-of-plane" with respect to a resonant mode refers to resonance that is primarily perpendicular to the plane of the resonator structure, 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 to drive the resonator to its target mode shape at a design frequency and / or to sense an electrical or electromechanical effect through capacitive coupling (e.g., between the resonator mass and one or more adjacent structures), although it should be noted that other types of electrodes and couplings (e.g., piezoelectric) may be used. Thus, in exemplary embodiments, the electrodes may include the resonator mass and one or more structures for driving and / or sensing the motion of the resonator mass.

[0028] Various exemplary embodiments are described below with reference to an XY-axis resonant accelerometer having four masses, but the present invention is not limited to this configuration. Two different exemplary operating modes are described. The first exemplary operating mode uses differential X / Y-axis sensing with weak or no coupling of the resonator masses. The second exemplary operating mode uses single-ended X / Y-axis sensing with strong coupling of the resonator masses.

[0029] Use weak or uncoupled differential X / Y axis sensing

[0030] Figure 1 Figure 1 is a schematic top view of the device layer structure of an XY-axis resonant accelerometer using X / Y-axis sensing with a weak or no resonant mass according to an exemplary embodiment of the present invention. In this exemplary embodiment, four resonator masses 101, 102, 103, and 104 are supported above an underlying substrate (not shown for convenience) and driven in the x- and y-axis directions parallel to the underlying substrate via a set of in-plane drive electrodes (drive electrodes DX1, DX2, DX3, and DX4 for driving x-axis motion; drive electrodes DY1, DY2, DY3, and DY4 for driving y-axis motion), which are directly or indirectly fixedly supported by the underlying substrate. The in-plane motion of the resonator masses parallel to the underlying substrate is achieved via a set of in-plane sense electrodes (sense electrodes SX1, SX2, SX3, and SX4 for sensing x-axis motion; and sense electrodes SY1, SY2, SY3, and SY4 for sensing y-axis motion), which are directly or indirectly fixedly supported by the underlying substrate. Figure 1 The x-axis and y-axis are depicted for reference purposes and are not part of the resonant accelerometer.

[0031] In this exemplary embodiment, each electrode is shown as a single elongated finger structure that is electrostatically coupled (i.e., through a small gap) to a finger structure extending from a corresponding resonator mass, but it should be noted that other electrode arrangements may be used in various alternative embodiments. For example, in certain alternative embodiments, each electrode may include a plurality of elongated fingers that are interleaved with one or more fingers extending from a corresponding resonator mass.

[0032] In this exemplary operating mode, the resonator masses have weak or no mechanical coupling. Opposing pairs of resonator masses are driven into anti-phase resonance with each other, and differential sensing is used to generate an accelerometer output for each sensitive axis based on the change in resonant frequency caused by the frequency pulling effect in the presence of an external acceleration, where one pair of resonator masses experiences an increase in resonant frequency, while the opposing pair of resonator masses experiences a decrease in resonant frequency in the presence of such external acceleration. The change in resonant frequency, and therefore the magnitude of the external acceleration, can be determined by the difference in resonant frequency between the two pairs of resonator masses. Generally, this differential sensing increases sensitivity and eliminates common-mode errors, such as frequency drift due to temperature, humidity, mechanical stress, and driver / detection circuit stability errors.

[0033] For x-axis motion in an exemplary embodiment, resonator masses 101 and 104 are alternately driven by drive electrodes DX1 and DX4 to move back and forth in phase with each other, while resonator masses 102 and 103 are alternately driven by drive electrodes DX2 and DX3 to move back and forth synchronously with each other but in opposite directions. Thus, for these x-axis motions, resonator masses 101 and 104 can be considered a single body, and resonator masses 102 and 103 can be considered a single body. In this example, the motion of resonator masses 101 / 104 and resonator masses 102 / 103 can be driven in phase with each other by drive electrodes DX1, DX2, DX3, and DX4, i.e., with the same drive signal applied to all of these drive electrodes. During one phase of the x-axis motion, resonator masses 101 and 104 move to the right (i.e., in the "x" direction) while resonator masses 102 and 103 move to the left (i.e., in the "-x" direction), and during the anti-phase of the x-axis motion, resonator masses 101 and 104 move to the left (i.e., in the "-x" direction) while resonator masses 102 and 103 move to the right (i.e., in the "x" direction).

[0034] In one exemplary embodiment, for y-axis motion, resonator masses 101 and 102 are alternately driven by drive electrodes DY1 and DY2 to move back and forth in phase with each other, while resonator masses 103 and 104 are alternately driven by drive electrodes DY3 and DY4 to move back and forth in phase with each other but in anti-phase with respect to resonator masses 101 and 102. Therefore, for these y-axis motions, resonator masses 101 and 102 can be considered as a single entity, and resonator masses 103 and 104 can be considered as a single entity. In this example, the motion of resonator masses 101 / 102 and resonator masses 103 / 104 can be achieved by driving drive electrodes DY1, DY2, DY3, and DY4 in phase, i.e., applying the same drive signal to all of these drive electrodes. During one phase of the y-axis motion, resonator masses 101 and 102 move toward the top (i.e., in the "y" direction) while resonator masses 103 and 104 move toward the bottom (i.e., in the "-y" direction). During the anti-phase of the y-axis motion, resonator masses 101 and 102 move toward the bottom (i.e., in the "-y" direction) while resonator masses 103 and 104 move toward the top (i.e., in the "y" direction).

[0035] As described above, the resonator masses can be configured to resonate such that the x-axis resonant frequency and the y-axis resonant frequency are substantially different, for example to help mitigate mode injection and locking issues. Because the force on each resonator mass will include unequal x-axis and y-axis components (e.g., due to different drive frequencies for the two axes), the driven motion of the resonator masses will generally be nonlinear and therefore each resonator mass will generally experience a slight amount of rotation as it moves back and forth from resonance.

[0036] An acceleration in a particular direction acts on all four resonator masses and effectively changes the electrostatic gaps between the four masses and the drive / sense electrodes associated with that particular axis of sensitivity, which in turn effectively changes the electrostatic spring stiffness of the resonator masses, which in turn effectively changes the resonant frequencies of the resonator masses. Specifically, the resonant frequency of one pair of resonator masses increases, while the resonant frequency of the opposing mass decreases. For convenience, each pair of resonator masses may be referred to herein as a "resonator," so that the accelerometer may be considered to have two resonators for each sensitive axis (i.e., for the X-axis, resonator masses 101 and 104 constitute one resonator, and resonator masses 102 and 103 constitute another resonator; for the Y-axis, resonator masses 101 and 102 constitute one resonator, and resonator masses 103 and 104 constitute another resonator).

[0037] The resonant frequency of the resonator can be characterized by the following formula and is affected by the mechanical spring constant K 机电 and electrostatic spring constant K 静电Impact:

[0038]

[0039] The resonant frequency of each resonator can be sensed, and an output signal can be generated based on the difference in resonant frequency. Generally, the relationship between input acceleration and change in resonant frequency is expressed in Hz / G (for example, a particular accelerometer may be designed to operate with a scale factor such as 50 Hz / G or 100 Hz / G). Therefore, the input acceleration (in terms of G-force) can be determined from the change in resonant frequency (in Hz) according to the scale factor. Different sensitivity axes may have the same scale factor or may have different scale factors.

[0040] To operate the resonant accelerometer, in this exemplary embodiment, the resonator mass, drive electrodes, and sense electrodes must be placed at different potentials. For example, the resonator mass can be placed at a fixed potential (referred to herein as VDC_BULK), which can be a non-zero voltage or ground. The drive electrodes associated with a particular sensitivity axis can be biased with a DC bias voltage (referred to herein as VDC_DRIVEX for the x-axis and VDC_DRIVEY for the y-axis) plus a small AC voltage (referred to herein as VAC_DRIVEX for the x-axis and VAC_DRIVEY for the y-axis). That is, the drive electrodes DX1, DX2, DX3, and DX4 are biased with VDC_DRIVEX + VAC_DRIVEX to excite x-axis motion of the resonator masses 101-104, and the drive electrodes DY1, DY2, DY3, and DY4 are biased with VDC_DRIVEY + VAC_DRIVEY to excite y-axis motion of the resonator masses 101-104. The sense electrodes associated with a particular sensitivity axis can be biased with different DC voltages (referred to herein as VDC_SENSE X for the x-axis and VDC_SENSE Y for the y-axis) plus a small AC voltage corresponding to the sensitivity axis (referred to herein as VAC_SENSE X for the x-axis and VAC_SENSE Y for the y-axis). That is, sense electrodes SX1, SX2, SX3, and SX4 are biased with VDC_SENSE X + VAC_SENSE X, and sense electrodes SY1, SY2, SY3, and SY4 are biased with VDC_SENSE Y + VAC_SENSE Y. Importantly, VDC_DRIVEX and VDC_SENSE X are unequal to each other and to VDC_BULK, and VDC_DRIVEY and VDC_SENSE Y are unequal to each other and to VDC_BULK. In various alternative embodiments, VDC_DRIVEX can be equal to or different from VDC_DRIVEY, VDC_SENSE X can be equal to or different from VDC_SENSE Y, and VAC_DRIVEX can be equal to or different from VAC_DRIVEY. In this exemplary embodiment, VAC_DRIVE X and VAC_SENSING X are 180 degrees out of phase with each other, and VAC_DRIVE Y and VAC_SENSING Y are 180 degrees out of phase with each other. For simplicity, VAC_DRIVE X and VAC_SENSING X can have the same amplitude as each other, and VAC_DRIVE Y and VAC_SENSING Y can have the same amplitude as each other, although the amplitudes can be different in alternative embodiments.

[0041] The X-axis motion of the resonator masses 101-104 is sensed by changing the capacitance between each resonator mass 101-104 and its corresponding sense electrode SX1-SX4. The changing capacitance induces a correspondingly changing current in the sense electrode. The sensed current is used as a feedback signal (e.g., via a phase-locked loop) to drive the X-axis motion of the resonator mass and sense the resonant frequency of the resonator mass. Because the drive electrodes DX1, DX2, DX3, and DX4 are all driven in phase, in this exemplary embodiment, the electrostatic force will resonate the proof masses 101 and 104 in the X direction, but will cause the proof masses 102 and 103 to resonate out of phase (180° phase shift) with the proof masses 101 and 104 in the X direction.

[0042] Similarly, the Y-axis motion of resonator masses 101-104 is sensed by changing the capacitance between each resonator mass 101-104 and its corresponding sense electrode SY1-SY4. The changing capacitance induces a correspondingly changing current in the sense electrode. The sensed current can be used as a feedback signal (e.g., via a phase-locked loop) to drive the Y-axis motion of the resonator mass and sense the resonant frequency of the resonator mass. Because drive electrodes DY1, DY2, DY3, and DY4 are all driven in phase, in this exemplary embodiment, the electrostatic force will resonate with proof masses 101 and 102 in the Y direction, but proof masses 103 and 104 will resonate out of phase (180° phase shift) with proof masses 101 and 102 in the Y direction.

[0043] Under external acceleration relative to a given sensitivity axis, all four resonator masses will move in opposite directions relative to that sensitivity axis. Due to the frequency-pull effect, one pair of resonator masses will experience an increase in resonant frequency, while the opposing pair of resonator masses will experience a decrease in resonant frequency relative to that sensitivity axis. The resonant frequency of each pair of resonator masses can be sensed by corresponding sensing electrodes, and an output signal can be generated based on the difference in resonant frequency between the two pairs of resonator masses.

[0044] Thus, for example, under an external X-axis acceleration in the -X direction, all four proof masses will move in the +X direction while stationary, while still being driven into resonance. The gap between proof mass 101 and drive electrode DX1 and the gap between proof mass 104 and drive electrode DX4 will become smaller. Due to the K 静电 Proportional to 1 / gap^3, when the gap becomes smaller, K 静电will increase. According to equation (1), the resonant frequency Fx of the detection masses 101 and 104 will decrease. This resonant frequency change is sensed by the sensing electrodes SX1 and SX4 respectively. Under the same conditions, the gap between the detection mass 102 and the drive electrode DX2 and the gap between the detection mass 103 and the drive electrode DX3 will become larger. Due to the K 静电 Proportional to 1 / gap^3, when the gap becomes larger, K 静电 According to equation (1), the resonant frequency Fx of the detection masses 102 and 103 will increase. This resonant frequency change is detected by SX2 and SX3 respectively.

[0045] Under external X-axis acceleration in the +X direction, the opposite situation occurs, that is, the gap between the detection mass 101 and the drive electrode DX1 and the gap between the detection mass 104 and the drive electrode DX4 will become larger, so the resonant frequency Fx of the detection masses 101 and 104 will increase and be detected by SX1 and SX4, respectively, while the gap between the detection mass 102 and the drive electrode DX2 and the gap between the detection mass 103 and the drive electrode DX3 will become smaller, so the resonant frequency Fx of the detection masses 102 and 103 will decrease and be detected by SX2 and SX3, respectively.

[0046] Similarly, under an external Y-axis acceleration in the -Y direction, all four proof masses will move in the +Y direction while stationary, while still being driven into resonance. The gap between proof mass 101 and drive electrode DY1, and the gap between proof mass 102 and drive electrode DY2, will become smaller. 静电 Proportional to 1 / gap^3, when the gap becomes smaller, K 静电 will increase. According to equation (1), the resonant frequency Fy of the detection masses 101 and 102 will decrease. This resonant frequency change is detected by SY1 and SY2 respectively. Under the same conditions, the gap between the detection mass 103 and the drive electrode DY3 and the gap between the detection mass 104 and the drive electrode DY4 will become larger. Due to the K 静电 Proportional to 1 / gap^3, when the gap becomes larger, K 静电 According to equation (1), the resonant frequency Fy of the detection masses 103 and 104 will increase. This resonant frequency change is detected by SY3 and SY4 respectively.

[0047] Under external Y-axis acceleration in the +Y direction, the opposite situation occurs, that is, the gap between the detection mass block 101 and the drive electrode DY1 and the gap between the detection mass block 102 and the drive electrode DY2 will become larger, so the resonant frequency Fy of the detection masses 101 and 102 will increase and be detected by the sensing electrodes SY1 and SY2, respectively, while the gap between the detection mass block 103 and the drive electrode DY3 and the gap between the detection mass block 104 and the drive electrode DY4 will become smaller, so the resonant frequency Fy of the detection masses 103 and 104 will decrease and be detected by the sensing electrodes SY3 and SY4, respectively.

[0048] As a result, the resonant frequency of one pair of masses increases, while the resonant frequency of the other pair of masses decreases for that particular sensitivity axis. The relative change in resonant frequency in a particular sensitivity axis will manifest as a change in the combined differential output for that particular sensitivity axis, which can be sensed to provide an accelerometer output signal representative of acceleration.

[0049] Figure 2 FIG2 is a schematic diagram illustrating an embodiment of a frequency pulling effect of an acceleration in the -X direction (i.e., -Ax) for differential sensing in the -X direction, causing a corresponding displacement of the resonator mass in the +X direction, according to one example. In this example, the frequency pulling effect is illustrated for half of the X-axis (i.e., for resonator masses 101 and 102 relative to electrodes DX1, SX1, DX2, and SX2), although the same effect applies to the other half of the X-axis (i.e., for resonator masses 103 and 104 relative to electrodes DX3, SX3, DX4, and SX4), and a similar effect applies to the Y-axis. Because resonator masses 101 and 102 have weak or no coupling, they may have slightly different resonant frequencies. Consequently, resonator mass 101 has a resonant frequency fr101, while resonator mass 102 has a resonant frequency fr102.

[0050] The initial capacitance between a given resonator mass and the corresponding electrode can be expressed as:

[0051]

[0052] where d o is the nominal gap between the electrode and the corresponding finger-like structure extending from the corresponding resonator mass.

[0053] The rate of change of capacitance when the resonator mass moves a distance x (e.g., nanometers) can be expressed as:

[0054]

[0055] The force on a given resonator mass from the corresponding drive electrode due to dC / dx can be expressed as:

[0056] Fd = (1 / 2)(dC / dx)(VDC_drive – VDC_bulk) 2

[0057] The force on a given resonator mass from the corresponding sensing electrode due to dC / dx can be expressed as:

[0058] Fs = (1 / 2)(dC / dx)(VDC_sense – VDC_bulk) 2

[0059] The electrostatic stiffness caused by dC / dx can be expressed as:

[0060]

[0061] where Vr is the voltage placed on a given electrode and V is the potential placed on the resonator mass.

[0062] The total stiffness of the resonator mass as the gap changes in x can be expressed as (Keq-Ke), where Keq is the initial mechanical stiffness.

[0063] The frequency shift caused by the stiffness change can be expressed as:

[0064]

[0065] like Figure 2 As shown, an acceleration in the -X direction (ie, -Ax) causes a corresponding displacement of the resonator mass in the +X direction. The gap associated with electrodes DX2 and SX1 increases (ie, reaches d o +x) and thus the dC / dx associated with these electrodes decreases, while the gaps associated with electrodes SX2 and DX1 decrease (i.e., to d o =-x), so the dC / dx associated with these electrodes increases. As a result, the X-axis resonant frequency fr101 of the resonator mass 101 decreases, while the X-axis resonant frequency fr102 of the resonator mass 102 increases.

[0066] The resonant frequency of the resonator mass 101 relative to the SX1 and DX1 electrodes can be expressed as:

[0067]

[0068]

[0069] Where Gee is the input acceleration (in meters per square), f0 is the nominal resonant frequency of the resonator mass, Vres is the resonator voltage, Vs is the SX voltage, and Vd is the DX voltage.

[0070] The resonant frequency of the resonator mass 102 relative to the SX2 and DX2 electrodes can be expressed as:

[0071]

[0072]

[0073] Where Gee is the input acceleration (in meters per square), f0 is the nominal resonant frequency of the resonator mass, Vres is the resonator voltage, Vs is the SX voltage, and Vd is the DX voltage.

[0074] The resonant frequency of the resonator mass 104 relative to the SX4 and DX4 electrodes should be the same or nearly the same as that of the resonator mass 101 .

[0075] The resonant frequency of the resonator mass 103 relative to the SX3 and DX3 electrodes should be the same or nearly the same as the resonant frequency of the resonator mass 102 .

[0076] The frequency shift of the resonator mass 101 can be expressed as:

[0077] dfr101(Gee):=(fr101_SX1(0)–fr101_SX1(Gee))+(fr101_DX1(0)–fr101_DX1(Gee))

[0078] The frequency shift of the resonator mass 102 can be expressed as:

[0079] dfr102(Gee):=(fr102_SX2(0)–fr102_SX2(Gee))+(fr102_DX2(0)–fr102_DX2(Gee))

[0080] The frequency shift of the resonator mass 104 should be the same or nearly the same as the frequency shift of the resonator 101, which can be expressed as follows:

[0081] dfr104(Gee):=(fr104_SX4(0)–fr104_SX4(Gee))+(fr104_DX4(0)–fr104_DX4(Gee))

[0082] The frequency shift of the resonator mass 103 should be the same or almost the same as the frequency shift of the resonator 102, which can be expressed as:

[0083] dfr103(Gee):=(fr103_SX3(0)–fr103_SX3(Gee))+(fr103_DX3(0)–fr103_DX3(Gee))

[0084] It is worth noting that both the DX electrode and the SX electrode contribute to the resonant frequency change, and the larger the voltage difference between the DX and SX electrodes, the larger the resonant frequency change.

[0085] Figure 3 FIG2 is a schematic block diagram of a single-axis accelerometer control circuit 300 for differential sensing according to an exemplary embodiment. The accelerometer control circuit 300 includes a first drive circuit 302, a first measurement circuit 306, a first excitation feedback circuit 308, a second drive circuit 312, a second measurement circuit 316, a second excitation feedback circuit 318, and a differential frequency circuit 320. Generally speaking, the first and second drive circuits 302 and 312 drive the resonator masses of the first and second resonators 304 and 314, respectively. The excitation feedback circuits 308 and 318 provide control signals to the first drive circuit 302 and the second drive circuit 312, respectively, based on signals sensed by the first and second measurement circuits 306 and 316 via sensing electrodes associated with the first and second resonators 304 and 314, to maintain the resonance of the first and second resonators 304 and 314 at a desired resonant frequency. First and second measurement circuits 306 and 316 measure the resonant frequencies F1 and F2 of first and second resonators 304 and 314, respectively. As described above, in the exemplary embodiment, F1 and F2 change in opposite directions in the presence of an external acceleration. Difference frequency circuit 320 provides an output signal 330 based on the difference between the measured resonant frequencies of first resonator 304 and second resonator 314 from first measurement circuit 306 and second measurement circuit 316 (i.e., based on F1-F2). For example, output signal 330 can be the difference in resonant frequencies (i.e., F1-F2), or it can be an acceleration calculated from the different resonant frequencies and a scale factor for a particular sensitivity axis (e.g., if the scale factor for a particular gyroscope is 100 Hz / G and the frequency change is 50 Hz, then output signal 330 may be 0.5 G).

[0086] For example, for an X-axis accelerometer, first resonator 304 may include resonator masses 101 and 104, while second resonator 314 may include resonator masses 102 and 103. First drive circuit 302 provides drive signals to drive electrodes DX1 and DX4, while second drive circuit 312 provides drive signals to drive electrodes DX2 and DX3. First measurement circuit 306 measures the resonant frequency of resonator masses 101 and 104 of first resonator 304 via sense electrodes SX1 and SX4, while second measurement circuit 316 measures the resonant frequency of resonator masses 102 and 103 of second resonator 314 via sense electrodes SX2 and SX3. Difference frequency circuit 320 provides output signal 330 based on the difference between the measured resonant frequencies of first resonator 304 and second resonator 314 from first and second measurement circuits 306 and 316.

[0087] Similarly, for the Y-axis accelerometer, the first resonator 304 may include resonator masses 101 and 102, while the second resonator 314 may include resonator masses 103 and 104. A first drive circuit 302 provides drive signals to drive electrodes DY1 and DY2, while a second drive circuit 312 provides drive signals to drive electrodes DY3 and DY4. A first measurement circuit 306 measures the resonant frequency of resonator masses 101 and 102 of the first resonator 304 via sense electrodes SY1 and SY2, while a second measurement circuit 316 measures the resonant frequency of resonator masses 103 and 104 of the second resonator 314 via sense electrodes SY3 and SY4. A difference frequency circuit 320 provides an output signal 330 based on the difference between the measured resonant frequencies of the first resonator 304 and the second resonator 314 from the first and second measurement circuits 306 and 316.

[0088] Thus, exemplary embodiments generally include a separate accelerometer control circuit 300 for each axis of sensitivity.

[0089] In an exemplary embodiment, each resonator mass may be supported by a plurality of folded spring-type flexures configured to allow each mass to move in both the x-axis and the y-axis directions. For example, in one operating phase, resonator mass 101 moves upward and rightward, resonator mass 102 moves upward and leftward, resonator mass 103 moves downward and leftward, and resonator mass 104 moves downward and rightward (i.e., all masses move away from the center in the x-axis and y-axis directions), while in another operating phase, resonator mass 101 moves downward and leftward, resonator mass 102 moves downward and rightward, resonator mass 103 moves upward and rightward, and resonator mass 104 moves upward and leftward (i.e., all masses move toward the center in the x-axis and y-axis directions). The flexures may be configured such that resonator masses 101 and 104 move synchronously with each other in the x-axis direction, resonator masses 102 and 103 move synchronously with each other in the x-axis direction, resonator masses 101 and 102 move synchronously with each other in the y-axis direction, and resonator masses 103 and 104 move synchronously with each other in the y-axis direction.

[0090] In an exemplary embodiment, each drive / sense electrode may include a set of elongated fingers that are interleaved with corresponding fingers extending from a respective resonator mass.Such interdigitated electrostatic transducers are well known in the art.

[0091] Single-ended X / Y-axis sensing with strong coupling

[0092] Uses strongly coupled single-ended X / Y axis sensing

[0093] Figure 4 is a schematic top view of the device layer structure for an XY axis resonant accelerometer using strongly coupled anti-phase drive and single-ended X / Y axis sensing of a resonator mass according to an exemplary embodiment of the present invention. In this exemplary operating mode, the resonator mass and electrodes are substantially as Figure 1 The configuration shown is similar to that shown in the preceding text, but the resonator masses have strong mechanical coupling (e.g., via one or more tethered resonator masses marked with an * between each pair of adjacent ones) so that the four resonator masses effectively act as a single body with one resonant frequency, such as a single x-axis resonant frequency and a single y-axis resonant frequency. Single-ended sensing is used to generate an accelerometer output for each sensitivity axis based on a change in resonant frequency caused by a frequency-pull effect in the presence of an external acceleration, where the entire body experiences a change in resonant frequency when the external acceleration occurs. The change in resonant frequency, and therefore the magnitude of the external acceleration, can be determined by comparing the body's resonant frequency to a reference frequency.

[0094] For x-axis motion in an exemplary embodiment, the resonator masses 101-104 are alternately driven by drive electrodes DX1 / DX4 and DX2 / DX3 to move back and forth in phase with each other. During one phase of the x-axis motion, the resonator masses 101-104 move to the right (i.e., in the "x" direction), and during the opposite phase of the x-axis motion, the resonator masses 101-104 move to the left (i.e., in the "-x" direction).

[0095] For y-axis motion in an exemplary embodiment, the resonator masses 101-104 are alternately driven by drive electrodes DY1 / DY2 and DY3 / DY4 to move back and forth in phase with each other. During one phase of the y-axis motion, the resonator masses 101-104 move upward (i.e., in the "y" direction), and during the anti-phase phase of the y-axis motion, the resonator masses 101-104 move toward the bottom (i.e., in the "-y" direction).

[0096] As described above, the resonator mass can be configured to resonate such that the x-axis resonant frequency and the y-axis resonant frequency are substantially different, for example to help alleviate mode injection and locking issues.

[0097] An acceleration in a particular direction acts on all four resonator masses and effectively changes the electrostatic gaps between the four masses and the drive / sense electrodes associated with that particular sensitivity axis, which in turn effectively changes the electrostatic spring stiffness of the resonator masses, which in turn effectively changes the resonant frequency of the resonator masses. For convenience, the four coupled resonator masses may be referred to herein as "resonators," such that the accelerometer may be considered to have one resonator for each sensitivity axis.

[0098] The resonant frequency of a single resonator can be sensed, and an output signal can be generated based on the difference between the sensed resonant frequency and a reference frequency. Generally, the relationship between input acceleration and the change in resonant frequency is expressed in Hz / G (for example, a particular accelerometer may be designed to operate with a scale factor such as 50 Hz / G or 100 Hz / G). Therefore, the input acceleration (in terms of G-force) can be determined from the change in resonant frequency (in Hz) according to the scale factor. Different sensitivity axes may have the same scale factor or may have different scale factors.

[0099] To operate the resonant accelerometer, in this exemplary embodiment, the resonator mass, drive electrodes, and sense electrodes must be placed at different potentials. For example, the resonator mass can be placed at a fixed potential (referred to herein as VDC_BULK), which can be a non-zero voltage or ground. The drive electrodes associated with a particular sensitivity axis can be biased with a high DC bias voltage (referred to herein as VDC_DRIVEX for the x-axis and VDC_DRIVEY for the y-axis) plus a small AC voltage (referred to herein as VAC_DRIVEX for the x-axis and VAC_DRIVEY for the y-axis). That is, the drive electrodes DX1, DX2, DX3, and DX4 are biased with VDC_DRIVEX + VAC_DRIVEX to excite x-axis motion of the resonator masses 101-104, and the drive electrodes DY1, DY2, DY3, and DY4 are biased with VDC_DRIVEY + VAC_DRIVEY to excite y-axis motion of the resonator masses 101-104. The sense electrodes associated with a particular sensitivity axis can be biased with different DC voltages (referred to herein as VDC_SENSE X for the x-axis and VDC_SENSE Y for the y-axis) plus a small AC voltage corresponding to the sensitivity axis (referred to herein as VAC_SENSE X for the x-axis and VAC_SENSE Y for the y-axis). That is, sense electrodes SX1, SX2, SX3, and SX4 are biased with VDC_SENSE X + VAC_SENSE X, and sense electrodes SY1, SY2, SY3, and SY4 are biased with VDC_SENSE Y + VAC_SENSE Y. Importantly, VDC_DRIVEX and VDC_SENSE X are unequal to each other and to VDC_BULK, while VDC_DRIVEY and VDC_SENSE Y are unequal to each other and to VDC_BULK. In various alternative embodiments, VDC_DRIVEX can be equal to or different from VDC_DRIVEY, VDC_SENSE X can be equal to or different from VDC_SENSE Y, and VAC_DRIVEX can be equal to or different from VAC_DRIVEY. In this exemplary embodiment, VAC_DRIVE X and VAC_SENSING X are 180 degrees out of phase with each other, and VAC_DRIVE Y and VAC_SENSING Y are 180 degrees out of phase with each other. For simplicity, VAC_DRIVE X and VAC_SENSING X can have the same amplitude as each other, and VAC_DRIVE Y and VAC_SENSING Y can have the same amplitude as each other, although the amplitudes can be different in alternative embodiments.

[0100] The X-axis motion of the resonator masses 101-104 is sensed by changing the capacitance between each resonator mass 101-104 and its corresponding measurement electrode SX1-SX4. The changing capacitance induces a correspondingly changing current in the sensing electrode. The sensed current can be used as a feedback signal (e.g., via a phase-locked loop) to drive the X-axis motion of the resonator mass and sense the resonant frequency of the resonator.

[0101] Similarly, the Y-axis motion of the resonator masses 101-104 is sensed by changing the capacitance between each resonator mass 101-104 and its corresponding sensing electrode SY1-SY4. The changing capacitance induces a correspondingly changing current on the sensing electrode. The sensed current can be used as a feedback signal (e.g., via a phase-locked loop) to drive the Y-axis motion of the resonator mass and sense the resonant frequency of the resonator.

[0102] Under external acceleration relative to a given sensitivity axis, all four resonator masses will move in opposite directions relative to that sensitivity axis. Due to the frequency-pull effect, the resonant body will experience a change in resonant frequency. The resonant frequency of the resonant body can be sensed by sensing electrodes, and an output signal can be generated based on the difference between the sensed resonant frequency and a reference frequency.

[0103] Thus, for example, under an external X-axis acceleration in the -X direction, all four proof masses will move in the +X direction while stationary, while still being driven into resonance. The gaps between proof mass 101 and drive electrode DX1, and between proof mass 104 and drive electrode DX4, will decrease. Under the same conditions, the gaps between proof mass 102 and drive electrode DX2, and between proof mass 103 and drive electrode DX3, will increase.

[0104] Under an external X-axis acceleration in the +X direction, the opposite situation occurs, i.e., the gap between the detection mass 101 and the drive electrode DX1 and the gap between the detection mass 104 and the drive electrode DX4 will increase, while the gap between the detection mass 102 and the drive electrode DX2 and the gap between the detection mass 103 and the drive electrode DX3 will decrease.

[0105] Similarly, under an external Y-axis acceleration in the -Y direction, all four proof masses will move in the +Y direction while stationary, while still being driven into resonance. The gaps between proof mass 101 and drive electrode DY1, and between proof mass 102 and drive electrode DY2, will decrease. Under the same conditions, the gaps between proof mass 103 and drive electrode DY3, and between proof mass 104 and drive electrode DY4, will increase.

[0106] Under external Y-axis acceleration in the +Y direction, the opposite situation occurs, that is, the gap between the detection mass block 101 and the drive electrode DY1 and the gap between the detection mass block 102 and the drive electrode DY2 will become larger, while the gap between the detection mass block 103 and the drive electrode DY3 and the gap between the detection mass block 104 and the drive electrode DY4 will become smaller.

[0107] As a result, the resonant frequency of the resonator changes.

[0108] Figure 5 FIG2 is a diagram illustrating the frequency pulling effect of an acceleration in the -X direction (i.e., -Ax) on a resonator mass producing a corresponding displacement in the +X direction for single-ended sensing according to an exemplary embodiment. In this example, the frequency pulling effect is explained for half of the X axis (i.e., for resonator masses 101 and 102 relative to electrodes DX1, SX1, DX2, and SX2), although the same effect applies to the other half of the X axis (i.e., for resonator masses 103 and 104 relative to electrodes DX3, SX3, DX4, and SX4), and a similar effect applies to the Y axis. Because the resonator masses 101-104 have strong coupling in this exemplary embodiment, each resonator mass will have the same resonant frequency (at Figure 5 is represented as "fr" in Chinese).

[0109] The initial capacitance between a given resonator mass and the corresponding electrode can be expressed as:

[0110]

[0111] where d o is the nominal gap between the electrode and the corresponding finger-like structure extending from the corresponding resonator mass.

[0112] The rate of change of capacitance when the resonator mass moves a distance x (e.g., nanometers) can be expressed as:

[0113] The force on a given resonator mass from the corresponding drive electrode due to dC / dx can be expressed as:

[0114] Fd = (1 / 2)(dC / dx)(VDC_drive – VDC_bulk) 2

[0115] The force on a given resonator mass from the corresponding sensing electrode due to dC / dx can be expressed as:

[0116] Fs = (1 / 2)(dC / dx)(VDC_sense – VDC_bulk) 2

[0117] The electrostatic stiffness caused by dC / dx can be expressed as:

[0118]

[0119] where Vr is the voltage placed on a given electrode and V is the potential placed on the resonator mass.

[0120] The total stiffness of the resonator mass as the gap changes in x can be expressed as (Keq-Ke), where Keq is the initial mechanical stiffness.

[0121] The frequency shift caused by the stiffness change can be expressed as:

[0122]

[0123] like Figure 5 As shown, an acceleration in the -X direction (ie, -Ax) causes a corresponding displacement of the resonator mass in the +X direction. The gaps associated with electrodes DX2 and SX1 increase (ie, to d o +x) and thus the dC / dx associated with these electrodes decreases, while the gaps associated with electrodes SX2 and DX1 decrease (i.e., to d o =-x), so dC / dx associated with these electrodes increases. As a result, the X-axis resonance frequency fr of the resonator mass 101 decreases, and the X-axis resonance frequency fr of the resonator mass 102 also decreases.

[0124] The resonant frequency fr relative to the SX1 and SX2 electrodes can be expressed as:

[0125]

[0126]

[0127] where Gee is the input acceleration (in meters per square), f0 is the nominal resonant frequency of the resonator mass, Vres is the resonator voltage, and Vs is the SX voltage.

[0128] The resonant frequency fr relative to the DX1 and DX2 electrodes can be expressed as:

[0129]

[0130]

[0131] where Gee is the input acceleration (in meters per square), f0 is the nominal resonant frequency of the resonator mass, Vres is the resonator voltage, and Vd is the DX voltage.

[0132] The resonant frequency fr about the SX4 and DX4 electrodes should be the same or nearly the same as that of the SX1 and DX1 electrodes.

[0133] The resonant frequency fr with respect to the SX3 and DX3 electrodes should be the same or nearly the same as the resonant frequency of the SX2 and DX2 electrodes.

[0134] The frequency shift contribution of the SX electrode can be expressed as:

[0135] dfrSX(Gee):=(frSX1(0)–frSX1(Gee))+(frSX2(0)–frSX2(Gee))+(frSX3(0)–frSX3(Gee))+(frSX4(0)–frSX4(Gee))

[0136] The frequency shift contribution of the DX electrode can be expressed as:

[0137] dfrDX(Gee):=(frDX1(0)–frDX1(Gee))+(frDX2(0)–frDX2(Gee))+(frDX3(0)–frDX3(Gee))+(frDX4(0)–frDX4(Gee))

[0138] The total X-axis frequency shift under Gee input acceleration can be expressed as follows:

[0139] dfrX(Gee):=dfrDX(Gee)+dfrSX(Gee)

[0140] It is worth noting that both the DX electrode and the SX electrode contribute to the resonant frequency change, and the larger the voltage difference between the DX and SX electrodes, the larger the resonant frequency change.

[0141] Figure 6 FIG1 is a schematic block diagram of a single-axis accelerometer control circuit 800 for single-ended sensing according to an exemplary embodiment. Accelerometer control circuit 800 includes a drive circuit 802, a measurement circuit 806, an excitation feedback circuit 808, a reference frequency circuit 818, and a difference frequency circuit 820. Generally speaking, drive circuit 802 drives the resonator mass of resonator 804. Excitation feedback circuit 808 provides a control signal to drive circuit 802 based on a signal sensed by measurement circuit 806 via a sensing electrode to maintain the resonance of the resonator mass at a desired resonant frequency. Measurement circuit 806 measures the resonant frequency F1 of resonator 804, which, as described above, changes in the presence of an external acceleration. Difference frequency circuit 820 provides an output signal 830 based on the difference between the measured resonant frequency of the resonator from measurement circuit 806 and a reference frequency provided by reference frequency circuit 818 (i.e., based on F1 minus F2). For example, output signal 330 may be the difference in resonant frequencies (i.e., F1 - F2), or may be an acceleration calculated from the different resonant frequencies and a scale factor for a particular sensitivity axis (e.g., if the scale factor for a particular gyroscope is 100 Hz / G and the frequency change is 50 Hz, then output signal 330 may be 0.5 G).

[0142] Exemplary embodiments generally include a separate accelerometer control circuit 800 for each axis of sensitivity.

[0143] Figure 7 1 is a schematic top view of a device layer structure for an XY-axis resonant accelerometer for strongly coupled in-phase driving and single-ended X / Y-axis sensing using a resonator mass according to an exemplary embodiment of the present invention. Figure 4-6 As with the described exemplary embodiments, the resonator masses have strong mechanical coupling (e.g., via one or more tethers marked "*" between each pair of adjacent resonator masses) such that the four resonator masses effectively act as a single resonant frequency for each sensitivity axis, such as a single x-axis resonant frequency and a single y-axis resonant frequency. Single-ended sensing is used to generate an accelerometer output for each sensitivity axis based on a change in resonant frequency caused by a frequency-pull effect in the presence of an external acceleration, where the entire body experiences a change in resonant frequency when the external acceleration occurs. The change in resonant frequency, and therefore the magnitude of the external acceleration, can be determined by comparing the body's resonant frequency to a reference frequency.

[0144] For x-axis motion in one exemplary embodiment, the resonator masses 101-104 are driven by drive electrodes DX1-DX4 to move back and forth in phase with one another. In this example, the motion of the resonator masses 101-104 can be achieved by driving the drive electrodes DX1, DX2, DX3, and DX4 in phase with one another, i.e., the same drive signal is applied to all of these drive electrodes. During one phase of the x-axis motion, the resonator masses 101-104 move to the right (i.e., in the "x" direction), and during the opposite phase of the x-axis motion, the resonator masses 101-104 move to the left (i.e., in the "-x" direction).

[0145] For y-axis motion in one exemplary embodiment, the resonator masses 101-104 are driven by drive electrodes DY1-DY4 to move back and forth in phase with one another. In this example, the motion of the resonator masses 101-104 can be accomplished by driving drive electrodes DY1, DY2, DY3, and DY4 in phase, i.e., the same drive signal is applied to all of these drive electrodes. During one phase of the y-axis motion, the resonator masses 101-104 move upward (i.e., in the "y" direction), and during the anti-phase phase of the y-axis motion, the resonator masses 101-104 move toward the bottom (i.e., in the "-y" direction).

[0146] As described above, the resonator mass can be configured to resonate such that the x-axis resonant frequency and the y-axis resonant frequency are substantially different, for example to help alleviate mode injection and locking issues.

[0147] Under external acceleration relative to a given sensitivity axis, all four resonator masses will move in opposite directions relative to that sensitivity axis. Due to the frequency-pull effect, the resonant body will experience a change in resonant frequency. The resonant frequency of the resonant body can be sensed by sensing electrodes, and an output signal can be generated based on the difference between the sensed resonant frequency and a reference frequency.

[0148] So, for example, under an external X-axis acceleration in the -X direction, all four proof masses will move in the +X direction while stationary, while still being driven into resonance. The gap between each proof mass and its corresponding X-axis drive electrode will decrease, while the gap between each proof mass and its corresponding X-axis sense electrode will increase.

[0149] Under external X-axis acceleration in the +X direction, the opposite situation occurs, that is, the gap between each detection mass and its corresponding X-axis drive electrode becomes larger, while the gap between each detection mass and its corresponding X-axis sense electrode becomes smaller.

[0150] Similarly, under an external Y-axis acceleration in the -Y direction, all four proof masses move in the +Y direction while stationary, while still being driven into resonance. The gap between each proof mass and its corresponding Y-axis drive electrode decreases, while the gap between each proof mass and its corresponding Y-axis sense electrode increases.

[0151] Under external Y-axis acceleration in the +Y direction, the opposite situation occurs, that is, the gap between each detection mass block and its corresponding Y-axis drive electrode will become larger, while the gap between each detection mass block and its corresponding Y-axis sense electrode will become smaller.

[0152] As a result, the resonant frequency of the resonator changes.

[0153] Figure 8 is based on Figure 7 The exemplary embodiment of FIG. 1 shows a diagram illustrating the frequency pulling effect of an acceleration in the -X direction (i.e., -Ax) on a resonator mass producing a corresponding displacement in the +X direction for single-ended sensing. In this example, the frequency pulling effect is explained for half of the X axis (i.e., for resonator masses 101 and 102 relative to electrodes DX1, SX1, DX2, and SX2), but the same effect also applies to the other half of the X axis (i.e., for resonator masses 103 and 104 relative to electrodes DX3, SX3, DX4, and SX4), and a similar effect applies to the Y axis. Because the resonator masses 101-104 have strong coupling in this exemplary embodiment, each resonator mass will have the same resonant frequency (at Figure 8 is represented as "fr" in Chinese).

[0154] like Figure 8 As shown, an acceleration in the -X direction (ie, -Ax) causes a corresponding displacement of the resonator mass in the +X direction. The gaps associated with electrodes SX1 and SX2 increase (ie, to d o +x), and thus the dC / dx associated with these electrodes decreases, while the gap associated with electrodes DX1 and DX2 decreases (i.e., to d o =-x), and thus the dC / dx associated with these electrodes increases. As a result, the X-axis resonant frequency fr of the resonator mass 101 decreases, and the X-axis resonant frequency fr of the resonator mass 102 also decreases.

[0155] In this example using in-phase drive, the resonant frequencies of all drive electrodes DX1-DX4 should be the same, and the resonant frequencies of all sense electrodes SX1-SX4 should be the same. Figure 4-6 As discussed, the resonant frequency change can be determined differentially.

[0156] Z-axis sensing

[0157] In various exemplary embodiments, the multi-axis resonant accelerometer also includes Z-axis sensing. For Z-axis sensing, the multi-axis resonant accelerometer includes at least one z-axis sensor element, wherein each z-axis sensor element is part of a unique resonator mass and moves with the rest of the resonator mass in the X-axis and Y-axis directions, and is further configured to resonate up and down in the z-axis (i.e., out-of-plane) direction when driven by a set of drive electrodes below and / or above the z-axis sensor element. Out-of-plane motion of the z-axis sensor element is sensed using a set of sense electrodes below and / or above the z-axis sensor element. Signals from the z-axis sense electrodes are combined to generate the accelerometer's z-axis output signal. As with the x-axis and y-axis sensors discussed above, the z-axis sensor can operate using differential sensing or single-ended sensing.

[0158] In certain exemplary embodiments, the Z-axis sensor element is a seesaw element configured to resonate with a "teeter-totter" for "teeter-totter" motion, although alternative embodiments may use other Z-axis sensor element configurations, including configurations in which the entire resonator mass resonates in the Z-axis direction. In certain exemplary embodiments, the seesaw element is large and constitutes the majority of the moving mass of the resonator mass for both the x-axis and y-axis motions.

[0159] Figure 9FIG2 is a schematic top view of a device layer structure for a triaxial resonant accelerometer according to an exemplary embodiment. In this exemplary embodiment, four resonator masses 501, 502, 503, and 504 are supported above an underlying substrate (not shown for convenience) and driven to resonate simultaneously in the X-axis, Y-axis, and Z-axis directions relative to the underlying substrate.

[0160] The operation of the resonant accelerometer for the X and Y axes is essentially as described above with reference to Figure 1-3 Specifically, the resonator mass is driven in the X- and Y-axis directions relative to an underlying substrate via a set of in-plane drive electrodes, which are directly or indirectly fixedly supported by the underlying substrate. The in-plane motion of the resonator mass relative to the underlying substrate is sensed by a set of in-plane sense electrodes, which are also directly or indirectly fixedly supported by the underlying substrate. The X- and Y-axis sensors can operate using either differential or single-ended sensing.

[0161] Figure 10 Shown according to Figure 9 Details of the seesaw element of an embodiment (this specifically shows Figure 9 Detail of the seesaw element of resonator mass 502 is shown, although the other seesaw elements are identical but oriented in different directions due to the symmetry of the structure. Specifically, each seesaw element includes two lugs 602 and 604 supported by a central pivot flexure 606 that allows lugs 602 and 604 to move in the z-direction in anti-phase with each other (i.e., lobe 602 moves upward when lobe 604 moves downward, and lobe 602 moves downward when lobe 604 moves upward) via a "seesaw" or "teeter-totter" motion about an axis labeled "a."

[0162] Figure 11is a diagram illustrating the relative positions of the driver "D" and sense "S" electrodes under the seesaw elements according to an exemplary embodiment. In this example, each seesaw element has one Z-axis drive electrode and one Z-axis sense electrode. In this example, the seesaw elements of resonator masses 501 and 503 are driven in phase with each other, while the seesaw elements of resonator masses 502 and 504 are driven in phase with each other and in antiphase with the seesaw elements of resonator masses 501 and 503. This causes the blades of the seesaw elements of resonator masses 501 and 503 to move downward toward the underlying substrate when their protrusions overlie drive electrodes D1 and D3, while the blades of the seesaw elements of resonator masses 502 and 504 overlie sense electrodes S2 and S4. When the protrusions of the seesaw elements of resonator masses 501 and 503 overlie drive electrodes D1 and D3, they move upward from the underlying substrate, while the blades of the seesaw elements of resonator masses 502 and 504 overlie sense electrodes S2 and S4. This is accomplished by driving drive electrodes D1, D2, D3, and D4 in phase with each other.

[0163] According to equation (1), when the blades of the seesaw elements of resonator masses 501 and 503 are overlaid on drive electrodes D1 and D3, they face the substrate below, K 静电 will increase, and the resonant frequency of the detection masses 501 and 503 will decrease. This resonant frequency change is sensed using sensing electrodes S1 and S3, respectively. At the same time, the blades of the seesaw element of the resonator masses 502 and 504 on the drive electrodes D2 and D4 move upward from the bottom substrate, so K 静电 will decrease, and the resonant frequency of proof masses 502 and 504 will increase. This resonant frequency change is sensed using sensing electrodes S2 and S4, respectively. Similar to the X and Y axes, a Z-axis accelerometer output signal can be generated based on the change in resonant frequency.

[0164] In a particular exemplary embodiment, Figure 9 A three-axis resonant accelerometer of the type shown operates with an x-axis resonant frequency of 39 KHz, a y-axis resonant frequency of 42 KHz, and a z-axis resonant frequency of 43 KHz, although the axes may operate at different resonant frequencies, which may be the same or different from one another.

[0165] Similar to X-axis and Y-axis acceleration, Z-axis acceleration acts on all four seesaw elements and effectively changes the gap between the blades and the corresponding Z-axis drive / sense electrodes, which in turn effectively changes the spring constant of the central pivot flexure 606 supporting the lobe. As a result, the resonant frequency of one pair of lobes increases, while the resonant frequency of the other pair of lobes decreases. This relative change in resonant frequency can be detected differentially using the Z-axis sense electrodes.

[0166] For example, during one phase of operation, Z-axis acceleration pulling all four masses downward will effectively lower the resonant frequency of the blade moving downward, while effectively increasing the resonant frequency of the blade moving upward. This relative change in resonant frequency will manifest as a change in the combined differential output from the Z-axis sense electrodes, which can be sensed to provide an accelerometer output signal representing acceleration while also filtering out any cross-coupling with other axes based on the substantial difference in resonant frequency.

[0167] Because Z-axis sensor elements are typically not mechanically interconnected to ensure that they resonate at the same nominal Z-axis resonant frequency, certain embodiments may include additional electrodes and circuitry to adjust the resonant frequency of one or more Z-axis sensor elements so that the Z-axis sensor elements resonate in synchronization with each other.

[0168] It should be noted that embodiments of accelerometers of the type described herein can be very compact, for example having a sensor size of approximately 1 mm x 1 mm. Due to the compact size and, in embodiments using differential sensing, the use of differential sensing, it is desirable for such accelerometers to have minimal offset displacement from package stress. Importantly, such accelerometers can operate in a vacuum or very low pressure (e.g., with a lid) and can therefore be integrated with gyroscopes, for example, to achieve a six-degree-of-freedom inertial sensor under a single lid.

[0169] Without departing from the true scope of the invention, the present invention may be implemented in other specific forms, and based on the teachings herein, many changes and modifications will be obvious to those skilled in the art. Unless the context requires otherwise, any reference to the "invention" is intended to refer to exemplary embodiments of the present invention and should not be construed as referring to all embodiments of the present invention. The described embodiments are to be considered in all respects only as illustrative and not restrictive.

Claims

1. A multi-axis resonant accelerometer comprising: A resonator comprising four proof masses arranged in a device plane, each of the four proof masses comprising a first finger structure extending in the y-axis direction and a second finger structure extending in the x-axis direction; The first finger structure of each of the four detection masses is located between a corresponding x-axis drive electrode and a corresponding x-axis sense electrode that are arranged opposite to each other in the x-axis direction to form a part of: an x-axis drive capacitor configured to drive x-axis motion of the proof mass in the plane of the device; and an x-axis sensing capacitor configured to sense a change in the x-axis resonant frequency of the proof mass based on electrostatic spring tuning in the presence of x-axis acceleration; and The second finger structure of each of the four detection masses is located between a corresponding y-axis drive electrode and a corresponding y-axis sense electrode that are arranged opposite to each other in the y-axis direction to form a part of: a y-axis drive capacitor configured to drive y-axis motion of the proof mass in the plane of the device; and A y-axis sensing capacitor is configured to sense a change in a y-axis resonant frequency of the proof mass based on electrostatic spring tuning in the presence of a y-axis acceleration.

2. The multi-axis resonant accelerometer according to claim 1, wherein: A portion of the x-axis sensing capacitor formed by a first proof mass of the four proof masses and a portion of the x-axis sensing capacitor formed by a second proof mass of the four proof masses are collectively configured to differentially sense a change in resonant frequency, the first proof mass and the second proof mass being adjacent to and offset from each other along the x-axis.

3. The multi-axis resonant accelerometer of claim 1, wherein the x-axis motion and the y-axis motion are driven at the same resonant frequency.

4. The multi-axis resonant accelerometer of claim 1, wherein the x-axis motion and the y-axis motion are driven at different resonant frequencies.

5. The multi-axis resonant accelerometer of claim 1, further comprising circuitry configured to determine a change in x-axis resonant frequency by detecting a voltage between the x-axis drive capacitor and the x-axis sense capacitor.

6. The multi-axis resonant accelerometer of claim 1 , wherein the resonator further comprises a z-axis sensor element configured to resonate with z-axis motion perpendicular to the device plane, wherein the multi-axis resonant accelerometer further comprises: a z-axis driving electrode configured to drive a z-axis motion of the z-axis sensor element; and A z-axis sensing electrode is configured to sense a change in a z-axis resonant frequency of the z-axis sensor element based on electrostatic spring tuning in the presence of a z-axis acceleration.

7. The multi-axis resonant accelerometer of claim 6, wherein the z-axis sensor element comprises a seesaw sensor element.

8. A method for operating a multi-axis resonant accelerometer, wherein the multi-axis resonant accelerometer is the multi-axis resonant accelerometer according to any one of claims 1 to 7, the method comprising: driving each of the four proof masses to resonate with x-axis motion in the plane of the device; driving each of the four proof masses to resonate with y-axis motion in the plane of the device; sensing a change in an x-axis resonant frequency of each of the four proof masses based on electrostatic spring tuning in the presence of an x-axis acceleration; and A change in the y-axis resonant frequency of each of the four proof masses is sensed based on electrostatic spring tuning in the presence of y-axis acceleration.

9. The method of claim 8 , wherein driving each of the four proof masses to resonate with the x-axis motion comprises driving a first proof mass of the four proof masses with a first phase and driving a second proof mass of the four proof masses with a second phase opposite to the first phase.

10. The method of claim 8, wherein driving each of the four proof masses to resonate with x-axis motion in the device plane comprises: A first proof mass of the four proof masses is driven and a second proof mass of the four proof masses is driven, the first proof mass and the second proof mass being adjacent to each other along the x-axis and offset from each other such that differential sensing of the resonant frequency change is performed.

11. The method of claim 8 , wherein driving each of the four proof masses to resonate with x-axis motion comprises driving each of the four proof masses to resonate with x-axis motion at a first resonant frequency, and wherein driving each of the four proof masses to resonate with y-axis motion comprises driving each of the four proof masses to resonate with y-axis motion at the first resonant frequency.

12. The method of claim 8 , wherein driving each of the four proof masses to resonate with x-axis motion comprises driving each of the four proof masses to resonate with x-axis motion at a first resonant frequency, and wherein driving each of the four proof masses to resonate with y-axis motion comprises driving each of the four proof masses to resonate with y-axis motion at a second resonant frequency different from the first resonant frequency.

13. The method of claim 8, further comprising inferring a change in x-axis resonant frequency based on a voltage difference between an x-axis drive capacitor and an x-axis sense capacitor.

14. The method of claim 8, wherein the multi-axis resonant accelerometer further comprises a z-axis sensor element configured to resonate with z-axis motion perpendicular to the device plane, wherein the method further comprises: driving the z-axis motion of the z-axis sensor element; and Changes in the z-axis resonant frequency of the z-axis sensor element are sensed based on electrostatic spring tuning in the presence of z-axis acceleration.

15. A multi-axis resonant accelerometer comprising: A resonator comprising four proof masses arranged in a device plane, each of the four proof masses comprising a first finger structure extending in the y-axis direction and a second finger structure extending in the x-axis direction; The first finger structure of each of the four detection masses is located between a corresponding x-axis drive electrode and a corresponding x-axis sense electrode that are arranged opposite to each other in the x-axis direction to form a part of: means for driving the respective proof masses to resonate with x-axis motion in the plane of the device; and means for sensing a change in the x-axis resonant frequency of the respective proof masses based on electrostatic spring tuning in the presence of x-axis acceleration; and The second finger structure of each of the four detection masses is located between a corresponding y-axis drive electrode and a corresponding y-axis sense electrode that are arranged opposite to each other in the y-axis direction to form a part of: means for driving the respective proof masses to resonate with y-axis motion in the plane of the device; Means for sensing a change in a y-axis resonant frequency of a respective proof mass based on electrostatic spring tuning in the presence of a y-axis acceleration.

16. The multi-axis resonant accelerometer of claim 15, wherein the x-axis motion and the y-axis motion are driven at the same resonant frequency.

17. The multi-axis resonant accelerometer of claim 15, wherein the x-axis motion and the y-axis motion are driven at different resonant frequencies.

18. The multi-axis resonant accelerometer of claim 15, further comprising circuitry configured to determine a change in the x-axis resonant frequency by detecting a voltage between the x-axis drive capacitor and the x-axis sense capacitor.

19. The multi-axis resonant accelerometer of claim 15, wherein the resonator further comprises a z-axis sensor element configured to resonate with z-axis motion perpendicular to the device plane, wherein the multi-axis resonant accelerometer further comprises: a member for driving z-axis motion of the z-axis sensor element; and For sensing a change in a z-axis resonant frequency of the z-axis sensor element based on electrostatic spring tuning in the presence of a z-axis acceleration.

20. The multi-axis resonant accelerometer of claim 19, wherein the z-axis sensor element comprises a seesaw sensor element.

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