CN112782428A - Vibrating beam accelerometer with pressure damping - Google Patents

Abstract

The invention provides a vibrating beam accelerometer with pressure damping. This disclosure describes techniques for damping proof mass motion of an accelerometer while implementing an underdamped resonator. In the example of an in-plane microelectromechanical system (MEMS) VBA, the proof mass can include one or more damping combs that include one or more sets of rotor comb fingers attached to the proof mass. The rotor comb fingers may be interdigitated with stator comb fingers attached to a fixed geometry. The damping comb fingers can provide air damping for the proof mass when the MEMS die is placed in a package containing a pressure above vacuum. The geometry of the damping comb has a reduced air gap and a large overlap area between the rotor comb fingers and the stator comb fingers. The geometry of the resonator of the VBA of the present disclosure may be configured to avoid air damping.

Description

Vibrating beam accelerometer with pressure damping

The present patent application claims the following benefits:

us provisional patent application 62/932,397 filed on 7/11/2019, and

us provisional patent application 62/932,298 filed 2019, 11, 7, each of which is hereby incorporated by reference in its entirety.

Technical Field

The present disclosure relates to vibrating beam accelerometers.

Background

Accelerometers function by detecting the displacement of a proof mass under inertial forces. In one example, an accelerometer can detect displacement of a proof mass by changes in the frequency of a resonator connected between the proof mass and a support base. The resonator may be designed to change the frequency in proportion to the load applied to the resonator by the proof mass under acceleration. The resonator may be electrically coupled to a signal generating circuit forming an oscillator that causes the resonator to vibrate, and in some examples, at a resonant frequency of the resonator.

Disclosure of Invention

In general, the present disclosure provides techniques for improving the functionality of a Vibrating Beam Accelerometer (VBA). In one example, the present disclosure describes techniques for damping proof mass motion of an accelerometer while implementing an underdamped resonator. In the example of an in-plane microelectromechanical system (MEMS) VBA, the proof mass can include one or more damping combs that include one or more sets of movable comb fingers attached to the proof mass. The movable comb fingers can be interdigitated with anchoring comb fingers attached to a fixed geometry. The damping comb fingers can provide air damping for the proof mass when the MEMS die is placed into a pressure chamber of a package containing a pressure above vacuum. In some examples, the MEMS die may be placed into a ceramic package containing a pressure of about 1 torr. The geometry of the damping comb can minimize the air gap and maximize the overlap area between the movable comb fingers and the anchoring comb fingers. The geometry of the resonator of the VBA of the present disclosure may be configured to avoid air damping.

In other examples, the present disclosure describes techniques to configure a capacitive comb of an accelerometer resonator as discrete electrodes having a drive electrode and at least two sense electrodes. The techniques of this disclosure also describe the routing of electrical signals on the die and on the analog electronics board, which are designed to produce approximately equal parasitic feed-through capacitance. The at least two sensing electrodes can be placed on opposite sides of the moving resonator beam such that the magnitude of the capacitance change (e.g., dC/dx) with respect to displacement is approximately equal and opposite in sign. This may result in a sense current that is also opposite in sign and in that the feed-through current will have the same sign. The sense output from the resonator may be connected to a differential front end amplifier (such as a transimpedance or charge amplifier) that handles differences in output current. Processing this difference in output current may mitigate the effects of the feedthrough current and eliminate parasitic feedthrough capacitance. Parasitic feedthrough capacitance can result in increased accelerometer noise and reduced bias stability.

In other examples, the present disclosure describes an accelerometer device comprising: a support base; a resonator comprising an anchor portion and a release portion, wherein the anchor portion of the resonator is mechanically connected to the support base; a proof mass mechanically connected to the released portion of the resonator, the proof mass comprising one or more damping combs, wherein the damping combs: including movable comb fingers and anchoring comb fingers, wherein the anchoring comb fingers of the one or more damping combs are mechanically connected to the support base, wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and wherein a spacing between the movable comb fingers of the one or more damping combs and the anchoring comb fingers of the one or more damping combs is configured to provide air damping for the proof mass; and a pressure chamber, wherein the pressure chamber contains the support base, the resonator, the proof mass, and the one or more damping combs.

In other examples, the present disclosure describes a system for determining acceleration, the system comprising: a suspended mass Vibrating Beam Accelerometer (VBA) comprising: a support base; a resonator comprising an anchor portion and a release portion, wherein the anchor portion of the resonator is mechanically connected to the support base; a proof mass mechanically connected to the released portion of the resonator, the proof mass comprising one or more damping combs, wherein the damping combs: including movable comb fingers and anchoring comb fingers, wherein the anchoring comb fingers of the one or more damping combs are mechanically connected to the support base, wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and wherein a spacing between the movable comb fingers of the one or more damping combs and the anchoring comb fingers of the one or more damping combs is configured to provide air damping for the proof mass; and a pressure chamber, wherein the pressure chamber contains the support base, the resonator, the proof mass, and the one or more damping combs; a resonator drive circuit operatively connected to the suspended mass VBA; and a processing circuit operatively connected to the suspended mass VBA via the resonator drive circuit, wherein: the resonator drive circuit is configured to output a first signal that causes the resonators of the suspended mass VBA to vibrate at a respective resonant frequency of each of the resonators, acceleration of the suspended mass VBA in a direction substantially parallel to a second plane causes rotation of the suspended proof mass about hinge flexures parallel to the second plane, the resonators are configured to receive a force in response to the rotation of the suspended proof mass such that the force causes a respective change in the resonant frequency of the resonators, and the processing circuit is configured to receive a second signal from the suspended mass VBA indicative of the respective change in the resonant frequency and determine an acceleration measurement based on the respective change in the resonant frequency.

In other examples, the present disclosure describes a method comprising: receiving, by a processing circuit, one or more electrical signals indicative of a frequency of a first resonator beam and a frequency of a second resonator beam from a Vibrating Beam Accelerometer (VBA), wherein the VBA comprises: a support base; a resonator comprising an anchor portion and a release portion, wherein the anchor portion of the resonator is mechanically connected to the support base; a proof mass mechanically connected to the released portion of the resonator, the proof mass comprising one or more damping combs, wherein the damping combs: including movable comb fingers and anchoring comb fingers, wherein the anchoring comb fingers of the one or more damping combs are mechanically connected to the support base, wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and wherein a spacing between the movable comb fingers of the one or more damping combs and the anchoring comb fingers of the one or more damping combs is configured to provide air damping for the proof mass; and a pressure chamber, wherein the pressure chamber contains the support base, the resonator, the proof mass, and the one or more damping combs; determining, by the processing circuit and based on the one or more electrical signals, the frequency of the first resonator beam and the frequency of the second resonator beam; and calculating, by the processing circuit and based on the frequency of the first resonator beam and the frequency of the second resonator beam, an acceleration of the VBA.

Drawings

Fig. 1 is a conceptual diagram illustrating a pendulous VBA with a support flexure, an X-direction resonator, and a damping comb.

Fig. 2 is a conceptual diagram illustrating a cross-sectional view of a pendulous VBA with a support flexure and with an X-direction resonator.

Fig. 3A is a block diagram illustrating a system including a pendulous VBA in accordance with one or more techniques of the present disclosure.

Figure 3B is a block diagram illustrating an accelerometer system according to one or more techniques of this disclosure.

Fig. 4 is a conceptual diagram illustrating an example of resonator electrode placement and electrical signal routing to avoid the effects of parasitic feed-through capacitance on accelerometer performance.

Fig. 5A and 5B are schematic diagrams illustrating an exemplary MEMS VBA configured with a single sense electrode.

Fig. 6A and 6B are schematic diagrams illustrating an example MEMS VBA configured with two sense electrodes in accordance with one or more techniques of the present disclosure.

Fig. 7A is a conceptual diagram illustrating a first resonator with an additional mass according to one or more techniques of this disclosure.

Fig. 7B is a conceptual diagram illustrating a portion of the first resonator of fig. 7A including an additional mass according to one or more techniques of the present disclosure.

Fig. 8A is a conceptual diagram illustrating a second resonator forming a gap according to one or more techniques of the present disclosure.

Fig. 8B is a conceptual diagram illustrating a portion of the second resonator of fig. 5A including a gap according to one or more techniques of this disclosure.

Fig. 9 is a graph illustrating a first graph representing a second order nonlinear coefficient as a function of additional mass position and a second graph representing a zero acceleration resonant frequency difference as a function of additional mass position, according to one or more techniques of the present disclosure.

FIG. 10 is a flow diagram illustrating exemplary operations for determining acceleration of the VBA in accordance with one or more techniques of the present disclosure.

Detailed Description

The techniques of this disclosure may be incorporated into a variety of VBAs. For example, the techniques described by U.S. patent application 16/041,244 (which is hereby incorporated by reference in its entirety) for planar geometry and a single primary mechanical anchor between the support base and the VBA may be combined with the techniques of this disclosure.

Fig. 1 is a conceptual diagram illustrating a pendulous VBA with a support flexure and with an X-direction resonator. FIG. 1 is a top view of the VBA30 showing the anchor 14 to a support base, but the support base is not shown in FIG. 1. VBA30 includes a suspended proof mass 32 having a damping comb 40 and resonators 18A and 18B connected to anchor 14 and resonator connecting structure 16 at hinge flexure 22. Fig. 1 also shows a section a-a' extending along the long axis of the resonator connection structure 16 and through the anchor 14. In the present disclosure, the resonator connection structure 16 may also be referred to as a rigid anchor connection 16.

The suspended proof mass 32 includes a support flexure and is connected to the resonator connection structure 16 at anchor 14 by hinge flexure 22. The hinge flexure 22 suspends the proof mass at the anchor 14, and the point at which the hinge flexure 22 connects to the anchor 14 is the center of rotation of the proof mass 32. The left resonator 18A and the right resonator 18B are connected to the same primary anchor 14 by a resonator connection structure 16. Resonators 18A and 18B are connected to proof mass 12 at a distance r1 from the center of rotation of proof mass 32. Proof mass 12 has center of mass 24 which is a distance r2 from the center of rotation of proof mass 12. The arrangement of VBA30 causes the inertial force of proof mass 12 on the release beams of resonator beams 19A and 19B to be amplified by the leverage ratio r2/r 1.

In exemplary FIG. 1, the VBA30 may be implemented as a planar microelectromechanical system (MEMS) VBA. Proof mass 32 may include one or more damping combs 40 comprising one or more sets of movable comb fingers 42 attached to proof mass 32. The movable comb fingers 42 may be interdigitated with anchoring comb fingers 44 attached to a fixed geometry, such as anchors 46. These damping comb fingers 42 and 44 lie in the same plane as proof mass 32 and can provide air damping for proof mass 32 when the MEMS die is placed into a package containing a pressure above vacuum. In some examples, the MEMS die may be placed into a ceramic package containing an internal pressure of about 1 torr. Pressure changes may change the degree of damping. In the present disclosure, "movable comb fingers 42" may be referred to as "rotor comb fingers 42". Additionally, "anchor comb fingers 44" may be referred to as "stator comb fingers 44".

In the present disclosure, air damping may include damping caused by two surfaces sliding past each other, such as couette damping. In other examples, the air damping may include two surfaces in proximity to each other, such as squeeze film damping. In some examples, one type of air damping may have a greater effect than other types of air damping, and may depend on VBA geometry.

The geometry of the damping comb 40 may minimize air gaps and maximize the overlap area between the movable comb fingers 42 and the anchoring comb fingers 44. As shown in fig. 1, a first one of the movable comb fingers is adjacent to a first one and a second one of the anchor comb fingers. The overlapping portions have a total linear distance. The total linear distance is the sum of the first length and the second length. The first length is a linear distance that a first edge of a first one of the movable comb fingers overlaps a first edge of a first one of the anchoring comb fingers. The second length is a linear distance that a second edge of a first one of the movable comb fingers overlaps a first edge of a second one of the anchoring comb fingers. The example of fig. 1 shows six damping combs. However, in other examples, the VBA may include more or fewer damping combs. More damping combs can result in a larger overlap and thus a longer overall linear distance. Longer overall linear distances may result in greater damping. Similarly, more fingers per damping comb may result in longer overall linear distance and greater damping. The movable comb fingers and the anchoring comb fingers may be configured with a plurality of widths in the X direction. Thinner (e.g., slimmer) fingers may result in more fingers, greater overall linear distance, and greater damping. In addition, the movable comb fingers and the anchoring comb fingers may be configured with a plurality of lengths in the Y direction. Longer fingers may result in greater overall linear distance and greater damping. Because the quality factor depends on the damping and the mass and stiffness of the VBA30, a designer may consider the amount of damping desired and the mechanical and structural strength of the VBA30 when selecting the geometry of the damping comb 40.

Proof mass 32 may include one or more support flexures to increase the stiffness of proof mass 32 in the out-of-plane (z) direction. In other words, the support flexures (e.g., flexures 33) coupled to proof mass 32 are configured to limit out-of-plane motion of the suspended proof mass relative to an X-Y plane parallel to proof mass 32 and resonator connecting structure 16. These flexures are configured to be significantly more flexible in the in-plane (x and y) directions than a rigid resonator connection structure or than the axial stiffness of the resonator. For example, the flexure 33 includes an anchor portion connected to a support base (not shown in fig. 1) similar to the primary anchor 14 and the anchor 46. Flexure 33 may include a compliant portion 36C connected between anchor portion 33 and proof mass 32. Compliant portion 36C may be of the same or similar material as the material of proof mass 32. The configuration of the one or more support flexures may reduce out-of-plane movement while avoiding bias caused by forces applied to the accelerometer mechanism (e.g., proof mass 32 and resonators 18A and 18B), which may be caused by CTE mismatch between the base and the accelerometer mechanism.

Proof mass 32 may include additional support flexures, such as a flexure having anchor portions 34A and 34B and compliant portions 36A and 36B. As described above for flexures 33, compliant portions 36A and 36B may be of the same or similar material as proof mass 32. The location of anchor portions 34A and 34B and the shape and configuration of compliant portions 36A and 36B shown in fig. 1 are merely one exemplary technique for providing support flexures to enhance movement of proof mass 32 in the out-of-plane (z) direction. In other examples, the flexible portions 36A and 36B may have different shapes, such as a straight beam or an S-shape. In other examples, the VBA30 may have more or fewer support flexures. The anchoring portions of the support flexures of the present disclosure will not exert significant force on proof mass 32, so the mechanism of VBA30 will still be connected to the structure of the support base primarily through a single anchoring region (e.g., anchor 14). Advantages of the geometry of the VBA30 may include a reduction in bias errors that may otherwise result from thermal expansion mismatch between the glass substrate (support base) and the silicon mechanism (e.g., the suspended proof mass 32).

The use of a single primary mechanical anchor 14 may reduce or prevent bias errors that may be caused by external mechanical forces applied to the circuit board, package, and/or substrate (including the accelerometer mechanism). Since the source of these forces may be unavoidable (e.g., thermal expansion mismatch between the substrate and the mechanism), the geometry of the VBA of the present disclosure may mechanically isolate sensitive components. Another advantage may include reduced cost and complexity by achieving mechanical isolation within the MEMS mechanism, which may avoid the need for additional manufacturing steps or components, such as discrete isolation stages.

Damping comb 40 is an exemplary technique for damping the proof mass motion of an accelerometer while implementing an underdamped resonator. A Vibrating Beam Accelerometer (VBA) functions by using a proof mass to apply inertial forces to a vibrating beam (also referred to as resonators 18A and 18B) such that the applied acceleration can be measured as a change in the resonant frequency of the vibrating beam.

A high quality factor may provide the benefit of mitigating the phase shift inherent to the resonator control electronics. This phase shift may cause a frequency shift, which ultimately manifests as an offset error. A large quality factor (Q), i.e., substantially under-damped, may also reduce the applied voltage required to achieve a particular displacement amplitude. However, to minimize Vibration Rectification Error (VRE), the motion of the proof mass may be substantially damped, and in some examples may be critically damped, i.e., return to equilibrium as quickly as possible without oscillation. Without sufficient proof mass damping, the accelerometer output may exhibit unacceptable bias error in the presence of ambient vibrations.

In contrast to damping comb 40, the geometry of resonators 18A and 18B of VBA30 of the present disclosure may be designed to avoid air damping. The geometry and partial pressure of the components of the MEMS VBA of the present disclosure may enable an under-damped resonator to have a relatively high quality factor Q, but damp the proof mass such that the proof mass Q is relatively low when compared to the Q of the resonator. For example, the reduced total linear distance of the combs on the resonator 18 may configure the relative Q between the combs of the resonator 18 and the damping comb 40 when compared to the total linear distance of the damping comb 40. Similarly, the air gap between the anchor and release portions of the resonator 18 and the air gap between the rotor comb fingers 42 and the stator comb fingers 44 of the damping comb 40 may also affect the relative Q.

A quality factor Q is typically assigned to a damped oscillator, where Q is the ratio of the energy stored in the oscillator to the energy dissipated per radian. In an over-damped system, the system returns to equilibrium without oscillation. The critical damping system returns to equilibrium as quickly as possible without oscillation. The under-damped system may oscillate (at a reduced frequency compared to the undamped case) with a gradual reduction in amplitude to zero. The quality factor can be written as:

Q＝E/[-dE/dθ]

when dE/d θ is written as (dE/dt)/(d θ/dt), the formula becomes: q ═ E/[ -dE/dt/d θ/dt ]. Since dE/dt is P (power dissipated) and d θ/dt is the angular frequency ω, this can be written as:

q ═ ω E/[ -dE/dt ] ═ ω E/P ═ ω (stored energy/dissipated power).

The frequency can be further described as: omega₁Is under-resistanceDamping oscillation frequency (slightly less than undamped frequency omega)₀)：ω₁ ²＝ω₀ ²-β²。

The techniques of this disclosure may be applied to, for example, a micro-electro-mechanical system (MEMS) Vibrating Beam Accelerometer (VBA), which represents one of many possible scenarios capable of achieving desired accelerometer performance. The techniques of this disclosure may improve the basic operation of the VBA. In existing MEMS VBAs, the resonator may be substantially under-damped (with Q in the range of 100 to perhaps 100,000), which may reduce the effect of phase shift from the control electronics on the closed loop resonant frequency. As discussed above, the underdamped resonator contrasts with the second design goal of the damped proof mass. These techniques may provide a way to implement an under-damped resonator (Q about 1000) while also damping the proof mass, which represents an advantage over other alternative solutions.

There are alternative solutions for proof mass partial damping, but some have the disadvantage of limiting performance, cost, and the required combination of size, weight, and power (SWaP). A first alternative example may include sealing both the proof mass and the resonator under a complete atmosphere. The complete atmosphere solution can be used for larger plants. But the air damping of the resonator becomes excessive after scaling down in size to typical MEMS dimensions. Excessive air damping can limit the ability of electrostatic drives and increase the susceptibility of the device to phase errors from the control electronics.

A second alternative example may include sealing the proof mass and resonator in separate cavities such that the proof mass is encapsulated under a complete atmosphere and the resonator is encapsulated under vacuum. This alternative example can significantly complicate device manufacturing and thus can ultimately increase costs.

A third alternative example may include sealing the proof mass and resonator under vacuum. A third alternative may mitigate vibration rectification errors by setting the proof mass resonant frequency significantly higher than the ambient vibration frequency. Unfortunately, the available die size and minimum resonator beam width dimension may prevent this solution from becoming viable. Under current constraints, significantly increasing the proof mass frequency can result in a low scaling factor, which can ultimately lead to poor bias performance.

A fourth example may include sealing the proof mass and resonator under vacuum. A force rebalance actuator that actively dampens vibrations may mitigate vibration rectification errors. Additional actuation electrodes may be included to counteract vibrations at high frequencies (> 100Hz) while allowing the proof mass to deflect at lower frequencies (< 100 Hz). This solution may be feasible, but introduces additional complexity to both the mechanical equipment and the auxiliary electronics and assumes the cost of introduction.

In contrast to the prior art, the techniques of this disclosure may provide a way to damp the proof mass while making the resonator significantly under-damped. This damping is achieved by gas damping without the need for separate chambers for different pressures. Finally, the techniques of this disclosure may enable a navigation-level accelerometer with reduced cost and SWaP to maintain bias repeatability in the presence of ambient vibrations. These techniques may avoid separate pressure chambers and/or more complex auxiliary electronics, both of which may result in higher costs.

Using partial pressure damping may include integrating the following features into the VBA design:

1. the proof mass may have a large area defining a small air gap (typically on the order of a few microns) between the proof mass and the anchoring geometry. Given sufficient gas pressure, this gap can generate air damping and ultimately reduce the Q of the proof mass motion.

2. The resonator may have only a small partial area contributing to air damping, which may enable relatively high Q resonator motion.

MEMS devices can be packaged at a partial voltage that, in combination with proof mass damping, results in a relatively high Q resonator (Q of about 100 or higher) and a low Q proof mass (Q < 100).

In some examples, the voltage division technique may be implemented within an in-plane MEMS VBA. As shown in fig. 1, proof mass 32, which includes sets of movable comb fingers 42 interdigitated with anchoring comb fingers 44, may be attached to a fixed geometry portion 46 of the accelerometer. The fingers of damping combs 40 provide air damping for proof masses 32. To maximize damping, the air gap can be reduced while maximizing the overlap area between comb fingers 42 and 44. Unlike damping combs, resonators can be configured to avoid air damping. The MEMS die is placed into a ceramic package containing a pressure of about 1 torr. This voltage division may cause the resonator to have a relatively high Q (about 1000), but keeps the proof mass Q slightly damped (Q about 10).

The same concepts can be applied to out-of-plane MEMS VBAs, in addition to in-plane MEMS VBAs. Such an apparatus may use a parallel plate gap between the proof mass and the anchoring geometry (rather than interdigitated comb fingers). The basic concept may be the same, i.e. air damping will damp the proof mass while giving the resonator a relatively high Q. A similar partial pressure of about 1 torr would likely result in sufficient damping with respect to typical air gaps and device geometries.

It should be noted that the techniques of this disclosure are applicable to VBAs that operate with different actuation methods. For example, piezoelectric actuation of a resonator may alleviate the need for a small capacitive air gap within the resonator geometry. A larger capacitive air gap may enable even greater differentiation between the resonator Q and the proof mass Q. In some examples, the VBA may provide proof-mass damping via sets of damping combs embedded within the proof-mass block, although other geometries and configurations may achieve similar effects in theory. In some examples, the damping combs can be attached to the sides of the proof mass rather than embedded in the middle. For some designs, only the edges of the proof mass itself with a small enough air gap may be sufficient to provide proof mass damping.

Fig. 2 is a conceptual diagram illustrating a cross-sectional view of a pendulous VBA with a support flexure and with an X-direction resonator. Fig. 2 shows a section a-a' of the VBA30 depicted in fig. 1 extending down the long axis of the resonator connection structure 16 and through the anchor 14. Parts in fig. 2 having the same reference numerals as in fig. 1 have the same description, characteristics and functions as described above. For example, the VBA 50 includes a suspended proof mass 32 (not shown in fig. 2) connected to the resonator connection structure 16 at the anchor 14. Fig. 2 also shows the anchoring portions of anchoring combs 26C and 20C, and the anchoring portions of support flexures 34A and 34B. The anchor 46 of the damping comb 40 may also be mechanically connected to the support base 36 (not shown in fig. 2).

As with VBA30 described above with respect to FIG. 1, VBA 50 can be fabricated using a silicon mask and a glass mask such that both proof mass 32 and resonator connection structure 16 are anchored primarily to a single region, such as anchor 14. The release silicon mechanical structure of the VBA 50 may be tethered to a support base 36, which may be a glass substrate, such as a quartz substrate or a silicon substrate. Proof mass 32 may also be tethered at other anchor regions (e.g., anchor portions 34A and 34B) configured to allow free movement of the released silicon portions, such as proof mass 32 and resonator beams 19A and 19B (not shown in fig. 2) of resonators 18A and 18B, relative to support base 36.

The support base 36 can include an encapsulating structure, such as structures 38A and 38B, that can surround the released portion of the VBA 30. In some examples, the VBA30 may include a lower support base 36 and an upper support (not shown in fig. 2). In some examples, an anchor portion, such as the anchor 14, may be mechanically connected to both the lower support base 36 and the upper support. The support base 36 can define a second plane that is also substantially parallel to the X-Y plane, which is different from the plane of the released portion of the VBA 30. The plane defined by the released portions of VBA30 (e.g., resonator beams 19A-19B and proof mass 32) may be substantially parallel to a second plane defined by support base 36. As described above with respect to fig. 1, the air gap between the plane of the proof mass and the plane of the support base 36 may allow the silicon portion (such as the proof mass) to move freely relative to the substrate.

The resonator connection structure 16 may be configured to be more rigid than the resonator. The rigid structure of the resonator connection structure 16 is connected to the resonator and branches back to the primary mechanical anchor 14, which is connected to the support base 36. As described above, the resonator connection structure 16 is sized to have a stiffness greater than the axial spring constant of the resonator and to support the resonator in the in-plane (e.g., x and y) directions. In some examples, the resonator connection structure 16 may be an order of magnitude stiffer than the resonator beams 19A-19B. The single primary anchor 14 allows mechanical attachment of the released portion of the VBA30 for thermal expansion at different rates or directions of the support base 36, without being constrained by other attachments that may result in offset and inaccurate support bases 36.

The support base 36 can include metal layers deposited onto a glass substrate (not shown in fig. 2) that define electrical lines connecting the silicon electrodes to the wire bond pads. In some examples, support base 36 may include bond pads and other metal structures (e.g., as shown by the arrows from 36) on the bottom surface of support base 36, such as conductive paths 37A and 37B. In some examples, the support base 36 may include a metal layer on a top surface (e.g., on a surface opposite the bottom surface), and in other examples, the support base 36 may include an intermediate metal layer (not shown in fig. 2) between the top and bottom surfaces. In some examples, the metal layers may be electrically connected to each other using vias or other types of connections through the support base 36. In some examples, the wire may also be defined by other conductive materials besides metal. As described above with respect to fig. 1, a metal layer or other conductive material may define electrical paths, such as conductive paths 37A and 37B, for carrying signals to and from VBA 30.

As described above with respect to fig. 1, each of the one or more resonators may include a resonator beam (e.g., 19A) having a release comb and an anchor comb (e.g., 20C and 26C). As shown in fig. 2, the anchoring portions of anchoring combs 20C and 26C extend from the plane of support base 36 to the plane of the release portion of VBA 30. Comb portions of anchor combs 20C and 26C are supported in the same plane as resonator beams 19A-19B and proof masses 12 and 32, as described above with respect to fig. 1.

Fig. 3A is a functional block diagram illustrating a system including a pendulous VBA in accordance with one or more techniques of the present disclosure. The functional blocks of system 100 are but one example of a system that may include a VBA according to the present disclosure. In other examples, the functional blocks may be combined, or the functions may be grouped in a different manner than shown in FIG. 3A. Other circuitry 113 may include power supply circuitry and other processing circuitry that may use the output of accelerometer 110 to perform various functions (e.g., inertial navigation and motion sensing).

System 100 may include processing circuitry 102, resonator drive circuits 104A and 104B, and accelerometer 110. The accelerometer 110 may comprise any VBA, including the suspended proof mass VBA accelerometer described above with respect to fig. 1-4.

In the example of fig. 3A, resonator drive circuits 104A and 104B are operatively connected to accelerometer 110, and can send drive signals 106A and 106B to accelerometer 110 and receive sense signals 108A and 108B from accelerometer 110. In the example of fig. 3A, the resonator drive circuit 104A may be coupled to one resonator (e.g., the resonator 18A depicted in fig. 1) and the resonator drive circuit 104B may be coupled to a second resonator (e.g., the resonator 18B). The resonator drive circuits 104A and 104B may be configured to output signals that cause the resonators of the accelerometer 110 to vibrate at the respective resonant frequency of each resonator. In some examples, the vibration device excites and maintains mechanical motion of each resonator through electrostatic actuation. In some examples, the resonator drive circuits 104A and 104B may include one or more oscillator circuits. In some examples, the signal to the accelerometer 110 may travel along a conductive path along or within a support base of the accelerometer (such as the support base 36 described above with respect to fig. 2). Signals from resonator drive circuits 104A and 104B may provide a patterned electric field to cause the resonator of accelerometer 110 to remain resonant. The processing circuit 102 in combination with the resonator drive circuits 104A and 104B may be an example of the control electronics described above with respect to fig. 1.

The resonator drive circuit 104A may output the drive signal 106A at a different frequency than the drive signal 106B from the resonator drive circuit 104B. The example of fig. 3A may be configured to determine a differential frequency signal based on the sense signals 108A and 108B. The resonator drive circuits 104A and 104B may adjust the output of the drive signals 106A and 106B based on a feedback loop from the sense signals 108A and 108B, for example, to maintain the resonators at respective resonant frequencies. As described above, a VBA according to the present disclosure may include one resonator or more than two resonators, and may also include fewer or additional resonator drive circuits.

In the present disclosure, a "differential frequency" measurement may include a combination of frequencies other than simple subtraction. In some examples, the output of the first resonator may be weighted differently than the output of the second resonator or the third resonator as part of the differential frequency measurement. For example, as part of determining the differential frequency measurement, a first resonator may be weighted to 98% of the resonator output compared to other resonators. In other examples, the output of each resonator may be squared or otherwise processed as part of determining the differential frequency measurement. In other examples, any combination of weighting, squaring, square root, reciprocal, or other processing may be part of determining the differential frequency measurement.

As described above with respect to fig. 1 and 2, acceleration of the suspended mass VBA, e.g., in a direction substantially parallel to the plane of the proof mass, can cause rotation of the suspended proof mass about the hinge flexures parallel to the plane of the proof mass. The resonators of accelerometer 110 may be configured to receive a force in response to rotation of the proof mass such that the force causes the resonators to bend in the plane of the proof mass and cause a corresponding change in the resonant frequency of at least one of the resonators.

The processing circuit 102 may be in communication with the resonator drive circuits 104A and 104B. The processing circuit 102 may include various signal processing functions such as filtering, amplification, and analog-to-digital conversion (ADC). The filtering function may include high-pass, band-pass, or other types of signal filtering. In some examples, the resonator drive circuits 104A and 104B may also include signal processing functions, such as amplification and filtering. The processing circuit 102 may output the processed signal received from the accelerometer 110 to the other circuitry 113 as an analog signal or a digital signal. Processing circuitry 102 may also receive signals from other circuitry 113, such as command signals, calibration signals, and the like.

The processing circuit 102 may be operatively connected to the accelerometer 110, for example, via the resonator drive circuits 104A and 104B. The processing circuit 102 may be configured to receive a signal from the accelerometer 110 that may be indicative of a corresponding change in a resonant frequency of at least one resonator of the accelerometer 110. Based on the corresponding change in the resonant frequency, the processing circuit 102 may determine an acceleration measurement. In other examples (not shown in fig. 3A), the processing circuit 102 may be part of a feedback loop from the accelerometer 110, and may control the drive signals 106A and 106B to maintain the motion of the resonator at its resonant frequency.

Figure 3B is a block diagram illustrating the accelerometer system 101 according to one or more techniques of the present disclosure. As shown in fig. 3B, the accelerometer system 101 includes a processing circuit 103, resonator drive circuits 105A-105B (collectively "resonator drive circuits 105"), and a proof mass assembly 111. Proof mass assembly 111 includes proof mass 112, resonator connecting structure 116, first resonator 120, and second resonator 130. The first resonator 120 includes first and second mechanical beams 124A, 124B (collectively "mechanical beams 124"), and first, second, and third sets of electrodes 128A, 128B, 128C (collectively "electrodes 128"). The second resonator 130 includes third and fourth mechanical beams 134A, 134B (collectively "mechanical beams 134"), and fourth, fifth, and sixth sets of electrodes 138A, 138B, 138C (collectively "electrodes 138").

In some examples, accelerometer system 101 may be configured to determine an acceleration associated with an object (not shown in fig. 3B) based on a measured vibration frequency of one or both of first resonator 120 and second resonator 130 connected to proof mass 112. In some cases, the vibrations of the first resonator 120 and the second resonator 130 are caused by the driving signals emitted by the resonator driving circuit 105A and the resonator driving circuit 105B, respectively. In turn, the first resonator 120 may output a first set of sense signals and the second resonator 130 may output a second set of sense signals, and the processing circuit 103 may determine the acceleration of the object based on the first and second sets of sense signals.

In some examples, the processing circuitry 103 may include one or more processors configured to implement functions and/or processing instructions for execution within the accelerometer system 101. For example, the processing circuit 103 can process instructions stored in a memory device. The processing circuit 103 may comprise, for example, a microprocessor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or an equivalent discrete or integrated logic circuit, or a combination of any of the preceding devices or circuits. Thus, the processing circuit 103 may include any suitable structure, whether in hardware, software, firmware, or any combination thereof, to perform the functions attributed herein to the processing circuit 103.

The memory (not shown in figure 3B) may be configured to store information within the accelerometer system 101 during operation. The memory may include a computer-readable storage medium or a computer-readable storage device. In some examples, the memory includes one or more of short term memory or long term memory. The memory may include, for example, Random Access Memory (RAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), magnetic disks, optical disks, flash memory, or forms of electrically programmable memory (EPROM) or electrically erasable programmable memory (EEPROM). In some examples, the memory is to store program instructions for execution by the processing circuit 103.

In some examples, the resonator drive circuit 105A may be electrically coupled to the first resonator 120. Resonator drive circuit 105A may output a first set of drive signals to first resonator 120 such that first resonator 120 vibrates at a resonant frequency. Additionally, in some examples, resonator drive circuit 105A may receive a first set of sense signals from first resonator 120, where the first set of sense signals may be indicative of a mechanical vibration frequency of first resonator 120. Resonator drive circuit 105A may output the first set of sense signals to processing circuit 103 for analysis. In some examples, the first set of sense signals may represent a data stream such that the processing circuit 103 may determine the mechanical vibration frequency of the first resonator 120 in real time or near real time.

In some examples, the resonator drive circuit 105B may be electrically coupled to the second resonator 130. Resonator drive circuit 105B may output a second set of drive signals to second resonator 130 such that second resonator 130 vibrates at a resonant frequency. Additionally, in some examples, resonator drive circuit 105B may receive a second set of sense signals from second resonator 130, where the second set of sense signals may be indicative of a mechanical vibration frequency of first resonator 130. Resonator drive circuit 105B may output the second set of sense signals to processing circuit 103 for analysis. In some examples, the second set of sense signals may represent a data stream such that processing circuit 103 may determine the mechanical vibration frequency of second resonator 130 in real time or near real time.

Proof mass assembly 111 may use first resonator 120 and second resonator 130 to secure proof mass 112 to resonator connection structure 116. Proof mass 112 may be secured to resonator connection structure 116 in a first direction using hinge flexures 114, for example. Proof mass 112 may be secured to resonator connection structure 116 in a second direction using first resonator 120 and resonator 130. Proof mass 112 may be configured to pivot about hinge flexure 114 to apply pressure to first resonator 120 and second resonator 130 in a second direction. For example, if proof mass 112 pivots toward first resonator 120, proof mass 112 applies a compressive force to first resonator 120 and a tensile force to second resonator 130. If proof mass 112 pivots toward second resonator 130, proof mass 112 applies a tensile force to first resonator 120 and a compressive force to second resonator 130.

The acceleration of proof mass assembly 111 may affect the degree to which proof mass 112 pivots about hinge flexures 114. In this way, the magnitude of the force applied to the first resonator 120 and the magnitude of the force applied to the second resonator 130 can be determined by examining the acceleration of the mass block assembly 111. The amount of force (e.g., compressive or tensile) applied to the resonators 120, 130 can be related to the acceleration vector of the proof-mass assembly 111, where the acceleration vector is perpendicular to the hinge flexure 114.

In some examples, the magnitude of the force applied to first resonator 120 may be related to a resonant frequency at which first resonator 120 vibrates in response to resonator drive circuit 105A outputting the first set of drive signals to first resonator 120. For example, the first resonator 120 may include a mechanical beam 124. As such, the first resonator 120 may represent a double-ended tuning fork (DETF) structure, wherein each of the mechanical beams 124 vibrates at a resonant frequency in response to receiving the first set of drive signals. The electrodes 128 may generate electrical signals indicative of the mechanical vibration frequency of the first mechanical beam 124A and the mechanical vibration frequency of the second mechanical beam 124B. For example, a first set of electrodes 128A may generate a first electrical signal, a second set of electrodes 128B may generate a second electrical signal, and a third set of electrodes 128C may generate a third electrical signal. The electrode 128 may output a first electrical signal, a second electrical signal, and a third electrical signal to the processing circuit 103.

The processing circuit 103 may determine a difference between the first electrical signal and the second electrical signal and determine a mechanical vibration frequency of the first mechanical beam 124A based on the difference between the first electrical signal and the second electrical signal. Additionally or alternatively, the processing circuit 103 may determine a difference between the second electrical signal and the third electrical signal, and determine the mechanical vibration frequency of the second mechanical beam 124B based on the difference between the second electrical signal and the third electrical signal. In some examples, the mechanical vibration frequencies of the first mechanical beam 124A and the second mechanical beam 124B are substantially the same when the resonator drive circuit 105A outputs the first set of drive signals to the first resonator 120. For example, the mechanical vibration frequency of first mechanical beam 124A and the mechanical vibration frequency of second mechanical beam 124B may both represent the resonant frequency of first resonator 120, where the resonant frequency is related to the amount of force applied to first resonator 120 by proof mass 112. The amount of force applied by proof mass 112 to first resonator 120 may be related to the acceleration of proof mass assembly 111 relative to the long axis of resonator connecting structure 116. In this way, processing circuitry 103 may calculate the acceleration of proof-mass 112 relative to the long axis of resonator connection structure 116 based on the detected mechanical vibration frequency of mechanical beams 124.

In some examples, the magnitude of the force applied to second resonator 130 may be related to the resonant frequency at which second resonator 130 vibrates in response to resonator drive circuit 105B outputting the second set of drive signals to second resonator 130. For example, the second resonator 130 may include a mechanical beam 134. As such, the second resonator 130 may represent a double-ended tuning fork (DETF) structure, wherein each of the mechanical beams 134 vibrates at a resonant frequency in response to receiving the second set of drive signals. The electrodes 138 may generate electrical signals indicative of the mechanical vibration frequency of the third mechanical beam 134A and the mechanical vibration frequency of the fourth mechanical beam 134B. For example, the fourth set of electrodes 138A may generate a fourth electrical signal, the fifth set of electrodes 138B may generate a fifth electrical signal, and the sixth set of electrodes 138C may generate a sixth electrical signal. The electrode 138 may output the fourth, fifth, and sixth electrical signals to the processing circuit 103.

The processing circuit 103 may determine a difference between the fourth electrical signal and the fifth electrical signal and determine a mechanical vibration frequency of the third mechanical beam 134A based on the difference between the fourth electrical signal and the fifth electrical signal. Additionally or alternatively, the processing circuit 103 may determine a difference between the fifth electrical signal and the sixth electrical signal, and determine the mechanical vibration frequency of the fourth mechanical beam 134B based on the difference between the fifth electrical signal and the sixth electrical signal. In some examples, the mechanical vibration frequencies of the third mechanical beam 134A and the fourth mechanical beam 134B are substantially the same when the resonator drive circuit 105B outputs the second set of drive signals to the second resonator 130. For example, the mechanical vibration frequency of third mechanical beam 134A and the mechanical vibration frequency of fourth mechanical beam 134B may both represent the resonant frequency of second resonator 130, where the resonant frequency is related to the amount of force applied to second resonator 130 by proof mass 112. The amount of force applied by proof mass 112 to second resonator 130 may be related to the acceleration of proof mass assembly 111 relative to the long axis of resonator connecting structure 116. In this way, processing circuitry 103 may calculate the acceleration of proof-mass 112 relative to the long axis of resonator connection structure 116 based on the detected mechanical vibration frequency of mechanical beams 134.

In some cases, processing circuitry 103 may calculate the acceleration of proof mass assembly 111 relative to the long axis of resonator connection structure 116 based on the difference between the detected mechanical vibration frequency of mechanical beam 124 and the detected mechanical vibration frequency of mechanical beam 134. When proof mass assembly 111 is accelerated in a first direction along the long axis of resonator connection structure 116, proof mass 112 pivots toward first resonator 120 such that proof mass 112 applies a compressive force to first resonator 120 and a tensile force to second resonator 130. When proof mass assembly 111 is accelerated in a second direction along the long axis of resonator connection structure 116, proof mass 112 pivots toward second resonator 130 such that proof mass 112 applies a tensile force to first resonator 120 and a compressive force to second resonator 130. When the first compressive force is less than the second compressive force, the resonant frequency of the resonator to which the first compressive force is applied may be greater than the resonant frequency of the resonator to which the second compressive force is applied. When the first tension is greater than the second tension, the resonance frequency of the resonator to which the first tension is applied may be greater than the resonance frequency of the resonator to which the second tension is applied.

Although accelerometer system 101 is shown as including resonator connection structure 116, in some examples not shown in figure 3B, proof mass 112, first resonator 120, and second resonator 130 are not connected to a resonator connection structure. In some such examples, proof mass 112, first resonator 120, and second resonator 130 are connected to a substrate. For example, hinge flexures 114 may secure proof mass 112 to the substrate such that proof mass 112 may pivot about hinge flexures 114, thereby exerting a tensile and/or compressive force on first resonator 120 and second resonator 130.

In some examples, the difference between the resonant frequency of first resonator 120 and the resonant frequency of second resonator 130 may have an approximately linear relationship to the acceleration of proof mass assembly 111. In some examples, the relationship between the difference in resonant frequencies of resonators 120, 130 and the acceleration of proof mass assembly 111 may not be perfectly linear. For example, the relationship may include a quadratic nonlinear coefficient (K) representing a nonlinear relationship between the difference in resonant frequencies of resonators 120, 130 and the acceleration of proof mass assembly 111₂). It may be advantageous for the quadratic non-linearity coefficient to be zero or close to zero, such that processing circuitry 103 is configured to accurately determine the acceleration of proof mass assembly 111 based on the relationship between the difference in resonant frequencies of resonators 120, 130 and the acceleration of proof mass assembly 111. One type of error is vibrationDynamic rectification error (VRE). VRE may be provided as a zero gravity output or change in accelerometer bias that occurs during vibration. VRE may be caused by non-linearities in the accelerometer input to output transfer function. Generally, the most dominant source is the quadratic nonlinear coefficient (K)₂). To avoid VRE, it may be beneficial to mitigate this quadratic nonlinearity.

Additionally, it may be advantageous when the acceleration of the proof mass assembly 111 is zero m/s²When the difference between the resonance frequency of the first resonator 120 and the resonance frequency of the second resonator 130 is not zero. Compared to systems where the difference in the respective resonant frequencies of the first and second resonators at zero acceleration is zero or closer to zero than the systems described herein, it may be advantageous that the difference in the respective resonant frequencies of the resonators 120, 130 is not zero when the proof mass assembly 111 is not accelerating in order to reduce interference between the first and second resonators 120, 130.

In some examples, the accelerometer system 101 may ensure that the quadratic non-linearity coefficient is close to zero and that the zero acceleration difference for the respective resonant frequencies of the resonators 120, 130 is not zero by including an additional mass on the first resonator 120. For example, the first mechanical beam 124A and the second mechanical beam 124B may each include one or more additional masses, wherein the one or more additional masses affect the resonant frequency and the second order nonlinear coefficient of the first resonator 120. The third mechanical beam 134A and the fourth mechanical beam 134B may each form one or more gaps, while additional masses are located on the first mechanical beam 124A and the second mechanical beam 124B. In some examples, the first resonator 120 and the second resonator 130 are substantially identical, except that the first resonator 120 includes an additional mass on the first mechanical beam 124A and an additional mass on the second mechanical beam 124B, while the third mechanical beam 134A includes a gap corresponding to the additional mass on the first mechanical beam 124A, and the fourth mechanical beam 134B includes a gap corresponding to the additional mass on the second mechanical beam 124B. Such a difference between first resonator 120 and second resonator 130 may ensure that the second order non-linearity coefficient is close to zero (e.g., less than 5 μ g/g)²) And ensures the resonators 120,130 is not zero.

For a VBA with two identical resonators, even-order nonlinearities (e.g., quadratic nonlinearity, fourth-order nonlinearity) are common-mode error sources that are nominally cancelled by the differential output. However, mismatched resonators (such as first resonator 120 and second resonator 130) may result in the K of the accelerometer₂Not necessarily set to zero. Unmatched resonators may be required to avoid operating both resonators at the same frequency. Driving two resonators at similar frequencies can cause the resonators to interfere with each other (both mechanically and electrically), which ultimately reduces the output of the VBA. The resonators 120 and 130 may ensure K₂Is zero or close to zero and reduces such disturbances that degrade the output of the VBA.

Although the accelerometer system 101 is described as having two resonators, in other examples not shown in figure 3B, the accelerometer system may include less than two resonators or more than two resonators. For example, an accelerometer system may include a resonator. Another accelerometer system may include four resonators.

Fig. 4 is a conceptual diagram illustrating an example of resonator electrode placement and electrical signal routing to avoid the effects of parasitic feed-through capacitance on accelerometer performance. VBA 830 is an example of VBA30, VBA 50, and VBA 430 described above with respect to FIGS. 1,2, and 4. Suspended proof mass 832, resonator 818, resonator beams 819, flexure 833 and mechanical anchor 814 are examples of proof mass 32, resonators 18A and 18B, resonator beams 19A and 19B, flexure 33 and mechanical anchor 14 described above with respect to fig. 1 and 4, and thus may have the same descriptions, characteristics and functions as described above. The example of VBA 830 in fig. 4 includes a damping comb 840. However, in other examples, VBA 830 may not have damping comb 840.

Electrodes and routing within both the electronics and the VBA mechanism may create some parasitic capacitance between the drive and sense electrodes. Examples of VBA 830 include resonator electrodes, such as drive electrodes 838 and 839, configured to mitigate the effects of parasitic capacitance inherent in VBA resonators. In this way, if the feed-through capacitance between each drive electrode and sense electrode is similar, the feed-through currents will be out of phase with each other, resulting in a zero net current.

Control electronics may be connected to resonator drive electrodes (such as drive electrodes 838 and 839) to maintain movement of the vibrating beam 819. Electrodes and routing within both the electronics and the VBA mechanism may create some parasitic capacitance between the drive and sense electrodes. In the example of fig. 4, two different drive electrodes 838 and 839 may receive voltage signals of opposite polarity. The drive electrodes 838 and 839 may be located on both sides of the moving MEMS element (e.g., the resonator 818) such that the actuator may push or pull to drive the resonator 818. In some examples, the inverted drive signal may be generated by analog electronics within the control electronics of the VBA. In this way, if the feed-through capacitance between each drive electrode and sense electrode is similar, the feed-through currents will be out of phase with each other, resulting in a zero net current.

In some alternative examples, such as configurations with a single drive and sense electrode, this parasitic feedthrough capacitance may result in a feedthrough current between the drive and sense electrodes. The feed-through current may be summed with the motional current caused by the motion of the mechanical resonator. This total output current is read by the front-end electronics and ultimately used to maintain and sense the frequency of the mechanical oscillation. Thus, the feedthrough current caused by the feedthrough capacitance may affect the resonator transfer function and the operation of the VBA.

For moderate feedthrough capacitances, the magnitude and phase of the resonator transfer function may degrade, which may result in increased accelerometer noise. If the resonator is driven too far away from mechanical resonance, the stability of the accelerometer bias may deteriorate as the resonator frequency will be more susceptible to any phase shift in the electronic device. Thus, avoiding the effects of this parasitic feedthrough capacitance can ultimately improve accelerometer performance.

The techniques of this disclosure may include configuring the capacitive comb of resonator 818 into discrete electrodes including drive electrodes 838 and 839 and two sense electrodes (sense-856 and sense + 858). The sense electrodes (i.e., sense-856 and sense +858) may be coupled to an anchor portion of resonator 818. Furthermore, the routing of electrical signals 850, 852, and 854 on the die and on the analog electronics board may be configured to produce approximately equal parasitic feedthrough capacitances Cf + and Cf-. In some examples, one or more of the electrical signals may include additional routing 824 to ensure that the parasitic feed-through capacitances Cf + and Cf-are approximately equal. Electrical signals 850, 852, and 854 may be connected to terminals, such as drive 820, sense-802, and sense + 810, respectively.

The two sense electrodes on the VBA may be placed on opposite sides of the moving MEMS resonator beam 819 such that the capacitance change (dCs/dx) with respect to displacement is approximately equal in magnitude and opposite in sign. Then, the current (i) is sensed_s+And i_s-) Will be opposite in sign but feed-through current (i)_f+And i_f-) Will have the same sign. The sense outputs 802 and 810 may be connected to a differential front end amplifier (such as a transimpedance or charge amplifier) that handles differences in output current. In this way, the feed-through currents substantially cancel each other out, and the effect can be mitigated.

Alternative solutions may exist to avoid feedthrough capacitance effects, but those alternatives involve additional electronics complexity that may increase cost. Some exemplary alternatives may include driving the resonator with a sinusoidal voltage at half the mechanical resonance frequency. Since electrostatic force is proportional to the square of the voltage, an electrostatic actuator may generate a force at twice the frequency of the sinusoidal voltage. This alternative solution may eliminate the possibility of driving to the sense capacitor feed-through if the second harmonic content of the drive signal is small, since the drive signal and the sense signal have different frequencies. However, this alternative solution would make it possible to use a microcontroller within the resonator feedback loop. The addition of a digital microcontroller would likely result in an accelerometer that is significantly larger and more expensive than an accelerometer with an analog control loop.

Another alternative example may use two different sensing electrodes biased by voltages of opposite polarity. The resulting output current may then be differentiated to eliminate the effect of the feed-through capacitance. However, sensing electrodes with opposite polarities may have the disadvantage of requiring two large bias voltages instead of only one.

A third alternative may use two different drive electrodes receiving inverted voltage signals. If the feed-through capacitance between each drive electrode and sense electrode is similar, the feed-through currents will be out of phase with each other, resulting in a zero net current. This configuration requires moving the drive electrodes on both sides of the MEMS element so that the actuator can push and pull to drive the resonator. The inverted drive signal may be generated by analog electronics and may have the disadvantage of requiring two separate drive circuits.

Measurement test results of the resonator configuration techniques of the present disclosure show an improvement in the open loop phase response of the analog electronics, which is expected to improve noise and in some examples, bias stability. These techniques may be unique compared to other exemplary techniques, as VBA typically uses one drive electrode and one sense electrode for each resonator in some examples. Given a driving and a sensing configuration, there is no means for eliminating any feedthrough capacitance that may occur. Rather, other examples may simply attempt to minimize this capacitance.

Technical benefits of the techniques of this disclosure may eliminate or reduce the effects of driving to sensing feed-through capacitances. The reduced capacitance may improve the open loop phase response of the resonator in combination with the electronics, which in turn enables the electronics to directly drive the resonator at mechanical resonance. In some examples, these techniques may make the accelerometer device easier to integrate with small changes in the electronics, which ultimately relaxes the requirements on the electronics themselves. In addition, prior to the development of readout electronics, there may be some concern that the feedthrough capacitance will be detrimental to the electronics performance. The readout circuit is a circuit that can be configured to convert information on a capacitance change caused by external acceleration into a voltage signal. Test measurements have shown that the elimination of these feed-through currents can lead to an improvement in the open loop response of the resonator.

The techniques of the present disclosure for eliminating feedthrough currents may be incorporated into a MEMS VBA. Each resonator 818 may have an electrode wired to its corresponding bond pad. The input to each resonator 818 may be a single drive voltage, while the output may be configured as two sense electrodes 841 and 842 containing nominally out-of-phase currents representative of the physical motion of the MEMS resonator.

In the example of a double ended tuning fork resonator, each resonator has two moving parts that oscillate in opposite directions. The drive electrodes (e.g., drive electrodes 838 and 839) may supply a drive voltage that excites mechanical motion at resonance. VBA 830 may include additional drive electrodes not shown in FIG. 4. When the two resonator tines are separated, a positive sense electrode (e.g., 858) may generate a positive current. When the two resonator tines move together, a negative sense electrode (e.g., 856) may generate a positive current. Thus, the sense electrodes are oriented to have dC/dx of similar magnitude but opposite sign. The routing of electrical signals 850, 852 and 854 on the MEMS die may be configured to have similar feed-through capacitances between the drive electrodes and the sense electrodes.

Fig. 5A and 5B are schematic diagrams illustrating an exemplary MEMS VBA configured with a single sense electrode. FIG. 5A shows a mechanical model of an exemplary single sense electrode VBA, and FIG. 5B shows an equivalent circuit.

In the example of fig. 5A, the DC bias voltage Vb 902 is connected to the MEMS electrodes at the proof mass 910, where the proof mass 910 represents the proof mass of the resonator beam, not the proof mass of the VBA. The mass 910 is connected to an attachment point 922 through a spring 916 having a spring constant K, to an attachment point 923 through a variable drive capacitance Cd912, and to an attachment point 924 through a variable sense capacitance Cs 914. As described above with respect to, for example, fig. 1, the capacitance may change as the resonator tines for the release region move relative to the resonator tines for the anchor region.

The AC drive voltage Vd 904 is connected to the drive electrodes at attachment points 923 to excite mechanical motion in the resonator and cause the mass 910 to move along the X-axis 918. As described above with respect to fig. 4, the electrode position and signal routing may create some parasitic capacitance between the drive and sense electrodes, such as the feed-through capacitance Cf 908. In an exemplary configuration of the resonator 900 having a single drive and sense electrode, this parasitic feedthrough capacitance Cf908 may result in a feedthrough current between the drive and sense electrodes that may be received by an amplifier connected to VBA.

The circuit 950 in the example of fig. 5B is an equivalent circuit of the resonator 900 depicted in fig. 5A. The mass and other components of resonator 900 may be modeled as an RLC circuit of MEMS 952. MEMS 952 includes a resistor R932 connected in series with an inductor L930 and a capacitor C934. A first terminal of the resistor R932 is connected to the AC driving voltage Vd 904. A second terminal of resistor R932 is connected to a first terminal of inductor L930. A second terminal of the inductor L930 is connected to a first terminal of a capacitor C934. A second terminal of capacitor C934 is connected to a node 942 that also includes connections to feed-through capacitance Cf908, resistor R935, and capacitor Cblock 940. The other terminal of Cblock 940 is connected to a terminal that can output a sense signal to an amplifier. The bias voltage Vb 902 is connected to the same node 942 through a resistor R935.

Motional or sensed current i caused by AC drive voltage 904_m958 move through the MEMS 952. Electrode and electrical conductor geometries can lead to unwanted feed-through currents i_f956. Feed-through current i _f956 adds to the motional current i caused by the motion of the mechanical resonator at node 942_m958, and as i_m+i_f954 to an amplifier. This total output current can be read by the front-end electronics. The total current may cause the resonator transfer function to degrade, which may result in increased accelerometer noise. The additional feed-through current may degrade the stability of the accelerometer bias if the resonator is driven away from mechanical resonance.

Fig. 6A and 6B are schematic diagrams illustrating an exemplary MEMS VBA configured with two sense electrodes. FIG. 6A shows a mechanical model of an exemplary single sense electrode VBA, and FIG. 6B shows an equivalent circuit. The arrangement of resonator 1000 and circuit 1050 may eliminate at least some of the unwanted feedthrough currents and reduce the effects of feedthrough capacitance.

In the example of fig. 6A, the proof mass 1010 is connected to an attachment point 1022 through a spring 1016 having a spring constant K and to an attachment point 1023 through a variable drive capacitance Cd 1012. For the sense electrodes, proof mass 1010 is connected to attachment point 1024 by variable sense capacitance Cs-1015 and to attachment point 1025 by variable sense capacitance Cs + 1014.

An AC drive voltage Vd 1004 is connected to the drive electrodes at attachment point 1023 to excite mechanical motion in the resonator and cause the proof mass 1010 to move along the X-axis 1018. As described above with respect to FIG. 4, electrode position and signal routing may create some parasitic capacitance between the drive and sense electrodes. In the example of resonator 1000, the positive feedthrough capacitance Cf +1008 may be caused by parasitic capacitance between the drive and sense circuits including Cs + 1014. The negative feedthrough capacitance Cf-1018 may be caused by parasitic capacitance between the drive circuitry, including Cs-1015, and the sense circuitry.

As described above with respect to fig. 4, when the resonator tines move apart, the positive sense electrode of the resonator (represented by Cs + 1014) may generate a positive current. When the resonator tines move together, the negative sense electrode (represented by Cs-1015) may generate a positive current. Thus, the sense electrodes are oriented to have dC/dx of similar magnitude but opposite sign. The routing of electrical signals 850, 852, and 854 on the MEMS die may be configured to have similar feed-through capacitances between the drive electrode and the positive and negative sense electrodes, such that Cf +1008 and Cf-1018 are approximately equal. Substantially equal in this disclosure means equal within manufacturing and measurement tolerances. Small variations in materials, processes, etc. during fabrication may result in small differences such that, for example, CF-1018 and CF +1008 may be approximately equal, rather than exactly equal. The sense output from the resonator 1000 may be processed by a differential amplifier 1020 such that the positive and negative feed-through currents may substantially cancel each other.

In the example of fig. 6B, circuit 1050 is an equivalent circuit of resonator 1000 depicted in fig. 6A. The mass and other components of the resonator 900 may be modeled as two RLC circuits of the MEMS 1052. For the positive sense branch, MEMS 1052 includes a resistor R1032 connected in series with an inductor L1030 and a capacitor C1034. A first terminal of the resistor R1032 is connected to the AC drive voltage + Vd 1040. A second terminal of resistor R1032 is connected to a first terminal of inductor L1030. A second terminal of inductor L1030 is connected to a first terminal of capacitor C1034. A second terminal of the capacitor C1034 is connected to an output node 1042 that also includes a connection to the feedthrough capacitance Cf + 1008. The AC drive voltage + Vd 1040 and the AC drive voltage-Vd 1041 indicate that the drive voltages are opposite in phase. Although depicted as two separate AC sources in the example of circuit 1050, in other examples a single AC source may provide the drive signals, and the analog circuit may output AC drive signals having opposite phases, for example. For example, the resonator drive circuits 103A, 103B, 104A, and 104B described above in connection with fig. 3A and 3B may include AC drive circuits configured to provide drive signals having opposite phases to the resonators.

For the negative sense branch, MEMS 1052 includes a resistor R1033 connected in series with an inductor L1031 and a capacitor C1035. A first terminal of the resistor R1033 is connected to the AC drive voltage-Vd 1041. A second terminal of the resistor R1033 is connected to a first terminal of the inductor L1031. A second terminal of inductor L1031 is connected to a first terminal of capacitor C1035. A second terminal of capacitor C1035 is connected to an output node 1043, which also includes a connection to the feed-through capacitance Cf-1018.

The motional current caused by the AC drive voltages 1040 and 1041 moves through the positive branch of MEMS 1052 (which includes R1032, e.g., i @_m+1058) And through a negative branch (which includes R1033, e.g. i)_m-1059) And both. Electrode and electrical conductor geometries can lead to unwanted feed-through currents i_f+1056 and i_f-1057. On the positive side, the feed-through current i_f+1056 added to the motional current i caused by the motion of the mechanical resonator _m+1058, and as i_m++i_f+1054 is output to one input of a differential amplifier 1020. On the negative side, the feed-through current i_f-1057 to the motional current i _m-1059 and as i_m-+i_f+1055 is output to a second input of the differential amplifier 1020. In formula form, the result can be described as:

positive and negative sense currents are approximately equal: i.e. i_m+＝-i_m-

Positive and negative feedthrough capacitances are approximately equal:

thus, the output of the differential amplifier is:

i_diff＝i_m++i_f+-(i_f-+i_m-)＝2*i_m+

fig. 7A is a conceptual diagram illustrating a first resonator 1120 with an additional mass according to one or more techniques of the present disclosure. The first resonator 1120 may be an example of the resonator 18 of fig. 1 and the first resonator 120 of fig. 3B. The first resonator 1120 may include anchoring combs 1122A-1122C (collectively, "anchoring combs 1122"), a first mechanical beam 1124A, and a second mechanical beam 1124 (collectively, "mechanical beams 1124"). The first machine beam 1124A may include additional masses 1162A-1162D (collectively, "additional masses 1162"). The second machine beam 1124B may include additional masses 1164A-1164D (collectively "additional masses 1164").

In some examples, anchoring comb 1122A includes one or more anchoring comb portions, anchoring comb 1122B includes one or more anchoring comb portions, and anchoring comb 1122C includes one or more anchoring comb portions. In some examples, any one or combination of the anchoring comb portions of anchoring comb 1122A can comprise one or more electrodes of a first set of electrodes (e.g., first set of electrodes 128A of fig. 3B). In some examples, any one or combination of the anchoring comb portions of anchoring comb 1122B can include one or more electrodes of the second set of electrodes (e.g., second set of electrodes 128A). In some examples, any one or combination of the anchoring comb portions of anchoring comb 1122C can include one or more electrodes of the third set of electrodes (e.g., third set of electrodes 128C).

In some examples, the resonator drive circuit may transmit a drive signal to the first resonator 1120 via any one or combination of the first, second, and third sets of electrodes such that the first resonator 1120 vibrates at a resonant frequency. For example, the first mechanical beam 1124A and the second mechanical beam 1124B may vibrate at the resonant frequency described above. In turn, the first set of electrodes may generate a first electrical signal, the second set of electrodes may generate a second electrical signal, and the third set of electrodes may generate a third electrical signal. The first resonator 1120 may output the first, second, and third electrical signals to a processing circuit (not shown in fig. 7A) configured to determine a resonant frequency of the first resonator 1120 based on the first, second, and third electrical signals.

In some examples, the resonant frequency of the first resonator 1120 may be related to the amount of force applied to the first resonator 1120 by a proof mass (such as proof mass 32 of fig. 1 and proof mass 112 of fig. 3B). For example, a first end 1182 of the first resonator 1120 may be secured to a resonator connection structure (e.g., resonator connection structure 16 of fig. 1 and resonator connection structure 116 of fig. 3B), and a second end 1184 of the first resonator 1120 may be secured to a proof mass. If the proof mass rotates toward the first resonator 1120 in response to an acceleration in a first direction, the proof mass may apply a compressive force to the first resonator 1120. If the proof mass rotates away from the first resonator 1120 in response to acceleration in a second direction, the proof mass may apply tension to the first resonator 1120. In some examples, if the acceleration is zero m/s²The proof mass may not apply a force to the first resonator 1120. As the compressive force exerted by the proof mass increases in response to an increase in acceleration in the first direction, the resonant frequency of first resonator 1120 may decrease, and as the tensile force exerted by the proof mass increases in response to an increase in acceleration in the second direction, the resonant frequency of first resonator 1120 may increase. As such, there may be a relationship between the resonant frequency of the first resonator 1120 and the acceleration of the accelerometer including the first resonator 1120.

The additional masses 1162, 1164 may affect the relationship between the acceleration and the resonant frequency of the first resonator 1120. For example, the quadratic non-linear coefficient defining the relationship between acceleration and the resonant frequency of the first resonator 1120 may be smaller than the quadratic non-linear coefficient defining the relationship between acceleration and the resonant frequency of a resonator that does not include the additional mass 1162 and the additional mass 1164. It may be advantageous for the relationship between the acceleration and the resonant frequency of the first resonator 1120 to be as close to linear as possible (e.g., the quadratic non-linearity coefficient is as small as possible) in order to ensure that the electrical signal generated by the first resonator 1120 allows the processing circuitry to accurately determine the acceleration.

In some examples, the additional mass 1162A and the additional mass 1162B may be placed at a location along the first mechanical beam 1124A that is in a range of 25% to 45% of the length along the first end 1156 to the second end 1157 of the first mechanical beam 1124A. For example, the additional mass 1162A and the additional mass 1162B may be placed at a position that is 35% of the distance between the first end 1156 and the second end 1157. In some examples, the additional masses 1162C and 1162D may be placed at a location along the first mechanical beam 1124A that is in a range of 55% to 75% of a length along the first end 1156 to the second end 1157 of the first mechanical beam 1124A. For example, the additional mass 1162C and the additional mass 1162D may be placed at a position that is 65% of the distance between the first end 1156 and the second end 1157.

In some examples, the additional masses 1164A and 1164B may be placed at a location along the second mechanical beam 1124B that is in a range of 25% to 45% of the length along the first end 1158 to the second end 1159 of the second mechanical beam 1124B. For example, the additional mass 1164A and the additional mass 1164B may be placed at a position that is 35% of the distance between the first end 1158 and the second end 1159. In some examples, the additional masses 1164C and 1164D may be placed at a location along the second mechanical beam 1124B that is in a range of 55% to 75% of the length along the first end 1158 to the second end 1159 of the second mechanical beam 1124B. For example, additional mass 1164C and additional mass 1164D may be placed at 65% of the distance between first end 1158 and second end 1159.

Fig. 7B is a conceptual diagram illustrating a portion of the first resonator 1120 of fig. 7A including additional masses 1162A and 1162B in accordance with one or more techniques of the present disclosure. For example, the first mechanical beam 301124a includes a primary member 1190 and a set of secondary members 1192A-1192D (collectively referred to as "set of secondary members 1192"). As shown in fig. 7B, each secondary member of the set of secondary members 1192 extends perpendicular to the primary member 1190. The first mechanical beam 1124A may include additional secondary members and additional other components not shown in fig. 7B. Each secondary member of the set of secondary members 1192 may be substantially identical, except that secondary member 1192C includes an additional mass 1162A and an additional mass 1162B.

Fig. 8A is a conceptual diagram illustrating a gapped second resonator 1230 according to one or more techniques of this disclosure. The second resonator 1230 may be an example of the second resonator 130 of fig. 3B. The second resonator 1230 may include anchoring combs 1232A-1232C (collectively, "anchoring combs 1232"), a third mechanical beam 1234A, and a fourth mechanical beam 1234B (collectively, "mechanical beams 1234"). Third mechanical beam 1234A may form gaps 1262A-1262D (collectively "gaps 1262"). Fourth mechanical beam 1234B may form gaps 1264A-1264D (collectively "gaps 1264").

In some examples, the anchoring comb 1232A can include one or more anchoring comb portions, the anchoring comb 1232B can include one or more anchoring comb portions, and the anchoring comb can include one or more anchoring comb portions. In some examples, any one or combination of the anchoring comb portions of the anchoring comb 1232A can include one or more electrodes of a fourth set of electrodes (e.g., the fourth set of electrodes 138A of fig. 3B). In some examples, any one or combination of the anchoring comb portions of the anchoring comb 1232B can include one or more electrodes of the fifth set of electrodes (e.g., the fifth set of electrodes 138B). In some examples, any one or combination of the anchoring comb portions of the anchoring comb 1232C can include one or more electrodes of a sixth set of electrodes (e.g., the sixth set of electrodes 138C).

In some examples, the resonator drive circuit may transmit a drive signal to the second resonator 1230 via any one or combination of the fourth, fifth, and sixth sets of electrodes, causing the second resonator 1230 to vibrate at a resonant frequency. For example, the third mechanical beam 1234A and the fourth mechanical beam 1234B may vibrate at a resonant frequency of the second resonator 1230. In turn, the fourth set of electrodes may generate a fourth electrical signal, the fifth set of electrodes may generate a fifth electrical signal, and the sixth set of electrodes may generate a sixth electrical signal. The second resonator 1230 may output the fourth, fifth, and sixth electrical signals to a processing circuit (not shown in fig. 8A) configured to determine a resonant frequency of the second resonator 1230 based on the fourth, fifth, and sixth electrical signals.

In some examples, the resonant frequency of second resonator 1230 may be related to the amount of force applied to second resonator 1230 by a proof mass (such as proof mass 112 of fig. 3B). For example, a first end 1282 of the second resonator 1230 may be secured to the proof mass and a second end 1284 of the second resonator 1230 may be secured to a resonator connection structure (e.g., resonator connection structure 116 of fig. 3B). If the proof mass rotates away from the second resonator 1230 in response to an acceleration in a first direction, the proof mass may apply a tension to the second resonator 1230. If the proof mass rotates toward the second resonator 1230 in response to an acceleration in a second direction, the proof mass may apply a compressive force to the second resonator 1230. In some examples, if the acceleration is zero m/s²The proof mass may not apply a force to the second resonator 1230. The resonant frequency of second resonator 1230 may decrease as the compressive force exerted by the proof mass increases in response to an increase in acceleration in the second direction, and the resonant frequency of second resonator 1230 may increase as the tensile force exerted by the proof mass increases in response to an increase in acceleration in the first direction. As such, there may be a relationship between the resonant frequency of the second resonator 1230 and the acceleration of the accelerometer comprising the second resonator 1230.

The gaps 1262 and 1264 may affect the relationship between the acceleration and the resonant frequency of the second resonator 1230. For example, the quadratic non-linear coefficient defining the relationship between the acceleration and the resonant frequency of second resonator 1230 may be smaller than the quadratic non-linear coefficient defining the relationship between the acceleration and the resonant frequency of a resonator that does not include gap 1262 and gap 1264. It may be advantageous for the relationship between the acceleration and the resonant frequency of the second resonator 1230 to be as close to linear as possible (e.g., the quadratic non-linearity coefficient is as small as possible) in order to ensure that the electrical signal generated by the second resonator 1230 allows the processing circuitry to accurately determine the acceleration. In some examples, the gap 1262 represents an "aperture" and the additional mass 1162 is included on the first resonator 1120 of fig. 7A-7B. In some examples, the gap 1264 represents an aperture and the additional mass 1164 is included on the first resonator 1120 of fig. 7A-7B. The gap or aperture of the additional mass above the resonator is different from the aperture in the proof mass configured to tune the mechanical mode, as described above with respect to fig. 4.

In some examples, gaps 1262A and 1262B may be placed at a location along third machine beam 1234A that is in the range of 25% to 45% of the length along first end 1256 to second end 1257 of third machine beam 1234A. For example, gap 1262A and gap 1262B may be placed at a location that is 35% of the distance between first end 1256 and second end 1257. In some examples, gaps 1262C and 1262D may be placed at a location along third machine beam 1234A that is in the range of 55% to 75% of the length along first end 1256 to second end 1257 of third machine beam 1234A. For example, gap 1262C and gap 1262D may be placed at 65% of the distance between first end 1256 and second end 1257.

In some examples, gaps 1264A and 1264B may be placed at a location along fourth machine beam 1234B that is in the range of 25% to 45% of the length along first end 1258 to second end 1259 of fourth machine beam 1234B. For example, gap 1264A and gap 1264B may be placed at a location that is 35% of the distance between first end 1258 and second end 1259. In some examples, gap 1264C and gap 1264D may be placed at a location along fourth machine beam 1234B that is in the range of 55% to 75% of the length along first end 1258 to second end 1259 of fourth machine beam 1234B. For example, gap 1264C and gap 1264D may be placed at 65% of the distance between first end 1258 and second end 1259.

Fig. 8B is a conceptual diagram illustrating a portion of the second resonator 1230 of fig. 8A including a gap 1262A and a gap 1262B in accordance with one or more techniques of the present disclosure. For example, the third mechanical beam 1234A includes a primary member 1290 and a set of secondary members 1292A-1292D (collectively referred to as a "set of secondary members 1292"). As shown in fig. 8B, each minor member of the set of minor members 1292 extends perpendicular to the major member 1290. Third mechanical beam 1234A may include additional secondary members and additional other components not shown in fig. 8B. Each minor member of the set of minor members 1292 may be substantially identical except that the distance between the minor member 1292C and the minor member 1292D is greater than the distance between any other pair of consecutive minor members of the set of minor members 1292.

Fig. 9 is a graph illustrating a first graph 1310 representing a second order nonlinear coefficient as a function of additional mass position and a second graph 1320 representing a zero acceleration resonant frequency difference as a function of additional mass position, in accordance with one or more techniques of the present disclosure. For example, as depicted in fig. 7A, "Location of Added masses" may represent the Location of additional masses, such as additional Mass 1162A and additional Mass 1162B, on the first mechanical beam 1124A as a percentage of the length of the first end 1156 to second end 1157 of the first mechanical beam 1124A. As shown in the first graph 610 of fig. 6, when the additional masses 1162A and 1162B are positioned at 35% of the length of the first mechanical beam 1124A, the second order nonlinear coefficient (K) is₂) Is zero. In addition, as seen at point 1330 of the second graph 1320, when the positions of the additional mass 1162A and the additional mass 1162B are 35% of the length of the first mechanical beam 1124A, the difference between the resonant frequency of the first resonator 1120 and the resonant frequency of the second resonator 1230 is not zero. Thus, because the second order non-linear coefficient is zero and the frequency difference is not zero, it may be advantageous for the additional mass 1162A and the additional mass 1162B to be located 35% of the length of the first mechanical beam 1124A.

In some examples, point 1330 may represent an ideal position of additional masses 1162A and 1162B along first mechanical beam 1124A. In some examples, the resonant frequency of the first resonator 1120 at zero acceleration may be in the range of 25 kilohertz (KHz) to 30 KHz. In some examples, the resonant frequency of the second resonator 1230 at zero acceleration may be in the range of 25 kilohertz (KHz) to 30 KHz. In some examples, when the additional mass 1162A and the additional mass 1162B are placed 35% of the length of the first mechanical beam 1124A, the difference between the resonant frequency of the first resonator 1120 at zero acceleration and the resonant frequency of the second resonator 1230 at zero acceleration may be in the range of 250 hertz (Hz) to 3500 Hz.

FIG. 10 is a flow diagram illustrating exemplary operations for determining acceleration of the VBA in accordance with one or more techniques of the present disclosure. Fig. 7 is described with respect to the processing circuit 102, resonator drive circuit 104, and proof mass block assembly 111 of fig. 3B. However, the technique of fig. 7 may be performed by system 101, different components of system 100 of fig. 3A, or by additional or alternative accelerometer systems.

The resonator drive circuit 104A may transmit a set of drive signals to the first resonator 120 (1402). The resonator drive circuit 104A may be electrically coupled to the first resonator 120. The resonator drive circuit 104A may output the set of drive signals to the first resonator 120 such that the first resonator 120 vibrates at a resonant frequency. The processing circuit 102 may receive one or more electrical signals indicative of the frequency of the first mechanical beam 124A and the second mechanical beam 124B via the resonator drive circuit 104A (1404). Subsequently, processing circuitry 102 may determine the frequency of first mechanical beam 124A and second mechanical beam 124B based on the one or more electrical signals (1406). The mechanical vibration frequency of the first mechanical beam 124A and the mechanical vibration frequency of the second mechanical beam 124B may represent the resonance frequency of the first resonator 120. The resonant frequency of the first resonator 120 may be related to the acceleration of a VBA (such as VBA 110 of fig. 2). As such, processing circuitry 102 may calculate an acceleration of VBA 110 based on the frequency of first mechanical beam 124A and the frequency of second mechanical beam 124B (1408).

Although the above example operations are described with respect to the first resonator 120, the processing circuit 102 may additionally or alternatively determine the resonant frequency of the second resonator 130. In some examples, processing circuitry 102 may be configured to determine a difference between the resonant frequency of first resonator 120 and the resonant frequency of second resonator 130, and calculate the acceleration based on the difference in resonant frequencies.

In one or more examples, the accelerometers described herein may utilize hardware, software, firmware, or any combination thereof to implement the described functionality. Those functions implemented in software may be stored on or transmitted over as one or more instructions or code on a computer-readable medium and executed by a hardware-based processing unit. Computer readable media may include computer readable storage media corresponding to tangible media, such as data storage media, or communication media including any medium that facilitates transfer of a computer program from one place to another, for example, according to a communication protocol. As such, the computer-readable medium may generally correspond to: (1) a non-transitory, tangible computer-readable storage medium, or (2) a communication medium such as a signal or carrier wave. A data storage medium may be any available medium that can be accessed by one or more computers or one or more processors to retrieve instructions, code and/or data structures for implementing the techniques described in this disclosure.

The instructions may be executed by one or more processors within the accelerometer or communicatively coupled to the accelerometer. The one or more processors may, for example, comprise one or more DSPs, general purpose microprocessors, Application Specific Integrated Circuits (ASICs), FPGAs, or other equivalent integrated or discrete logic circuitry. Thus, the term "processor," as used herein may refer to any of the foregoing structure or any other structure suitable for implementation of the techniques described herein. Further, in some aspects, the functions described herein may be provided within dedicated hardware and/or software modules configured to perform the techniques described herein. Furthermore, the techniques may be implemented entirely within one or more circuits or logic elements.

The techniques of this disclosure may be implemented in various devices or apparatuses including an Integrated Circuit (IC) or a group of ICs (e.g., a chipset). Various components, modules, or units are described in this disclosure to emphasize functional aspects of devices configured to perform the disclosed techniques, but do not necessarily require implementation by different hardware units. Rather, the various units may be combined with or provided by a collection of interoperative hardware units (including one or more processors as described above) in combination with suitable software and/or firmware.

Various examples of the present disclosure have been described. These embodiments and other embodiments are within the scope of the following claims.

Claims (7)

1. An accelerometer device, the device comprising:

a support base;

a resonator comprising an anchor portion and a release portion, wherein the anchor portion of the resonator is mechanically connected to the support base;

a proof mass mechanically connected to the released portion of the resonator, the proof mass comprising one or more damping combs, wherein the damping combs:

comprising a movable comb finger and an anchoring comb finger,

wherein the anchoring comb fingers of the one or more damping combs are mechanically connected to the support base,

wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and

wherein a spacing between the movable comb fingers of the one or more damping combs and the anchoring comb fingers of the one or more damping combs is configured to provide air damping for the proof mass; and

a pressure chamber, wherein the pressure chamber contains the support base, the resonator, the proof mass, and the one or more damping combs.

2. The apparatus of claim 1, wherein:

the proof mass defines a plane;

the movable comb fingers of the one or more damping combs lie in the plane of the proof mass;

the anchoring comb fingers of the one or more damping combs are located in the plane of the proof mass;

the movable comb fingers overlap the anchoring comb fingers in the defined plane of the proof mass in overlapping portions of the one or more damping combs;

the overlapping portion comprises an air gap;

the overlapping portion has a total linear distance, wherein the total linear distance is the sum of a first length and a second length, wherein:

the first length is a linear distance that a first edge of a first finger of the first plurality of comb fingers overlaps a first edge of a first finger of the second plurality of comb fingers,

the second length is a linear distance that a second edge of the first finger of the first plurality of fingers overlaps a first edge of a second finger of the second plurality of fingers, and

the first comb finger of the first plurality of comb fingers is adjacent to the first comb finger and the second comb finger of the second plurality of comb fingers.

3. The apparatus of claim 2, wherein the anchor portion and the release portion of the resonator comprise overlapping resonator comb fingers, and wherein the total linear distance of the damping comb is greater than a total linear distance of the overlapping resonator comb fingers.

4. The apparatus of claim 1, further comprising a support flexure coupled to the suspended proof mass, wherein the support flexure is configured to constrain out-of-plane motion of the suspended proof mass relative to the second plane.

5. The apparatus as set forth in claim 1, wherein,

wherein the resonator is a first resonator, the apparatus further comprising at least a second resonator, wherein each of the first resonator and the second resonator vibrates at a respective drive resonant frequency,

wherein movement of the proof mass causes the first resonator to receive a tensile force and the second resonator to receive a compressive force, and

wherein the first resonator and the second resonator provide differential frequency measurements.

6. A method, comprising:

receiving, by a processing circuit, one or more electrical signals indicative of a frequency of a first resonator beam and a frequency of a second resonator beam from a Vibrating Beam Accelerometer (VBA), wherein the VBA comprises:

a support base;

a resonator comprising an anchor portion and a release portion, wherein the anchor portion of the resonator is mechanically connected to the support base;

a proof mass mechanically connected to the released portion of the resonator, the proof mass comprising one or more damping combs, wherein the damping combs:

comprising a movable comb finger and an anchoring comb finger,

wherein the anchoring comb fingers of the one or more damping combs are mechanically connected to the support base,

wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and

wherein a spacing between the movable comb fingers of the one or more damping combs and the anchoring comb fingers of the one or more damping combs is configured to provide air damping for the proof mass; and

a pressure chamber, wherein the pressure chamber contains the support base, the resonator, the proof mass, and the one or more damping combs;

determining, by the processing circuit and based on the one or more electrical signals, the frequency of the first resonator beam and the frequency of the second resonator beam; and

calculating, by the processing circuit and based on the frequency of the first resonator beam and the frequency of the second resonator beam, an acceleration of the VBA.

7. The method of claim 6, wherein the anchor portion and the release portion of the resonator comprise overlapping resonator comb fingers, and wherein the total linear distance of the damping comb is greater than a total linear distance of the overlapping resonator comb fingers.

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